formula_id,family,primary_subject,name_en,name_zh,unit,precision,expression,latex,math_type,math_types,modes,sample_count
CMF001,carbon_nitrogen_cycle,carbon-nitrogen cycling photosynthesis,carbon-nitrogen cycling CO2 fertilization factor,作物二氧化碳施肥因子,multiplier,3,1 + Coef_B_CO2 * ln(CO2 / 340),F_{CO2}=1+B\ln(CO2/340),Logarithmic,Logarithmic,direct;sensitivity,14
CMF002,carbon_nitrogen_cycle,carbon-nitrogen cycling photosynthesis,carbon-nitrogen cycling gross primary production,总初级生产力,g C/m2/day,3,Photo_Rate_opt * F_T * F_Water * F_CO2 * Day_Length_hour * 0.0432,GPP=P_{opt}F_TF_WF_{CO2}DL\cdot0.0432,Multiplicative conversion,Multiplicative conversion,sensitivity;direct;chain_2,20
CMF003,carbon_nitrogen_cycle,Nitrogen,Nitrogen use efficiency,氮利用效率,kg grain/kg N,2,GrainYield / NUptake,NUE=\frac{GrainYield}{NUptake},Ratio,Ratio,direct;sensitivity,14
CMF004,carbon_nitrogen_cycle,carbon-nitrogen cycling nitrogen,carbon-nitrogen cycling crop nitrogen demand,作物需氮量,g N/m2/day,3,"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)","N_d=C_uN_{shoot}\;\text{or}\;\min(N_{max},r_NNPP)",Piecewise minimum,Piecewise minimum,chain_2;direct;branch;sensitivity,25
CMF005,carbon_nitrogen_cycle,carbon-nitrogen cycling nitrogen,carbon-nitrogen cycling shoot nitrogen allocation,地上部氮分配量,g N/m2,3,Plant_TN_uptake * Biom_shoot / (Biom_shoot + Biom_root),N_{shoot}=N_{uptake}\frac{B_{shoot}}{B_{shoot}+B_{root}},Biomass-weighted allocation,Biomass-weighted allocation,sensitivity;direct,13
CMF006,carbon_nitrogen_cycle,carbon-nitrogen cycling photosynthesis,carbon-nitrogen cycling canopy absorbed PAR,冠层吸收光合有效辐射,umol/m2/s,2,Radi * 0.44 * 4.6 * (1-Coef_rou) * (1-exp(-Coef_K*LAI)) / (Coef_K*LAI),PAR=Radi\cdot0.44\cdot4.6(1-\rho)\frac{1-e^{-KLAI}}{KLAI},Exponential ratio,Exponential ratio,direct;chain_2;sensitivity,19
CMF007,carbon_nitrogen_cycle,carbon-nitrogen cycling photosynthesis,carbon-nitrogen cycling optimal photosynthetic rate,最适光合速率,umol CO2/m2/s,3,(Coef_alfa * Leaf_N) * PAR / (PAR + Coef_beta),P_{opt}=\alpha N_{leaf}\frac{PAR}{PAR+\beta},Michaelis-Menten response,Michaelis-Menten response,sensitivity;chain_2;direct,21
CMF008,carbon_nitrogen_cycle,carbon-nitrogen cycling respiration,carbon-nitrogen cycling plant maintenance respiration,植株维持呼吸,g C/m2/day,3,0.0432*24*(Biom_plant_yesterday/0.45)*Coef_Rm*2^((Tmn-25)/10) / (if DVI>1: DVI^2; else: 1),R_m=0.0432\cdot24(Biom/0.45)C_m2^{(T-25)/10},Q10 with DVI correction,Q10 with DVI correction,branch;direct;sensitivity,20
CMF009,carbon_nitrogen_cycle,carbon-nitrogen cycling soil carbon,carbon-nitrogen cycling carbon pool respiration loss,碳库呼吸损失,g C/m2/day,3,Pool*Coef_K_Decom*F_temp*F_water*F_texture*F_pH*F_notill*(1-Coef_K_Trans),R=PoolK F_TF_WF_{texture}F_{pH}F_{notill}(1-K_{trans}),Chained multiplicative decomposition,Chained multiplicative decomposition,direct;sensitivity;chain_2,19
CMF010,carbon_nitrogen_cycle,carbon-nitrogen cycling soil carbon,carbon-nitrogen cycling soil pH decomposition factor,土壤pH分解因子,fraction,3,1 / (1 + exp(2.5 * (5 - pH))),F_{pH}=\frac{1}{1+e^{2.5(5-pH)}},Logistic,Logistic,direct;sensitivity,13
