answer stringlengths 4 6 | benchmark_version stringclasses 1
value | change dict | distractor_formula_ids listlengths 2 2 | effective_parameters unknown | family stringclasses 4
values | formula dict | id stringlengths 21 26 | is_gold bool 1
class | knowledge_distractor stringlengths 1.95k 3.54k | knowledge_domain stringlengths 530 1.23k | knowledge_formula stringlengths 381 1.03k | knowledge_formula_expr stringlengths 216 407 | knowledge_name stringlengths 269 491 | knowledge_wrong stringlengths 638 1.34k | level int64 1 4 | math_type stringclasses 50
values | mode stringclasses 4
values | parameters unknown | problem stringlengths 105 438 | prompts dict | solution stringlengths 321 682 | split stringclasses 1
value | subject stringclasses 17
values | template_id int64 0 2 | wrong_formula_id stringlengths 6 6 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
6.247 | cropmath-v1 | null | [
"CMF014",
"CMF011"
] | {
"Biom_plant_yesterday": 704.9,
"Coef_Rm": 0.0039000000000000003,
"DVI": 0.48,
"Tmn": 24.8
} | carbon_nitrogen_cycle | {
"expression": "0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)",
"id": "CMF008",
"latex": "R_m=0.0432\\cdot24(Biom/0.45)C_m2^{(T-25)/10}",
"name": "植株维持呼吸",
"name_en": "carbon-nitrogen cycling plant maintenance respiration",
"precision": 3,
"unit": "g C/m2/day"... | CMF008_direct_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Wa... | Formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸)
Formula (LaTeX): R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | Formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸)
Formula (LaTeX): R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸).
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_W... | 2 | Q10 with DVI correction | direct | {
"Biom_plant_yesterday": 704.9,
"Coef_Rm": 0.0039000000000000003,
"DVI": 0.48,
"Tmn": 24.8
} | A carbon-nitrogen cycling respiration calculation estimates carbon-nitrogen cycling plant maintenance respiration. The measured inputs are Biom_plant_yesterday=704.9 g C/m2, Coef_Rm=0.0039 g C/g C/s, Tmn=24.8 C, DVI=0.48 dimensionless. What is the carbon-nitrogen cycling plant maintenance respiration? Give the final nu... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling plant maintenance respiration.
Use the verified formula:
\[R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}\]
In calculation-friendly notation, this is:
Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1).
Substitute the rel... | dev | carbon-nitrogen cycling respiration | 0 | CMF014 |
72.07 | cropmath-v1 | {
"new_value": 30,
"old_value": 29.3,
"parameter": "To"
} | [
"CMF033",
"CMF037"
] | {
"ABIOMASS": 13378,
"PDT": 7,
"Q10": 2.18,
"T": 24.3,
"To": 30
} | growth_yield | {
"expression": "(0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)",
"id": "CMF048",
"latex": "RM=(0.0091-0.0001\\cdot PDT)\\cdot ABIOMASS\\cdot Q_{10}^{(T-T_o)/10}",
"name": "维持呼吸",
"name_en": "Maintenance respiration",
"precision": 2,
"unit": "kg/ha/day"
} | CMF048_sensitivity_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Potential leaf area index (潜在叶面积指数)
Formula (LaTeX): LAI_P=LAI_0e^{RP\cdot GDD}
Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means... | Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logari... | Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logari... | Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | Relevant formula name: Maintenance respiration (维持呼吸).
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Daily dry matter increment (日干物质增量)
Formula (LaTeX): GCR=\frac{DTGA-RM-RG}{1-b}
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | 3 | Product with Q10 temperature response | sensitivity | {
"ABIOMASS": 13378,
"PDT": 7,
"Q10": 2.18,
"T": 24.3,
"To": 29.3
} | In respiration, we analyze how Maintenance respiration responds to parameter changes. Baseline: PDT=7.0 physiological days, ABIOMASS=13378.0 kg/ha, Q10=2.18 dimensionless, T=24.3 C, To=29.3 C. After changing To from 29.3 to 30.0, compute the new Maintenance respiration. Give the numeric value in kg/ha/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Maintenance respiration.
Use the verified formula:
\[RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}\]
In calculation-friendly notation, this is:
RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10).
Substitute the relevant values:
PDT=7.0 physiological days, ABI... | dev | Respiration | 2 | CMF033 |
28.34 | cropmath-v1 | {
"new_value": 31.5,
"old_value": 28.6,
"parameter": "Tair"
} | [
"CMF025",
"CMF023"
] | {
"Tair": 31.5
} | methane_emission | {
"expression": "4.4 + 0.76 * Tair",
"id": "CMF024",
"latex": "T_{soil}=4.4+0.76T_{air}",
"name": "土壤温度估算",
"name_en": "Soil temperature from air temperature",
"precision": 2,
"unit": "C"
} | CMF024_sensitivity_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Soil temperature from air temperature (土壤温度估算)
Formula (LaTeX): T_{soil}=4.4+0.76T_{air}
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ... | Formula name: Soil temperature from air temperature (土壤温度估算)
Formula (LaTeX): T_{soil}=4.4+0.76T_{air}
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output un... | Formula name: Soil temperature from air temperature (土壤温度估算)
Formula (LaTeX): T_{soil}=4.4+0.76T_{air}
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output un... | Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C | Relevant formula name: Soil temperature from air temperature (土壤温度估算).
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means divi... | 2 | Linear | sensitivity | {
"Tair": 28.6
} | Given current measurements Tair=28.6 C in methane, what would the Soil temperature from air temperature be if Tair were adjusted to 31.5? Provide the numeric value in C. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Soil temperature from air temperature.
Use the verified formula:
\[T_{soil}=4.4+0.76T_{air}\]
In calculation-friendly notation, this is:
Tsoil = 4.4 + 0.76 * Tair.
Substitute the relevant values:
Tair=31.5 C.
The computed value is 28.34 C.
Therefore, the final numeric answer is \boxed{28... | dev | Methane | 1 | CMF025 |
0.708 | cropmath-v1 | null | [
"CMF024",
"CMF023"
] | {
"WaterC": 0.606
} | methane_emission | {
"expression": "0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)",
"id": "CMF025",
"latex": "WI=0.49e^{3.88W_c-5.4W_c^2}",
"name": "水分分解因子",
"name_en": "Water-content decomposition factor",
"precision": 3,
"unit": "fraction"
} | CMF025_direct_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ ... | Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/l... | Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/l... | Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Water-content decomposition factor (水分分解因子).
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Soil temperature from air temperature (土壤温度估算)
Formula (LaTeX): T_{soil}=4.4+0.76T_{air}
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means po... | 1 | Exponential quadratic | direct | {
"WaterC": 0.606
} | In a methane, the Water-content decomposition factor is computed as part of methane modeling. With WaterC=0.606 fraction, determine the numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Water-content decomposition factor.
Use the verified formula:
\[WI=0.49e^{3.88W_c-5.4W_c^2}\]
In calculation-friendly notation, this is:
WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2).
Substitute the relevant values:
WaterC=0.606 fraction.
The computed value is 0.708 fraction.
Therefore... | dev | Methane | 2 | CMF024 |
50.61 | cropmath-v1 | null | [
"CMF002",
"CMF010"
] | {
"GrainYield": 8113,
"NUptake": 160.3
} | carbon_nitrogen_cycle | {
"expression": "GrainYield / NUptake",
"id": "CMF003",
"latex": "NUE=\\frac{GrainYield}{NUptake}",
"name": "氮利用效率",
"name_en": "Nitrogen use efficiency",
"precision": 2,
"unit": "kg grain/kg N"
} | CMF003_direct_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0... | Formula name: Nitrogen use efficiency (氮利用效率)
Formula (LaTeX): NUE=\frac{GrainYield}{NUptake}
Formula: NUE = GrainYield / NUptake
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg g... | Formula name: Nitrogen use efficiency (氮利用效率)
Formula (LaTeX): NUE=\frac{GrainYield}{NUptake}
Formula: NUE = GrainYield / NUptake
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg g... | Formula: NUE = GrainYield / NUptake
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg grain/kg N | Relevant formula name: Nitrogen use efficiency (氮利用效率).
Formula: NUE = GrainYield / NUptake
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg grain/kg N | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Oper... | 1 | Ratio | direct | {
"GrainYield": 8113,
"NUptake": 160.3
} | Given GrainYield=8113.0 kg/ha, NUptake=160.3 kg N/ha, calculate the Nitrogen use efficiency for a nitrogen. The result should be in kg grain/kg N. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Nitrogen use efficiency.
Use the verified formula:
\[NUE=\frac{GrainYield}{NUptake}\]
In calculation-friendly notation, this is:
NUE = GrainYield / NUptake.
Substitute the relevant values:
GrainYield=8113.0 kg/ha, NUptake=160.3 kg N/ha.
The computed value is 50.61 kg grain/kg N.
Therefor... | dev | Nitrogen | 1 | CMF002 |
1.04 | cropmath-v1 | {
"new_value": 0.59,
"old_value": 0.65,
"parameter": "beta"
} | [
"CMF030",
"CMF034"
] | {
"Cx": 363,
"beta": 0.59
} | growth_yield | {
"expression": "1 + beta * ln(Cx / 340)",
"id": "CMF029",
"latex": "F_{CO2}=1+\\beta\\ln(C_x/340)",
"name": "二氧化碳影响因子",
"name_en": "CO2 response factor",
"precision": 2,
"unit": "multiplier"
} | CMF029_sensitivity_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multipli... | Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: frac... | Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: frac... | Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: CO2 response factor (二氧化碳影响因子).
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / ... | 2 | Logarithmic | sensitivity | {
"Cx": 363,
"beta": 0.65
} | In photosynthesis, we analyze how CO2 response factor responds to parameter changes. Baseline: Cx=363.0 ppm, beta=0.65 dimensionless. After changing beta from 0.65 to 0.59, compute the new CO2 response factor. Give the numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as CO2 response factor.
Use the verified formula:
\[F_{CO2}=1+\beta\ln(C_x/340)\]
In calculation-friendly notation, this is:
FCO2 = 1 + beta * ln(Cx / 340).
Substitute the relevant values:
Cx=363.0 ppm, beta=0.59 dimensionless.
The computed value is 1.04 fraction.
Therefore, the final numer... | dev | Photosynthesis | 2 | CMF030 |
183.14 | cropmath-v1 | {
"new_value": 223.6,
"old_value": 248.4,
"parameter": "SLAc"
} | [
"CMF051",
"CMF044"
] | {
"GDD": 611.2,
"SLAc": 223.6
} | growth_yield | {
"expression": "if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)",
"id": "CMF053",
"latex": "SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)",
"name": "比叶面积",
"name_en": "Specific leaf area",
"precision": 2,
"unit": "cm2/g"
} | CMF053_sensitivity_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Specific leaf area (比叶面积)
Formula (LaTeX): SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Op... | Formula name: Specific leaf area (比叶面积)
Formula (LaTeX): SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural log... | Formula name: Specific leaf area (比叶面积)
Formula (LaTeX): SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural log... | Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: cm2/g | Relevant formula name: Specific leaf area (比叶面积).
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
O... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Relative thermal effectiveness (相对热效应)
Formula (LaTeX): RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}
Formula: RTE = (((T - Tb)/(To - Tb)) * (((... | 3 | Piecewise polynomial | sensitivity | {
"GDD": 611.2,
"SLAc": 248.4
} | In leaf area growth, we analyze how Specific leaf area responds to parameter changes. Baseline: GDD=611.2 C day, SLAc=248.4 cm2/g. After changing SLAc from 248.4 to 223.6, compute the new Specific leaf area. Give the numeric value in cm2/g. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Specific leaf area.
Use the verified formula:
\[SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)\]
In calculation-friendly notation, this is:
SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200).
Substitute the relevant values:
GDD=611.2 C day, SLAc=223.6 ... | dev | Leaf area growth | 2 | CMF051 |
0.35 | cropmath-v1 | null | [
"CMF036",
"CMF053"
] | {
"PDT": 47.6,
"a": 0.053
} | growth_yield | {
"expression": "if PDT<28: 1; else: exp(-a*(PDT-28))",
"id": "CMF030",
"latex": "F_{PA}=1\\;(PDT<28),\\quad e^{-a(PDT-28)}\\;(PDT\\ge 28)",
"name": "生理年龄因子",
"name_en": "Physiological age factor",
"precision": 2,
"unit": "fraction"
} | CMF030_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power,... | Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the... | Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the... | Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Physiological age factor (生理年龄因子).
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) me... | 2 | Piecewise exponential decay | direct | {
"PDT": 47.6,
"a": 0.053
} | A photosynthesis calculation estimates Physiological age factor. The measured inputs are PDT=47.6 physiological days, a=0.053 dimensionless. What is the physiological age factor? Give the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Physiological age factor.
Use the verified formula:
\[F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)\]
In calculation-friendly notation, this is:
FPA = if PDT<28: 1; else: exp(-a*(PDT-28)).
Substitute the relevant values:
PDT=47.6 physiological days, a=0.053 dimensionless.
The comp... | dev | Photosynthesis | 0 | CMF036 |
56.2 | cropmath-v1 | null | [
"CMF048",
"CMF042"
] | {
"SDEPTH": 1.6
} | growth_yield | {
"expression": "45 + 7 * SDEPTH",
"id": "CMF028",
"latex": "EMGDD=45+7SDEPTH",
"name": "出苗热量需求",
"name_en": "Emergence thermal requirement",
"precision": 1,
"unit": "C day"
} | CMF028_direct_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Opera... | Formula name: Emergence thermal requirement (出苗热量需求)
Formula (LaTeX): EMGDD=45+7SDEPTH
Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day
Paramete... | Formula name: Emergence thermal requirement (出苗热量需求)
Formula (LaTeX): EMGDD=45+7SDEPTH
Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day
Paramete... | Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day | Relevant formula name: Emergence thermal requirement (出苗热量需求).
Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes:... | 1 | Linear | direct | {
"SDEPTH": 1.6
} | In a phenology, the Emergence thermal requirement is computed as part of phenology modeling. With SDEPTH=1.6 cm, determine the numeric value in C day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Emergence thermal requirement.
Use the verified formula:
\[EMGDD=45+7SDEPTH\]
In calculation-friendly notation, this is:
EMGDD = 45 + 7 * SDEPTH.
Substitute the relevant values:
SDEPTH=1.6 cm.
The computed value is 56.2 C day.
Therefore, the final numeric answer is \boxed{56.2}.
#### 56.... | dev | Phenology | 2 | CMF048 |
0.09 | cropmath-v1 | {
"new_value": 44.7,
"old_value": 38.9,
"parameter": "PDT"
} | [
"CMF032",
"CMF038"
] | {
"PDT": 44.7
} | growth_yield | {
"expression": "1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)",
"id": "CMF043",
"latex": "PIRO=1-PISH",
"name": "地下部分配指数",
"name_en": "Root partitioning index",
"precision": 2,
"unit": "fraction"
} | CMF043_sensitivity_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Temperature response factor (温度响应因子)
Formula (LaTeX): F_T=\sin(\frac{T-T_b}{T_{ol}-T_b}\frac{\pi}{2}); 1; \cos(\frac{T-T_{ou}}{T_{max}-T_{ou}}\frac{\pi}{2})
Formula: F_T = if Tb<=T<Tol: si... | Formula name: Root partitioning index (地下部分配指数)
Formula (LaTeX): PIRO=1-PISH
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | Formula name: Root partitioning index (地下部分配指数)
Formula (LaTeX): PIRO=1-PISH
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Root partitioning index (地下部分配指数).
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Temperature response factor (温度响应因子)
Formula (LaTeX): F_T=\sin(\frac{T-T_b}{T_{ol}-T_b}\frac{\pi}{2}); 1; \cos(\frac{T-T_{ou}}{T_{max}-T_{ou}}\frac{\pi}{2})
Formula: F_T = if Tb<=T<Tol: sin(pi/2*(T-... | 2 | Residual from shoot partitioning | sensitivity | {
"PDT": 38.9
} | A dry matter partitioning calculation involves sensitivity analysis. The current measurements are PDT=38.9 physiological days. A field technician asks what the root partitioning index would become if PDT changed to 44.7. Report the new final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Root partitioning index.
Use the verified formula:
\[PIRO=1-PISH\]
In calculation-friendly notation, this is:
PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63).
Substitute the relevant values:
PDT=44.7 physiological days.
The computed value is 0.09 fraction.
Therefore, the final numeric an... | dev | Dry matter partitioning | 0 | CMF032 |
0.241 | cropmath-v1 | null | [
"CMF045",
"CMF035"
] | {
"PDT": 2.2
} | growth_yield | {
"expression": "0.0087 * PDT + 0.2222",
"id": "CMF036",
"latex": "K=0.0087PDT+0.2222",
"name": "冠层消光系数",
"name_en": "Canopy extinction coefficient",
"precision": 3,
"unit": "dimensionless"
} | CMF036_direct_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power,... | Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: dimensionl... | Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: dimensionl... | Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: dimensionless | Relevant formula name: Canopy extinction coefficient (冠层消光系数).
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: dimensionless | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Stem partitioning index (茎鞘分配指数)
Formula (LaTeX): PIS=1-PIGL-PIP
Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))
Ope... | 1 | Linear | direct | {
"PDT": 2.2
} | In a photosynthesis, the Canopy extinction coefficient is computed as part of photosynthesis modeling. With PDT=2.2 physiological days, determine the numeric value in dimensionless. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Canopy extinction coefficient.
Use the verified formula:
\[K=0.0087PDT+0.2222\]
In calculation-friendly notation, this is:
K = 0.0087 * PDT + 0.2222.
Substitute the relevant values:
PDT=2.2 physiological days.
The computed value is 0.241 dimensionless.
Therefore, the final numeric answer... | dev | Photosynthesis | 2 | CMF045 |
0.763 | cropmath-v1 | null | [
"CMF015",
"CMF017"
] | {
"Com": 3.488,
"Cr": 4.31,
"FEh": 0.428,
"TI": 0.722
} | methane_emission | {
"expression": "max(0, 0.27 * FEh * (TI * Cr + Com))",
"id": "CMF022",
"latex": "P=\\max(0,0.27F_{Eh}(TI\\cdot C_r+Com))",
"name": "甲烷产生量",
"name_en": "Methane production",
"precision": 3,
"unit": "g CH4/m2/day"
} | CMF022_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Methane production (甲烷产生量)
Formula (LaTeX): P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division... | Formula name: Methane production (甲烷产生量)
Formula (LaTeX): P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
O... | Formula name: Methane production (甲烷产生量)
Formula (LaTeX): P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
O... | Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g CH4/m2/day | Relevant formula name: Methane production (甲烷产生量).
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g CH4/m2/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Root-exudate carbon substrate (根系分泌碳底物)
Formula (LaTeX): C_r=0.0018VI\cdot SI\cdot W^{1.25}
Formula: Cr = 0.0018 * VI * SI * W ** 1.25
Operator notes: * means multiplication, / means division, ** or... | 1 | Maximum with chained drivers | direct | {
"Com": 3.488,
"Cr": 4.31,
"FEh": 0.428,
"TI": 0.722
} | A methane calculation estimates Methane production. The measured inputs are FEh=0.428 fraction, TI=0.722 fraction, Cr=4.31 g C/m2/day, Com=3.488 g C/m2/day. What is the methane production? Give the final numeric value in g CH4/m2/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Methane production.
Use the verified formula:
\[P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))\]
In calculation-friendly notation, this is:
P = max(0, 0.27 * FEh * (TI * Cr + Com)).
Substitute the relevant values:
FEh=0.428 fraction, TI=0.722 fraction, Cr=4.31 g C/m2/day, Com=3.488 g C/m2/day.
Th... | dev | Methane | 0 | CMF015 |
0.993 | cropmath-v1 | null | [
"CMF007",
"CMF011"
] | {
"Crop_Water_max": 0.42,
"Crop_Water_min": 0.22,
"Soil_Water": 0.428,
"Wilt_point": 0.08
} | carbon_nitrogen_cycle | {
"expression": "if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1+(1-Soil_Water)/(1-Crop_Water_max))",
"id": "CMF014",
"latex": "F_W=f(\\theta,\\theta_{wp},\\theta_{min},\\theta_{max})",
"name": "作物水分胁迫... | CMF014_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling optimal photosynthetic rate (最适光合速率)
Formula (LaTeX): P_{opt}=\alpha N_{leaf}\frac{PAR}{PAR+\beta}
Formula: Photo_Rate_opt = (Coef_alfa * Leaf_N) * PAR / (PAR + Coe... | Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1... | Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1... | Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1+(1-Soil_Water)/(1-Crop_Water_max))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) mean... | Relevant formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子).
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1+(1-Soil_Water)/(1-Crop_Water_max))
Operator notes: * means... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling optimal photosynthetic rate (最适光合速率)
Formula (LaTeX): P_{opt}=\alpha N_{leaf}\frac{PAR}{PAR+\beta}
Formula: Photo_Rate_opt = (Coef_alfa * Leaf_N) * PAR / (PAR + Coef_beta)
Op... | 2 | Piecewise water response | direct | {
"Crop_Water_max": 0.42,
"Crop_Water_min": 0.22,
"Soil_Water": 0.428,
"Wilt_point": 0.08
} | A carbon-nitrogen cycling water calculation estimates carbon-nitrogen cycling crop water stress factor. The measured inputs are Soil_Water=0.428 cm3/cm3, Crop_Water_max=0.42 cm3/cm3, Crop_Water_min=0.22 cm3/cm3, Wilt_point=0.08 cm3/cm3. What is the carbon-nitrogen cycling crop water stress factor? Give the final numeri... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling crop water stress factor.
Use the verified formula:
\[F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})\]
In calculation-friendly notation, this is:
F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wil... | dev | carbon-nitrogen cycling water | 0 | CMF007 |
244.63 | cropmath-v1 | null | [
"CMF041",
"CMF026"
] | {
"DTGA": 432.5,
"RG": 115.5,
"RM": 84.6,
"b": 0.05
} | growth_yield | {
"expression": "(DTGA - RM - RG) / (1 - b)",
"id": "CMF033",
"latex": "GCR=\\frac{DTGA-RM-RG}{1-b}",
"name": "日干物质增量",
"name_en": "Daily dry matter increment",
"precision": 2,
"unit": "kg/ha/day"
} | CMF033_direct_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes... | Formula name: Daily dry matter increment (日干物质增量)
Formula (LaTeX): GCR=\frac{DTGA-RM-RG}{1-b}
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula name: Daily dry matter increment (日干物质增量)
Formula (LaTeX): GCR=\frac{DTGA-RM-RG}{1-b}
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | Relevant formula name: Daily dry matter increment (日干物质增量).
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Green leaf partitioning index (绿叶分配指数)
Formula (LaTeX): PIGL=0.54-0.0046PDT\;(PDT<26),\quad1.4532e^{-0.0492PDT}\;(PDT\ge26)
Formula: PIGL = if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)
... | 1 | Subtraction and conversion | direct | {
"DTGA": 432.5,
"RG": 115.5,
"RM": 84.6,
"b": 0.05
} | In a respiration, the Daily dry matter increment is computed as part of respiration modeling. With DTGA=432.5 kg/ha/day, RM=84.6 kg/ha/day, RG=115.5 kg/ha/day, b=0.05 fraction, determine the numeric value in kg/ha/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Daily dry matter increment.
Use the verified formula:
\[GCR=\frac{DTGA-RM-RG}{1-b}\]
In calculation-friendly notation, this is:
GCR = (DTGA - RM - RG) / (1 - b).
Substitute the relevant values:
DTGA=432.5 kg/ha/day, RM=84.6 kg/ha/day, RG=115.5 kg/ha/day, b=0.05 fraction.
The computed val... | dev | Respiration | 2 | CMF041 |
1.30 | cropmath-v1 | {
"new_value": 0.55,
"old_value": 0.5,
"parameter": "beta"
} | [
"CMF037",
"CMF043"
] | {
"Cx": 583,
"beta": 0.55
} | growth_yield | {
"expression": "1 + beta * ln(Cx / 340)",
"id": "CMF029",
"latex": "F_{CO2}=1+\\beta\\ln(C_x/340)",
"name": "二氧化碳影响因子",
"name_en": "CO2 response factor",
"precision": 2,
"unit": "multiplier"
} | CMF029_sensitivity_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Potential leaf area index (潜在叶面积指数)
Formula (LaTeX): LAI_P=LAI_0e^{RP\cdot GDD}
Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means... | Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: frac... | Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: frac... | Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: CO2 response factor (二氧化碳影响因子).
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Potential leaf area index (潜在叶面积指数)
Formula (LaTeX): LAI_P=LAI_0e^{RP\cdot GDD}
Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means power, ex... | 2 | Logarithmic | sensitivity | {
"Cx": 583,
"beta": 0.5
} | In photosynthesis, we analyze how CO2 response factor responds to parameter changes. Baseline: Cx=583.0 ppm, beta=0.5 dimensionless. After changing beta from 0.5 to 0.55, compute the new CO2 response factor. Give the numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as CO2 response factor.
Use the verified formula:
\[F_{CO2}=1+\beta\ln(C_x/340)\]
In calculation-friendly notation, this is:
FCO2 = 1 + beta * ln(Cx / 340).
Substitute the relevant values:
Cx=583.0 ppm, beta=0.55 dimensionless.
The computed value is 1.30 fraction.
