The EPIC Crop Growth Model - Agricultural Research Service

crop parameters and determine the sigmoid relationshipdescribed by equation [9] for crop j . The parameters ahj,and ahj2 are calculated by simultaneous solution ofequation [9] using the two pairs of values for H U F andHUI.From the start of leaf decline to the end of the growingseason, LAI is estimated with the equation/ 1. - HUI: \ ad;) LAL LAI ( V L - HUI. /The economic yield of most grain, pulse, and tubercrops is a reproductive organ. Crops have a variety ofmechanisms which insure that their production is neithertoo great to be supported by the vegetative componentsnor too small to insure survival of the species. As a result,harvest index (economic yield/above-ground biomass) isoften a relatively stable value across a range ofenvironmental conditions. In EPIC, crop yield isestimated using the harvest index concept.[1 0][15]YLDj ( H I J ) ( B A G )where ad is a parameter that governs LAI decline rate forcrop j and HUI is the value of H U I when LAI startsdeclining.Crop height is estimated with the relationshipCHTi HMXj VHUFi[11]where CHT is the crop height in m and H M X is themaximum height for crop j .The fraction of total biomass partitioned to rootsystem normally decreases from 0.3 to 0.5 in the seedlingto 0.05 to 0.20 at maturity (Jones, 1985). The modelestimates the fraction of crop growth that is partitionedto the root system to range linearly from 0.4 atemergency to 0.2 at maturity. Thus, the potential dailychange in root system weight is computed with theequationwhere YLD is the amount of economic yield that could beremoved from the field in t-ha S HI is the harvest index,and BAG is the above-ground biomass in t-ha for crop j .For non-stressed conditions, harvest index increases nonlinearly from zero at planting to HI at maturity using theequationHIAi HIj S AHUFHj j[16]where HIA is the harvest index on day i and H U F H is theheat unit factor that affects harvest index.The harvest index heat unit factor is computed withthe equationHUI,ARWT- ABp i(0.4 - 0.2 HUI )[12]where ARWT is the change in root weight in t-ha onday i. The distribution of root growth through the rootzone is simulated as a function of plant water use in eachlayer of soil using the equationARWi g (ARWTi)U;i,C[13]MZ u i,CHUFH,HUIj e x p ( 6 . 5 0 - 1 0 . 0 H U I i )[17]The constants in equation 17 are set to allow HUFHj toincrease from 0.1 at HUIi 0.5 to 0.92 at H U I i 0 . 9 .This is consistent with economic yield development ofgrain crops which produce most economic yield in thesecond half of the growing season. The effects of stresseson harvest index are discussed in the section on growthconstraints.2 1where RW is the root weight in soil layer i in t-ha S M isthe total number of soil layers, and u is the daily wateruse in layer i in m m .As discussed in the section describing water use, thismethod of estimating root growth produces realisticexponential decreases in root weight with depth when soilwater and other properties do not constrain growth.When a soil layer is dry or root stress factors (strength,aluminum saturation, or aeration) limit root function,both water use and root growth in the layer are reduced.Rooting depth normally increases rapidly from theseeding depth to a crop-specific maximum. In manycrops, the maximum is usually attained well beforephysiological maturity (Borg and Grimes, 1986). Rootingdepth is simulated as a function of heat units andpotential root zone depth.RDi 2.5(RDMXj)(HUIi),RD- RZj-PiLALEoi(-r-)'Epi Eo[18]where E is the potential evaporation and LAI is the leafarea-index on day i.The potential water use from the soil surface to anyroot depth is estimated with the functionUPi Pi(l--exp(-A( )))1. - exp(-A)[19][14]where RD is the root depth in m, R D M X is themaximum root depth for crop j in ideal soil in m, RZ isthe soil profile depth in m, and the constant 2.5 allowsroot depth to reach its maximum when HUI reaches 0.4.Vol. 32(2):March-April, 1989Water UseThe potential water use, Ep, is estimated as a fractionof the potential evaporation using the leaf-area-indexrelationship developed by Ritchie (1972).where Up is the total water used in m m to depth Z in mon day i, RZ is the root zone depth in m, and ' is a wateruse distribution parameter. The amount used in ap a r t i c u l a r layer can b e calculated by t a k i n g t h edifference between Upj values at the layer boundaries.499