CMF011,carbon_nitrogen_cycle,carbon-nitrogen cycling soil carbon,carbon-nitrogen cycling soil carbon temperature factor,土壤碳分解温度因子,multiplier,3,if is_soil_temp>=0.5: 2.4**((Temp-10)*0.1); else: 2.4**((4.4+0.76*Temp-10)*0.1),F_T=2.4^{(T_{soil}-10)/10}\;\text{where}\;T_{soil}=T\;\text{or}\;4.4+0.76T,Q10 temperature response,Q10 temperature response,sensitivity;direct;branch,18
CMF012,carbon_nitrogen_cycle,carbon-nitrogen cycling soil carbon,carbon-nitrogen cycling soil carbon water factor,土壤碳分解水分因子,fraction,3,if Soil_Water>=Saturate_Water: 0.65; else: 0.49*exp(3.88*(Soil_Water/BD)-5.4*(Soil_Water/BD)^2),F_W=0.49e^{3.88W-5.4W^2},Piecewise exponential,Piecewise exponential,sensitivity;branch;direct,20
CMF013,carbon_nitrogen_cycle,carbon-nitrogen cycling stress,carbon-nitrogen cycling crop temperature activity factor,作物温度活性因子,response factor,3,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),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},Beta temperature response,Beta temperature response,direct;branch;sensitivity,18
CMF014,carbon_nitrogen_cycle,carbon-nitrogen cycling water,carbon-nitrogen cycling crop water stress factor,作物水分胁迫因子,fraction,3,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)),"F_W=f(\theta,\theta_{wp},\theta_{min},\theta_{max})",Piecewise water response,Piecewise water response,sensitivity;branch;direct,19
CMF015,methane_emission,Methane,Root-exudate carbon substrate,根系分泌碳底物,g C/m2/day,3,0.0018 * VI * SI * W ** 1.25,C_r=0.0018VI\cdot SI\cdot W^{1.25},Power product,Power product,direct;sensitivity,12
CMF016,methane_emission,Methane,Methane ebullition emission,甲烷冒泡排放,g CH4/m2/day,3,"min(0.7 * ln(t_soil) / Wr, 0.9) * P","E_{bl}=\min(0.7\ln(t_{soil})/W_r,0.9)P",Logarithmic minimum,Logarithmic minimum,chain_2;sensitivity;direct,21
CMF017,methane_emission,Methane,Total methane emission,甲烷总排放,g CH4/m2/day,3,Ebl + P * CH4RiceEfC * (1 - W/Wmax)^0.25,E=E_{bl}+P\cdot C(1-W/W_{max})^{0.25},Chained sum,Chained sum,chain_2;sensitivity;direct,19
CMF018,methane_emission,Methane,Redox potential factor,氧化还原电位因子,fraction,3,if Eh<-150: 1; else: exp(-1.7*(1+Eh/150)),"F_{Eh}=1\;(Eh<-150),\quad e^{-1.7(1+Eh/150)}",Piecewise exponential,Piecewise exponential,direct;sensitivity;branch,21
CMF019,methane_emission,Methane,Plant methane transport factor,植株传输因子,fraction,3,CH4RiceEfC * (1 - W / Wmax) ** 0.25,F_p=C(1-W/W_{max})^{0.25},Power attenuation,Power attenuation,sensitivity;direct,14
CMF020,methane_emission,Methane,Fresh organic matter carbon decomposition,新鲜有机质碳分解量,g C/m2/day,3,WI * SI * TI * 0.027 * OMN,OMNC=WI\cdot SI\cdot TI\cdot0.027\cdot OMN,Multiplicative,Multiplicative,direct;sensitivity;chain_2,20
CMF021,methane_emission,Methane,Soil organic matter carbon decomposition,土壤有机质碳分解量,g C/m2/day,3,WI * SI * TI * 0.003 * OMS,OMSC=WI\cdot SI\cdot TI\cdot0.003\cdot OMS,Multiplicative,Multiplicative,chain_2;sensitivity;direct,19
CMF022,methane_emission,Methane,Methane production,甲烷产生量,g CH4/m2/day,3,"max(0, 0.27 * FEh * (TI * Cr + Com))","P=\max(0,0.27F_{Eh}(TI\cdot C_r+Com))",Maximum with chained drivers,Maximum with chained drivers,chain_2;sensitivity;direct,18