Therefore, the final numer... | dev | Photosynthesis | 2 | CMF037 |
1.00 | cropmath-v1 | null | [
"CMF034",
"CMF030"
] | {
"GDD": 203.4,
"LAI0": 0.279,
"RP": 0.0063
} | growth_yield | {
"expression": "LAI0 * exp(RP * GDD)",
"id": "CMF037",
"latex": "LAI_P=LAI_0e^{RP\\cdot GDD}",
"name": "潜在叶面积指数",
"name_en": "Potential leaf area index",
"precision": 2,
"unit": "m2/m2"
} | CMF037_direct_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Harvest index (收获指数)
Formula (LaTeX): HI=\frac{Y_{grain}}{B_{above}}
Formula: HI = Y_grain / B_above
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) m... | Formula name: Potential leaf area index (潜在叶面积指数)
Formula (LaTeX): LAI_P=LAI_0e^{RP\cdot GDD}
Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: m2/... | Formula name: Potential leaf area index (潜在叶面积指数)
Formula (LaTeX): LAI_P=LAI_0e^{RP\cdot GDD}
Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: m2/... | Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: m2/m2 | Relevant formula name: Potential leaf area index (潜在叶面积指数).
Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: m2/m2 | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Harvest index (收获指数)
Formula (LaTeX): HI=\frac{Y_{grain}}{B_{above}}
Formula: HI = Y_grain / B_above
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | 1 | Exponential growth | direct | {
"GDD": 203.4,
"LAI0": 0.279,
"RP": 0.0063
} | Given LAI0=0.279 m2/m2, RP=0.0063 d-1, GDD=203.4 C day, calculate the Potential leaf area index for a leaf area growth. The result should be in m2/m2. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Potential leaf area index.
Use the verified formula:
\[LAI_P=LAI_0e^{RP\cdot GDD}\]
In calculation-friendly notation, this is:
LAIP = LAI0 * exp(RP * GDD).
Substitute the relevant values:
LAI0=0.279 m2/m2, RP=0.0063 d-1, GDD=203.4 C day.
The computed value is 1.00 m2/m2.
Therefore, the f... | dev | Leaf area growth | 1 | CMF034 |
12.52 | cropmath-v1 | null | [
"CMF053",
"CMF038"
] | {
"PS": 0.246,
"Po": 10.5
} | growth_yield | {
"expression": "Po + sqrt(1 / PS)",
"id": "CMF040",
"latex": "P_c=P_o+\\sqrt{1/PS}",
"name": "临界日长",
"name_en": "Critical daylength",
"precision": 2,
"unit": "h"
} | CMF040_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Leaf area index from SLA (比叶面积法叶面积指数)
Formula (LaTeX): LAI=SLA\cdot AWL
Formula: LAI = SLA * AWL
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means... | Formula name: Critical daylength (临界日长)
Formula (LaTeX): P_c=P_o+\sqrt{1/PS}
Formula: Pc = Po + sqrt(1 / PS)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: h
Parameters:
- Po: optim... | Formula name: Critical daylength (临界日长)
Formula (LaTeX): P_c=P_o+\sqrt{1/PS}
Formula: Pc = Po + sqrt(1 / PS)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: h
Parameters:
- Po: optim... | Formula: Pc = Po + sqrt(1 / PS)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: h | Relevant formula name: Critical daylength (临界日长).
Formula: Pc = Po + sqrt(1 / PS)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: h | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Specific leaf area (比叶面积)
Formula (LaTeX): SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Operator not... | 1 | Power response | direct | {
"PS": 0.246,
"Po": 10.5
} | A phenology calculation estimates Critical daylength. The measured inputs are Po=10.5 h, PS=0.246 dimensionless. What is the critical daylength? Give the final numeric value in h. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Critical daylength.
Use the verified formula:
\[P_c=P_o+\sqrt{1/PS}\]
In calculation-friendly notation, this is:
Pc = Po + sqrt(1 / PS).
Substitute the relevant values:
Po=10.5 h, PS=0.246 dimensionless.
The computed value is 12.52 h.
Therefore, the final numeric answer is \boxed{12.52}.... | dev | Phenology | 0 | CMF053 |
1.222 | cropmath-v1 | {
"new_value": 551,
"old_value": 501,
"parameter": "CO2"
} | [
"CMF014",
"CMF008"
] | {
"CO2": 551,
"Coef_B_CO2": 0.46
} | carbon_nitrogen_cycle | {
"expression": "1 + Coef_B_CO2 * ln(CO2 / 340)",
"id": "CMF001",
"latex": "F_{CO2}=1+B\\ln(CO2/340)",
"name": "作物二氧化碳施肥因子",
"name_en": "carbon-nitrogen cycling CO2 fertilization factor",
"precision": 3,
"unit": "multiplier"
} | CMF001_sensitivity_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子)
Formula (LaTeX): F_{CO2}=1+B\ln(CO2/340)
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplicatio... | Formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子)
Formula (LaTeX): F_{CO2}=1+B\ln(CO2/340)
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smal... | Formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子)
Formula (LaTeX): F_{CO2}=1+B\ln(CO2/340)
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smal... | Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子).
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_W... | 2 | Logarithmic | sensitivity | {
"CO2": 501,
"Coef_B_CO2": 0.46
} | A carbon-nitrogen cycling photosynthesis calculation involves sensitivity analysis. The current measurements are CO2=501.0 ppm, Coef_B_CO2=0.46 dimensionless. A field technician asks what the carbon-nitrogen cycling co2 fertilization factor would become if CO2 changed to 551.0. Report the new final numeric value in fra... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling CO2 fertilization factor.
Use the verified formula:
\[F_{CO2}=1+B\ln(CO2/340)\]
In calculation-friendly notation, this is:
F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340).
Substitute the relevant values:
CO2=551.0 ppm, Coef_B_CO2=0.46 dimensionless.
The computed value is 1... | dev | carbon-nitrogen cycling photosynthesis | 0 | CMF014 |
0.802 | cropmath-v1 | {
"new_value": 33.3,
"old_value": 29,
"parameter": "Td"
} | [
"CMF008",
"CMF010"
] | {
"Coef_T_M": 0.13,
"Td": 33.3,
"Tmax_active": 42,
"Tmin_active": 3,
"Topt_active": 25
} | carbon_nitrogen_cycle | {
"expression": "if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^(1+Coef_T_M) * ((Tmax_active-Td)/(Tmax_active-Topt_active))^(1-Coef_T_M)",
"id": "CMF013",
"latex": "F_T=\\left(\\frac{T_d-T_{min}}{T_{opt}-T_{min}}\\right)^{1+M}\\left(\\frac{T_{max}-T_d}{T_{max}-T_{opt}... | CMF013_sensitivity_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸)
Formula (LaTeX): R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^(... | Formula name: carbon-nitrogen cycling crop temperature activity factor (作物温度活性因子)
Formula (LaTeX): F_T=\left(\frac{T_d-T_{min}}{T_{opt}-T_{min}}\right)^{1+M}\left(\frac{T_{max}-T_d}{T_{max}-T_{opt}}\right)^{1-M}
Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^... | Formula name: carbon-nitrogen cycling crop temperature activity factor (作物温度活性因子)
Formula (LaTeX): F_T=\left(\frac{T_d-T_{min}}{T_{opt}-T_{min}}\right)^{1+M}\left(\frac{T_{max}-T_d}{T_{max}-T_{opt}}\right)^{1-M}
Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^... | Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^(1+Coef_T_M) * ((Tmax_active-Td)/(Tmax_active-Topt_active))^(1-Coef_T_M)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max... | Relevant formula name: carbon-nitrogen cycling crop temperature activity factor (作物温度活性因子).
Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^(1+Coef_T_M) * ((Tmax_active-Td)/(Tmax_active-Topt_active))^(1-Coef_T_M)
Operator notes: * means multiplication, / means... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸)
Formula (LaTeX): R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/1... | 3 | Beta temperature response | sensitivity | {
"Coef_T_M": 0.13,
"Td": 29,
"Tmax_active": 42,
"Tmin_active": 3,
"Topt_active": 25
} | In carbon-nitrogen cycling stress, we analyze how carbon-nitrogen cycling crop temperature activity factor responds to parameter changes. Baseline: Td=29.0 C, Tmin_active=3.0 C, Topt_active=25.0 C, Tmax_active=42.0 C, Coef_T_M=0.13 dimensionless. After changing Td from 29.0 to 33.3, compute the new carbon-nitrogen cycl... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling crop temperature activity factor.
Use the verified formula:
\[F_T=\left(\frac{T_d-T_{min}}{T_{opt}-T_{min}}\right)^{1+M}\left(\frac{T_{max}-T_d}{T_{max}-T_{opt}}\right)^{1-M}\]
In calculation-friendly notation, this is:
F_T = if Td<=Tmin_active or Td>=Tmax_active:... | dev | carbon-nitrogen cycling stress | 2 | CMF008 |
0.265 | cropmath-v1 | null | [
"CMF036",
"CMF050"
] | {
"BFF": 1.17,
"DTE": 0.265,
"IE": 0.85,
"PDT": 18.9,
"RPE": 0.6000000000000001
} | growth_yield | {
"expression": "if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0",
"id": "CMF027",
"latex": "DPE=DTE\\cdot IE,\\;DTE\\cdot RPE,\\;DTE,\\;DTE\\cdot BFF",
"name": "每日生理效应",
"name_en": "Daily physiological effectiveness",
"precision": 3,
"unit": "physiological days/day"
} | CMF027_branch_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<... | Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: physiological days/day | Relevant formula name: Daily physiological effectiveness (每日生理效应).
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the small... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) me... | 4 | Stage-dependent product | branch | {
"BFF": 1.17,
"DTE": 0.265,
"IE": 0.85,
"PDT": 18.9,
"RPE": 0.6000000000000001
} | For phenology, compute the Daily physiological effectiveness. The inputs are PDT=18.9 physiological days, DTE=0.265 fraction, IE=0.85 dimensionless, RPE=0.6 fraction, BFF=1.17 dimensionless. Note that this formula uses piecewise logic depending on parameter values. Report the final numeric value in physiological days/d... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Daily physiological effectiveness.
Use the verified formula:
\[DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF\]
In calculation-friendly notation, this is:
DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0.
Substitute the relevant values:
PDT=18.... | dev | Phenology | 1 | CMF036 |
0.687 | cropmath-v1 | null | [
"CMF023",
"CMF020"
] | {
"WaterC": 0.617
} | methane_emission | {
"expression": "0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)",
"id": "CMF025",
"latex": "WI=0.49e^{3.88W_c-5.4W_c^2}",
"name": "水分分解因子",
"name_en": "Water-content decomposition factor",
"precision": 3,
"unit": "fraction"
} | CMF025_direct_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ ... | Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/l... | Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/l... | Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Water-content decomposition factor (水分分解因子).
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | 1 | Exponential quadratic | direct | {
"WaterC": 0.617
} | Given WaterC=0.617 fraction, calculate the Water-content decomposition factor for a methane. The result should be in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Water-content decomposition factor.
Use the verified formula:
\[WI=0.49e^{3.88W_c-5.4W_c^2}\]
In calculation-friendly notation, this is:
WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2).
Substitute the relevant values:
WaterC=0.617 fraction.
The computed value is 0.687 fraction.
Therefore... | dev | Methane | 1 | CMF023 |
0.329 | cropmath-v1 | null | [
"CMF025",
"CMF023"
] | {
"CH4RiceEfC": 0.39,
"W": 5043,
"Wmax": 10266
} | methane_emission | {
"expression": "CH4RiceEfC * (1 - W / Wmax) ** 0.25",
"id": "CMF019",
"latex": "F_p=C(1-W/W_{max})^{0.25}",
"name": "植株传输因子",
"name_en": "Plant methane transport factor",
"precision": 3,
"unit": "fraction"
} | CMF019_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ ... | Formula name: Plant methane transport factor (植株传输因子)
Formula (LaTeX): F_p=C(1-W/W_{max})^{0.25}
Formula: Fp = CH4RiceEfC * (1 - W / Wmax) ** 0.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
... | Formula name: Plant methane transport factor (植株传输因子)
Formula (LaTeX): F_p=C(1-W/W_{max})^{0.25}
Formula: Fp = CH4RiceEfC * (1 - W / Wmax) ** 0.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
... | Formula: Fp = CH4RiceEfC * (1 - W / Wmax) ** 0.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Plant methane transport factor (植株传输因子).
Formula: Fp = CH4RiceEfC * (1 - W / Wmax) ** 0.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means divi... | 1 | Power attenuation | direct | {
"CH4RiceEfC": 0.39,
"W": 5043,
"Wmax": 10266
} | A methane calculation estimates Plant methane transport factor. The measured inputs are CH4RiceEfC=0.39 fraction, W=5043.0 kg/ha, Wmax=10266.0 kg/ha. What is the plant methane transport factor? Give the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Plant methane transport factor.
Use the verified formula:
\[F_p=C(1-W/W_{max})^{0.25}\]
In calculation-friendly notation, this is:
Fp = CH4RiceEfC * (1 - W / Wmax) ** 0.25.
Substitute the relevant values:
CH4RiceEfC=0.39 fraction, W=5043.0 kg/ha, Wmax=10266.0 kg/ha.
The computed value is... | dev | Methane | 0 | CMF025 |
1.000 | cropmath-v1 | null | [
"CMF023",
"CMF016"
] | {
"Eh": -204.5
} | methane_emission | {
"expression": "if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))",
"id": "CMF018",
"latex": "F_{Eh}=1\\;(Eh<-150),\\quad e^{-1.7(1+Eh/150)}",
"name": "氧化还原电位因子",
"name_en": "Redox potential factor",
"precision": 3,
"unit": "fraction"
} | CMF018_direct_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Methane ebullition emission (甲烷冒泡排放)
Formula (LaTeX): E_{bl}=\min(0.7\ln(t_{soil})/W_r,0.9)P
Formula: Ebl = min(0.7 * ln(t_soil) / Wr, 0.9) * P
Operator notes: * means multiplication, / me... | Formula name: Redox potential factor (氧化还原电位因子)
Formula (LaTeX): F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the sm... | Formula name: Redox potential factor (氧化还原电位因子)
Formula (LaTeX): F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the sm... | Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Redox potential factor (氧化还原电位因子).
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | 2 | Piecewise exponential | direct | {
"Eh": -204.5
} | Given Eh=-204.5 mV, calculate the Redox potential factor for a methane. The result should be in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Redox potential factor.
Use the verified formula:
\[F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}\]
In calculation-friendly notation, this is:
FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150)).
Substitute the relevant values:
Eh=-204.5 mV.
The computed value is 1.000 fraction.
Therefore, th... | dev | Methane | 1 | CMF023 |
0.637 | cropmath-v1 | null | [
"CMF058",
"CMF060"
] | {
"I50A": 483.6,
"I50B": 435.8,
"TT": 912.5,
"Tsum": 2171,
"fSolarMax": 0.9500000000000001,
"fSolar_water": 0.68
} | environmental_response | {
"expression": "min(fSolarMax/(1+exp(-0.01*(TT-I50A))), fSolarMax/(1+exp(0.01*(TT-(Tsum-I50B))))) * min(fSolar_water, 1)",
"id": "CMF059",
"latex": "fSolar=\\min(f_1,f_2)F_{solar,water}",
"name": "环境响应光截获比例",
"name_en": "environmental-response solar interception fraction",
"precision": 3,
"unit": "fracti... | CMF059_chain_2_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: environmental-response heat stress response (环境响应高温响应)
Formula (LaTeX): F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}
Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0;... | Formula name: environmental-response solar interception fraction (环境响应光截获比例)
Formula (LaTeX): fSolar=\min(f_1,f_2)F_{solar,water}
Formula: fSolar = min(fSolarMax/(1+exp(-0.01*(TT-I50A))), fSolarMax/(1+exp(0.01*(TT-(Tsum-I50B))))) * min(fSolar_water, 1)
Operator notes: * means multiplication, / means division, ** or ^ m... | Formula name: environmental-response solar interception fraction (环境响应光截获比例)
Formula (LaTeX): fSolar=\min(f_1,f_2)F_{solar,water}
Formula: fSolar = min(fSolarMax/(1+exp(-0.01*(TT-I50A))), fSolarMax/(1+exp(0.01*(TT-(Tsum-I50B))))) * min(fSolar_water, 1)
Operator notes: * means multiplication, / means division, ** or ^ m... | Formula: fSolar = min(fSolarMax/(1+exp(-0.01*(TT-I50A))), fSolarMax/(1+exp(0.01*(TT-(Tsum-I50B))))) * min(fSolar_water, 1)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: environmental-response solar interception fraction (环境响应光截获比例).
Formula: fSolar = min(fSolarMax/(1+exp(-0.01*(TT-I50A))), fSolarMax/(1+exp(0.01*(TT-(Tsum-I50B))))) * min(fSolar_water, 1)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means n... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: environmental-response heat stress response (环境响应高温响应)
Formula (LaTeX): F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}
Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max... | 4 | Double logistic | chain_2 | {
"I50A": 483.6,
"I50B": 435.8,
"TT": 912.5,
"Tsum": 2171,
"fSolarMax": 0.9500000000000001,
"fSolar_water": 0.68
} | Given fSolarMax=0.95 fraction, TT=912.5 C day, I50A=483.6 C day, I50B=435.8 C day, Tsum=2171.0 C day, fSolar_water=0.68 fraction, compute environmental-response solar interception fraction in environmental-response formula system. This requires sequential calculation through intermediate variables. Report the final num... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as environmental-response solar interception fraction.
Use the verified formula:
\[fSolar=\min(f_1,f_2)F_{solar,water}\]
In calculation-friendly notation, this is:
fSolar = min(fSolarMax/(1+exp(-0.01*(TT-I50A))), fSolarMax/(1+exp(0.01*(TT-(Tsum-I50B))))) * min(fSolar_water, 1).
Substitute t... | dev | environmental-response formula system | 1 | CMF058 |
0.007 | cropmath-v1 | {
"new_value": 36,
"old_value": 32.3,
"parameter": "t_soil"
} | [
"CMF025",
"CMF022"
] | {
"P": 2.174,
"Wr": 735.6,
"t_soil": 36
} | methane_emission | {
"expression": "min(0.7 * ln(t_soil) / Wr, 0.9) * P",
"id": "CMF016",
"latex": "E_{bl}=\\min(0.7\\ln(t_{soil})/W_r,0.9)P",
"name": "甲烷冒泡排放",
"name_en": "Methane ebullition emission",
"precision": 3,
"unit": "g CH4/m2/day"
} | CMF016_sensitivity_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Methane ebullition emission (甲烷冒泡排放)
Formula (LaTeX): E_{bl}=\min(0.7\ln(t_{soil})/W_r,0.9)P
Formula: Ebl = min(0.7 * ln(t_soil) / Wr, 0.9) * P
Operator notes: * means multiplication, / me... | Formula name: Methane ebullition emission (甲烷冒泡排放)
Formula (LaTeX): E_{bl}=\min(0.7\ln(t_{soil})/W_r,0.9)P
Formula: Ebl = min(0.7 * ln(t_soil) / Wr, 0.9) * P
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/lar... | Formula name: Methane ebullition emission (甲烷冒泡排放)
Formula (LaTeX): E_{bl}=\min(0.7\ln(t_{soil})/W_r,0.9)P
Formula: Ebl = min(0.7 * ln(t_soil) / Wr, 0.9) * P
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/lar... | Formula: Ebl = min(0.7 * ln(t_soil) / Wr, 0.9) * P
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g CH4/m2/day | Relevant formula name: Methane ebullition emission (甲烷冒泡排放).
Formula: Ebl = min(0.7 * ln(t_soil) / Wr, 0.9) * P
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g CH4/m2/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means divi... | 2 | Logarithmic minimum | sensitivity | {
"P": 2.174,
"Wr": 735.6,
"t_soil": 32.3
} | In methane, we analyze how Methane ebullition emission responds to parameter changes. Baseline: P=2.174 g CH4/m2/day, t_soil=32.3 C, Wr=735.6 kg/ha. After changing t_soil from 32.3 to 36.0, compute the new Methane ebullition emission. Give the numeric value in g CH4/m2/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Methane ebullition emission.
Use the verified formula:
\[E_{bl}=\min(0.7\ln(t_{soil})/W_r,0.9)P\]
In calculation-friendly notation, this is:
Ebl = min(0.7 * ln(t_soil) / Wr, 0.9) * P.
Substitute the relevant values:
P=2.174 g CH4/m2/day, t_soil=36.0 C, Wr=735.6 kg/ha.
The computed value ... | dev | Methane | 2 | CMF025 |
1.898 | cropmath-v1 | null | [
"CMF001",
"CMF008"
] | {
"Day_Length_hour": 15.26,
"F_CO2": 1.25,
"F_T": 0.73,
"F_Water": 0.49,
"Photo_Rate_opt": 6.44
} | carbon_nitrogen_cycle | {
"expression": "Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432",
"id": "CMF002",
"latex": "GPP=P_{opt}F_TF_WF_{CO2}DL\\cdot0.0432",
"name": "总初级生产力",
"name_en": "carbon-nitrogen cycling gross primary production",
"precision": 3,
"unit": "g C/m2/day"
} | CMF002_direct_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子)
Formula (LaTeX): F_{CO2}=1+B\ln(CO2/340)
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplicatio... | Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means nat... | Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means nat... | Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: carbon-nitrogen cycling gross primary production (总初级生产力).
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smalle... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子)
Formula (LaTeX): F_{CO2}=1+B\ln(CO2/340)
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means... | 2 | Multiplicative conversion | direct | {
"Day_Length_hour": 15.26,
"F_CO2": 1.25,
"F_T": 0.73,
"F_Water": 0.49,
"Photo_Rate_opt": 6.44
} | A carbon-nitrogen cycling photosynthesis calculation estimates carbon-nitrogen cycling gross primary production. The measured inputs are Photo_Rate_opt=6.44 umol CO2/m2/s, F_T=0.73 fraction, F_Water=0.49 fraction, F_CO2=1.25 fraction, Day_Length_hour=15.26 h. What is the carbon-nitrogen cycling gross primary production... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling gross primary production.
Use the verified formula:
\[GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432\]
In calculation-friendly notation, this is:
GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432.
Substitute the relevant values:
Photo_Rate_opt=6.44 um... | dev | carbon-nitrogen cycling photosynthesis | 0 | CMF001 |
195.60 | cropmath-v1 | null | [
"CMF037",
"CMF047"
] | {
"DTGA": 489,
"Rg": 0.4
} | growth_yield | {
"expression": "Rg * DTGA",
"id": "CMF046",
"latex": "RG=R_g\\cdot DTGA",
"name": "生长呼吸",
"name_en": "Growth respiration",
"precision": 2,
"unit": "kg/ha/day"
} | CMF046_direct_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) m... | Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day
Parameters:
- Rg: growth r... | Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day
Parameters:
- Rg: growth r... | Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | Relevant formula name: Growth respiration (生长呼吸).
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Potential leaf area index (潜在叶面积指数)
Formula (LaTeX): LAI_P=LAI_0e^{RP\cdot GDD}
Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means power, ex... | 1 | Product | direct | {
"DTGA": 489,
"Rg": 0.4
} | In a respiration, the Growth respiration is computed as part of respiration modeling. With Rg=0.4 fraction, DTGA=489.0 kg/ha/day, determine the numeric value in kg/ha/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Growth respiration.
Use the verified formula:
\[RG=R_g\cdot DTGA\]
In calculation-friendly notation, this is:
RG = Rg * DTGA.
Substitute the relevant values:
Rg=0.4 fraction, DTGA=489.0 kg/ha/day.
The computed value is 195.60 kg/ha/day.
Therefore, the final numeric answer is \boxed{195.6... | dev | Respiration | 2 | CMF037 |
20.022 | cropmath-v1 | {
"new_value": 3240.2,
"old_value": 3600.2,
"parameter": "W"
} | [
"CMF022",
"CMF018"
] | {
"SI": 0.65,
"VI": 0.7000000000000001,
"W": 3240.2
} | methane_emission | {
"expression": "0.0018 * VI * SI * W ** 1.25",
"id": "CMF015",
"latex": "C_r=0.0018VI\\cdot SI\\cdot W^{1.25}",
"name": "根系分泌碳底物",
"name_en": "Root-exudate carbon substrate",
"precision": 3,
"unit": "g C/m2/day"
} | CMF015_sensitivity_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Redox potential factor (氧化还原电位因子)
Formula (LaTeX): F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplicat... | Formula name: Root-exudate carbon substrate (根系分泌碳底物)
Formula (LaTeX): C_r=0.0018VI\cdot SI\cdot W^{1.25}
Formula: Cr = 0.0018 * VI * SI * W ** 1.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value... | Formula name: Root-exudate carbon substrate (根系分泌碳底物)
Formula (LaTeX): C_r=0.0018VI\cdot SI\cdot W^{1.25}
Formula: Cr = 0.0018 * VI * SI * W ** 1.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value... | Formula: Cr = 0.0018 * VI * SI * W ** 1.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: Root-exudate carbon substrate (根系分泌碳底物).
Formula: Cr = 0.0018 * VI * SI * W ** 1.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Methane production (甲烷产生量)
Formula (LaTeX): P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ ... | 2 | Power product | sensitivity | {
"SI": 0.65,
"VI": 0.7000000000000001,
"W": 3600.2
} | In methane, we analyze how Root-exudate carbon substrate responds to parameter changes. Baseline: VI=0.7 fraction, SI=0.65 fraction, W=3600.2 kg/ha. After changing W from 3600.2 to 3240.2, compute the new Root-exudate carbon substrate. Give the numeric value in g C/m2/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Root-exudate carbon substrate.
Use the verified formula:
\[C_r=0.0018VI\cdot SI\cdot W^{1.25}\]
In calculation-friendly notation, this is:
Cr = 0.0018 * VI * SI * W ** 1.25.
Substitute the relevant values:
VI=0.7 fraction, SI=0.65 fraction, W=3240.2 kg/ha.