-Pi PEexp(-A(-( -FCn - WPol. exp(-A(—))1. - exp(-A)Un U P Cl 'O)[20]where Up is the potential water use from layer I in mm.Equation 20 represents a soil that provides poorconditions for root development when A is set a highvalue like 10. The high A value gives high water use nearthe surface and very low use in the lower half of the rootzone. Since there is no provision for water deficiencycompensation in any layer, considerable water stress mayresult using equation [20]. To overcome this problem,equation [20] was modified to allow plants to compensatefor water deficiency in a layer by using more water fromother layers. Total compensation can be accomplished bytaking the difference between Upj at the bottom of a layerand the sum of water use above a layer. -Pi P (l.-exp(-A( )))1. -exp(-A)C-1[21]sw, 4. WPg[24]where SW is the soil water content in layer i on day i inmm and FC and WP are the soil water contents at fieldcapacity and wilting point for layer i .Nutrient uptakeNitrogenCrop use of N is estimated using a supply and demandapproach. The daily crop N demand is the differencebetween the crop N content and the ideal N content forday i. The demand is estimated with the equationUNDi (cNB)i(B)ii l2 UN,K l[25]*where UND is the N demand of the crop in kg-ha UNis the actual N uptake in kg-ha S C B is the optimal Nconcentration of the crop in kg t and B is theaccumulated biomass in t-ha" for day i. The optimalcrop N concentration declines with increasing growthstage (Jones, 1983a) and is computed as a function ofgrowth stage using the equation NBi 1 2 e x p ( - b n 3 HUI )[26]K lwhere u is the actual water use in mm for all layersabove layer i. Thus, any deficit can be overcome if alayer is encountered that has adequate water storage.Neither equation [20] (no compensation) nor equation[21] (total compensation) is satisfactory to simulate awide range of soil conditions. A combination of the twoequations, however, provides a very general water usefunction. -Pi- pe1. - exp(-A (1. - exp(A)e-i(1. - UC) ( . . - , .p(-A( UCi: XXyrK l [22]where UC ranges (0.0 to 1.0) and is the water deficitcompensation factor. In soils with a good rootingenvironment, UC 1. gives total compensation. Theother extreme, poor conditions, allow no compensation(UC 0.). The procedure for estimating UC is describedin the Growth Constraints section.The potential water use in each layer (neglecting theeffects of root constraints) calculated with equation [22]is reduced when the soil water storage is less than 25% ofplant-available soil water (Jones and Kiniry, 1986) usingthe equation.Ug Upg e x pf(4.(SWBi-WPg)(FC,-WP,) ) )where HUI (heat unit index) is the fraction of thegrowing season and bnj, bn2, and bnj are parameterscalculated from crop-specific concentrations of N in theplant at the seedling stage, halfway through the season,and at maturity.Mineral nutrients move to plant roots primarily bymass flow and diffusion. Mass flow is the movement ofnutrients to roots in the soil water absorbed andtranspired by the plant. Mass flow rarely provides exactlythe amount of nutrient absorbed by the plant; therefore,the concentration of nutrient near the root may increaseor decrease in response to the balance between mass flowand absorption (Barber, 1984). Diffusion causes thenutrient concentration gradient between the root to thebulk soil to decrease, and when soil solutionconcentrations are low it can provide a significantfraction of N absorbed by the plant. Barber (1984)suggests that mass flow normally accounts for about80% of the N uptake of corn roots, and a combination ofmass flow and diffusion can reduce soil NO3—N to verylow levels.In EPIC, mass flow of NO3—N to the roots is used todistribute potential N uptake among soil layersWN03oU N o ,i c,i(SWnwhere UN is the amount of N supplied by the soil inkg-ha-S WN03 is the amount of NO3-N in kg-ha- ,SW is the soil water content in mm, u is water use in mm,and subscript i refers to the soil layers. The total Navailable for uptake by mass flow is estimated bysumming mass flow of all layers.FCg-WPgSWgi WPo[23][27]UNS: M2 UN,fi,i[28]K l500TRANSACTIONS of the ASAE