CMF023,methane_emission,Methane,Methane temperature index,甲烷温度指数,multiplier,3,"Q10^((min(t_soil,30)-30)/10)",TI=Q_{10}^{(t_{sl}-30)/10},Q10 with temperature clipping,Q10 with temperature clipping,sensitivity;direct;branch,20
CMF024,methane_emission,Methane,Soil temperature from air temperature,土壤温度估算,C,2,4.4 + 0.76 * Tair,T_{soil}=4.4+0.76T_{air},Linear,Linear,direct;sensitivity,13
CMF025,methane_emission,Methane,Water-content decomposition factor,水分分解因子,fraction,3,0.49 * exp(3.88 * WaterC - 5.4 * WaterC^2),WI=0.49e^{3.88W_c-5.4W_c^2},Exponential quadratic,Exponential quadratic,sensitivity;direct,12
CMF026,growth_yield,Photosynthesis,Actual maximum assimilation rate,实际最大同化速率,kg CO2/ha/h,2,"Am * FCO2 * FPA * FT * min(NNI, WDF)","AMAX=Am\cdot F_{CO2}\cdot F_{PA}\cdot F_T\cdot\min(NNI,WDF)",Multiplicative with minimum stress,Multiplicative with minimum stress,sensitivity;direct;chain_2,20
CMF027,growth_yield,Phenology,Daily physiological effectiveness,每日生理效应,physiological days/day,3,if PDT<8: DTE*IE; if PDT<18: DTE*RPE; if PDT<32: DTE; if PDT<57: DTE*BFF; else: 0,"DPE=DTE\cdot IE,\;DTE\cdot RPE,\;DTE,\;DTE\cdot BFF",Stage-dependent product,Stage-dependent product,chain_2;sensitivity;branch;direct,24
CMF028,growth_yield,Phenology,Emergence thermal requirement,出苗热量需求,C day,1,45 + 7 * SDEPTH,EMGDD=45+7SDEPTH,Linear,Linear,direct;sensitivity,11
CMF029,growth_yield,Photosynthesis,CO2 response factor,二氧化碳影响因子,multiplier,2,1 + beta * ln(Cx / 340),F_{CO2}=1+\beta\ln(C_x/340),Logarithmic,Logarithmic,direct;sensitivity,14
CMF030,growth_yield,Photosynthesis,Physiological age factor,生理年龄因子,fraction,2,if PDT<28: 1; else: exp(-a*(PDT-28)),"F_{PA}=1\;(PDT<28),\quad e^{-a(PDT-28)}\;(PDT\ge 28)",Piecewise exponential decay,Piecewise exponential decay,direct;branch;sensitivity,20
CMF031,growth_yield,Photosynthesis,Light interception fraction,光能截获率,fraction,2,1 - exp(-k * LAI),fPAR = 1 - e^{-k \cdot LAI},Exponential saturation,Exponential saturation,direct;sensitivity,13
CMF032,growth_yield,Temperature response,Temperature response factor,温度响应因子,fraction,2,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,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}),Piecewise trigonometric,Piecewise trigonometric,direct;branch;sensitivity,18
CMF033,growth_yield,Respiration,Daily dry matter increment,日干物质增量,kg/ha/day,2,(DTGA - RM - RG) / (1 - b),GCR=\frac{DTGA-RM-RG}{1-b},Subtraction and conversion,Subtraction and conversion,chain_2;sensitivity;direct,21
CMF034,growth_yield,Dry matter partitioning,Harvest index,收获指数,fraction,2,Y_grain / B_above,HI=\frac{Y_{grain}}{B_{above}},Ratio,Ratio,direct;sensitivity,12
CMF035,growth_yield,Temperature stress,High-temperature fertility factor,高温结实因子,fraction,2,if 32<=PDT<=39 and Tmax_day>36.6: 1/(1+exp(0.853*(Tmax_day-36.6))); else: 1,HTF=\frac{1}{1+e^{0.853(T_m-36.6)}},Piecewise logistic,Piecewise logistic,sensitivity;branch;direct,20
CMF036,growth_yield,Photosynthesis,Canopy extinction coefficient,冠层消光系数,dimensionless,3,0.0087 * PDT + 0.2222,K=0.0087PDT+0.2222,Linear,Linear,sensitivity;direct,13
CMF037,growth_yield,Leaf area growth,Potential leaf area index,潜在叶面积指数,m2/m2,2,LAI0 * exp(RP * GDD),LAI_P=LAI_0e^{RP\cdot GDD},Exponential growth,Exponential growth,sensitivity;chain_2;direct,22