The computed value is 20.022 g ... | dev | Methane | 2 | CMF022 |
0.580 | cropmath-v1 | {
"new_value": 13.5,
"old_value": 11.7,
"parameter": "Tmn"
} | [
"CMF012",
"CMF006"
] | {
"Biom_plant_yesterday": 279.1,
"Coef_Rm": 0.002,
"DVI": 0.51,
"Tmn": 13.5
} | carbon_nitrogen_cycle | {
"expression": "0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)",
"id": "CMF008",
"latex": "R_m=0.0432\\cdot24(Biom/0.45)C_m2^{(T-25)/10}",
"name": "植株维持呼吸",
"name_en": "carbon-nitrogen cycling plant maintenance respiration",
"precision": 3,
"unit": "g C/m2/day"... | CMF008_sensitivity_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling soil carbon water factor (土壤碳分解水分因子)
Formula (LaTeX): F_W=0.49e^{3.88W-5.4W^2}
Formula: F_W_soil = if Soil_Water>=Saturate_Water: 0.65; else: 0.49*exp(3.88*(Soil_Wa... | Formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸)
Formula (LaTeX): R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | Formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸)
Formula (LaTeX): R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸).
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling soil carbon water factor (土壤碳分解水分因子)
Formula (LaTeX): F_W=0.49e^{3.88W-5.4W^2}
Formula: F_W_soil = if Soil_Water>=Saturate_Water: 0.65; else: 0.49*exp(3.88*(Soil_Water/BD)-5.... | 3 | Q10 with DVI correction | sensitivity | {
"Biom_plant_yesterday": 279.1,
"Coef_Rm": 0.002,
"DVI": 0.51,
"Tmn": 11.7
} | Given current measurements Biom_plant_yesterday=279.1 g C/m2, Coef_Rm=0.002 g C/g C/s, Tmn=11.7 C, DVI=0.51 dimensionless in carbon-nitrogen cycling respiration, what would the carbon-nitrogen cycling plant maintenance respiration be if Tmn were adjusted to 13.5? Provide the numeric value in g C/m2/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling plant maintenance respiration.
Use the verified formula:
\[R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}\]
In calculation-friendly notation, this is:
Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1).
Substitute the rel... | dev | carbon-nitrogen cycling respiration | 1 | CMF012 |
1.00 | cropmath-v1 | null | [
"CMF028",
"CMF038"
] | {
"T": 30.6,
"Tb": 10,
"Tmax": 45,
"Tol": 24,
"Tou": 34
} | growth_yield | {
"expression": "if Tb<=T<Tol: sin(pi/2*(T-Tb)/(Tol-Tb)); if Tol<=T<Tou: 1; if Tou<=T<Tmax: cos(pi/2*(T-Tou)/(Tmax-Tou)); else: 0",
"id": "CMF032",
"latex": "F_T=\\sin(\\frac{T-T_b}{T_{ol}-T_b}\\frac{\\pi}{2}); 1; \\cos(\\frac{T-T_{ou}}{T_{max}-T_{ou}}\\frac{\\pi}{2})",
"name": "温度响应因子",
"name_en": "Temperatu... | CMF032_branch_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Temperature response factor (温度响应因子)
Formula (LaTeX): F_T=\sin(\frac{T-T_b}{T_{ol}-T_b}\frac{\pi}{2}); 1; \cos(\frac{T-T_{ou}}{T_{max}-T_{ou}}\frac{\pi}{2})
Formula: F_T = if Tb<=T<Tol: si... | Formula name: Temperature response factor (温度响应因子)
Formula (LaTeX): F_T=\sin(\frac{T-T_b}{T_{ol}-T_b}\frac{\pi}{2}); 1; \cos(\frac{T-T_{ou}}{T_{max}-T_{ou}}\frac{\pi}{2})
Formula: F_T = if Tb<=T<Tol: sin(pi/2*(T-Tb)/(Tol-Tb)); if Tol<=T<Tou: 1; if Tou<=T<Tmax: cos(pi/2*(T-Tou)/(Tmax-Tou)); else: 0
Operator notes: * mea... | Formula name: Temperature response factor (温度响应因子)
Formula (LaTeX): F_T=\sin(\frac{T-T_b}{T_{ol}-T_b}\frac{\pi}{2}); 1; \cos(\frac{T-T_{ou}}{T_{max}-T_{ou}}\frac{\pi}{2})
Formula: F_T = if Tb<=T<Tol: sin(pi/2*(T-Tb)/(Tol-Tb)); if Tol<=T<Tou: 1; if Tou<=T<Tmax: cos(pi/2*(T-Tou)/(Tmax-Tou)); else: 0
Operator notes: * mea... | Formula: F_T = if Tb<=T<Tol: sin(pi/2*(T-Tb)/(Tol-Tb)); if Tol<=T<Tou: 1; if Tou<=T<Tmax: cos(pi/2*(T-Tou)/(Tmax-Tou)); else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fracti... | Relevant formula name: Temperature response factor (温度响应因子).
Formula: F_T = if Tb<=T<Tol: sin(pi/2*(T-Tb)/(Tol-Tb)); if Tol<=T<Tou: 1; if Tou<=T<Tmax: cos(pi/2*(T-Tou)/(Tmax-Tou)); else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Emergence thermal requirement (出苗热量需求)
Formula (LaTeX): EMGDD=45+7SDEPTH
Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means ... | 4 | Piecewise trigonometric | branch | {
"T": 30.6,
"Tb": 10,
"Tmax": 45,
"Tol": 24,
"Tou": 34
} | Calculate Temperature response factor in temperature response with these inputs: T=30.6 C, Tb=10.0 C, Tol=24.0 C, Tou=34.0 C, Tmax=45.0 C. The computation may follow different paths based on piecewise thresholds. Give the numeric result in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Temperature response factor.
Use the verified formula:
\[F_T=\sin(\frac{T-T_b}{T_{ol}-T_b}\frac{\pi}{2}); 1; \cos(\frac{T-T_{ou}}{T_{max}-T_{ou}}\frac{\pi}{2})\]
In calculation-friendly notation, this is:
F_T = if Tb<=T<Tol: sin(pi/2*(T-Tb)/(Tol-Tb)); if Tol<=T<Tou: 1; if Tou<=T<Tmax: co... | dev | Temperature response | 2 | CMF028 |
1.00 | cropmath-v1 | null | [
"CMF048",
"CMF043"
] | {
"P": 10.17,
"PS": 0.121,
"Po": 10.5
} | growth_yield | {
"expression": "if P<=Po: 1; if P<=Po+sqrt(1/PS): 1-PS*(P-Po)^2; else: 0",
"id": "CMF050",
"latex": "RPE=1,\\;1-PS(P-P_o)^2,\\;0",
"name": "相对光周期效应",
"name_en": "Relative photoperiod effectiveness",
"precision": 2,
"unit": "fraction"
} | CMF050_chain_2_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Relative photoperiod effectiveness (相对光周期效应)
Formula (LaTeX): RPE=1,\;1-PS(P-P_o)^2,\;0
Formula: RPE = if P<=Po: 1; if P<=Po+sqrt(1/PS): 1-PS*(P-Po)^2; else: 0
Operator notes: * means mult... | Formula name: Relative photoperiod effectiveness (相对光周期效应)
Formula (LaTeX): RPE=1,\;1-PS(P-P_o)^2,\;0
Formula: RPE = if P<=Po: 1; if P<=Po+sqrt(1/PS): 1-PS*(P-Po)^2; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select... | Formula name: Relative photoperiod effectiveness (相对光周期效应)
Formula (LaTeX): RPE=1,\;1-PS(P-P_o)^2,\;0
Formula: RPE = if P<=Po: 1; if P<=Po+sqrt(1/PS): 1-PS*(P-Po)^2; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select... | Formula: RPE = if P<=Po: 1; if P<=Po+sqrt(1/PS): 1-PS*(P-Po)^2; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Relative photoperiod effectiveness (相对光周期效应).
Formula: RPE = if P<=Po: 1; if P<=Po+sqrt(1/PS): 1-PS*(P-Po)^2; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes:... | 4 | Piecewise quadratic | chain_2 | {
"P": 10.17,
"PS": 0.121,
"Po": 10.5
} | Given P=10.17 h, Po=10.5 h, PS=0.121 dimensionless, compute Relative photoperiod effectiveness in phenology. This requires sequential calculation through intermediate variables. Report the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Relative photoperiod effectiveness.
Use the verified formula:
\[RPE=1,\;1-PS(P-P_o)^2,\;0\]
In calculation-friendly notation, this is:
RPE = if P<=Po: 1; if P<=Po+sqrt(1/PS): 1-PS*(P-Po)^2; else: 0.
Substitute the relevant values:
P=10.17 h, Po=10.5 h, PS=0.121 dimensionless.
The compute... | dev | Phenology | 1 | CMF048 |
0.196 | cropmath-v1 | null | [
"CMF005",
"CMF007"
] | {
"Coef_Plant_TN_uptake": 0.058,
"DVI": 0.29,
"NPP": 13.98,
"N_requirement_max_day": 1.44,
"N_shoot": 4.79,
"Ratio_N_C_photo_product": 0.014
} | carbon_nitrogen_cycle | {
"expression": "if NPP<0: 0; if N_shoot<3.5 and DVI<0.3: Coef_Plant_TN_uptake*N_shoot; else: min(N_requirement_max_day, Ratio_N_C_photo_product*NPP)",
"id": "CMF004",
"latex": "N_d=C_uN_{shoot}\\;\\text{or}\\;\\min(N_{max},r_NNPP)",
"name": "作物需氮量",
"name_en": "carbon-nitrogen cycling crop nitrogen demand",
... | CMF004_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling shoot nitrogen allocation (地上部氮分配量)
Formula (LaTeX): N_{shoot}=N_{uptake}\frac{B_{shoot}}{B_{shoot}+B_{root}}
Formula: N_shoot = Plant_TN_uptake * Biom_shoot / (Bio... | Formula name: carbon-nitrogen cycling crop nitrogen demand (作物需氮量)
Formula (LaTeX): N_d=C_uN_{shoot}\;\text{or}\;\min(N_{max},r_NNPP)
Formula: N_demand = if NPP<0: 0; if N_shoot<3.5 and DVI<0.3: Coef_Plant_TN_uptake*N_shoot; else: min(N_requirement_max_day, Ratio_N_C_photo_product*NPP)
Operator notes: * means multiplic... | Formula name: carbon-nitrogen cycling crop nitrogen demand (作物需氮量)
Formula (LaTeX): N_d=C_uN_{shoot}\;\text{or}\;\min(N_{max},r_NNPP)
Formula: N_demand = if NPP<0: 0; if N_shoot<3.5 and DVI<0.3: Coef_Plant_TN_uptake*N_shoot; else: min(N_requirement_max_day, Ratio_N_C_photo_product*NPP)
Operator notes: * means multiplic... | Formula: N_demand = if NPP<0: 0; if N_shoot<3.5 and DVI<0.3: Coef_Plant_TN_uptake*N_shoot; else: min(N_requirement_max_day, Ratio_N_C_photo_product*NPP)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger v... | Relevant formula name: carbon-nitrogen cycling crop nitrogen demand (作物需氮量).
Formula: N_demand = if NPP<0: 0; if N_shoot<3.5 and DVI<0.3: Coef_Plant_TN_uptake*N_shoot; else: min(N_requirement_max_day, Ratio_N_C_photo_product*NPP)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) mean... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling shoot nitrogen allocation (地上部氮分配量)
Formula (LaTeX): N_{shoot}=N_{uptake}\frac{B_{shoot}}{B_{shoot}+B_{root}}
Formula: N_shoot = Plant_TN_uptake * Biom_shoot / (Biom_shoot + ... | 3 | Piecewise minimum | direct | {
"Coef_Plant_TN_uptake": 0.058,
"DVI": 0.29,
"NPP": 13.98,
"N_requirement_max_day": 1.44,
"N_shoot": 4.79,
"Ratio_N_C_photo_product": 0.014
} | A carbon-nitrogen cycling nitrogen calculation estimates carbon-nitrogen cycling crop nitrogen demand. The measured inputs are N_shoot=4.79 g N/m2, Coef_Plant_TN_uptake=0.058 d-1, N_requirement_max_day=1.44 g N/m2/day, NPP=13.98 g C/m2/day, Ratio_N_C_photo_product=0.014 g N/g C, DVI=0.29 dimensionless. What is the carb... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling crop nitrogen demand.
Use the verified formula:
\[N_d=C_uN_{shoot}\;\text{or}\;\min(N_{max},r_NNPP)\]
In calculation-friendly notation, this is:
N_demand = if NPP<0: 0; if N_shoot<3.5 and DVI<0.3: Coef_Plant_TN_uptake*N_shoot; else: min(N_requirement_max_day, Rati... | dev | carbon-nitrogen cycling nitrogen | 0 | CMF005 |
1.028 | cropmath-v1 | null | [
"CMF011",
"CMF003"
] | {
"Coef_T_M": 0.52,
"Td": 25.7,
"Tmax_active": 42,
"Tmin_active": 3,
"Topt_active": 25
} | carbon_nitrogen_cycle | {
"expression": "if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^(1+Coef_T_M) * ((Tmax_active-Td)/(Tmax_active-Topt_active))^(1-Coef_T_M)",
"id": "CMF013",
"latex": "F_T=\\left(\\frac{T_d-T_{min}}{T_{opt}-T_{min}}\\right)^{1+M}\\left(\\frac{T_{max}-T_d}{T_{max}-T_{opt}... | CMF013_branch_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling soil carbon temperature factor (土壤碳分解温度因子)
Formula (LaTeX): F_T=2.4^{(T_{soil}-10)/10}\;\text{where}\;T_{soil}=T\;\text{or}\;4.4+0.76T
Formula: F_T_soil = if is_soi... | Formula name: carbon-nitrogen cycling crop temperature activity factor (作物温度活性因子)
Formula (LaTeX): F_T=\left(\frac{T_d-T_{min}}{T_{opt}-T_{min}}\right)^{1+M}\left(\frac{T_{max}-T_d}{T_{max}-T_{opt}}\right)^{1-M}
Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^... | Formula name: carbon-nitrogen cycling crop temperature activity factor (作物温度活性因子)
Formula (LaTeX): F_T=\left(\frac{T_d-T_{min}}{T_{opt}-T_{min}}\right)^{1+M}\left(\frac{T_{max}-T_d}{T_{max}-T_{opt}}\right)^{1-M}
Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^... | Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^(1+Coef_T_M) * ((Tmax_active-Td)/(Tmax_active-Topt_active))^(1-Coef_T_M)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max... | Relevant formula name: carbon-nitrogen cycling crop temperature activity factor (作物温度活性因子).
Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^(1+Coef_T_M) * ((Tmax_active-Td)/(Tmax_active-Topt_active))^(1-Coef_T_M)
Operator notes: * means multiplication, / means... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling soil carbon temperature factor (土壤碳分解温度因子)
Formula (LaTeX): F_T=2.4^{(T_{soil}-10)/10}\;\text{where}\;T_{soil}=T\;\text{or}\;4.4+0.76T
Formula: F_T_soil = if is_soil_temp>=0.... | 4 | Beta temperature response | branch | {
"Coef_T_M": 0.52,
"Td": 25.7,
"Tmax_active": 42,
"Tmin_active": 3,
"Topt_active": 25
} | For carbon-nitrogen cycling stress, compute the carbon-nitrogen cycling crop temperature activity factor. The inputs are Td=25.7 C, Tmin_active=3.0 C, Topt_active=25.0 C, Tmax_active=42.0 C, Coef_T_M=0.52 dimensionless. Note that this formula uses piecewise logic depending on parameter values. Report the final numeric ... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling crop temperature activity factor.
Use the verified formula:
\[F_T=\left(\frac{T_d-T_{min}}{T_{opt}-T_{min}}\right)^{1+M}\left(\frac{T_{max}-T_d}{T_{max}-T_{opt}}\right)^{1-M}\]
In calculation-friendly notation, this is:
F_T = if Td<=Tmin_active or Td>=Tmax_active:... | dev | carbon-nitrogen cycling stress | 1 | CMF011 |
0.278 | cropmath-v1 | null | [
"CMF055",
"CMF058"
] | {
"Tbase": 6.6,
"Tmean": 12.5,
"Topt": 27.8
} | environmental_response | {
"expression": "if Tmean>=Topt: 1; else: max((Tmean-Tbase)/(Topt-Tbase), 0)",
"id": "CMF060",
"latex": "F_T=1\\;\\text{or}\\;\\max((T-T_b)/(T_o-T_b),0)",
"name": "环境响应温度响应",
"name_en": "environmental-response temperature response",
"precision": 3,
"unit": "fraction"
} | CMF060_direct_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: environmental-response heat stress response (环境响应高温响应)
Formula (LaTeX): F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}
Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0;... | Formula name: environmental-response temperature response (环境响应温度响应)
Formula (LaTeX): F_T=1\;\text{or}\;\max((T-T_b)/(T_o-T_b),0)
Formula: F_Temp = if Tmean>=Topt: 1; else: max((Tmean-Tbase)/(Topt-Tbase), 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means nat... | Formula name: environmental-response temperature response (环境响应温度响应)
Formula (LaTeX): F_T=1\;\text{or}\;\max((T-T_b)/(T_o-T_b),0)
Formula: F_Temp = if Tmean>=Topt: 1; else: max((Tmean-Tbase)/(Topt-Tbase), 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means nat... | Formula: F_Temp = if Tmean>=Topt: 1; else: max((Tmean-Tbase)/(Topt-Tbase), 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: environmental-response temperature response (环境响应温度响应).
Formula: F_Temp = if Tmean>=Topt: 1; else: max((Tmean-Tbase)/(Topt-Tbase), 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larg... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: environmental-response daily biomass increment (环境响应日生物量增量)
Formula (LaTeX): dB=10RUEfSolarSRADF_{CO2}F_T\min(F_W,F_H)
Formula: dBiomass = 10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F_Water, F_... | 2 | Piecewise linear | direct | {
"Tbase": 6.6,
"Tmean": 12.5,
"Topt": 27.8
} | In an environmental-response formula system, the environmental-response temperature response is computed as part of environmental-response formula calculation. With Tmean=12.5 C, Tbase=6.6 C, Topt=27.8 C, determine the numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as environmental-response temperature response.
Use the verified formula:
\[F_T=1\;\text{or}\;\max((T-T_b)/(T_o-T_b),0)\]
In calculation-friendly notation, this is:
F_Temp = if Tmean>=Topt: 1; else: max((Tmean-Tbase)/(Topt-Tbase), 0).
Substitute the relevant values:
Tmean=12.5 C, Tbase=6.6 ... | dev | environmental-response formula system | 2 | CMF055 |
0.0020 | cropmath-v1 | {
"new_value": 0.45,
"old_value": 0.5,
"parameter": "NNI"
} | [
"CMF037",
"CMF041"
] | {
"NNI": 0.45,
"RP": 0.0044,
"WDF": 0.92
} | growth_yield | {
"expression": "RP * min(NNI, WDF)",
"id": "CMF052",
"latex": "R=RP\\cdot\\min(NNI,WDF)",
"name": "实际叶面积相对增长率",
"name_en": "Actual LAI relative growth rate",
"precision": 4,
"unit": "d-1"
} | CMF052_sensitivity_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Green leaf partitioning index (绿叶分配指数)
Formula (LaTeX): PIGL=0.54-0.0046PDT\;(PDT<26),\quad1.4532e^{-0.0492PDT}\;(PDT\ge26)
Formula: PIGL = if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.... | Formula name: Actual LAI relative growth rate (实际叶面积相对增长率)
Formula (LaTeX): R=RP\cdot\min(NNI,WDF)
Formula: R = RP * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: d-1... | Formula name: Actual LAI relative growth rate (实际叶面积相对增长率)
Formula (LaTeX): R=RP\cdot\min(NNI,WDF)
Formula: R = RP * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: d-1... | Formula: R = RP * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: d-1 | Relevant formula name: Actual LAI relative growth rate (实际叶面积相对增长率).
Formula: R = RP * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: d-1 | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Potential leaf area index (潜在叶面积指数)
Formula (LaTeX): LAI_P=LAI_0e^{RP\cdot GDD}
Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means power, ex... | 2 | Minimum stress multiplier | sensitivity | {
"NNI": 0.5,
"RP": 0.0044,
"WDF": 0.92
} | In leaf area growth, we analyze how Actual LAI relative growth rate responds to parameter changes. Baseline: RP=0.0044 d-1, NNI=0.5 fraction, WDF=0.92 fraction. After changing NNI from 0.5 to 0.45, compute the new Actual LAI relative growth rate. Give the numeric value in d-1. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Actual LAI relative growth rate.
Use the verified formula:
\[R=RP\cdot\min(NNI,WDF)\]
In calculation-friendly notation, this is:
R = RP * min(NNI, WDF).
Substitute the relevant values:
RP=0.0044 d-1, NNI=0.45 fraction, WDF=0.92 fraction.
The computed value is 0.0020 d-1.
Therefore, the f... | dev | Leaf area growth | 2 | CMF037 |
0.867 | cropmath-v1 | null | [
"CMF004",
"CMF005"
] | {
"Crop_Water_max": 0.42,
"Crop_Water_min": 0.22,
"Soil_Water": 0.5740000000000001,
"Wilt_point": 0.08
} | carbon_nitrogen_cycle | {
"expression": "if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1+(1-Soil_Water)/(1-Crop_Water_max))",
"id": "CMF014",
"latex": "F_W=f(\\theta,\\theta_{wp},\\theta_{min},\\theta_{max})",
"name": "作物水分胁迫... | CMF014_branch_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling crop nitrogen demand (作物需氮量)
Formula (LaTeX): N_d=C_uN_{shoot}\;\text{or}\;\min(N_{max},r_NNPP)
Formula: N_demand = if NPP<0: 0; if N_shoot<3.5 and DVI<0.3: Coef_Pl... | Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1... | Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1... | Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1+(1-Soil_Water)/(1-Crop_Water_max))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) mean... | Relevant formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子).
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1+(1-Soil_Water)/(1-Crop_Water_max))
Operator notes: * means... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling crop nitrogen demand (作物需氮量)
Formula (LaTeX): N_d=C_uN_{shoot}\;\text{or}\;\min(N_{max},r_NNPP)
Formula: N_demand = if NPP<0: 0; if N_shoot<3.5 and DVI<0.3: Coef_Plant_TN_upt... | 4 | Piecewise water response | branch | {
"Crop_Water_max": 0.42,
"Crop_Water_min": 0.22,
"Soil_Water": 0.5740000000000001,
"Wilt_point": 0.08
} | Calculate carbon-nitrogen cycling crop water stress factor in carbon-nitrogen cycling water with these inputs: Soil_Water=0.574 cm3/cm3, Crop_Water_max=0.42 cm3/cm3, Crop_Water_min=0.22 cm3/cm3, Wilt_point=0.08 cm3/cm3. The computation may follow different paths based on piecewise thresholds. Give the numeric result in... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling crop water stress factor.
Use the verified formula:
\[F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})\]
In calculation-friendly notation, this is:
F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wil... | dev | carbon-nitrogen cycling water | 2 | CMF004 |
0.999 | cropmath-v1 | null | [
"CMF007",
"CMF014"
] | {
"pH": 7.85
} | carbon_nitrogen_cycle | {
"expression": "1 / (1 + exp(2.5 * (5 - pH)))",
"id": "CMF010",
"latex": "F_{pH}=\\frac{1}{1+e^{2.5(5-pH)}}",
"name": "土壤pH分解因子",
"name_en": "carbon-nitrogen cycling soil pH decomposition factor",
"precision": 3,
"unit": "fraction"
} | CMF010_direct_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling soil pH decomposition factor (土壤pH分解因子)
Formula (LaTeX): F_{pH}=\frac{1}{1+e^{2.5(5-pH)}}
Formula: F_pH = 1 / (1 + exp(2.5 * (5 - pH)))
Operator notes: * means mult... | Formula name: carbon-nitrogen cycling soil pH decomposition factor (土壤pH分解因子)
Formula (LaTeX): F_{pH}=\frac{1}{1+e^{2.5(5-pH)}}
Formula: F_pH = 1 / (1 + exp(2.5 * (5 - pH)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select... | Formula name: carbon-nitrogen cycling soil pH decomposition factor (土壤pH分解因子)
Formula (LaTeX): F_{pH}=\frac{1}{1+e^{2.5(5-pH)}}
Formula: F_pH = 1 / (1 + exp(2.5 * (5 - pH)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select... | Formula: F_pH = 1 / (1 + exp(2.5 * (5 - pH)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: carbon-nitrogen cycling soil pH decomposition factor (土壤pH分解因子).
Formula: F_pH = 1 / (1 + exp(2.5 * (5 - pH)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling optimal photosynthetic rate (最适光合速率)
Formula (LaTeX): P_{opt}=\alpha N_{leaf}\frac{PAR}{PAR+\beta}
Formula: Photo_Rate_opt = (Coef_alfa * Leaf_N) * PAR / (PAR + Coef_beta)
Op... | 1 | Logistic | direct | {
"pH": 7.85
} | A carbon-nitrogen cycling soil carbon calculation estimates carbon-nitrogen cycling soil pH decomposition factor. The measured inputs are pH=7.85 pH. What is the carbon-nitrogen cycling soil ph decomposition factor? Give the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling soil pH decomposition factor.
Use the verified formula:
\[F_{pH}=\frac{1}{1+e^{2.5(5-pH)}}\]
In calculation-friendly notation, this is:
F_pH = 1 / (1 + exp(2.5 * (5 - pH))).
Substitute the relevant values:
pH=7.85 pH.
The computed value is 0.999 fraction.