Since mass flow rarely provides the exact amount of Nrequired by the crop, UN values obtained from equation[27] are adjusted.UNDUNaei UNgi (UNS:UNag i WN03e i. . . [29]where UNa is the adjusted N supply in kg-hg- for layerL Equation 29 assures that actual N uptake cannotexceed the plant demand when mass flow exceedsdemand. It also provides for increased N supply from thelayer (by diffusion) when mass flow does not meet cropdemand but NO3—N is available in the soil.Nitrogen Fixation: Daily N fixation is estimated as afraction of daily plant N demand by legumes.WFXi FXRi UND ,WFX 6.0[30]where WFX is the amount of N fixation in kg-ha andFXR is the fraction of uptake for day i. The fraction,FXR, is estimated as a function of soil NO3 and watercontent and plant growth stage.FXR min (1.0, FXW, FXN) FXG[31]where FXG is the growth stage factor, FXW is the soilwater content factor, and FXN is the soil NO3 contentfactor. The growth stage factor inhibits N fixation inyoung plants prior to development of functional nodulesand in old plants with senescent nodules (Patterson andLaRue, 1983).FXGi -0' U i -15, HUI 0.75FXGi 6-67 HUIi - 1.0,FXG- 1.0,0.15 HUIi 0.3 . . . [33]0.3 HUIi 0.55FXGi 3.75 - 5.0 HUIi,. . . . [32]where HUI is the heat unit index for day i. The soil watercontent factor reduces N fixation when the water contentat the top 0.3 m is less than 85% of field capacity(Albrecht et al., 1984; Bouniols et al., 1985) using theequationSW3i - WP3FXU 0.85(FC3-WP3)FXN 1.0,Vol. 32(2):March-April, 1989WN03 100. kg-ha-l-m-l,[39]Where W N 0 3 is the weight of NO3—N in the root zonein kg-ha- and RD is the root depth in m. This approachreduces N fixation when the NO3—N content of the rootzone is greater than 100 kg-ha" and prohibits N fixationat N contents greater than 300 kg-ha" PhosphorusCrop use of P is estimated with the supply and demandapproach described in the N model. The daily plantdemand is computed with equation [25] written in theformUPDi (cpB)i(B)i-[40]2 UPKK— 1where UPD is the P demand for the plant in kg-ha S U Pis the actual P uptake in kg-ha S and Cpg is the optimalP concentration for the plant. As in the case of N, theoptimal plant P concentration is computed with equation[26] in written in the formCpBi Pl t)p2 exp(-bp3 HUIj)[41]where bpi, bp2, and bp3 are parameters calculated fromcrop-specific optimum P concentrations at the seedlingstage, halfway through the season and at maturity. Soilsupply of P is estimated using the equationUPS:MRWo1.5 UPDi X (LF )e ([42]where UPS is the amount of P supplied by the soil inkg'ha \ LFu is the labile P factor for uptake, RW is theroot weight in layer i in kg ha and RWT is the totalroot weight on day i in kg-ha The constant 1.5 allows2 / 3 of the roots to meet the P demand of the plant iflabile P is not limiting. This approach is consistent withstudies suggesting that roots of P-deficient plants (orplants whose root systems have been pruned) can absorbP faster than the roots of normal plants (Andrews andNewman, 1970; DeJager, 1979; Jungk and Barber,1974).The labile P factor for uptake ranges from 0.1 to 1.0according to the equation[36]where SW3, WP3, and FC3 are the water contents in thetop 0.3 m of soil on day i, at wilting point, and at fieldcapacity.The amount of NO3 in the root zone can affect Nfixation (Harper, 1976; Bouniols et al., 1985) determinesthe soil NO3 factor, FXN.WN03 300. kg-hsT -m- 100. WNO3 300.RlT[38]L F , , 0.1 FXN 0.,WN03[34]0.55 HUIi 0.75 . . [35]SW3 0.85 (FC3 - WP3) WP3FXN 1 . 5 - 0 . 0 0 5 ([37]0.9 c LPfi. . . . [43]CLPC 117. exp(-0.283 CLPC)where CLP is the labile P concentration in soil layer i ing-t . Equation 43 allows optimum uptake rates whenCLP is above 20 g-t This is consistent with critical labileP concentrations for a range of crops and soils (Sharpleyet al., 1989). Sharpley et al. (1984, 1985) describedmethods of estimating CLP from soil test P and other soilcharacteristics.501