CMF038,growth_yield,Leaf area growth,Leaf area index from SLA,比叶面积法叶面积指数,m2/m2,2,SLA * AWL,LAI=SLA\cdot AWL,Product,Product,direct;sensitivity,13
CMF039,growth_yield,Temperature stress,Low-temperature fertility factor,低温结实因子,fraction,2,if 26<=PDT<=39 and Tmean<22: 1-(4.6+0.054*Qt^1.56)/100; else: 1,LTF=1-\frac{4.6+0.054Q_t^{1.56}}{100},Piecewise power penalty,Piecewise power penalty,branch;sensitivity;direct,20
CMF040,growth_yield,Phenology,Critical daylength,临界日长,h,2,Po + sqrt(1 / PS),P_c=P_o+\sqrt{1/PS},Power response,Power response,direct;sensitivity;chain_2,20
CMF041,growth_yield,Dry matter partitioning,Green leaf partitioning index,绿叶分配指数,fraction,2,if PDT<26: 0.54-0.0046*PDT; else: 1.4532*exp(-0.0492*PDT),"PIGL=0.54-0.0046PDT\;(PDT<26),\quad1.4532e^{-0.0492PDT}\;(PDT\ge26)",Piecewise linear/exponential,Piecewise linear/exponential,sensitivity;direct;branch,21
CMF042,growth_yield,Dry matter partitioning,Panicle partitioning index,穗分配指数,fraction,2,(Y_grain / B_above / 0.87) / (1 + exp(-0.2804 * (PDT - 39))),PIP=\frac{HI/0.87}{1+e^{-0.2804(PDT-39)}},Multi-step sigmoid,Multi-step sigmoid,direct;branch;sensitivity,23
CMF043,growth_yield,Dry matter partitioning,Root partitioning index,地下部分配指数,fraction,2,1 - (-0.0000842*PDT^2 + 0.01*PDT + 0.63),PIRO=1-PISH,Residual from shoot partitioning,Residual from shoot partitioning,chain_2;sensitivity;direct,18
CMF044,growth_yield,Dry matter partitioning,Shoot partitioning index,地上部分配指数,fraction,2,-0.0000842 * PDT^2 + 0.01 * PDT + 0.63,PISH=-8.42\times10^{-5}PDT^2+0.01PDT+0.63,Quadratic polynomial,Quadratic polynomial,sensitivity;direct,15
CMF045,growth_yield,Dry matter partitioning,Stem partitioning index,茎鞘分配指数,fraction,2,1 - (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))),PIS=1-PIGL-PIP,Residual with piecewise components,Residual with piecewise components,chain_2;sensitivity;direct,19
CMF046,growth_yield,Respiration,Growth respiration,生长呼吸,kg/ha/day,2,Rg * DTGA,RG=R_g\cdot DTGA,Product,Product,direct;sensitivity,11
CMF047,growth_yield,Photosynthesis,Intercepted photosynthetically active radiation,截获光合有效辐射,MJ/m2/day,2,PAR * (1 - exp(-k * LAI)),IPAR = PAR \cdot (1 - e^{-k \cdot LAI}),Product with exponential saturation,Product with exponential saturation,direct;sensitivity,13
CMF048,growth_yield,Respiration,Maintenance respiration,维持呼吸,kg/ha/day,2,(0.0091 - 0.0001 * PDT) * ABIOMASS * Q10**((T-To)/10),RM=(0.0091-0.0001\cdot PDT)\cdot ABIOMASS\cdot Q_{10}^{(T-T_o)/10},Product with Q10 temperature response,Product with Q10 temperature response,chain_2;direct;sensitivity,20
CMF049,growth_yield,Respiration,Maintenance respiration coefficient at optimum temperature,最适温度维持呼吸系数,d-1,4,0.0091 - 0.0001 * PDT,RM(T_o)=0.0091-0.0001PDT,Linear decline,Linear decline,direct;sensitivity,12
CMF050,growth_yield,Phenology,Relative photoperiod effectiveness,相对光周期效应,fraction,2,if P<=Po: 1; if P<=Po+sqrt(1/PS): 1-PS*(P-Po)^2; else: 0,"RPE=1,\;1-PS(P-P_o)^2,\;0",Piecewise quadratic,Piecewise quadratic,sensitivity;branch;direct;chain_2,29