Therefor... | dev | carbon-nitrogen cycling soil carbon | 0 | CMF007 |
83.94 | cropmath-v1 | {
"new_value": 299.8,
"old_value": 260.7,
"parameter": "DTGA"
} | [
"CMF035",
"CMF049"
] | {
"DTGA": 299.8,
"Rg": 0.28
} | growth_yield | {
"expression": "Rg * DTGA",
"id": "CMF046",
"latex": "RG=R_g\\cdot DTGA",
"name": "生长呼吸",
"name_en": "Growth respiration",
"precision": 2,
"unit": "kg/ha/day"
} | CMF046_sensitivity_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Maintenance respiration coefficient at optimum temperature (最适温度维持呼吸系数)
Formula (LaTeX): RM(T_o)=0.0091-0.0001PDT
Formula: RMTo = 0.0091 - 0.0001 * PDT
Operator notes: * means multiplicati... | Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day
Parameters:
- Rg: growth r... | Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day
Parameters:
- Rg: growth r... | Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | Relevant formula name: Growth respiration (生长呼吸).
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: High-temperature fertility factor (高温结实因子)
Formula (LaTeX): HTF=\frac{1}{1+e^{0.853(T_m-36.6)}}
Formula: HTF = if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1
Operator no... | 2 | Product | sensitivity | {
"DTGA": 260.7,
"Rg": 0.28
} | Given current measurements Rg=0.28 fraction, DTGA=260.7 kg/ha/day in respiration, what would the Growth respiration be if DTGA were adjusted to 299.8? Provide the numeric value in kg/ha/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Growth respiration.
Use the verified formula:
\[RG=R_g\cdot DTGA\]
In calculation-friendly notation, this is:
RG = Rg * DTGA.
Substitute the relevant values:
Rg=0.28 fraction, DTGA=299.8 kg/ha/day.
The computed value is 83.94 kg/ha/day.
Therefore, the final numeric answer is \boxed{83.94... | dev | Respiration | 1 | CMF035 |
0.960 | cropmath-v1 | null | [
"CMF047",
"CMF027"
] | {
"T": 26.9,
"TS": 1.35,
"Tb": 10,
"Tm": 42,
"To": 30
} | growth_yield | {
"expression": "(((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** TS",
"id": "CMF051",
"latex": "RTE=\\left[\\frac{T-T_b}{T_o-T_b}\\left(\\frac{T_m-T}{T_m-T_o}\\right)^{(T_m-T_o)/(T_o-T_b)}\\right]^{TS}",
"name": "相对热效应",
"name_en": "Relative thermal effectiveness",
"precision": 3... | CMF051_direct_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Intercepted photosynthetically active radiation (截获光合有效辐射)
Formula (LaTeX): IPAR = PAR \cdot (1 - e^{-k \cdot LAI})
Formula: IPAR = PAR * (1 - exp(-k * LAI))
Operator notes: * means multip... | Formula name: Relative thermal effectiveness (相对热效应)
Formula (LaTeX): RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}
Formula: RTE = (((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** TS
Operator notes: * means multiplication, / means division... | Formula name: Relative thermal effectiveness (相对热效应)
Formula (LaTeX): RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}
Formula: RTE = (((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** TS
Operator notes: * means multiplication, / means division... | Formula: RTE = (((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** TS
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Relative thermal effectiveness (相对热效应).
Formula: RTE = (((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** TS
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larg... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Intercepted photosynthetically active radiation (截获光合有效辐射)
Formula (LaTeX): IPAR = PAR \cdot (1 - e^{-k \cdot LAI})
Formula: IPAR = PAR * (1 - exp(-k * LAI))
Operator notes: * means multiplication, ... | 2 | Beta temperature response | direct | {
"T": 26.9,
"TS": 1.35,
"Tb": 10,
"Tm": 42,
"To": 30
} | Given T=26.9 C, Tb=10.0 C, To=30.0 C, Tm=42.0 C, TS=1.35 dimensionless, calculate the Relative thermal effectiveness for a phenology. The result should be in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Relative thermal effectiveness.
Use the verified formula:
\[RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}\]
In calculation-friendly notation, this is:
RTE = (((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** T... | dev | Phenology | 1 | CMF047 |
8.259 | cropmath-v1 | null | [
"CMF015",
"CMF024"
] | {
"Com": 7.123,
"Cr": 61.55,
"FEh": 0.47800000000000004,
"TI": 0.924
} | methane_emission | {
"expression": "max(0, 0.27 * FEh * (TI * Cr + Com))",
"id": "CMF022",
"latex": "P=\\max(0,0.27F_{Eh}(TI\\cdot C_r+Com))",
"name": "甲烷产生量",
"name_en": "Methane production",
"precision": 3,
"unit": "g CH4/m2/day"
} | CMF022_direct_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Soil temperature from air temperature (土壤温度估算)
Formula (LaTeX): T_{soil}=4.4+0.76T_{air}
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ... | Formula name: Methane production (甲烷产生量)
Formula (LaTeX): P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
O... | Formula name: Methane production (甲烷产生量)
Formula (LaTeX): P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
O... | Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g CH4/m2/day | Relevant formula name: Methane production (甲烷产生量).
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g CH4/m2/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Root-exudate carbon substrate (根系分泌碳底物)
Formula (LaTeX): C_r=0.0018VI\cdot SI\cdot W^{1.25}
Formula: Cr = 0.0018 * VI * SI * W ** 1.25
Operator notes: * means multiplication, / means division, ** or... | 1 | Maximum with chained drivers | direct | {
"Com": 7.123,
"Cr": 61.55,
"FEh": 0.47800000000000004,
"TI": 0.924
} | In a methane, the Methane production is computed as part of methane modeling. With FEh=0.478 fraction, TI=0.924 fraction, Cr=61.55 g C/m2/day, Com=7.123 g C/m2/day, determine the numeric value in g CH4/m2/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Methane production.
Use the verified formula:
\[P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))\]
In calculation-friendly notation, this is:
P = max(0, 0.27 * FEh * (TI * Cr + Com)).
Substitute the relevant values:
FEh=0.478 fraction, TI=0.924 fraction, Cr=61.55 g C/m2/day, Com=7.123 g C/m2/day.
T... | dev | Methane | 2 | CMF015 |
0.326 | cropmath-v1 | null | [
"CMF015",
"CMF024"
] | {
"Q10": 3.52,
"t_soil": 21.1
} | methane_emission | {
"expression": "Q10^((min(t_soil,30)-30)/10)",
"id": "CMF023",
"latex": "TI=Q_{10}^{(t_{sl}-30)/10}",
"name": "甲烷温度指数",
"name_en": "Methane temperature index",
"precision": 3,
"unit": "multiplier"
} | CMF023_direct_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Root-exudate carbon substrate (根系分泌碳底物)
Formula (LaTeX): C_r=0.0018VI\cdot SI\cdot W^{1.25}
Formula: Cr = 0.0018 * VI * SI * W ** 1.25
Operator notes: * means multiplication, / means divis... | Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Methane temperature index (甲烷温度指数).
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Root-exudate carbon substrate (根系分泌碳底物)
Formula (LaTeX): C_r=0.0018VI\cdot SI\cdot W^{1.25}
Formula: Cr = 0.0018 * VI * SI * W ** 1.25
Operator notes: * means multiplication, / means division, ** or... | 1 | Q10 with temperature clipping | direct | {
"Q10": 3.52,
"t_soil": 21.1
} | In a methane, the Methane temperature index is computed as part of methane modeling. With Q10=3.52 dimensionless, t_soil=21.1 C, determine the numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Methane temperature index.
Use the verified formula:
\[TI=Q_{10}^{(t_{sl}-30)/10}\]
In calculation-friendly notation, this is:
TI = Q10^((min(t_soil,30)-30)/10).
Substitute the relevant values:
Q10=3.52 dimensionless, t_soil=21.1 C.
The computed value is 0.326 fraction.
Therefore, the fi... | dev | Methane | 2 | CMF015 |
0.11 | cropmath-v1 | null | [
"CMF031",
"CMF033"
] | {
"B_above": 17858,
"PDT": 34.4,
"Y_grain": 7851
} | growth_yield | {
"expression": "(Y_grain / B_above / 0.87) / (1 + exp(-0.2804 * (PDT - 39)))",
"id": "CMF042",
"latex": "PIP=\\frac{HI/0.87}{1+e^{-0.2804(PDT-39)}}",
"name": "穗分配指数",
"name_en": "Panicle partitioning index",
"precision": 2,
"unit": "fraction"
} | CMF042_direct_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Daily dry matter increment (日干物质增量)
Formula (LaTeX): GCR=\frac{DTGA-RM-RG}{1-b}
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ ... | Formula name: Panicle partitioning index (穗分配指数)
Formula (LaTeX): PIP=\frac{HI/0.87}{1+e^{-0.2804(PDT-39)}}
Formula: PIP = (Y_grain / B_above / 0.87) / (1 + exp(-0.2804 * (PDT - 39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/... | Formula name: Panicle partitioning index (穗分配指数)
Formula (LaTeX): PIP=\frac{HI/0.87}{1+e^{-0.2804(PDT-39)}}
Formula: PIP = (Y_grain / B_above / 0.87) / (1 + exp(-0.2804 * (PDT - 39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/... | Formula: PIP = (Y_grain / B_above / 0.87) / (1 + exp(-0.2804 * (PDT - 39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Panicle partitioning index (穗分配指数).
Formula: PIP = (Y_grain / B_above / 0.87) / (1 + exp(-0.2804 * (PDT - 39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit:... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Light interception fraction (光能截获率)
Formula (LaTeX): fPAR = 1 - e^{-k \cdot LAI}
Formula: fPAR = 1 - exp(-k * LAI)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(... | 1 | Multi-step sigmoid | direct | {
"B_above": 17858,
"PDT": 34.4,
"Y_grain": 7851
} | Given Y_grain=7851.0 kg/ha, B_above=17858.0 kg/ha, PDT=34.4 physiological days, calculate the Panicle partitioning index for a dry matter partitioning. The result should be in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Panicle partitioning index.
Use the verified formula:
\[PIP=\frac{HI/0.87}{1+e^{-0.2804(PDT-39)}}\]
In calculation-friendly notation, this is:
PIP = (Y_grain / B_above / 0.87) / (1 + exp(-0.2804 * (PDT - 39))).
Substitute the relevant values:
Y_grain=7851.0 kg/ha, B_above=17858.0 kg/ha, ... | dev | Dry matter partitioning | 1 | CMF031 |
0.00 | cropmath-v1 | null | [
"CMF061",
"CMF057"
] | {
"Tbase": 6.8,
"Tmean": 3
} | environmental_response | {
"expression": "max(Tmean - Tbase, 0)",
"id": "CMF056",
"latex": "dTT=\\max(T_{mean}-T_{base},0)",
"name": "每日有效积温",
"name_en": "environmental-response daily thermal time",
"precision": 2,
"unit": "C day"
} | CMF056_branch_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: environmental-response water stress response (环境响应水分响应)
Formula (LaTeX): F_W=\max(0,1-S_WARID)
Formula: F_Water = max(0, 1 - S_Water * ARID)
Operator notes: * means multiplication, / means... | Formula name: environmental-response daily thermal time (每日有效积温)
Formula (LaTeX): dTT=\max(T_{mean}-T_{base},0)
Formula: dTT = max(Tmean - Tbase, 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value... | Formula name: environmental-response daily thermal time (每日有效积温)
Formula (LaTeX): dTT=\max(T_{mean}-T_{base},0)
Formula: dTT = max(Tmean - Tbase, 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value... | Formula: dTT = max(Tmean - Tbase, 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day | Relevant formula name: environmental-response daily thermal time (每日有效积温).
Formula: dTT = max(Tmean - Tbase, 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: environmental-response water stress response (环境响应水分响应)
Formula (LaTeX): F_W=\max(0,1-S_WARID)
Formula: F_Water = max(0, 1 - S_Water * ARID)
Operator notes: * means multiplication, / means division,... | 3 | Maximum linear | branch | {
"Tbase": 6.8,
"Tmean": 3
} | Calculate environmental-response daily thermal time in environmental-response formula system with these inputs: Tmean=3.0 C, Tbase=6.8 C. The computation may follow different paths based on piecewise thresholds. Give the numeric result in C day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as environmental-response daily thermal time.
Use the verified formula:
\[dTT=\max(T_{mean}-T_{base},0)\]
In calculation-friendly notation, this is:
dTT = max(Tmean - Tbase, 0).
Substitute the relevant values:
Tmean=3.0 C, Tbase=6.8 C.
The computed value is 0.00 C day.
Therefore, the final ... | dev | environmental-response formula system | 2 | CMF061 |
29.939 | cropmath-v1 | null | [
"CMF002",
"CMF010"
] | {
"Coef_alfa": 27.9,
"Coef_beta": 146.2,
"Leaf_N": 1.58,
"PAR": 309.5
} | carbon_nitrogen_cycle | {
"expression": "(Coef_alfa * Leaf_N) * PAR / (PAR + Coef_beta)",
"id": "CMF007",
"latex": "P_{opt}=\\alpha N_{leaf}\\frac{PAR}{PAR+\\beta}",
"name": "最适光合速率",
"name_en": "carbon-nitrogen cycling optimal photosynthetic rate",
"precision": 3,
"unit": "umol CO2/m2/s"
} | CMF007_chain_2_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0... | Formula name: carbon-nitrogen cycling optimal photosynthetic rate (最适光合速率)
Formula (LaTeX): P_{opt}=\alpha N_{leaf}\frac{PAR}{PAR+\beta}
Formula: Photo_Rate_opt = (Coef_alfa * Leaf_N) * PAR / (PAR + Coef_beta)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means n... | Formula name: carbon-nitrogen cycling optimal photosynthetic rate (最适光合速率)
Formula (LaTeX): P_{opt}=\alpha N_{leaf}\frac{PAR}{PAR+\beta}
Formula: Photo_Rate_opt = (Coef_alfa * Leaf_N) * PAR / (PAR + Coef_beta)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means n... | Formula: Photo_Rate_opt = (Coef_alfa * Leaf_N) * PAR / (PAR + Coef_beta)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: umol CO2/m2/s | Relevant formula name: carbon-nitrogen cycling optimal photosynthetic rate (最适光合速率).
Formula: Photo_Rate_opt = (Coef_alfa * Leaf_N) * PAR / (PAR + Coef_beta)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/lar... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Oper... | 3 | Michaelis-Menten response | chain_2 | {
"Coef_alfa": 27.9,
"Coef_beta": 146.2,
"Leaf_N": 1.58,
"PAR": 309.5
} | In carbon-nitrogen cycling photosynthesis, the carbon-nitrogen cycling optimal photosynthetic rate is obtained by chaining intermediate calculations. With inputs Coef_alfa=27.9 umol CO2/gN/s, Coef_beta=146.2 umol/m2/s, PAR=309.5 umol/m2/s, Leaf_N=1.58 gN/m2, determine the numeric value in umol CO2/m2/s. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling optimal photosynthetic rate.
Use the verified formula:
\[P_{opt}=\alpha N_{leaf}\frac{PAR}{PAR+\beta}\]
In calculation-friendly notation, this is:
Photo_Rate_opt = (Coef_alfa * Leaf_N) * PAR / (PAR + Coef_beta).
Substitute the relevant values:
Coef_alfa=27.9 umol ... | dev | carbon-nitrogen cycling photosynthesis | 2 | CMF002 |
0.771 | cropmath-v1 | null | [
"CMF031",
"CMF039"
] | {
"BFF": 1.19,
"DTE": 0.771,
"IE": 1.24,
"PDT": 22.1,
"RPE": 0.81
} | growth_yield | {
"expression": "if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0",
"id": "CMF027",
"latex": "DPE=DTE\\cdot IE,\\;DTE\\cdot RPE,\\;DTE,\\;DTE\\cdot BFF",
"name": "每日生理效应",
"name_en": "Daily physiological effectiveness",
"precision": 3,
"unit": "physiological days/day"
} | CMF027_direct_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Low-temperature fertility factor (低温结实因子)
Formula (LaTeX): LTF=1-\frac{4.6+0.054Q_t^{1.56}}{100}
Formula: LTF = if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1
Operator not... | Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: physiological days/day | Relevant formula name: Daily physiological effectiveness (每日生理效应).
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the small... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Light interception fraction (光能截获率)
Formula (LaTeX): fPAR = 1 - e^{-k \cdot LAI}
Formula: fPAR = 1 - exp(-k * LAI)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(... | 2 | Stage-dependent product | direct | {
"BFF": 1.19,
"DTE": 0.771,
"IE": 1.24,
"PDT": 22.1,
"RPE": 0.81
} | In a phenology, the Daily physiological effectiveness is computed as part of phenology modeling. With PDT=22.1 physiological days, DTE=0.771 fraction, IE=1.24 dimensionless, RPE=0.81 fraction, BFF=1.19 dimensionless, determine the numeric value in physiological days/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Daily physiological effectiveness.
Use the verified formula:
\[DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF\]
In calculation-friendly notation, this is:
DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0.
Substitute the relevant values:
PDT=22.... | dev | Phenology | 2 | CMF031 |
5.724 | cropmath-v1 | {
"new_value": 0.004,
"old_value": 0.0037,
"parameter": "Coef_Rm"
} | [
"CMF013",
"CMF002"
] | {
"Biom_plant_yesterday": 941.4,
"Coef_Rm": 0.004,
"DVI": 0.78,
"Tmn": 19
} | carbon_nitrogen_cycle | {
"expression": "0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)",
"id": "CMF008",
"latex": "R_m=0.0432\\cdot24(Biom/0.45)C_m2^{(T-25)/10}",
"name": "植株维持呼吸",
"name_en": "carbon-nitrogen cycling plant maintenance respiration",
"precision": 3,
"unit": "g C/m2/day"... | CMF008_sensitivity_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸)
Formula (LaTeX): R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^(... | Formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸)
Formula (LaTeX): R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | Formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸)
Formula (LaTeX): R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: carbon-nitrogen cycling plant maintenance respiration (植株维持呼吸).
Formula: Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling crop temperature activity factor (作物温度活性因子)
Formula (LaTeX): F_T=\left(\frac{T_d-T_{min}}{T_{opt}-T_{min}}\right)^{1+M}\left(\frac{T_{max}-T_d}{T_{max}-T_{opt}}\right)^{1-M}
... | 3 | Q10 with DVI correction | sensitivity | {
"Biom_plant_yesterday": 941.4,
"Coef_Rm": 0.0037,
"DVI": 0.78,
"Tmn": 19
} | Given current measurements Biom_plant_yesterday=941.4 g C/m2, Coef_Rm=0.0037 g C/g C/s, Tmn=19.0 C, DVI=0.78 dimensionless in carbon-nitrogen cycling respiration, what would the carbon-nitrogen cycling plant maintenance respiration be if Coef_Rm were adjusted to 0.004? Provide the numeric value in g C/m2/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling plant maintenance respiration.
Use the verified formula:
\[R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10}\]
In calculation-friendly notation, this is:
Rm = 0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1).
Substitute the rel... | dev | carbon-nitrogen cycling respiration | 1 | CMF013 |
0.842 | cropmath-v1 | null | [
"CMF010",
"CMF004"
] | {
"BD": 1.26,
"Saturate_Water": 0.48,
"Soil_Water": 0.23900000000000002
} | carbon_nitrogen_cycle | {
"expression": "if Soil_Water>=Saturate_Water: 0.65; else: 0.49*exp(3.88*(Soil_Water/BD)-5.4*(Soil_Water/BD)^2)",
"id": "CMF012",
"latex": "F_W=0.49e^{3.88W-5.4W^2}",
"name": "土壤碳分解水分因子",
"name_en": "carbon-nitrogen cycling soil carbon water factor",
"precision": 3,
"unit": "fraction"
} | CMF012_branch_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling soil carbon water factor (土壤碳分解水分因子)
Formula (LaTeX): F_W=0.49e^{3.88W-5.4W^2}
Formula: F_W_soil = if Soil_Water>=Saturate_Water: 0.65; else: 0.49*exp(3.88*(Soil_Wa... | Formula name: carbon-nitrogen cycling soil carbon water factor (土壤碳分解水分因子)
Formula (LaTeX): F_W=0.49e^{3.88W-5.4W^2}
Formula: F_W_soil = if Soil_Water>=Saturate_Water: 0.65; else: 0.49*exp(3.88*(Soil_Water/BD)-5.4*(Soil_Water/BD)^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) m... | Formula name: carbon-nitrogen cycling soil carbon water factor (土壤碳分解水分因子)
Formula (LaTeX): F_W=0.49e^{3.88W-5.4W^2}
Formula: F_W_soil = if Soil_Water>=Saturate_Water: 0.65; else: 0.49*exp(3.88*(Soil_Water/BD)-5.4*(Soil_Water/BD)^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) m... | Formula: F_W_soil = if Soil_Water>=Saturate_Water: 0.65; else: 0.49*exp(3.88*(Soil_Water/BD)-5.4*(Soil_Water/BD)^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: carbon-nitrogen cycling soil carbon water factor (土壤碳分解水分因子).
Formula: F_W_soil = if Soil_Water>=Saturate_Water: 0.65; else: 0.49*exp(3.88*(Soil_Water/BD)-5.4*(Soil_Water/BD)^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural lo... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling soil pH decomposition factor (土壤pH分解因子)
Formula (LaTeX): F_{pH}=\frac{1}{1+e^{2.5(5-pH)}}
Formula: F_pH = 1 / (1 + exp(2.5 * (5 - pH)))
Operator notes: * means multiplication... | 4 | Piecewise exponential | branch | {
"BD": 1.26,
"Saturate_Water": 0.48,
"Soil_Water": 0.23900000000000002
} | Calculate carbon-nitrogen cycling soil carbon water factor in carbon-nitrogen cycling soil carbon with these inputs: Soil_Water=0.239 cm3/cm3, Saturate_Water=0.48 cm3/cm3, BD=1.26 g/cm3. The computation may follow different paths based on piecewise thresholds. Give the numeric result in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling soil carbon water factor.
Use the verified formula:
\[F_W=0.49e^{3.88W-5.4W^2}\]
In calculation-friendly notation, this is:
F_W_soil = if Soil_Water>=Saturate_Water: 0.65; else: 0.49*exp(3.88*(Soil_Water/BD)-5.4*(Soil_Water/BD)^2).
Substitute the relevant values:
... | dev | carbon-nitrogen cycling soil carbon | 2 | CMF010 |
0.978 | cropmath-v1 | null | [
"CMF021",
"CMF016"
] | {
"WaterC": 0.393
} | methane_emission | {
"expression": "0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)",
"id": "CMF025",
"latex": "WI=0.49e^{3.88W_c-5.4W_c^2}",
"name": "水分分解因子",
"name_en": "Water-content decomposition factor",
"precision": 3,
"unit": "fraction"
} | CMF025_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Methane ebullition emission (甲烷冒泡排放)
Formula (LaTeX): E_{bl}=\min(0.7\ln(t_{soil})/W_r,0.9)P
Formula: Ebl = min(0.7 * ln(t_soil) / Wr, 0.9) * P
Operator notes: * means multiplication, / me... | Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/l... | Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/l... | Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Water-content decomposition factor (水分分解因子).
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Soil organic matter carbon decomposition (土壤有机质碳分解量)
Formula (LaTeX): OMSC=WI\cdot SI\cdot TI\cdot0.003\cdot OMS
Formula: OMSC = WI * SI * TI * 0.003 * OMS
Operator notes: * means multiplication, / ... | 1 | Exponential quadratic | direct | {
"WaterC": 0.393
} | A methane calculation estimates Water-content decomposition factor. The measured inputs are WaterC=0.393 fraction. What is the water-content decomposition factor? Give the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Water-content decomposition factor.
Use the verified formula:
\[WI=0.49e^{3.88W_c-5.4W_c^2}\]
In calculation-friendly notation, this is:
WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2).
Substitute the relevant values:
WaterC=0.393 fraction.
The computed value is 0.978 fraction.
Therefore... | dev | Methane | 0 | CMF021 |
1.177 | cropmath-v1 | null | [
"CMF009",
"CMF005"
] | {
"CO2": 459,
"Coef_B_CO2": 0.59
} | carbon_nitrogen_cycle | {
"expression": "1 + Coef_B_CO2 * ln(CO2 / 340)",
"id": "CMF001",
"latex": "F_{CO2}=1+B\\ln(CO2/340)",
"name": "作物二氧化碳施肥因子",
"name_en": "carbon-nitrogen cycling CO2 fertilization factor",
"precision": 3,
"unit": "multiplier"
} | CMF001_direct_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling shoot nitrogen allocation (地上部氮分配量)
Formula (LaTeX): N_{shoot}=N_{uptake}\frac{B_{shoot}}{B_{shoot}+B_{root}}
Formula: N_shoot = Plant_TN_uptake * Biom_shoot / (Bio... | Formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子)
Formula (LaTeX): F_{CO2}=1+B\ln(CO2/340)
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smal... | Formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子)
Formula (LaTeX): F_{CO2}=1+B\ln(CO2/340)
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smal... | Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子).
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling carbon pool respiration loss (碳库呼吸损失)
Formula (LaTeX): R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans})
Formula: Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_textur... | 1 | Logarithmic | direct | {
"CO2": 459,
"Coef_B_CO2": 0.59
} | In a carbon-nitrogen cycling photosynthesis, the carbon-nitrogen cycling CO2 fertilization factor is computed as part of carbon-nitrogen cycling photosynthesis modeling. With CO2=459.0 ppm, Coef_B_CO2=0.59 dimensionless, determine the numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling CO2 fertilization factor.
Use the verified formula:
\[F_{CO2}=1+B\ln(CO2/340)\]
In calculation-friendly notation, this is:
F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340).
Substitute the relevant values:
CO2=459.0 ppm, Coef_B_CO2=0.59 dimensionless.