Growth ConstraintsPotential crop growth and yield are usually notachieved because of constraints imposed by the plantenvironment. The model estimates stresses caused bywater, nutrients, temperature, aeration, and radiation.These stresses range from 0.0 to 1.0 and affect plants inseveral ways. In EPIC, the stresses are considered inestimating constraints on biomass accumulation, rootgrowth, and yield. The biomass constraint is theminimum of the water, nutrient, temperature, andaeration stresses. The root growth constraint is theminimum of soil strength, temperature, and aluminumtoxicity. Though topsoil aluminum toxicity can have adirect effect on shoot growth, EPIC simulates only itsindirect effects through its inhibition of root growth andwater use. A description of the stress factors involved indetermining each constraint follows.optimal values. The stress factors vary non-linearly from1.0 at optimal N and P contents to 0. when N or P is halfthe optimal level (Jones, 1983a). In the case of N, thescaling equation is2 UN KK lSNs,i 2[47](cNB)i(S)iwhere SNs is a scaling factor for the N stress factor, C B isthe optimal N concentration of the crop on day i, B is theaccumulated biomass in kg-ha S and UN is the crop Nuptake on day K in kg-ha- . The N stress factor iscomputed with the equationSN S,iSN: 1 - -SNg i exp(3.39 - 10.93 SNg jBiomassThe potential biomass predicted with equation [4] isadjusted daily if any of the five plant stress factors is lessthan 1.0 using the equationAB (ABp) (REG)[44]where REG is the crop growth regulating factor (theminimum stress factor).Water Stress: The water stress factor is computed byconsidering supply and demand in the equation[48]where SN is the N stress factor for day i. The P stressfactor is computed with equations [47] and [48] writtenin P terms.Aeration Stress: When soil water content approachessaturation, plants may suffer from aeration stress. Thewater content of the top 1 m of soil is considered inestimating the degree of stress.SAT SWICAR[49]POIMWSi . 1""-'[45]-Piwhere WS is the water stress factor, u is the water use inlayer i, and Ep is the potential plant water use on day i.This is consistent with the concept that drought stresslimits biomass production in proportion to transpirationreduction (Hanks, 1983).Temperature Stress: The plant temperature stress isestimated with the equationTSrsine( t -i: )),0 TS, 1[46]where TS is the plant temperature stress factor Tg is theaverage daily soil surface temperature in C, T is thebase temperature for crop j , and T is the optimaltemperature for crop j . Equation [46] producessymmetrical plant growth stress about the optimaltemperature and it is driven by average daily soil surfacetemperature. This approach allows growth of smallplants to respond realistically to low soil surfacetemperatures found in temperate regions in the spring.The presence of soil residues can retard simulated soilwarming and reduce crop growth. As the crop canopydevelops, it shades the soil surface, and simulatedaverage soil surface temperature approaches average airtemperature. A more detailed description of the soiltemperature model is given in Williams et al. (1984).Nutrient Stress: The N and P stress factors are basedon the ratio of simulated plant N and P contents to the502SAT-, SAT 0.0AS: 1.