CMF051,growth_yield,Phenology,Relative thermal effectiveness,相对热效应,fraction,3,(((T - Tb)/(To - Tb)) * (((Tm - T)/(Tm - To)) ** ((Tm - To)/(To - Tb)))) ** TS,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},Beta temperature response,Beta temperature response,direct;branch;sensitivity,18
CMF052,growth_yield,Leaf area growth,Actual LAI relative growth rate,实际叶面积相对增长率,d-1,4,"RP * min(NNI, WDF)","R=RP\cdot\min(NNI,WDF)",Minimum stress multiplier,Minimum stress multiplier,chain_2;sensitivity;direct,21
CMF053,growth_yield,Leaf area growth,Specific leaf area,比叶面积,cm2/g,2,if GDD<=1200: (-0.0002*GDD^2-0.5604*GDD+581.04)*(SLAc/200); else: 200*(SLAc/200),SLA=(-0.0002GDD^2-0.5604GDD+581.04)(SLA_c/200),Piecewise polynomial,Piecewise polynomial,direct;sensitivity;branch,20
CMF054,growth_yield,Yield formation,Dry grain yield,稻谷干重产量,kg/ha,1,AWSP * grain_fraction,Y=AWSP\cdot f_{grain},Product,Product,sensitivity;direct,12
CMF055,environmental_response,environmental-response formula system,environmental-response daily biomass increment,环境响应日生物量增量,kg/ha/day,2,"10 * RUE * fSolar * SRAD * F_CO2 * F_Temp * min(F_Water, F_Heat)","dB=10RUEfSolarSRADF_{CO2}F_T\min(F_W,F_H)",Multiplicative minimum stress,Multiplicative minimum stress,direct;sensitivity;chain_2,18
CMF056,environmental_response,environmental-response formula system,environmental-response daily thermal time,每日有效积温,C day,2,"max(Tmean - Tbase, 0)","dTT=\max(T_{mean}-T_{base},0)",Maximum linear,Maximum linear,branch;direct;sensitivity,18
CMF057,environmental_response,environmental-response formula system,environmental-response CO2 response,环境响应二氧化碳响应,multiplier,3,"if CO2>=700: 1+CO2_RUE*350/100; else: max(CO2_RUE*CO2*0.01+1-0.01*350*CO2_RUE, 1)","F_{CO2}=f(CO2,CO2_{RUE})",Piecewise linear cap,Piecewise linear cap,branch;direct;sensitivity,21
CMF058,environmental_response,environmental-response formula system,environmental-response heat stress response,环境响应高温响应,fraction,3,"if Tmax<=MaxT: 1; if Tmax>ExtremeT: 0; else: max(1-(Tmax-MaxT)/(ExtremeT-MaxT), 0)","F_H=1,\;0,\;\text{or}\;1-\frac{T_{max}-MaxT}{ExtremeT-MaxT}",Piecewise linear stress,Piecewise linear stress,branch;sensitivity;direct,19
CMF059,environmental_response,environmental-response formula system,environmental-response solar interception fraction,环境响应光截获比例,fraction,3,"min(fSolarMax/(1+exp(-0.01*(TT-I50A))), fSolarMax/(1+exp(0.01*(TT-(Tsum-I50B))))) * min(fSolar_water, 1)","fSolar=\min(f_1,f_2)F_{solar,water}",Double logistic,Double logistic,chain_2;direct;sensitivity,18
CMF060,environmental_response,environmental-response formula system,environmental-response temperature response,环境响应温度响应,fraction,3,"if Tmean>=Topt: 1; else: max((Tmean-Tbase)/(Topt-Tbase), 0)","F_T=1\;\text{or}\;\max((T-T_b)/(T_o-T_b),0)",Piecewise linear,Piecewise linear,direct;branch;sensitivity,22
CMF061,environmental_response,environmental-response formula system,environmental-response water stress response,环境响应水分响应,response factor,3,"max(0, 1 - S_Water * ARID)","F_W=\max(0,1-S_WARID)",Maximum linear,Maximum linear,sensitivity;direct,14
CMF062,environmental_response,environmental-response formula system,environmental-response yield,环境响应产量,kg/ha,1,Biomass * HI,Yield=Biomass\cdot HI,Product,Product,direct;sensitivity,13