The computed value is 1... | dev | carbon-nitrogen cycling photosynthesis | 2 | CMF009 |
38.77 | cropmath-v1 | null | [
"CMF051",
"CMF047"
] | {
"Am": 41.5,
"FCO2": 1.05,
"FPA": 0.93,
"FT": 0.92,
"NNI": 1.04,
"WDF": 1.08
} | growth_yield | {
"expression": "Am * FCO2 * FPA * FT * min(NNI, WDF)",
"id": "CMF026",
"latex": "AMAX=Am\\cdot F_{CO2}\\cdot F_{PA}\\cdot F_T\\cdot\\min(NNI,WDF)",
"name": "实际最大同化速率",
"name_en": "Actual maximum assimilation rate",
"precision": 2,
"unit": "kg CO2/ha/h"
} | CMF026_chain_2_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes... | Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and ... | Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and ... | Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg CO2/ha/h | Relevant formula name: Actual maximum assimilation rate (实际最大同化速率).
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg CO2/ha/h | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Relative thermal effectiveness (相对热效应)
Formula (LaTeX): RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}
Formula: RTE = (((T - Tb)/(To - Tb)) * (((... | 4 | Multiplicative with minimum stress | chain_2 | {
"Am": 41.5,
"FCO2": 1.05,
"FPA": 0.93,
"FT": 0.92,
"NNI": 1.04,
"WDF": 1.08
} | A photosynthesis module estimates Actual maximum assimilation rate using intermediate drivers. Use the provided inputs in sequence. The measurements are Am=41.5 kg CO2/ha/h, FCO2=1.05 fraction, FPA=0.93 fraction, FT=0.92 fraction, NNI=1.04 fraction, WDF=1.08 fraction. Compute the actual maximum assimilation rate and gi... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Actual maximum assimilation rate.
Use the verified formula:
\[AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)\]
In calculation-friendly notation, this is:
AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF).
Substitute the relevant values:
Am=41.5 kg CO2/ha/h, FCO2=1.05 fraction, FPA... | dev | Photosynthesis | 0 | CMF051 |
5978.8 | cropmath-v1 | null | [
"CMF058",
"CMF055"
] | {
"Biomass": 16159,
"HI": 0.37
} | environmental_response | {
"expression": "Biomass * HI",
"id": "CMF062",
"latex": "Yield=Biomass\\cdot HI",
"name": "环境响应产量",
"name_en": "environmental-response yield",
"precision": 1,
"unit": "kg/ha"
} | CMF062_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: environmental-response daily biomass increment (环境响应日生物量增量)
Formula (LaTeX): dB=10RUEfSolarSRADF_{CO2}F_T\min(F_W,F_H)
Formula: dBiomass = 10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F... | Formula name: environmental-response yield (环境响应产量)
Formula (LaTeX): Yield=Biomass\cdot HI
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha
Paramet... | Formula name: environmental-response yield (环境响应产量)
Formula (LaTeX): Yield=Biomass\cdot HI
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha
Paramet... | Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha | Relevant formula name: environmental-response yield (环境响应产量).
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: environmental-response heat stress response (环境响应高温响应)
Formula (LaTeX): F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}
Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max... | 1 | Product | direct | {
"Biomass": 16159,
"HI": 0.37
} | A environmental-response formula system calculation estimates environmental-response yield. The measured inputs are Biomass=16159.0 kg/ha, HI=0.37 fraction. What is the simple yield? Give the final numeric value in kg/ha. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as environmental-response yield.
Use the verified formula:
\[Yield=Biomass\cdot HI\]
In calculation-friendly notation, this is:
Yield = Biomass * HI.
Substitute the relevant values:
Biomass=16159.0 kg/ha, HI=0.37 fraction.
The computed value is 5978.8 kg/ha.
Therefore, the final numeric ans... | dev | environmental-response formula system | 0 | CMF058 |
8.285 | cropmath-v1 | {
"new_value": 753.4,
"old_value": 684.9,
"parameter": "Biom_shoot"
} | [
"CMF006",
"CMF011"
] | {
"Biom_root": 24.1,
"Biom_shoot": 753.4,
"Plant_TN_uptake": 8.55
} | carbon_nitrogen_cycle | {
"expression": "Plant_TN_uptake * Biom_shoot / (Biom_shoot + Biom_root)",
"id": "CMF005",
"latex": "N_{shoot}=N_{uptake}\\frac{B_{shoot}}{B_{shoot}+B_{root}}",
"name": "地上部氮分配量",
"name_en": "carbon-nitrogen cycling shoot nitrogen allocation",
"precision": 3,
"unit": "g N/m2"
} | CMF005_sensitivity_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling shoot nitrogen allocation (地上部氮分配量)
Formula (LaTeX): N_{shoot}=N_{uptake}\frac{B_{shoot}}{B_{shoot}+B_{root}}
Formula: N_shoot = Plant_TN_uptake * Biom_shoot / (Bio... | Formula name: carbon-nitrogen cycling shoot nitrogen allocation (地上部氮分配量)
Formula (LaTeX): N_{shoot}=N_{uptake}\frac{B_{shoot}}{B_{shoot}+B_{root}}
Formula: N_shoot = Plant_TN_uptake * Biom_shoot / (Biom_shoot + Biom_root)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula name: carbon-nitrogen cycling shoot nitrogen allocation (地上部氮分配量)
Formula (LaTeX): N_{shoot}=N_{uptake}\frac{B_{shoot}}{B_{shoot}+B_{root}}
Formula: N_shoot = Plant_TN_uptake * Biom_shoot / (Biom_shoot + Biom_root)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula: N_shoot = Plant_TN_uptake * Biom_shoot / (Biom_shoot + Biom_root)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g N/m2 | Relevant formula name: carbon-nitrogen cycling shoot nitrogen allocation (地上部氮分配量).
Formula: N_shoot = Plant_TN_uptake * Biom_shoot / (Biom_shoot + Biom_root)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/la... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling canopy absorbed PAR (冠层吸收光合有效辐射)
Formula (LaTeX): PAR=Radi\cdot0.44\cdot4.6(1-\rho)\frac{1-e^{-KLAI}}{KLAI}
Formula: PAR = Radi * 0.44 * 4.6 * (1-Coef_rou) * (1-exp(-Coef_K*L... | 2 | Biomass-weighted allocation | sensitivity | {
"Biom_root": 24.1,
"Biom_shoot": 684.9,
"Plant_TN_uptake": 8.55
} | A carbon-nitrogen cycling nitrogen calculation involves sensitivity analysis. The current measurements are Plant_TN_uptake=8.55 g N/m2, Biom_shoot=684.9 g C/m2, Biom_root=24.1 g C/m2. A field technician asks what the carbon-nitrogen cycling shoot nitrogen allocation would become if Biom_shoot changed to 753.4. Report t... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling shoot nitrogen allocation.
Use the verified formula:
\[N_{shoot}=N_{uptake}\frac{B_{shoot}}{B_{shoot}+B_{root}}\]
In calculation-friendly notation, this is:
N_shoot = Plant_TN_uptake * Biom_shoot / (Biom_shoot + Biom_root).
Substitute the relevant values:
Plant_TN... | dev | carbon-nitrogen cycling nitrogen | 0 | CMF006 |
439.26 | cropmath-v1 | null | [
"CMF047",
"CMF049"
] | {
"DTGA": 565.5,
"RG": 53.7,
"RM": 94.5,
"b": 0.05
} | growth_yield | {
"expression": "(DTGA - RM - RG) / (1 - b)",
"id": "CMF033",
"latex": "GCR=\\frac{DTGA-RM-RG}{1-b}",
"name": "日干物质增量",
"name_en": "Daily dry matter increment",
"precision": 2,
"unit": "kg/ha/day"
} | CMF033_chain_2_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Daily dry matter increment (日干物质增量)
Formula (LaTeX): GCR=\frac{DTGA-RM-RG}{1-b}
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ ... | Formula name: Daily dry matter increment (日干物质增量)
Formula (LaTeX): GCR=\frac{DTGA-RM-RG}{1-b}
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula name: Daily dry matter increment (日干物质增量)
Formula (LaTeX): GCR=\frac{DTGA-RM-RG}{1-b}
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | Relevant formula name: Daily dry matter increment (日干物质增量).
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Intercepted photosynthetically active radiation (截获光合有效辐射)
Formula (LaTeX): IPAR = PAR \cdot (1 - e^{-k \cdot LAI})
Formula: IPAR = PAR * (1 - exp(-k * LAI))
Operator notes: * means multiplication, ... | 3 | Subtraction and conversion | chain_2 | {
"DTGA": 565.5,
"RG": 53.7,
"RM": 94.5,
"b": 0.05
} | In respiration, the Daily dry matter increment is obtained by chaining intermediate calculations. With inputs DTGA=565.5 kg/ha/day, RM=94.5 kg/ha/day, RG=53.7 kg/ha/day, b=0.05 fraction, determine the numeric value in kg/ha/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Daily dry matter increment.
Use the verified formula:
\[GCR=\frac{DTGA-RM-RG}{1-b}\]
In calculation-friendly notation, this is:
GCR = (DTGA - RM - RG) / (1 - b).
Substitute the relevant values:
DTGA=565.5 kg/ha/day, RM=94.5 kg/ha/day, RG=53.7 kg/ha/day, b=0.05 fraction.
The computed valu... | dev | Respiration | 2 | CMF047 |
12.90 | cropmath-v1 | null | [
"CMF058",
"CMF059"
] | {
"Tbase": 10.6,
"Tmean": 23.5
} | environmental_response | {
"expression": "max(Tmean - Tbase, 0)",
"id": "CMF056",
"latex": "dTT=\\max(T_{mean}-T_{base},0)",
"name": "每日有效积温",
"name_en": "environmental-response daily thermal time",
"precision": 2,
"unit": "C day"
} | CMF056_branch_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: environmental-response daily thermal time (每日有效积温)
Formula (LaTeX): dTT=\max(T_{mean}-T_{base},0)
Formula: dTT = max(Tmean - Tbase, 0)
Operator notes: * means multiplication, / means divis... | Formula name: environmental-response daily thermal time (每日有效积温)
Formula (LaTeX): dTT=\max(T_{mean}-T_{base},0)
Formula: dTT = max(Tmean - Tbase, 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value... | Formula name: environmental-response daily thermal time (每日有效积温)
Formula (LaTeX): dTT=\max(T_{mean}-T_{base},0)
Formula: dTT = max(Tmean - Tbase, 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value... | Formula: dTT = max(Tmean - Tbase, 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day | Relevant formula name: environmental-response daily thermal time (每日有效积温).
Formula: dTT = max(Tmean - Tbase, 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: environmental-response heat stress response (环境响应高温响应)
Formula (LaTeX): F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}
Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max... | 3 | Maximum linear | branch | {
"Tbase": 10.6,
"Tmean": 23.5
} | Calculate environmental-response daily thermal time in environmental-response formula system with these inputs: Tmean=23.5 C, Tbase=10.6 C. The computation may follow different paths based on piecewise thresholds. Give the numeric result in C day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as environmental-response daily thermal time.
Use the verified formula:
\[dTT=\max(T_{mean}-T_{base},0)\]
In calculation-friendly notation, this is:
dTT = max(Tmean - Tbase, 0).
Substitute the relevant values:
Tmean=23.5 C, Tbase=10.6 C.
The computed value is 12.90 C day.
Therefore, the fin... | dev | environmental-response formula system | 2 | CMF058 |
0.331 | cropmath-v1 | null | [
"CMF018",
"CMF017"
] | {
"OMS": 1246.5,
"SI": 1.15,
"TI": 0.28,
"WI": 0.275
} | methane_emission | {
"expression": "WI * SI * TI * 0.003 * OMS",
"id": "CMF021",
"latex": "OMSC=WI\\cdot SI\\cdot TI\\cdot0.003\\cdot OMS",
"name": "土壤有机质碳分解量",
"name_en": "Soil organic matter carbon decomposition",
"precision": 3,
"unit": "g C/m2/day"
} | CMF021_chain_2_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Soil organic matter carbon decomposition (土壤有机质碳分解量)
Formula (LaTeX): OMSC=WI\cdot SI\cdot TI\cdot0.003\cdot OMS
Formula: OMSC = WI * SI * TI * 0.003 * OMS
Operator notes: * means multipli... | Formula name: Soil organic matter carbon decomposition (土壤有机质碳分解量)
Formula (LaTeX): OMSC=WI\cdot SI\cdot TI\cdot0.003\cdot OMS
Formula: OMSC = WI * SI * TI * 0.003 * OMS
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the... | Formula name: Soil organic matter carbon decomposition (土壤有机质碳分解量)
Formula (LaTeX): OMSC=WI\cdot SI\cdot TI\cdot0.003\cdot OMS
Formula: OMSC = WI * SI * TI * 0.003 * OMS
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the... | Formula: OMSC = WI * SI * TI * 0.003 * OMS
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: Soil organic matter carbon decomposition (土壤有机质碳分解量).
Formula: OMSC = WI * SI * TI * 0.003 * OMS
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Redox potential factor (氧化还原电位因子)
Formula (LaTeX): F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplication, / mea... | 3 | Multiplicative | chain_2 | {
"OMS": 1246.5,
"SI": 1.15,
"TI": 0.28,
"WI": 0.275
} | In methane, the Soil organic matter carbon decomposition is obtained by chaining intermediate calculations. With inputs WI=0.275 fraction, SI=1.15 fraction, TI=0.28 fraction, OMS=1246.5 g C/m2, determine the numeric value in g C/m2/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Soil organic matter carbon decomposition.
Use the verified formula:
\[OMSC=WI\cdot SI\cdot TI\cdot0.003\cdot OMS\]
In calculation-friendly notation, this is:
OMSC = WI * SI * TI * 0.003 * OMS.
Substitute the relevant values:
WI=0.275 fraction, SI=1.15 fraction, TI=0.28 fraction, OMS=1246... | dev | Methane | 2 | CMF018 |
6.319 | cropmath-v1 | null | [
"CMF018",
"CMF016"
] | {
"CH4RiceEfC": 0.20800000000000002,
"Ebl": 4.391,
"P": 11.616,
"W": 5453.7,
"Wmax": 9178
} | methane_emission | {
"expression": "Ebl + P * CH4RiceEfC * (1 - W/Wmax)^0.25",
"id": "CMF017",
"latex": "E=E_{bl}+P\\cdot C(1-W/W_{max})^{0.25}",
"name": "甲烷总排放",
"name_en": "Total methane emission",
"precision": 3,
"unit": "g CH4/m2/day"
} | CMF017_direct_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Redox potential factor (氧化还原电位因子)
Formula (LaTeX): F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplicat... | Formula name: Total methane emission (甲烷总排放)
Formula (LaTeX): E=E_{bl}+P\cdot C(1-W/W_{max})^{0.25}
Formula: E = Ebl + P * CH4RiceEfC * (1 - W/Wmax)^0.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger ... | Formula name: Total methane emission (甲烷总排放)
Formula (LaTeX): E=E_{bl}+P\cdot C(1-W/W_{max})^{0.25}
Formula: E = Ebl + P * CH4RiceEfC * (1 - W/Wmax)^0.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger ... | Formula: E = Ebl + P * CH4RiceEfC * (1 - W/Wmax)^0.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g CH4/m2/day | Relevant formula name: Total methane emission (甲烷总排放).
Formula: E = Ebl + P * CH4RiceEfC * (1 - W/Wmax)^0.25
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g CH4/m2/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Redox potential factor (氧化还原电位因子)
Formula (LaTeX): F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplication, / mea... | 2 | Chained sum | direct | {
"CH4RiceEfC": 0.20800000000000002,
"Ebl": 4.391,
"P": 11.616,
"W": 5453.7,
"Wmax": 9178
} | In a methane, the Total methane emission is computed as part of methane modeling. With Ebl=4.391 g CH4/m2/day, P=11.616 g CH4/m2/day, CH4RiceEfC=0.208 fraction, W=5453.7 kg/ha, Wmax=9178.0 kg/ha, determine the numeric value in g CH4/m2/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Total methane emission.
Use the verified formula:
\[E=E_{bl}+P\cdot C(1-W/W_{max})^{0.25}\]
In calculation-friendly notation, this is:
E = Ebl + P * CH4RiceEfC * (1 - W/Wmax)^0.25.
Substitute the relevant values:
Ebl=4.391 g CH4/m2/day, P=11.616 g CH4/m2/day, CH4RiceEfC=0.208 fraction, W... | dev | Methane | 2 | CMF018 |
0.345 | cropmath-v1 | null | [
"CMF054",
"CMF049"
] | {
"BFF": 0.67,
"DTE": 0.515,
"IE": 1.24,
"PDT": 34.5,
"RPE": 0.49
} | growth_yield | {
"expression": "if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0",
"id": "CMF027",
"latex": "DPE=DTE\\cdot IE,\\;DTE\\cdot RPE,\\;DTE,\\;DTE\\cdot BFF",
"name": "每日生理效应",
"name_en": "Daily physiological effectiveness",
"precision": 3,
"unit": "physiological days/day"
} | CMF027_branch_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Maintenance respiration coefficient at optimum temperature (最适温度维持呼吸系数)
Formula (LaTeX): RM(T_o)=0.0091-0.0001PDT
Formula: RMTo = 0.0091 - 0.0001 * PDT
Operator notes: * means multiplicati... | Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: physiological days/day | Relevant formula name: Daily physiological effectiveness (每日生理效应).
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the small... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Dry grain yield (稻谷干重产量)
Formula (LaTeX): Y=AWSP\cdot f_{grain}
Formula: Y = AWSP * grain_fraction
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln... | 4 | Stage-dependent product | branch | {
"BFF": 0.67,
"DTE": 0.515,
"IE": 1.24,
"PDT": 34.5,
"RPE": 0.49
} | A phenology involves a stage that may fall on either side of a piecewise threshold. The measured inputs are PDT=34.5 physiological days, DTE=0.515 fraction, IE=1.24 dimensionless, RPE=0.49 fraction, BFF=0.67 dimensionless. Determine the daily physiological effectiveness and report the final numeric value in physiologic... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Daily physiological effectiveness.
Use the verified formula:
\[DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF\]
In calculation-friendly notation, this is:
DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0.
Substitute the relevant values:
PDT=34.... | dev | Phenology | 0 | CMF054 |
27.20 | cropmath-v1 | null | [
"CMF019",
"CMF016"
] | {
"Tair": 30
} | methane_emission | {
"expression": "4.4 + 0.76 * Tair",
"id": "CMF024",
"latex": "T_{soil}=4.4+0.76T_{air}",
"name": "土壤温度估算",
"name_en": "Soil temperature from air temperature",
"precision": 2,
"unit": "C"
} | CMF024_direct_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Plant methane transport factor (植株传输因子)
Formula (LaTeX): F_p=C(1-W/W_{max})^{0.25}
Formula: Fp = CH4RiceEfC * (1 - W / Wmax) ** 0.25
Operator notes: * means multiplication, / means divisio... | Formula name: Soil temperature from air temperature (土壤温度估算)
Formula (LaTeX): T_{soil}=4.4+0.76T_{air}
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output un... | Formula name: Soil temperature from air temperature (土壤温度估算)
Formula (LaTeX): T_{soil}=4.4+0.76T_{air}
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output un... | Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C | Relevant formula name: Soil temperature from air temperature (土壤温度估算).
Formula: Tsoil = 4.4 + 0.76 * Tair
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Plant methane transport factor (植株传输因子)
Formula (LaTeX): F_p=C(1-W/W_{max})^{0.25}
Formula: Fp = CH4RiceEfC * (1 - W / Wmax) ** 0.25
Operator notes: * means multiplication, / means division, ** or ^... | 1 | Linear | direct | {
"Tair": 30
} | A methane calculation estimates Soil temperature from air temperature. The measured inputs are Tair=30.0 C. What is the soil temperature from air temperature? Give the final numeric value in C. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Soil temperature from air temperature.
Use the verified formula:
\[T_{soil}=4.4+0.76T_{air}\]
In calculation-friendly notation, this is:
Tsoil = 4.4 + 0.76 * Tair.
Substitute the relevant values:
Tair=30.0 C.
The computed value is 27.20 C.
Therefore, the final numeric answer is \boxed{27... | dev | Methane | 0 | CMF019 |
0.700 | cropmath-v1 | null | [
"CMF004",
"CMF002"
] | {
"Crop_Water_max": 0.42,
"Crop_Water_min": 0.22,
"Soil_Water": 0.178,
"Wilt_point": 0.08
} | carbon_nitrogen_cycle | {
"expression": "if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1+(1-Soil_Water)/(1-Crop_Water_max))",
"id": "CMF014",
"latex": "F_W=f(\\theta,\\theta_{wp},\\theta_{min},\\theta_{max})",
"name": "作物水分胁迫... | CMF014_direct_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Wa... | Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1... | Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1... | Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1+(1-Soil_Water)/(1-Crop_Water_max))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) mean... | Relevant formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子).
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wilt_point); if Soil_Water<Crop_Water_max: 1; else: 0.5*(1+(1-Soil_Water)/(1-Crop_Water_max))
Operator notes: * means... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling crop nitrogen demand (作物需氮量)
Formula (LaTeX): N_d=C_uN_{shoot}\;\text{or}\;\min(N_{max},r_NNPP)
Formula: N_demand = if NPP<0: 0; if N_shoot<3.5 and DVI<0.3: Coef_Plant_TN_upt... | 2 | Piecewise water response | direct | {
"Crop_Water_max": 0.42,
"Crop_Water_min": 0.22,
"Soil_Water": 0.178,
"Wilt_point": 0.08
} | Given Soil_Water=0.178 cm3/cm3, Crop_Water_max=0.42 cm3/cm3, Crop_Water_min=0.22 cm3/cm3, Wilt_point=0.08 cm3/cm3, calculate the carbon-nitrogen cycling crop water stress factor for a carbon-nitrogen cycling water. The result should be in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling crop water stress factor.
Use the verified formula:
\[F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})\]
In calculation-friendly notation, this is:
F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_Water_min: (Soil_Water-Wilt_point)/(Crop_Water_min-Wil... | dev | carbon-nitrogen cycling water | 1 | CMF004 |
151.50 | cropmath-v1 | {
"new_value": 0.41,
"old_value": 0.36,
"parameter": "Rg"
} | [
"CMF033",
"CMF035"
] | {
"DTGA": 369.5,
"Rg": 0.41000000000000003
} | growth_yield | {
"expression": "Rg * DTGA",
"id": "CMF046",
"latex": "RG=R_g\\cdot DTGA",
"name": "生长呼吸",
"name_en": "Growth respiration",
"precision": 2,
"unit": "kg/ha/day"
} | CMF046_sensitivity_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) m... | Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day
Parameters:
- Rg: growth r... | Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day
Parameters:
- Rg: growth r... | Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | Relevant formula name: Growth respiration (生长呼吸).
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Daily dry matter increment (日干物质增量)
Formula (LaTeX): GCR=\frac{DTGA-RM-RG}{1-b}
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | 2 | Product | sensitivity | {
"DTGA": 369.5,
"Rg": 0.36
} | Given current measurements Rg=0.36 fraction, DTGA=369.5 kg/ha/day in respiration, what would the Growth respiration be if Rg were adjusted to 0.41? Provide the numeric value in kg/ha/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Growth respiration.
Use the verified formula:
\[RG=R_g\cdot DTGA\]
In calculation-friendly notation, this is:
RG = Rg * DTGA.
Substitute the relevant values:
Rg=0.41 fraction, DTGA=369.5 kg/ha/day.
The computed value is 151.50 kg/ha/day.
Therefore, the final numeric answer is \boxed{151.... | dev | Respiration | 1 | CMF033 |
0.475 | cropmath-v1 | {
"new_value": 1.22,
"old_value": 1.35,
"parameter": "ARID"
} | [
"CMF062",
"CMF056"
] | {
"ARID": 1.22,
"S_Water": 0.43
} | environmental_response | {
"expression": "max(0, 1 - S_Water * ARID)",
"id": "CMF061",
"latex": "F_W=\\max(0,1-S_WARID)",
"name": "环境响应水分响应",
"name_en": "environmental-response water stress response",
"precision": 3,
"unit": "response factor"
} | CMF061_sensitivity_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: environmental-response daily thermal time (每日有效积温)
Formula (LaTeX): dTT=\max(T_{mean}-T_{base},0)
Formula: dTT = max(Tmean - Tbase, 0)
Operator notes: * means multiplication, / means divis... | Formula name: environmental-response water stress response (环境响应水分响应)
Formula (LaTeX): F_W=\max(0,1-S_WARID)
Formula: F_Water = max(0, 1 - S_Water * ARID)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger... | Formula name: environmental-response water stress response (环境响应水分响应)
Formula (LaTeX): F_W=\max(0,1-S_WARID)
Formula: F_Water = max(0, 1 - S_Water * ARID)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger... | Formula: F_Water = max(0, 1 - S_Water * ARID)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: environmental-response water stress response (环境响应水分响应).
Formula: F_Water = max(0, 1 - S_Water * ARID)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: environmental-response yield (环境响应产量)
Formula (LaTeX): Yield=Biomass\cdot HI
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means... | 2 | Maximum linear | sensitivity | {
"ARID": 1.35,
"S_Water": 0.43
} | Given current measurements ARID=1.35 dimensionless, S_Water=0.43 dimensionless in environmental-response formula system, what would the environmental-response water stress response be if ARID were adjusted to 1.22? Provide the numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as environmental-response water stress response.
Use the verified formula:
\[F_W=\max(0,1-S_WARID)\]
In calculation-friendly notation, this is:
F_Water = max(0, 1 - S_Water * ARID).
Substitute the relevant values:
ARID=1.22 dimensionless, S_Water=0.43 dimensionless.