-SAT exp(-1.291 - 56.1 SAT)[50]where SAT is the saturation factor, SWl is the watercontent of the top 1 m of soil in mm, POl is the porosityof the top 1 m of soil in mm, CAP is the critical aerationfactor for crop j (ssO.85 for many crops), and AS is theaeration stress factor. This approach allows the model torestrict crop growth both when water tables are high (buta layer of aerated soil occurs near the surface) and whenslow internal drainage causes poor aeration near the soilsurface. Several studies suggest that when water-filledpore space (WFP) exceeds 60% (Linn and Doran, 1984;Grable and Seimer, 1968; Trouse, 1964), root growth isinhibited by poor aeration. EPIC produces similarresults when CAF 0.85, WFP exceeds 60% in thesurface 0.5 m, and the soil is saturated from 0.5 to 1.0 m.Growth of flood-tolerant crops like rice can be simulatedby setting CAF 1.0.Finally, the value of REG is determined as theminimum of WS, TS, SN, SP, and AS.Root GrowthAs described in equation [13], root growth isproportional to water use. Water use from a soil layer isestimated as a function of soil depth, water content, anda compensation factor using equation [22] and [23]. Soilstrength, temperature, and aluminum toxicity stressfactors are calculated from soil properties. Theminimum of these three stresses, the root growth stressTRANSACTIONS of the ASAE

factor, constains root growth by governing the water usecompensation factor.Cold soil temperature may limit root growth,especially when subsoil layers warm slowly in the spring(Taylor, 1983). Temperature stress for each soil layer iscomputed by substituting soil temperature at the centerof the layer for soil surface temperature in equation [46].Numerous studies have shown that root growth isaffected by soil strength. Three important strengthdeterminants are bulk density, texture, and watercontent (Eavis, 1972; Monteith and Banath, 1965;Taylor et al., 1966). All three of these variables areconsidered in estimating the EPIC soil strength stressfactor using the following equation.Aluminum ( A l ) toxicity can limit root growth in someacid soil layers, and A l saturation is a widely used indexof its effects (Abruna et al., 1982; Brenes and Pearson,1973; Pavan et al., 1982). Because crops and cultivarsdiffer in their sensitivities to A l toxicity (Foy et al., 1972,1974; Mugwira et al., 1980), EPIC considers both the A ltoxicity of the soil and crop sensitivity to it. Root growthstress caused by aluminum toxicity is estimated with theequationATS, ALSg ALOj[57]100-ALO:ATSn 1 . 0 ,ALSg ALOj[58]0.9 BDnSSg 0.1 [51]BDg exp(bti bt2(BDg))where SS is the soil strength factor in layer i , BD is thesoil bulk density adjusted for water content in t-m andbt, and bt2 are parameters dependent upon soil texture.T h e values of bt a n d bt2 are o b t a i n e d from asimultaneous solution of equation [51] by substitutingboundary conditions for stress. The lower boundarywhere essentially no stress occurs is given by the equation(Jones, 1983b)BDL 1.15 0.00445 SAN[52]where BDL is the bulk density near the lower boundary(SS 1.) for a particular percent sand, SAN. The upperboundary is given by equation (Jones, 1983b)BDU 1.5 0.05 SAN[53]where BDU is the bulk density near the upper boundary(SSJ5:0.2) for a particular percent sand, SAN. Theequations for estimating bt and bt2 arebtoln(0.112 BDL) - ln(8. BDU)BDL-BDUbt ln(0.0112 BDL) - (bt2)(BDL)[55]BDg i BD3 (BDD - BD3)FCg-SW,i.[56]where BD is the water content adjusted bulk density onday i, BD3 is the bulk density at 33 kPa water content,BDD is the oven dry bulk density, FC is the fieldcapacity, W P is the wilting point, and SW is the soilwater content for layer i on day i.Vol. 32(2):March-April, 1989ALOj 10 20(ALTj- 1)[59]where ALTj is the aluminum tolerance index number forcrop j . Values of ALT range from 1 to 5 (1 is sensitive; 5is tolerant) for various crops. Finally, the root growthstress factor, R G F , is the minimum of SS, ATS, and TS.Water usePlant water use is governed by the root growth stressfactor using the water deficit compensation factor ofequation [22]. Recall that the water deficit compensationfactor, UC, allows total compensation if the value is 1.0and no compensation at 0.0. The value of UC for anylayer is estimated as the product of the root growth stressfactor

Only one of the model components, crop growth, is described here. Since soil productivity is expressed in terms of crop yield, crop growth is one of the most important processes simulated by EPIC. To evaluate the effect of erosion on crop yield, the model must be sensitive to crop characteristics, weather, soil fertility, and other soil properties.