The computed value is 0.... | dev | environmental-response formula system | 1 | CMF062 |
0.08 | cropmath-v1 | null | [
"CMF051",
"CMF037"
] | {
"PDT": 51
} | growth_yield | {
"expression": "1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)",
"id": "CMF043",
"latex": "PIRO=1-PISH",
"name": "地下部分配指数",
"name_en": "Root partitioning index",
"precision": 2,
"unit": "fraction"
} | CMF043_direct_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Root partitioning index (地下部分配指数)
Formula (LaTeX): PIRO=1-PISH
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ me... | Formula name: Root partitioning index (地下部分配指数)
Formula (LaTeX): PIRO=1-PISH
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | Formula name: Root partitioning index (地下部分配指数)
Formula (LaTeX): PIRO=1-PISH
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Root partitioning index (地下部分配指数).
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Relative thermal effectiveness (相对热效应)
Formula (LaTeX): RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}
Formula: RTE = (((T - Tb)/(To - Tb)) * (((... | 1 | Residual from shoot partitioning | direct | {
"PDT": 51
} | Given PDT=51.0 physiological days, calculate the Root partitioning index for a dry matter partitioning. The result should be in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Root partitioning index.
Use the verified formula:
\[PIRO=1-PISH\]
In calculation-friendly notation, this is:
PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63).
Substitute the relevant values:
PDT=51.0 physiological days.
The computed value is 0.08 fraction.
Therefore, the final numeric an... | dev | Dry matter partitioning | 1 | CMF051 |
0.0077 | cropmath-v1 | null | [
"CMF042",
"CMF041"
] | {
"PDT": 14.5
} | growth_yield | {
"expression": "0.0091 - 0.0001 * PDT",
"id": "CMF049",
"latex": "RM(T_o)=0.0091-0.0001PDT",
"name": "最适温度维持呼吸系数",
"name_en": "Maintenance respiration coefficient at optimum temperature",
"precision": 4,
"unit": "d-1"
} | CMF049_direct_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Maintenance respiration coefficient at optimum temperature (最适温度维持呼吸系数)
Formula (LaTeX): RM(T_o)=0.0091-0.0001PDT
Formula: RMTo = 0.0091 - 0.0001 * PDT
Operator notes: * means multiplicati... | Formula name: Maintenance respiration coefficient at optimum temperature (最适温度维持呼吸系数)
Formula (LaTeX): RM(T_o)=0.0091-0.0001PDT
Formula: RMTo = 0.0091 - 0.0001 * PDT
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the sma... | Formula name: Maintenance respiration coefficient at optimum temperature (最适温度维持呼吸系数)
Formula (LaTeX): RM(T_o)=0.0091-0.0001PDT
Formula: RMTo = 0.0091 - 0.0001 * PDT
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the sma... | Formula: RMTo = 0.0091 - 0.0001 * PDT
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: d-1 | Relevant formula name: Maintenance respiration coefficient at optimum temperature (最适温度维持呼吸系数).
Formula: RMTo = 0.0091 - 0.0001 * PDT
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Panicle partitioning index (穗分配指数)
Formula (LaTeX): PIP=\frac{HI/0.87}{1+e^{-0.2804(PDT-39)}}
Formula: PIP = (Y_grain / B_above / 0.87) / (1 + exp(-0.2804 * (PDT - 39)))
Operator notes: * means mult... | 1 | Linear decline | direct | {
"PDT": 14.5
} | In a respiration, the Maintenance respiration coefficient at optimum temperature is computed as part of respiration modeling. With PDT=14.5 physiological days, determine the numeric value in d-1. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Maintenance respiration coefficient at optimum temperature.
Use the verified formula:
\[RM(T_o)=0.0091-0.0001PDT\]
In calculation-friendly notation, this is:
RMTo = 0.0091 - 0.0001 * PDT.
Substitute the relevant values:
PDT=14.5 physiological days.
The computed value is 0.0077 d-1.
There... | dev | Respiration | 2 | CMF042 |
0.34 | cropmath-v1 | null | [
"CMF052",
"CMF031"
] | {
"PDT": 50,
"a": 0.049
} | growth_yield | {
"expression": "if PDT<28: 1; else: exp(-a*(PDT-28))",
"id": "CMF030",
"latex": "F_{PA}=1\\;(PDT<28),\\quad e^{-a(PDT-28)}\\;(PDT\\ge 28)",
"name": "生理年龄因子",
"name_en": "Physiological age factor",
"precision": 2,
"unit": "fraction"
} | CMF030_branch_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Actual LAI relative growth rate (实际叶面积相对增长率)
Formula (LaTeX): R=RP\cdot\min(NNI,WDF)
Formula: R = RP * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means... | Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the... | Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the... | Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Physiological age factor (生理年龄因子).
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Actual LAI relative growth rate (实际叶面积相对增长率)
Formula (LaTeX): R=RP\cdot\min(NNI,WDF)
Formula: R = RP * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, ex... | 4 | Piecewise exponential decay | branch | {
"PDT": 50,
"a": 0.049
} | Calculate Physiological age factor in photosynthesis with these inputs: PDT=50.0 physiological days, a=0.049 dimensionless. The computation may follow different paths based on piecewise thresholds. Give the numeric result in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Physiological age factor.
Use the verified formula:
\[F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)\]
In calculation-friendly notation, this is:
FPA = if PDT<28: 1; else: exp(-a*(PDT-28)).
Substitute the relevant values:
PDT=50.0 physiological days, a=0.049 dimensionless.
The comp... | dev | Photosynthesis | 2 | CMF052 |
14.04 | cropmath-v1 | {
"new_value": 0.08,
"old_value": 0.083,
"parameter": "PS"
} | [
"CMF029",
"CMF045"
] | {
"PS": 0.08,
"Po": 10.5
} | growth_yield | {
"expression": "Po + sqrt(1 / PS)",
"id": "CMF040",
"latex": "P_c=P_o+\\sqrt{1/PS}",
"name": "临界日长",
"name_en": "Critical daylength",
"precision": 2,
"unit": "h"
} | CMF040_sensitivity_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means ... | Formula name: Critical daylength (临界日长)
Formula (LaTeX): P_c=P_o+\sqrt{1/PS}
Formula: Pc = Po + sqrt(1 / PS)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: h
Parameters:
- Po: optim... | Formula name: Critical daylength (临界日长)
Formula (LaTeX): P_c=P_o+\sqrt{1/PS}
Formula: Pc = Po + sqrt(1 / PS)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: h
Parameters:
- Po: optim... | Formula: Pc = Po + sqrt(1 / PS)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: h | Relevant formula name: Critical daylength (临界日长).
Formula: Pc = Po + sqrt(1 / PS)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: h | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp... | 2 | Power response | sensitivity | {
"PS": 0.083,
"Po": 10.5
} | In phenology, we analyze how Critical daylength responds to parameter changes. Baseline: Po=10.5 h, PS=0.083 dimensionless. After changing PS from 0.083 to 0.08, compute the new Critical daylength. Give the numeric value in h. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Critical daylength.
Use the verified formula:
\[P_c=P_o+\sqrt{1/PS}\]
In calculation-friendly notation, this is:
Pc = Po + sqrt(1 / PS).
Substitute the relevant values:
Po=10.5 h, PS=0.08 dimensionless.
The computed value is 14.04 h.
Therefore, the final numeric answer is \boxed{14.04}.
... | dev | Phenology | 2 | CMF029 |
1.000 | cropmath-v1 | null | [
"CMF025",
"CMF018"
] | {
"Q10": 2.2,
"t_soil": 39.9
} | methane_emission | {
"expression": "Q10^((min(t_soil,30)-30)/10)",
"id": "CMF023",
"latex": "TI=Q_{10}^{(t_{sl}-30)/10}",
"name": "甲烷温度指数",
"name_en": "Methane temperature index",
"precision": 3,
"unit": "multiplier"
} | CMF023_branch_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Redox potential factor (氧化还原电位因子)
Formula (LaTeX): F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplicat... | Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Methane temperature index (甲烷温度指数).
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / means divi... | 3 | Q10 with temperature clipping | branch | {
"Q10": 2.2,
"t_soil": 39.9
} | For methane, compute the Methane temperature index. The inputs are Q10=2.2 dimensionless, t_soil=39.9 C. Note that this formula uses piecewise logic depending on parameter values. Report the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Methane temperature index.
Use the verified formula:
\[TI=Q_{10}^{(t_{sl}-30)/10}\]
In calculation-friendly notation, this is:
TI = Q10^((min(t_soil,30)-30)/10).
Substitute the relevant values:
Q10=2.2 dimensionless, t_soil=39.9 C.
The computed value is 1.000 fraction.
Therefore, the fin... | dev | Methane | 1 | CMF025 |
1.18 | cropmath-v1 | null | [
"CMF052",
"CMF051"
] | {
"Cx": 419,
"beta": 0.86
} | growth_yield | {
"expression": "1 + beta * ln(Cx / 340)",
"id": "CMF029",
"latex": "F_{CO2}=1+\\beta\\ln(C_x/340)",
"name": "二氧化碳影响因子",
"name_en": "CO2 response factor",
"precision": 2,
"unit": "multiplier"
} | CMF029_direct_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Actual LAI relative growth rate (实际叶面积相对增长率)
Formula (LaTeX): R=RP\cdot\min(NNI,WDF)
Formula: R = RP * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means... | Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: frac... | Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: frac... | Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: CO2 response factor (二氧化碳影响因子).
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Actual LAI relative growth rate (实际叶面积相对增长率)
Formula (LaTeX): R=RP\cdot\min(NNI,WDF)
Formula: R = RP * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, ex... | 1 | Logarithmic | direct | {
"Cx": 419,
"beta": 0.86
} | Given Cx=419.0 ppm, beta=0.86 dimensionless, calculate the CO2 response factor for a photosynthesis. The result should be in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as CO2 response factor.
Use the verified formula:
\[F_{CO2}=1+\beta\ln(C_x/340)\]
In calculation-friendly notation, this is:
FCO2 = 1 + beta * ln(Cx / 340).
Substitute the relevant values:
Cx=419.0 ppm, beta=0.86 dimensionless.
The computed value is 1.18 fraction.
Therefore, the final numer... | dev | Photosynthesis | 1 | CMF052 |
0.198 | cropmath-v1 | {
"new_value": -7,
"old_value": -6.1,
"parameter": "Eh"
} | [
"CMF023",
"CMF021"
] | {
"Eh": -7
} | methane_emission | {
"expression": "if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))",
"id": "CMF018",
"latex": "F_{Eh}=1\\;(Eh<-150),\\quad e^{-1.7(1+Eh/150)}",
"name": "氧化还原电位因子",
"name_en": "Redox potential factor",
"precision": 3,
"unit": "fraction"
} | CMF018_sensitivity_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Redox potential factor (氧化还原电位因子)
Formula (LaTeX): F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplicat... | Formula name: Redox potential factor (氧化还原电位因子)
Formula (LaTeX): F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the sm... | Formula name: Redox potential factor (氧化还原电位因子)
Formula (LaTeX): F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the sm... | Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Redox potential factor (氧化还原电位因子).
Formula: FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | 3 | Piecewise exponential | sensitivity | {
"Eh": -6.1
} | A methane calculation involves sensitivity analysis. The current measurements are Eh=-6.1 mV. A field technician asks what the redox potential factor would become if Eh changed to -7.0. Report the new final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Redox potential factor.
Use the verified formula:
\[F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}\]
In calculation-friendly notation, this is:
FEh = if Eh<-150: 1; else: exp(-1.7*(1+Eh/150)).
Substitute the relevant values:
Eh=-7.0 mV.
The computed value is 0.198 fraction.
Therefore, the ... | dev | Methane | 0 | CMF023 |
71.6 | cropmath-v1 | {
"new_value": 3.8,
"old_value": 4.2,
"parameter": "SDEPTH"
} | [
"CMF033",
"CMF034"
] | {
"SDEPTH": 3.8
} | growth_yield | {
"expression": "45 + 7 * SDEPTH",
"id": "CMF028",
"latex": "EMGDD=45+7SDEPTH",
"name": "出苗热量需求",
"name_en": "Emergence thermal requirement",
"precision": 1,
"unit": "C day"
} | CMF028_sensitivity_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Harvest index (收获指数)
Formula (LaTeX): HI=\frac{Y_{grain}}{B_{above}}
Formula: HI = Y_grain / B_above
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) m... | Formula name: Emergence thermal requirement (出苗热量需求)
Formula (LaTeX): EMGDD=45+7SDEPTH
Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day
Paramete... | Formula name: Emergence thermal requirement (出苗热量需求)
Formula (LaTeX): EMGDD=45+7SDEPTH
Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day
Paramete... | Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day | Relevant formula name: Emergence thermal requirement (出苗热量需求).
Formula: EMGDD = 45 + 7 * SDEPTH
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: C day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Daily dry matter increment (日干物质增量)
Formula (LaTeX): GCR=\frac{DTGA-RM-RG}{1-b}
Formula: GCR = (DTGA - RM - RG) / (1 - b)
Operator notes: * means multiplication, / means division, ** or ^ means powe... | 2 | Linear | sensitivity | {
"SDEPTH": 4.2
} | Given current measurements SDEPTH=4.2 cm in phenology, what would the Emergence thermal requirement be if SDEPTH were adjusted to 3.8? Provide the numeric value in C day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Emergence thermal requirement.
Use the verified formula:
\[EMGDD=45+7SDEPTH\]
In calculation-friendly notation, this is:
EMGDD = 45 + 7 * SDEPTH.
Substitute the relevant values:
SDEPTH=3.8 cm.
The computed value is 71.6 C day.
Therefore, the final numeric answer is \boxed{71.6}.
#### 71.... | dev | Phenology | 1 | CMF033 |
10.69 | cropmath-v1 | null | [
"CMF031",
"CMF027"
] | {
"Am": 28.3,
"FCO2": 1.13,
"FPA": 0.91,
"FT": 0.54,
"NNI": 0.68,
"WDF": 0.73
} | growth_yield | {
"expression": "Am * FCO2 * FPA * FT * min(NNI, WDF)",
"id": "CMF026",
"latex": "AMAX=Am\\cdot F_{CO2}\\cdot F_{PA}\\cdot F_T\\cdot\\min(NNI,WDF)",
"name": "实际最大同化速率",
"name_en": "Actual maximum assimilation rate",
"precision": 2,
"unit": "kg CO2/ha/h"
} | CMF026_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Light interception fraction (光能截获率)
Formula (LaTeX): fPAR = 1 - e^{-k \cdot LAI}
Formula: fPAR = 1 - exp(-k * LAI)
Operator notes: * means multiplication, / means division, ** or ^ means p... | Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and ... | Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and ... | Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg CO2/ha/h | Relevant formula name: Actual maximum assimilation rate (实际最大同化速率).
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg CO2/ha/h | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Light interception fraction (光能截获率)
Formula (LaTeX): fPAR = 1 - e^{-k \cdot LAI}
Formula: fPAR = 1 - exp(-k * LAI)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(... | 2 | Multiplicative with minimum stress | direct | {
"Am": 28.3,
"FCO2": 1.13,
"FPA": 0.91,
"FT": 0.54,
"NNI": 0.68,
"WDF": 0.73
} | A photosynthesis calculation estimates Actual maximum assimilation rate. The measured inputs are Am=28.3 kg CO2/ha/h, FCO2=1.13 fraction, FPA=0.91 fraction, FT=0.54 fraction, NNI=0.68 fraction, WDF=0.73 fraction. What is the actual maximum assimilation rate? Give the final numeric value in kg CO2/ha/h. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Actual maximum assimilation rate.
Use the verified formula:
\[AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)\]
In calculation-friendly notation, this is:
AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF).
Substitute the relevant values:
Am=28.3 kg CO2/ha/h, FCO2=1.13 fraction, FPA... | dev | Photosynthesis | 0 | CMF031 |
0.962 | cropmath-v1 | null | [
"CMF045",
"CMF054"
] | {
"BFF": 1.04,
"DTE": 0.925,
"IE": 0.89,
"PDT": 48.6,
"RPE": 0.52
} | growth_yield | {
"expression": "if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0",
"id": "CMF027",
"latex": "DPE=DTE\\cdot IE,\\;DTE\\cdot RPE,\\;DTE,\\;DTE\\cdot BFF",
"name": "每日生理效应",
"name_en": "Daily physiological effectiveness",
"precision": 3,
"unit": "physiological days/day"
} | CMF027_chain_2_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Stem partitioning index (茎鞘分配指数)
Formula (LaTeX): PIS=1-PIGL-PIP
Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT... | Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: physiological days/day | Relevant formula name: Daily physiological effectiveness (每日生理效应).
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the small... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Stem partitioning index (茎鞘分配指数)
Formula (LaTeX): PIS=1-PIGL-PIP
Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))
Ope... | 4 | Stage-dependent product | chain_2 | {
"BFF": 1.04,
"DTE": 0.925,
"IE": 0.89,
"PDT": 48.6,
"RPE": 0.52
} | A phenology module estimates Daily physiological effectiveness using intermediate drivers. Use the provided inputs in sequence. The measurements are PDT=48.6 physiological days, DTE=0.925 fraction, IE=0.89 dimensionless, RPE=0.52 fraction, BFF=1.04 dimensionless. Compute the daily physiological effectiveness and give t... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Daily physiological effectiveness.
Use the verified formula:
\[DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF\]
In calculation-friendly notation, this is:
DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0.
Substitute the relevant values:
PDT=48.... | dev | Phenology | 0 | CMF045 |
0.07 | cropmath-v1 | {
"new_value": 57,
"old_value": 56.5,
"parameter": "PDT"
} | [
"CMF031",
"CMF036"
] | {
"PDT": 57
} | growth_yield | {
"expression": "1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)",
"id": "CMF043",
"latex": "PIRO=1-PISH",
"name": "地下部分配指数",
"name_en": "Root partitioning index",
"precision": 2,
"unit": "fraction"
} | CMF043_sensitivity_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Canopy extinction coefficient (冠层消光系数)
Formula (LaTeX): K=0.0087PDT+0.2222
Formula: K = 0.0087 * PDT + 0.2222
Operator notes: * means multiplication, / means division, ** or ^ means power,... | Formula name: Root partitioning index (地下部分配指数)
Formula (LaTeX): PIRO=1-PISH
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | Formula name: Root partitioning index (地下部分配指数)
Formula (LaTeX): PIRO=1-PISH
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Root partitioning index (地下部分配指数).
Formula: PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Light interception fraction (光能截获率)
Formula (LaTeX): fPAR = 1 - e^{-k \cdot LAI}
Formula: fPAR = 1 - exp(-k * LAI)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(... | 2 | Residual from shoot partitioning | sensitivity | {
"PDT": 56.5
} | A dry matter partitioning calculation involves sensitivity analysis. The current measurements are PDT=56.5 physiological days. A field technician asks what the root partitioning index would become if PDT changed to 57.0. Report the new final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Root partitioning index.
Use the verified formula:
\[PIRO=1-PISH\]
In calculation-friendly notation, this is:
PIRO = 1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63).
Substitute the relevant values:
PDT=57.0 physiological days.
The computed value is 0.07 fraction.
Therefore, the final numeric an... | dev | Dry matter partitioning | 0 | CMF031 |
0.982 | cropmath-v1 | null | [
"CMF048",
"CMF036"
] | {
"T": 27.7,
"TS": 1.07,
"Tb": 10,
"Tm": 42,
"To": 30
} | growth_yield | {
"expression": "(((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** TS",
"id": "CMF051",
"latex": "RTE=\\left[\\frac{T-T_b}{T_o-T_b}\\left(\\frac{T_m-T}{T_m-T_o}\\right)^{(T_m-T_o)/(T_o-T_b)}\\right]^{TS}",
"name": "相对热效应",
"name_en": "Relative thermal effectiveness",
"precision": 3... | CMF051_branch_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Relative thermal effectiveness (相对热效应)
Formula (LaTeX): RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}
Formula: RTE = (((T - Tb)/(To - ... | Formula name: Relative thermal effectiveness (相对热效应)
Formula (LaTeX): RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}
Formula: RTE = (((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** TS
Operator notes: * means multiplication, / means division... | Formula name: Relative thermal effectiveness (相对热效应)
Formula (LaTeX): RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}
Formula: RTE = (((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** TS
Operator notes: * means multiplication, / means division... | Formula: RTE = (((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** TS
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Relative thermal effectiveness (相对热效应).
Formula: RTE = (((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** TS
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larg... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes:... | 4 | Beta temperature response | branch | {
"T": 27.7,
"TS": 1.07,
"Tb": 10,
"Tm": 42,
"To": 30
} | A phenology involves a stage that may fall on either side of a piecewise threshold. The measured inputs are T=27.7 C, Tb=10.0 C, To=30.0 C, Tm=42.0 C, TS=1.07 dimensionless. Determine the relative thermal effectiveness and report the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Relative thermal effectiveness.
Use the verified formula:
\[RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}\]
In calculation-friendly notation, this is:
RTE = (((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** T... | dev | Phenology | 0 | CMF048 |
0.045 | cropmath-v1 | null | [
"CMF007",
"CMF003"
] | {
"Coef_K_Decom": 0.0057,
"Coef_K_Trans": 0.08600000000000001,
"F_notill": 0.93,
"F_pH": 0.101,
"F_temp": 1.373,
"F_texture": 0.899,
"F_water": 0.266,
"Pool": 281.7
} | carbon_nitrogen_cycle | {
"expression": "Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans)",
"id": "CMF009",
"latex": "R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans})",
"name": "碳库呼吸损失",
"name_en": "carbon-nitrogen cycling carbon pool respiration loss",
"precision": 3,
"unit": "g C/m2/day"
} | CMF009_direct_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Nitrogen use efficiency (氮利用效率)
Formula (LaTeX): NUE=\frac{GrainYield}{NUptake}
Formula: NUE = GrainYield / NUptake
Operator notes: * means multiplication, / means division, ** or ^ means ... | Formula name: carbon-nitrogen cycling carbon pool respiration loss (碳库呼吸损失)
Formula (LaTeX): R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans})
Formula: Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans)
Operator notes: * means multiplication, / means division, ** or ^ means pow... | Formula name: carbon-nitrogen cycling carbon pool respiration loss (碳库呼吸损失)
Formula (LaTeX): R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans})
Formula: Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans)
Operator notes: * means multiplication, / means division, ** or ^ means pow... | Formula: Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: carbon-nitrogen cycling carbon pool respiration loss (碳库呼吸损失).
Formula: Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/m... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling optimal photosynthetic rate (最适光合速率)
Formula (LaTeX): P_{opt}=\alpha N_{leaf}\frac{PAR}{PAR+\beta}
Formula: Photo_Rate_opt = (Coef_alfa * Leaf_N) * PAR / (PAR + Coef_beta)
Op... | 2 | Chained multiplicative decomposition | direct | {
"Coef_K_Decom": 0.0057,
"Coef_K_Trans": 0.08600000000000001,
"F_notill": 0.93,
"F_pH": 0.101,
"F_temp": 1.373,
"F_texture": 0.899,
"F_water": 0.266,
"Pool": 281.7
} | A carbon-nitrogen cycling soil carbon calculation estimates carbon-nitrogen cycling carbon pool respiration loss. The measured inputs are Pool=281.7 g C/m2, Coef_K_Decom=0.0057 d-1, F_temp=1.373 fraction, F_water=0.266 fraction, F_texture=0.899 fraction, F_pH=0.101 fraction, F_notill=0.93 fraction, Coef_K_Trans=0.086 f... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling carbon pool respiration loss.
Use the verified formula:
\[R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans})\]
In calculation-friendly notation, this is:
Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans).
Substitute the re... | dev | carbon-nitrogen cycling soil carbon | 0 | CMF007 |
0.17 | cropmath-v1 | null | [
"CMF037",
"CMF040"
] | {
"PDT": 33.5,
"Tmax_day": 38.5
} | growth_yield | {
"expression": "if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1",
"id": "CMF035",
"latex": "HTF=\\frac{1}{1+e^{0.853(T_m-36.6)}}",
"name": "高温结实因子",
"name_en": "High-temperature fertility factor",
"precision": 2,
"unit": "fraction"
} | CMF035_branch_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Critical daylength (临界日长)
Formula (LaTeX): P_c=P_o+\sqrt{1/PS}
Formula: Pc = Po + sqrt(1 / PS)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e... | Formula name: High-temperature fertility factor (高温结实因子)
Formula (LaTeX): HTF=\frac{1}{1+e^{0.853(T_m-36.6)}}
Formula: HTF = if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural lo... | Formula name: High-temperature fertility factor (高温结实因子)
Formula (LaTeX): HTF=\frac{1}{1+e^{0.853(T_m-36.6)}}
Formula: HTF = if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural lo... | Formula: HTF = if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: High-temperature fertility factor (高温结实因子).
Formula: HTF = if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/lar... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Potential leaf area index (潜在叶面积指数)
Formula (LaTeX): LAI_P=LAI_0e^{RP\cdot GDD}
Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means power, ex... | 4 | Piecewise logistic | branch | {
"PDT": 33.5,
"Tmax_day": 38.5
} | A temperature stress involves a stage that may fall on either side of a piecewise threshold. The measured inputs are PDT=33.5 physiological days, Tmax_day=38.5 C. Determine the high-temperature fertility factor and report the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as High-temperature fertility factor.
Use the verified formula:
\[HTF=\frac{1}{1+e^{0.853(T_m-36.6)}}\]
In calculation-friendly notation, this is:
HTF = if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1.
Substitute the relevant values:
PDT=33.5 physiological days, ... | dev | Temperature stress | 0 | CMF037 |
0.17 | cropmath-v1 | {
"new_value": 34.8,
"old_value": 38.7,
"parameter": "PDT"
} | [
"CMF037",
"CMF046"
] | {
"PDT": 34.8,
"Tmax_day": 38.5
} | growth_yield | {
"expression": "if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1",
"id": "CMF035",
"latex": "HTF=\\frac{1}{1+e^{0.853(T_m-36.6)}}",
"name": "高温结实因子",
"name_en": "High-temperature fertility factor",
"precision": 2,
"unit": "fraction"
} | CMF035_sensitivity_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) m... | Formula name: High-temperature fertility factor (高温结实因子)
Formula (LaTeX): HTF=\frac{1}{1+e^{0.853(T_m-36.6)}}
Formula: HTF = if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural lo... | Formula name: High-temperature fertility factor (高温结实因子)
Formula (LaTeX): HTF=\frac{1}{1+e^{0.853(T_m-36.6)}}
Formula: HTF = if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural lo... | Formula: HTF = if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: High-temperature fertility factor (高温结实因子).
Formula: HTF = if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/lar... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Potential leaf area index (潜在叶面积指数)
Formula (LaTeX): LAI_P=LAI_0e^{RP\cdot GDD}
Formula: LAIP = LAI0 * exp(RP * GDD)
Operator notes: * means multiplication, / means division, ** or ^ means power, ex... | 3 | Piecewise logistic | sensitivity | {
"PDT": 38.7,
"Tmax_day": 38.5
} | Given current measurements PDT=38.7 physiological days, Tmax_day=38.5 C in temperature stress, what would the High-temperature fertility factor be if PDT were adjusted to 34.8? Provide the numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as High-temperature fertility factor.
Use the verified formula:
\[HTF=\frac{1}{1+e^{0.853(T_m-36.6)}}\]
In calculation-friendly notation, this is:
HTF = if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1.
Substitute the relevant values:
PDT=34.8 physiological days, ... | dev | Temperature stress | 1 | CMF037 |
14.11 | cropmath-v1 | null | [
"CMF056",
"CMF058"
] | {
"F_CO2": 1.33,
"F_Heat": 0.84,
"F_Temp": 0.77,
"F_Water": 0.47000000000000003,
"RUE": 1.44,
"SRAD": 12.72,
"fSolar": 0.16
} | environmental_response | {
"expression": "10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F_Water, F_Heat)",
"id": "CMF055",
"latex": "dB=10RUEfSolarSRADF_{CO2}F_T\\min(F_W,F_H)",
"name": "环境响应日生物量增量",
"name_en": "environmental-response daily biomass increment",
"precision": 2,
"unit": "kg/ha/day"
} | CMF055_chain_2_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: environmental-response daily biomass increment (环境响应日生物量增量)
Formula (LaTeX): dB=10RUEfSolarSRADF_{CO2}F_T\min(F_W,F_H)
Formula: dBiomass = 10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F... | Formula name: environmental-response daily biomass increment (环境响应日生物量增量)
Formula (LaTeX): dB=10RUEfSolarSRADF_{CO2}F_T\min(F_W,F_H)
Formula: dBiomass = 10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F_Water, F_Heat)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x)... | Formula name: environmental-response daily biomass increment (环境响应日生物量增量)
Formula (LaTeX): dB=10RUEfSolarSRADF_{CO2}F_T\min(F_W,F_H)
Formula: dBiomass = 10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F_Water, F_Heat)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x)... | Formula: dBiomass = 10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F_Water, F_Heat)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | Relevant formula name: environmental-response daily biomass increment (环境响应日生物量增量).
Formula: dBiomass = 10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F_Water, F_Heat)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: environmental-response daily thermal time (每日有效积温)
Formula (LaTeX): dTT=\max(T_{mean}-T_{base},0)
Formula: dTT = max(Tmean - Tbase, 0)
Operator notes: * means multiplication, / means division, ** or... | 4 | Multiplicative minimum stress | chain_2 | {
"F_CO2": 1.33,
"F_Heat": 0.84,
"F_Temp": 0.77,
"F_Water": 0.47000000000000003,
"RUE": 1.44,
"SRAD": 12.72,
"fSolar": 0.16
} | In environmental-response formula system, the environmental-response daily biomass increment is obtained by chaining intermediate calculations. With inputs RUE=1.44 g/MJ, fSolar=0.16 fraction, SRAD=12.72 MJ/m2/day, F_CO2=1.33 fraction, F_Temp=0.77 fraction, F_Water=0.47 fraction, F_Heat=0.84 fraction, determine the num... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as environmental-response daily biomass increment.
Use the verified formula:
\[dB=10RUEfSolarSRADF_{CO2}F_T\min(F_W,F_H)\]
In calculation-friendly notation, this is:
dBiomass = 10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F_Water, F_Heat).
Substitute the relevant values:
RUE=1.44 g/MJ, f... | dev | environmental-response formula system | 2 | CMF056 |
0.58 | cropmath-v1 | null | [
"CMF051",
"CMF042"
] | {
"B_above": 12702,
"PDT": 26,
"Y_grain": 6715
} | growth_yield | {
"expression": "1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))",
"id": "CMF045",
"latex": "PIS=1-PIGL-PIP",
"name": "茎鞘分配指数",
"name_en": "Stem partitioning index",
"precision": 2,
"unit": "fraction"
} | CMF045_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Stem partitioning index (茎鞘分配指数)
Formula (LaTeX): PIS=1-PIGL-PIP
Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT... | Formula name: Stem partitioning index (茎鞘分配指数)
Formula (LaTeX): PIS=1-PIGL-PIP
Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means na... | Formula name: Stem partitioning index (茎鞘分配指数)
Formula (LaTeX): PIS=1-PIGL-PIP
Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means na... | Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: frac... | Relevant formula name: Stem partitioning index (茎鞘分配指数).
Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and m... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Relative thermal effectiveness (相对热效应)
Formula (LaTeX): RTE=\left[\frac{T-T_b}{T_o-T_b}\left(\frac{T_m-T}{T_m-T_o}\right)^{(T_m-T_o)/(T_o-T_b)}\right]^{TS}
Formula: RTE = (((T - Tb)/(To - Tb)) * (((... | 2 | Residual with piecewise components | direct | {
"B_above": 12702,
"PDT": 26,
"Y_grain": 6715
} | A dry matter partitioning calculation estimates Stem partitioning index. The measured inputs are PDT=26.0 physiological days, Y_grain=6715.0 kg/ha, B_above=12702.0 kg/ha. What is the stem partitioning index? Give the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Stem partitioning index.
Use the verified formula:
\[PIS=1-PIGL-PIP\]
In calculation-friendly notation, this is:
PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39))).
Substitute the relevant values:
PDT=26.0 physiologica... | dev | Dry matter partitioning | 0 | CMF051 |
0.327 | cropmath-v1 | {
"new_value": 1,
"old_value": 1.11,
"parameter": "SI"
} | [
"CMF019",
"CMF023"
] | {
"OMN": 23.3,
"SI": 1,
"TI": 0.749,
"WI": 0.6950000000000001
} | methane_emission | {
"expression": "WI * SI * TI * 0.027 * OMN",
"id": "CMF020",
"latex": "OMNC=WI\\cdot SI\\cdot TI\\cdot0.027\\cdot OMN",
"name": "新鲜有机质碳分解量",
"name_en": "Fresh organic matter carbon decomposition",
"precision": 3,
"unit": "g C/m2/day"
} | CMF020_sensitivity_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ ... | Formula name: Fresh organic matter carbon decomposition (新鲜有机质碳分解量)
Formula (LaTeX): OMNC=WI\cdot SI\cdot TI\cdot0.027\cdot OMN
Formula: OMNC = WI * SI * TI * 0.027 * OMN
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select th... | Formula name: Fresh organic matter carbon decomposition (新鲜有机质碳分解量)
Formula (LaTeX): OMNC=WI\cdot SI\cdot TI\cdot0.027\cdot OMN
Formula: OMNC = WI * SI * TI * 0.027 * OMN
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select th... | Formula: OMNC = WI * SI * TI * 0.027 * OMN
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: Fresh organic matter carbon decomposition (新鲜有机质碳分解量).
Formula: OMNC = WI * SI * TI * 0.027 * OMN
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Plant methane transport factor (植株传输因子)
Formula (LaTeX): F_p=C(1-W/W_{max})^{0.25}
Formula: Fp = CH4RiceEfC * (1 - W / Wmax) ** 0.25
Operator notes: * means multiplication, / means division, ** or ^... | 2 | Multiplicative | sensitivity | {
"OMN": 23.3,
"SI": 1.11,
"TI": 0.749,
"WI": 0.6950000000000001
} | Given current measurements WI=0.695 fraction, SI=1.11 fraction, TI=0.749 fraction, OMN=23.3 g C/m2 in methane, what would the Fresh organic matter carbon decomposition be if SI were adjusted to 1.0? Provide the numeric value in g C/m2/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Fresh organic matter carbon decomposition.
Use the verified formula:
\[OMNC=WI\cdot SI\cdot TI\cdot0.027\cdot OMN\]
In calculation-friendly notation, this is:
OMNC = WI * SI * TI * 0.027 * OMN.
Substitute the relevant values:
WI=0.695 fraction, SI=1.0 fraction, TI=0.749 fraction, OMN=23.... | dev | Methane | 1 | CMF019 |
14.86 | cropmath-v1 | {
"new_value": 0.95,
"old_value": 1,
"parameter": "FCO2"
} | [
"CMF047",
"CMF029"
] | {
"Am": 49.4,
"FCO2": 0.9500000000000001,
"FPA": 0.6900000000000001,
"FT": 0.85,
"NNI": 0.54,
"WDF": 0.66
} | growth_yield | {
"expression": "Am * FCO2 * FPA * FT * min(NNI, WDF)",
"id": "CMF026",
"latex": "AMAX=Am\\cdot F_{CO2}\\cdot F_{PA}\\cdot F_T\\cdot\\min(NNI,WDF)",
"name": "实际最大同化速率",
"name_en": "Actual maximum assimilation rate",
"precision": 2,
"unit": "kg CO2/ha/h"
} | CMF026_sensitivity_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Intercepted photosynthetically active radiation (截获光合有效辐射)
Formula (LaTeX): IPAR = PAR \cdot (1 - e^{-k \cdot LAI})
Formula: IPAR = PAR * (1 - exp(-k * LAI))
Operator notes: * means multip... | Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and ... | Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and ... | Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg CO2/ha/h | Relevant formula name: Actual maximum assimilation rate (实际最大同化速率).
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg CO2/ha/h | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Intercepted photosynthetically active radiation (截获光合有效辐射)
Formula (LaTeX): IPAR = PAR \cdot (1 - e^{-k \cdot LAI})
Formula: IPAR = PAR * (1 - exp(-k * LAI))
Operator notes: * means multiplication, ... | 3 | Multiplicative with minimum stress | sensitivity | {
"Am": 49.4,
"FCO2": 1,
"FPA": 0.6900000000000001,
"FT": 0.85,
"NNI": 0.54,
"WDF": 0.66
} | A photosynthesis calculation involves sensitivity analysis. The current measurements are Am=49.4 kg CO2/ha/h, FCO2=1.0 fraction, FPA=0.69 fraction, FT=0.85 fraction, NNI=0.54 fraction, WDF=0.66 fraction. A field technician asks what the actual maximum assimilation rate would become if FCO2 changed to 0.95. Report the n... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Actual maximum assimilation rate.
Use the verified formula:
\[AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)\]
In calculation-friendly notation, this is:
AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF).
Substitute the relevant values:
Am=49.4 kg CO2/ha/h, FCO2=0.95 fraction, FPA... | dev | Photosynthesis | 0 | CMF047 |
8.687 | cropmath-v1 | null | [
"CMF014",
"CMF005"
] | {
"Day_Length_hour": 15.46,
"F_CO2": 0.99,
"F_T": 0.39,
"F_Water": 0.66,
"Photo_Rate_opt": 51.04
} | carbon_nitrogen_cycle | {
"expression": "Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432",
"id": "CMF002",
"latex": "GPP=P_{opt}F_TF_WF_{CO2}DL\\cdot0.0432",
"name": "总初级生产力",
"name_en": "carbon-nitrogen cycling gross primary production",
"precision": 3,
"unit": "g C/m2/day"
} | CMF002_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0... | Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means nat... | Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means nat... | Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: carbon-nitrogen cycling gross primary production (总初级生产力).
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smalle... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling crop water stress factor (作物水分胁迫因子)
Formula (LaTeX): F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})
Formula: F_Water = if Soil_Water<=Wilt_point: 0; if Soil_Water<Crop_W... | 2 | Multiplicative conversion | direct | {
"Day_Length_hour": 15.46,
"F_CO2": 0.99,
"F_T": 0.39,
"F_Water": 0.66,
"Photo_Rate_opt": 51.04
} | A carbon-nitrogen cycling photosynthesis calculation estimates carbon-nitrogen cycling gross primary production. The measured inputs are Photo_Rate_opt=51.04 umol CO2/m2/s, F_T=0.39 fraction, F_Water=0.66 fraction, F_CO2=0.99 fraction, Day_Length_hour=15.46 h. What is the carbon-nitrogen cycling gross primary productio... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling gross primary production.
Use the verified formula:
\[GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432\]
In calculation-friendly notation, this is:
GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432.
Substitute the relevant values:
Photo_Rate_opt=51.04 u... | dev | carbon-nitrogen cycling photosynthesis | 0 | CMF014 |
6835.8 | cropmath-v1 | null | [
"CMF061",
"CMF057"
] | {
"Biomass": 12428.7,
"HI": 0.55
} | environmental_response | {
"expression": "Biomass * HI",
"id": "CMF062",
"latex": "Yield=Biomass\\cdot HI",
"name": "环境响应产量",
"name_en": "environmental-response yield",
"precision": 1,
"unit": "kg/ha"
} | CMF062_direct_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: environmental-response yield (环境响应产量)
Formula (LaTeX): Yield=Biomass\cdot HI
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, ex... | Formula name: environmental-response yield (环境响应产量)
Formula (LaTeX): Yield=Biomass\cdot HI
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha
Paramet... | Formula name: environmental-response yield (环境响应产量)
Formula (LaTeX): Yield=Biomass\cdot HI
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha
Paramet... | Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha | Relevant formula name: environmental-response yield (环境响应产量).
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: environmental-response water stress response (环境响应水分响应)
Formula (LaTeX): F_W=\max(0,1-S_WARID)
Formula: F_Water = max(0, 1 - S_Water * ARID)
Operator notes: * means multiplication, / means division,... | 1 | Product | direct | {
"Biomass": 12428.7,
"HI": 0.55
} | Given Biomass=12428.7 kg/ha, HI=0.55 fraction, calculate the environmental-response yield for an environmental-response formula system. The result should be in kg/ha. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as environmental-response yield.
Use the verified formula:
\[Yield=Biomass\cdot HI\]
In calculation-friendly notation, this is:
Yield = Biomass * HI.
Substitute the relevant values:
Biomass=12428.7 kg/ha, HI=0.55 fraction.
The computed value is 6835.8 kg/ha.
Therefore, the final numeric ans... | dev | environmental-response formula system | 1 | CMF061 |
0.904 | cropmath-v1 | {
"new_value": 0.63,
"old_value": 0.55,
"parameter": "RPE"
} | [
"CMF029",
"CMF037"
] | {
"BFF": 0.78,
"DTE": 0.904,
"IE": 1.23,
"PDT": 26.3,
"RPE": 0.63
} | growth_yield | {
"expression": "if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0",
"id": "CMF027",
"latex": "DPE=DTE\\cdot IE,\\;DTE\\cdot RPE,\\;DTE,\\;DTE\\cdot BFF",
"name": "每日生理效应",
"name_en": "Daily physiological effectiveness",
"precision": 3,
"unit": "physiological days/day"
} | CMF027_sensitivity_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means ... | Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ... | Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: physiological days/day | Relevant formula name: Daily physiological effectiveness (每日生理效应).
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the small... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: CO2 response factor (二氧化碳影响因子)
Formula (LaTeX): F_{CO2}=1+\beta\ln(C_x/340)
Formula: FCO2 = 1 + beta * ln(Cx / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp... | 3 | Stage-dependent product | sensitivity | {
"BFF": 0.78,
"DTE": 0.904,
"IE": 1.23,
"PDT": 26.3,
"RPE": 0.55
} | A phenology calculation involves sensitivity analysis. The current measurements are PDT=26.3 physiological days, DTE=0.904 fraction, IE=1.23 dimensionless, RPE=0.55 fraction, BFF=0.78 dimensionless. A field technician asks what the daily physiological effectiveness would become if RPE changed to 0.63. Report the new fi... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Daily physiological effectiveness.
Use the verified formula:
\[DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF\]
In calculation-friendly notation, this is:
DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0.
Substitute the relevant values:
PDT=26.... | dev | Phenology | 0 | CMF029 |
0.500 | cropmath-v1 | null | [
"CMF005",
"CMF007"
] | {
"Coef_K_Decom": 0.0026000000000000003,
"Coef_K_Trans": 0.197,
"F_notill": 0.97,
"F_pH": 0.43,
"F_temp": 0.649,
"F_texture": 0.875,
"F_water": 0.5660000000000001,
"Pool": 1787
} | carbon_nitrogen_cycle | {
"expression": "Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans)",
"id": "CMF009",
"latex": "R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans})",
"name": "碳库呼吸损失",
"name_en": "carbon-nitrogen cycling carbon pool respiration loss",
"precision": 3,
"unit": "g C/m2/day"
} | CMF009_chain_2_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling carbon pool respiration loss (碳库呼吸损失)
Formula (LaTeX): R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans})
Formula: Respiration = Pool*Coef_K_Decom*F_temp*F_wate... | Formula name: carbon-nitrogen cycling carbon pool respiration loss (碳库呼吸损失)
Formula (LaTeX): R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans})
Formula: Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans)
Operator notes: * means multiplication, / means division, ** or ^ means pow... | Formula name: carbon-nitrogen cycling carbon pool respiration loss (碳库呼吸损失)
Formula (LaTeX): R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans})
Formula: Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans)
Operator notes: * means multiplication, / means division, ** or ^ means pow... | Formula: Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: carbon-nitrogen cycling carbon pool respiration loss (碳库呼吸损失).
Formula: Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/m... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling shoot nitrogen allocation (地上部氮分配量)
Formula (LaTeX): N_{shoot}=N_{uptake}\frac{B_{shoot}}{B_{shoot}+B_{root}}
Formula: N_shoot = Plant_TN_uptake * Biom_shoot / (Biom_shoot + ... | 4 | Chained multiplicative decomposition | chain_2 | {
"Coef_K_Decom": 0.0026000000000000003,
"Coef_K_Trans": 0.197,
"F_notill": 0.97,
"F_pH": 0.43,
"F_temp": 0.649,
"F_texture": 0.875,
"F_water": 0.5660000000000001,
"Pool": 1787
} | Given Pool=1787.0 g C/m2, Coef_K_Decom=0.0026 d-1, F_temp=0.649 fraction, F_water=0.566 fraction, F_texture=0.875 fraction, F_pH=0.43 fraction, F_notill=0.97 fraction, Coef_K_Trans=0.197 fraction, compute carbon-nitrogen cycling carbon pool respiration loss in carbon-nitrogen cycling soil carbon. This requires sequenti... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling carbon pool respiration loss.
Use the verified formula:
\[R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans})\]
In calculation-friendly notation, this is:
Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans).
Substitute the re... | dev | carbon-nitrogen cycling soil carbon | 1 | CMF005 |
0.269 | cropmath-v1 | null | [
"CMF057",
"CMF056"
] | {
"ExtremeT": 43.5,
"MaxT": 33.1,
"Tmax": 40.7
} | environmental_response | {
"expression": "if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0)",
"id": "CMF058",
"latex": "F_H=1,\\;0,\\;\\text{or}\\;1-\\frac{T_{max}-MaxT}{ExtremeT-MaxT}",
"name": "环境响应高温响应",
"name_en": "environmental-response heat stress response",
"precision": 3,
"unit": "fraction... | CMF058_direct_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: environmental-response CO2 response (环境响应二氧化碳响应)
Formula (LaTeX): F_{CO2}=f(CO2,CO2_{RUE})
Formula: F_CO2 = if CO2>=700: 1+CO2_RUE*350/100; else: max(CO2_RUE*CO2*0.01+1-0.01*350*CO2_RUE, 1... | Formula name: environmental-response heat stress response (环境响应高温响应)
Formula (LaTeX): F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}
Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0)
Operator notes: * means multiplication, / means division, ** or ^ means p... | Formula name: environmental-response heat stress response (环境响应高温响应)
Formula (LaTeX): F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}
Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0)
Operator notes: * means multiplication, / means division, ** or ^ means p... | Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: environmental-response heat stress response (环境响应高温响应).
Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: environmental-response CO2 response (环境响应二氧化碳响应)
Formula (LaTeX): F_{CO2}=f(CO2,CO2_{RUE})
Formula: F_CO2 = if CO2>=700: 1+CO2_RUE*350/100; else: max(CO2_RUE*CO2*0.01+1-0.01*350*CO2_RUE, 1)
Operator... | 2 | Piecewise linear stress | direct | {
"ExtremeT": 43.5,
"MaxT": 33.1,
"Tmax": 40.7
} | A environmental-response formula system calculation estimates environmental-response heat stress response. The measured inputs are Tmax=40.7 C, MaxT=33.1 C, ExtremeT=43.5 C. What is the simple heat stress response? Give the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as environmental-response heat stress response.
Use the verified formula:
\[F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}\]
In calculation-friendly notation, this is:
F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0).
Substitute the re... | dev | environmental-response formula system | 0 | CMF057 |
0.37 | cropmath-v1 | {
"new_value": 0.044,
"old_value": 0.049,
"parameter": "a"
} | [
"CMF027",
"CMF028"
] | {
"PDT": 50.7,
"a": 0.044
} | growth_yield | {
"expression": "if PDT<28: 1; else: exp(-a*(PDT-28))",
"id": "CMF030",
"latex": "F_{PA}=1\\;(PDT<28),\\quad e^{-a(PDT-28)}\\;(PDT\\ge 28)",
"name": "生理年龄因子",
"name_en": "Physiological age factor",
"precision": 2,
"unit": "fraction"
} | CMF030_sensitivity_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<... | Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the... | Formula name: Physiological age factor (生理年龄因子)
Formula (LaTeX): F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the... | Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Physiological age factor (生理年龄因子).
Formula: FPA = if PDT<28: 1; else: exp(-a*(PDT-28))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Daily physiological effectiveness (每日生理效应)
Formula (LaTeX): DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF
Formula: DPE = if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BF... | 3 | Piecewise exponential decay | sensitivity | {
"PDT": 50.7,
"a": 0.049
} | A photosynthesis calculation involves sensitivity analysis. The current measurements are PDT=50.7 physiological days, a=0.049 dimensionless. A field technician asks what the physiological age factor would become if a changed to 0.044. Report the new final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Physiological age factor.
Use the verified formula:
\[F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)\]
In calculation-friendly notation, this is:
FPA = if PDT<28: 1; else: exp(-a*(PDT-28)).
Substitute the relevant values:
PDT=50.7 physiological days, a=0.044 dimensionless.
The comp... | dev | Photosynthesis | 0 | CMF027 |
0.57 | cropmath-v1 | null | [
"CMF048",
"CMF046"
] | {
"B_above": 18531,
"PDT": 40.8,
"Y_grain": 6146
} | growth_yield | {
"expression": "1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))",
"id": "CMF045",
"latex": "PIS=1-PIGL-PIP",
"name": "茎鞘分配指数",
"name_en": "Stem partitioning index",
"precision": 2,
"unit": "fraction"
} | CMF045_chain_2_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) m... | Formula name: Stem partitioning index (茎鞘分配指数)
Formula (LaTeX): PIS=1-PIGL-PIP
Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means na... | Formula name: Stem partitioning index (茎鞘分配指数)
Formula (LaTeX): PIS=1-PIGL-PIP
Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means na... | Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: frac... | Relevant formula name: Stem partitioning index (茎鞘分配指数).
Formula: PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39)))
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and m... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes:... | 4 | Residual with piecewise components | chain_2 | {
"B_above": 18531,
"PDT": 40.8,
"Y_grain": 6146
} | A dry matter partitioning module estimates Stem partitioning index using intermediate drivers. Use the provided inputs in sequence. The measurements are PDT=40.8 physiological days, Y_grain=6146.0 kg/ha, B_above=18531.0 kg/ha. Compute the stem partitioning index and give the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Stem partitioning index.
Use the verified formula:
\[PIS=1-PIGL-PIP\]
In calculation-friendly notation, this is:
PIS = 1 - (if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT)) - (Y_grain/B_above/0.87)/(1+exp(-0.2804*(PDT-39))).
Substitute the relevant values:
PDT=40.8 physiologica... | dev | Dry matter partitioning | 0 | CMF048 |
128.56 | cropmath-v1 | null | [
"CMF048",
"CMF043"
] | {
"DTGA": 321.4,
"Rg": 0.4
} | growth_yield | {
"expression": "Rg * DTGA",
"id": "CMF046",
"latex": "RG=R_g\\cdot DTGA",
"name": "生长呼吸",
"name_en": "Growth respiration",
"precision": 2,
"unit": "kg/ha/day"
} | CMF046_direct_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) m... | Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day
Parameters:
- Rg: growth r... | Formula name: Growth respiration (生长呼吸)
Formula (LaTeX): RG=R_g\cdot DTGA
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day
Parameters:
- Rg: growth r... | Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | Relevant formula name: Growth respiration (生长呼吸).
Formula: RG = Rg * DTGA
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha/day | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Maintenance respiration (维持呼吸)
Formula (LaTeX): RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10}
Formula: RM = (0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10)
Operator notes:... | 1 | Product | direct | {
"DTGA": 321.4,
"Rg": 0.4
} | A respiration calculation estimates Growth respiration. The measured inputs are Rg=0.4 fraction, DTGA=321.4 kg/ha/day. What is the growth respiration? Give the final numeric value in kg/ha/day. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Growth respiration.
Use the verified formula:
\[RG=R_g\cdot DTGA\]
In calculation-friendly notation, this is:
RG = Rg * DTGA.
Substitute the relevant values:
Rg=0.4 fraction, DTGA=321.4 kg/ha/day.
The computed value is 128.56 kg/ha/day.
Therefore, the final numeric answer is \boxed{128.5... | dev | Respiration | 0 | CMF048 |
4114.4 | cropmath-v1 | null | [
"CMF053",
"CMF032"
] | {
"AWSP": 4622.9,
"grain_fraction": 0.89
} | growth_yield | {
"expression": "AWSP * grain_fraction",
"id": "CMF054",
"latex": "Y=AWSP\\cdot f_{grain}",
"name": "稻谷干重产量",
"name_en": "Dry grain yield",
"precision": 1,
"unit": "kg/ha"
} | CMF054_direct_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Specific leaf area (比叶面积)
Formula (LaTeX): SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Op... | Formula name: Dry grain yield (稻谷干重产量)
Formula (LaTeX): Y=AWSP\cdot f_{grain}
Formula: Y = AWSP * grain_fraction
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha
Parameters:
- A... | Formula name: Dry grain yield (稻谷干重产量)
Formula (LaTeX): Y=AWSP\cdot f_{grain}
Formula: Y = AWSP * grain_fraction
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha
Parameters:
- A... | Formula: Y = AWSP * grain_fraction
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha | Relevant formula name: Dry grain yield (稻谷干重产量).
Formula: Y = AWSP * grain_fraction
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Specific leaf area (比叶面积)
Formula (LaTeX): SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Operator not... | 1 | Product | direct | {
"AWSP": 4622.9,
"grain_fraction": 0.89
} | Given AWSP=4622.9 kg/ha, grain_fraction=0.89 fraction, calculate the Dry grain yield for a yield formation. The result should be in kg/ha. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Dry grain yield.
Use the verified formula:
\[Y=AWSP\cdot f_{grain}\]
In calculation-friendly notation, this is:
Y = AWSP * grain_fraction.
Substitute the relevant values:
AWSP=4622.9 kg/ha, grain_fraction=0.89 fraction.
The computed value is 4114.4 kg/ha.
Therefore, the final numeric ans... | dev | Yield formation | 1 | CMF053 |
0.915 | cropmath-v1 | null | [
"CMF022",
"CMF018"
] | {
"Q10": 3.04,
"t_soil": 29.2
} | methane_emission | {
"expression": "Q10^((min(t_soil,30)-30)/10)",
"id": "CMF023",
"latex": "TI=Q_{10}^{(t_{sl}-30)/10}",
"name": "甲烷温度指数",
"name_en": "Methane temperature index",
"precision": 3,
"unit": "multiplier"
} | CMF023_direct_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Methane production (甲烷产生量)
Formula (LaTeX): P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division... | Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Methane temperature index (甲烷温度指数).
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Methane production (甲烷产生量)
Formula (LaTeX): P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))
Formula: P = max(0, 0.27 * FEh * (TI * Cr + Com))
Operator notes: * means multiplication, / means division, ** or ^ ... | 1 | Q10 with temperature clipping | direct | {
"Q10": 3.04,
"t_soil": 29.2
} | Given Q10=3.04 dimensionless, t_soil=29.2 C, calculate the Methane temperature index for a methane. The result should be in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Methane temperature index.
Use the verified formula:
\[TI=Q_{10}^{(t_{sl}-30)/10}\]
In calculation-friendly notation, this is:
TI = Q10^((min(t_soil,30)-30)/10).
Substitute the relevant values:
Q10=3.04 dimensionless, t_soil=29.2 C.
The computed value is 0.915 fraction.
Therefore, the fi... | dev | Methane | 1 | CMF022 |
3886.3 | cropmath-v1 | null | [
"CMF055",
"CMF058"
] | {
"Biomass": 14393.7,
"HI": 0.27
} | environmental_response | {
"expression": "Biomass * HI",
"id": "CMF062",
"latex": "Yield=Biomass\\cdot HI",
"name": "环境响应产量",
"name_en": "environmental-response yield",
"precision": 1,
"unit": "kg/ha"
} | CMF062_direct_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: environmental-response yield (环境响应产量)
Formula (LaTeX): Yield=Biomass\cdot HI
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, ex... | Formula name: environmental-response yield (环境响应产量)
Formula (LaTeX): Yield=Biomass\cdot HI
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha
Paramet... | Formula name: environmental-response yield (环境响应产量)
Formula (LaTeX): Yield=Biomass\cdot HI
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha
Paramet... | Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha | Relevant formula name: environmental-response yield (环境响应产量).
Formula: Yield = Biomass * HI
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg/ha | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: environmental-response daily biomass increment (环境响应日生物量增量)
Formula (LaTeX): dB=10RUEfSolarSRADF_{CO2}F_T\min(F_W,F_H)
Formula: dBiomass = 10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F_Water, F_... | 1 | Product | direct | {
"Biomass": 14393.7,
"HI": 0.27
} | In an environmental-response formula system, the environmental-response yield is computed as part of environmental-response formula calculation. With Biomass=14393.7 kg/ha, HI=0.27 fraction, determine the numeric value in kg/ha. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as environmental-response yield.
Use the verified formula:
\[Yield=Biomass\cdot HI\]
In calculation-friendly notation, this is:
Yield = Biomass * HI.
Substitute the relevant values:
Biomass=14393.7 kg/ha, HI=0.27 fraction.
The computed value is 3886.3 kg/ha.
Therefore, the final numeric ans... | dev | environmental-response formula system | 2 | CMF055 |
1.000 | cropmath-v1 | {
"new_value": 28.7,
"old_value": 25,
"parameter": "Tmax"
} | [
"CMF055",
"CMF057"
] | {
"ExtremeT": 47.1,
"MaxT": 34.3,
"Tmax": 28.7
} | environmental_response | {
"expression": "if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0)",
"id": "CMF058",
"latex": "F_H=1,\\;0,\\;\\text{or}\\;1-\\frac{T_{max}-MaxT}{ExtremeT-MaxT}",
"name": "环境响应高温响应",
"name_en": "environmental-response heat stress response",
"precision": 3,
"unit": "fraction... | CMF058_sensitivity_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: environmental-response daily biomass increment (环境响应日生物量增量)
Formula (LaTeX): dB=10RUEfSolarSRADF_{CO2}F_T\min(F_W,F_H)
Formula: dBiomass = 10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F... | Formula name: environmental-response heat stress response (环境响应高温响应)
Formula (LaTeX): F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}
Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0)
Operator notes: * means multiplication, / means division, ** or ^ means p... | Formula name: environmental-response heat stress response (环境响应高温响应)
Formula (LaTeX): F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}
Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0)
Operator notes: * means multiplication, / means division, ** or ^ means p... | Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: environmental-response heat stress response (环境响应高温响应).
Formula: F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: environmental-response daily biomass increment (环境响应日生物量增量)
Formula (LaTeX): dB=10RUEfSolarSRADF_{CO2}F_T\min(F_W,F_H)
Formula: dBiomass = 10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F_Water, F_... | 3 | Piecewise linear stress | sensitivity | {
"ExtremeT": 47.1,
"MaxT": 34.3,
"Tmax": 25
} | In environmental-response formula system, we analyze how environmental-response heat stress response responds to parameter changes. Baseline: Tmax=25.0 C, MaxT=34.3 C, ExtremeT=47.1 C. After changing Tmax from 25.0 to 28.7, compute the new environmental-response heat stress response. Give the numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as environmental-response heat stress response.
Use the verified formula:
\[F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}\]
In calculation-friendly notation, this is:
F_Heat = if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0).
Substitute the re... | dev | environmental-response formula system | 2 | CMF055 |
0.395 | cropmath-v1 | {
"new_value": 22.6,
"old_value": 20.5,
"parameter": "t_soil"
} | [
"CMF020",
"CMF025"
] | {
"Q10": 3.51,
"t_soil": 22.6
} | methane_emission | {
"expression": "Q10^((min(t_soil,30)-30)/10)",
"id": "CMF023",
"latex": "TI=Q_{10}^{(t_{sl}-30)/10}",
"name": "甲烷温度指数",
"name_en": "Methane temperature index",
"precision": 3,
"unit": "multiplier"
} | CMF023_sensitivity_t0_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Water-content decomposition factor (水分分解因子)
Formula (LaTeX): WI=0.49e^{3.88W_c-5.4W_c^2}
Formula: WI = 0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2)
Operator notes: * means multiplication, / ... | Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula name: Methane temperature index (甲烷温度指数)
Formula (LaTeX): TI=Q_{10}^{(t_{sl}-30)/10}
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit... | Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Methane temperature index (甲烷温度指数).
Formula: TI = Q10^((min(t_soil,30)-30)/10)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Fresh organic matter carbon decomposition (新鲜有机质碳分解量)
Formula (LaTeX): OMNC=WI\cdot SI\cdot TI\cdot0.027\cdot OMN
Formula: OMNC = WI * SI * TI * 0.027 * OMN
Operator notes: * means multiplication, /... | 2 | Q10 with temperature clipping | sensitivity | {
"Q10": 3.51,
"t_soil": 20.5
} | A methane calculation involves sensitivity analysis. The current measurements are Q10=3.51 dimensionless, t_soil=20.5 C. A field technician asks what the methane temperature index would become if t_soil changed to 22.6. Report the new final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Methane temperature index.
Use the verified formula:
\[TI=Q_{10}^{(t_{sl}-30)/10}\]
In calculation-friendly notation, this is:
TI = Q10^((min(t_soil,30)-30)/10).
Substitute the relevant values:
Q10=3.51 dimensionless, t_soil=22.6 C.
The computed value is 0.395 fraction.
Therefore, the fi... | dev | Methane | 0 | CMF020 |
3.432 | cropmath-v1 | null | [
"CMF012",
"CMF010"
] | {
"Day_Length_hour": 10.37,
"F_CO2": 1.28,
"F_T": 0.49,
"F_Water": 0.33,
"Photo_Rate_opt": 37.01
} | carbon_nitrogen_cycle | {
"expression": "Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432",
"id": "CMF002",
"latex": "GPP=P_{opt}F_TF_WF_{CO2}DL\\cdot0.0432",
"name": "总初级生产力",
"name_en": "carbon-nitrogen cycling gross primary production",
"precision": 3,
"unit": "g C/m2/day"
} | CMF002_chain_2_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling soil pH decomposition factor (土壤pH分解因子)
Formula (LaTeX): F_{pH}=\frac{1}{1+e^{2.5(5-pH)}}
Formula: F_pH = 1 / (1 + exp(2.5 * (5 - pH)))
Operator notes: * means mult... | Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means nat... | Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means nat... | Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: carbon-nitrogen cycling gross primary production (总初级生产力).
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smalle... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling soil carbon water factor (土壤碳分解水分因子)
Formula (LaTeX): F_W=0.49e^{3.88W-5.4W^2}
Formula: F_W_soil = if Soil_Water>=Saturate_Water: 0.65; else: 0.49*exp(3.88*(Soil_Water/BD)-5.... | 4 | Multiplicative conversion | chain_2 | {
"Day_Length_hour": 10.37,
"F_CO2": 1.28,
"F_T": 0.49,
"F_Water": 0.33,
"Photo_Rate_opt": 37.01
} | A carbon-nitrogen cycling photosynthesis module estimates carbon-nitrogen cycling gross primary production using intermediate drivers. Use the provided inputs in sequence. The measurements are Photo_Rate_opt=37.01 umol CO2/m2/s, F_T=0.49 fraction, F_Water=0.33 fraction, F_CO2=1.28 fraction, Day_Length_hour=10.37 h. Com... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling gross primary production.
Use the verified formula:
\[GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432\]
In calculation-friendly notation, this is:
GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432.
Substitute the relevant values:
Photo_Rate_opt=37.01 u... | dev | carbon-nitrogen cycling photosynthesis | 0 | CMF012 |
17.02 | cropmath-v1 | null | [
"CMF053",
"CMF028"
] | {
"Am": 31.1,
"FCO2": 1.2,
"FPA": 0.92,
"FT": 0.67,
"NNI": 0.74,
"WDF": 0.92
} | growth_yield | {
"expression": "Am * FCO2 * FPA * FT * min(NNI, WDF)",
"id": "CMF026",
"latex": "AMAX=Am\\cdot F_{CO2}\\cdot F_{PA}\\cdot F_T\\cdot\\min(NNI,WDF)",
"name": "实际最大同化速率",
"name_en": "Actual maximum assimilation rate",
"precision": 2,
"unit": "kg CO2/ha/h"
} | CMF026_chain_2_t1_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes... | Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and ... | Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and ... | Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg CO2/ha/h | Relevant formula name: Actual maximum assimilation rate (实际最大同化速率).
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: kg CO2/ha/h | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Specific leaf area (比叶面积)
Formula (LaTeX): SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200)
Formula: SLA = if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200)
Operator not... | 4 | Multiplicative with minimum stress | chain_2 | {
"Am": 31.1,
"FCO2": 1.2,
"FPA": 0.92,
"FT": 0.67,
"NNI": 0.74,
"WDF": 0.92
} | Given Am=31.1 kg CO2/ha/h, FCO2=1.2 fraction, FPA=0.92 fraction, FT=0.67 fraction, NNI=0.74 fraction, WDF=0.92 fraction, compute Actual maximum assimilation rate in photosynthesis. This requires sequential calculation through intermediate variables. Report the final numeric value in kg CO2/ha/h. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Actual maximum assimilation rate.
Use the verified formula:
\[AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)\]
In calculation-friendly notation, this is:
AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF).
Substitute the relevant values:
Am=31.1 kg CO2/ha/h, FCO2=1.2 fraction, FPA=... | dev | Photosynthesis | 1 | CMF053 |
1.310 | cropmath-v1 | {
"new_value": 0.68,
"old_value": 0.75,
"parameter": "Coef_B_CO2"
} | [
"CMF002",
"CMF013"
] | {
"CO2": 536,
"Coef_B_CO2": 0.68
} | carbon_nitrogen_cycle | {
"expression": "1 + Coef_B_CO2 * ln(CO2 / 340)",
"id": "CMF001",
"latex": "F_{CO2}=1+B\\ln(CO2/340)",
"name": "作物二氧化碳施肥因子",
"name_en": "carbon-nitrogen cycling CO2 fertilization factor",
"precision": 3,
"unit": "multiplier"
} | CMF001_sensitivity_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0... | Formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子)
Formula (LaTeX): F_{CO2}=1+B\ln(CO2/340)
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smal... | Formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子)
Formula (LaTeX): F_{CO2}=1+B\ln(CO2/340)
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smal... | Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子).
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: ... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Oper... | 2 | Logarithmic | sensitivity | {
"CO2": 536,
"Coef_B_CO2": 0.75
} | In carbon-nitrogen cycling photosynthesis, we analyze how carbon-nitrogen cycling CO2 fertilization factor responds to parameter changes. Baseline: CO2=536.0 ppm, Coef_B_CO2=0.75 dimensionless. After changing Coef_B_CO2 from 0.75 to 0.68, compute the new carbon-nitrogen cycling CO2 fertilization factor. Give the numeri... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling CO2 fertilization factor.
Use the verified formula:
\[F_{CO2}=1+B\ln(CO2/340)\]
In calculation-friendly notation, this is:
F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340).
Substitute the relevant values:
CO2=536.0 ppm, Coef_B_CO2=0.68 dimensionless.
The computed value is 1... | dev | carbon-nitrogen cycling photosynthesis | 2 | CMF002 |
0.94 | cropmath-v1 | null | [
"CMF050",
"CMF026"
] | {
"PDT": 28.5,
"Qt": 6.2,
"Tmean": 16.2
} | growth_yield | {
"expression": "if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1",
"id": "CMF039",
"latex": "LTF=1-\\frac{4.6+0.054Q_t^{1.56}}{100}",
"name": "低温结实因子",
"name_en": "Low-temperature fertility factor",
"precision": 2,
"unit": "fraction"
} | CMF039_branch_t1_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes... | Formula name: Low-temperature fertility factor (低温结实因子)
Formula (LaTeX): LTF=1-\frac{4.6+0.054Q_t^{1.56}}{100}
Formula: LTF = if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, an... | Formula name: Low-temperature fertility factor (低温结实因子)
Formula (LaTeX): LTF=1-\frac{4.6+0.054Q_t^{1.56}}{100}
Formula: LTF = if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, an... | Formula: LTF = if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Low-temperature fertility factor (低温结实因子).
Formula: LTF = if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Ou... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Relative photoperiod effectiveness (相对光周期效应)
Formula (LaTeX): RPE=1,\;1-PS(P-P_o)^2,\;0
Formula: RPE = if P<=Po: 1; if P<=Po+sqrt(1/PS): 1-PS*(P-Po)^2; else: 0
Operator notes: * means multiplication... | 4 | Piecewise power penalty | branch | {
"PDT": 28.5,
"Qt": 6.2,
"Tmean": 16.2
} | For temperature stress, compute the Low-temperature fertility factor. The inputs are PDT=28.5 physiological days, Tmean=16.2 C, Qt=6.2 C day. Note that this formula uses piecewise logic depending on parameter values. Report the final numeric value in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Low-temperature fertility factor.
Use the verified formula:
\[LTF=1-\frac{4.6+0.054Q_t^{1.56}}{100}\]
In calculation-friendly notation, this is:
LTF = if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1.
Substitute the relevant values:
PDT=28.5 physiological days, Tmean=16.2 ... | dev | Temperature stress | 1 | CMF050 |
0.900 | cropmath-v1 | null | [
"CMF009",
"CMF008"
] | {
"Coef_T_M": 0.16,
"Td": 19.3,
"Tmax_active": 42,
"Tmin_active": 3,
"Topt_active": 25
} | carbon_nitrogen_cycle | {
"expression": "if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^(1+Coef_T_M) * ((Tmax_active-Td)/(Tmax_active-Topt_active))^(1-Coef_T_M)",
"id": "CMF013",
"latex": "F_T=\\left(\\frac{T_d-T_{min}}{T_{opt}-T_{min}}\\right)^{1+M}\\left(\\frac{T_{max}-T_d}{T_{max}-T_{opt}... | CMF013_direct_t0_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling crop temperature activity factor (作物温度活性因子)
Formula (LaTeX): F_T=\left(\frac{T_d-T_{min}}{T_{opt}-T_{min}}\right)^{1+M}\left(\frac{T_{max}-T_d}{T_{max}-T_{opt}}\rig... | Formula name: carbon-nitrogen cycling crop temperature activity factor (作物温度活性因子)
Formula (LaTeX): F_T=\left(\frac{T_d-T_{min}}{T_{opt}-T_{min}}\right)^{1+M}\left(\frac{T_{max}-T_d}{T_{max}-T_{opt}}\right)^{1-M}
Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^... | Formula name: carbon-nitrogen cycling crop temperature activity factor (作物温度活性因子)
Formula (LaTeX): F_T=\left(\frac{T_d-T_{min}}{T_{opt}-T_{min}}\right)^{1+M}\left(\frac{T_{max}-T_d}{T_{max}-T_{opt}}\right)^{1-M}
Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^... | Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^(1+Coef_T_M) * ((Tmax_active-Td)/(Tmax_active-Topt_active))^(1-Coef_T_M)
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max... | Relevant formula name: carbon-nitrogen cycling crop temperature activity factor (作物温度活性因子).
Formula: F_T = if Td<=Tmin_active or Td>=Tmax_active: 0; else: ((Td-Tmin_active)/(Topt_active-Tmin_active))^(1+Coef_T_M) * ((Tmax_active-Td)/(Tmax_active-Topt_active))^(1-Coef_T_M)
Operator notes: * means multiplication, / means... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling carbon pool respiration loss (碳库呼吸损失)
Formula (LaTeX): R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans})
Formula: Respiration = Pool*Coef_K_Decom*F_temp*F_water*F_textur... | 2 | Beta temperature response | direct | {
"Coef_T_M": 0.16,
"Td": 19.3,
"Tmax_active": 42,
"Tmin_active": 3,
"Topt_active": 25
} | A carbon-nitrogen cycling stress calculation estimates carbon-nitrogen cycling crop temperature activity factor. The measured inputs are Td=19.3 C, Tmin_active=3.0 C, Topt_active=25.0 C, Tmax_active=42.0 C, Coef_T_M=0.16 dimensionless. What is the carbon-nitrogen cycling crop temperature activity factor? Give the final... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling crop temperature activity factor.
Use the verified formula:
\[F_T=\left(\frac{T_d-T_{min}}{T_{opt}-T_{min}}\right)^{1+M}\left(\frac{T_{max}-T_d}{T_{max}-T_{opt}}\right)^{1-M}\]
In calculation-friendly notation, this is:
F_T = if Td<=Tmin_active or Td>=Tmax_active:... | dev | carbon-nitrogen cycling stress | 0 | CMF009 |
0.95 | cropmath-v1 | null | [
"CMF026",
"CMF046"
] | {
"PDT": 30.8,
"Qt": 4.3,
"Tmean": 20.6
} | growth_yield | {
"expression": "if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1",
"id": "CMF039",
"latex": "LTF=1-\\frac{4.6+0.054Q_t^{1.56}}{100}",
"name": "低温结实因子",
"name_en": "Low-temperature fertility factor",
"precision": 2,
"unit": "fraction"
} | CMF039_branch_t2_0001 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes... | Formula name: Low-temperature fertility factor (低温结实因子)
Formula (LaTeX): LTF=1-\frac{4.6+0.054Q_t^{1.56}}{100}
Formula: LTF = if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, an... | Formula name: Low-temperature fertility factor (低温结实因子)
Formula (LaTeX): LTF=1-\frac{4.6+0.054Q_t^{1.56}}{100}
Formula: LTF = if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, an... | Formula: LTF = if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: fraction | Relevant formula name: Low-temperature fertility factor (低温结实因子).
Formula: LTF = if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Ou... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: Actual maximum assimilation rate (实际最大同化速率)
Formula (LaTeX): AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)
Formula: AMAX = Am * FCO2 * FPA * FT * min(NNI, WDF)
Operator notes: * means ... | 4 | Piecewise power penalty | branch | {
"PDT": 30.8,
"Qt": 4.3,
"Tmean": 20.6
} | Calculate Low-temperature fertility factor in temperature stress with these inputs: PDT=30.8 physiological days, Tmean=20.6 C, Qt=4.3 C day. The computation may follow different paths based on piecewise thresholds. Give the numeric result in fraction. | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as Low-temperature fertility factor.
Use the verified formula:
\[LTF=1-\frac{4.6+0.054Q_t^{1.56}}{100}\]
In calculation-friendly notation, this is:
LTF = if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1.
Substitute the relevant values:
PDT=30.8 physiological days, Tmean=20.6 ... | dev | Temperature stress | 2 | CMF026 |
3.943 | cropmath-v1 | {
"new_value": 10.12,
"old_value": 11.24,
"parameter": "Day_Length_hour"
} | [
"CMF001",
"CMF007"
] | {
"Day_Length_hour": 10.12,
"F_CO2": 1.15,
"F_T": 0.64,
"F_Water": 0.44,
"Photo_Rate_opt": 27.85
} | carbon_nitrogen_cycle | {
"expression": "Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432",
"id": "CMF002",
"latex": "GPP=P_{opt}F_TF_WF_{CO2}DL\\cdot0.0432",
"name": "总初级生产力",
"name_en": "carbon-nitrogen cycling gross primary production",
"precision": 3,
"unit": "g C/m2/day"
} | CMF002_sensitivity_t2_0000 | false | Candidate formulas are listed below. Select the physiologically appropriate formula before calculating.
Candidate 1:
Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0... | Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means nat... | Formula name: carbon-nitrogen cycling gross primary production (总初级生产力)
Formula (LaTeX): GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means nat... | Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smaller/larger value.
Output unit: g C/m2/day | Relevant formula name: carbon-nitrogen cycling gross primary production (总初级生产力).
Formula: GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432
Operator notes: * means multiplication, / means division, ** or ^ means power, exp(x) means e^x, ln(x) means natural logarithm, and min/max select the smalle... | A retrieved formula is listed below. It may look relevant, but use it only if it truly matches the problem.
Formula name: carbon-nitrogen cycling CO2 fertilization factor (作物二氧化碳施肥因子)
Formula (LaTeX): F_{CO2}=1+B\ln(CO2/340)
Formula: F_CO2 = 1 + Coef_B_CO2 * ln(CO2 / 340)
Operator notes: * means multiplication, / means... | 3 | Multiplicative conversion | sensitivity | {
"Day_Length_hour": 11.24,
"F_CO2": 1.15,
"F_T": 0.64,
"F_Water": 0.44,
"Photo_Rate_opt": 27.85
} | In carbon-nitrogen cycling photosynthesis, we analyze how carbon-nitrogen cycling gross primary production responds to parameter changes. Baseline: Photo_Rate_opt=27.85 umol CO2/m2/s, F_T=0.64 fraction, F_Water=0.44 fraction, F_CO2=1.15 fraction, Day_Length_hour=11.24 h. After changing Day_Length_hour from 11.24 to 10.... | {
"C": "<|im_start|>system\nYou are a scientific reasoning assistant. Solve the following problem step by step. Show your reasoning clearly, then end with exactly one line in this format: The answer is [number].\nDo not write multiple answers. Do not include units in the final line.\nExample:\nStep 1: ...\nStep 2: ..... | Identify the target quantity as carbon-nitrogen cycling gross primary production.
Use the verified formula:
\[GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432\]
In calculation-friendly notation, this is:
GPP = Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432.
Substitute the relevant values:
Photo_Rate_opt=27.85 u... | dev | carbon-nitrogen cycling photosynthesis | 2 | CMF001 |
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