Note: This page is no longer being maintained and is kept for archival purposes only.
For current information see our main page.
Garden with Insight Kurtz-Fernhout Software
Developers of custom software and educational simulations.
Home ... News ... Products ... Download ... Order ... Support ... Consulting ... Company
Garden with Insight
Product area
Help System
Quick start

Garden with Insight v1.0 Help: Plant Growth - Constraints

Potential crop growth and yield are usually not achieved because of constraints imposed by the plant environment. The model estimates stresses caused by water, nutrients, temperature, aeration, and radiation. These stresses range from 0.0 to 1.0 and affect plants in several ways. In EPIC, the stresses are considered in estimating constraints on biomass accumulation, root growth, and yield. The biomass constraint is the minimum of the water, nutrient, temperature, and aeration stresses. The root growth constraint is the minimum of soil strength, temperature, and aluminum toxicity. Though topsoil aluminum toxicity can have a direct effect on shoot growth, EPIC simulates only its indirect effects through its inhibition of root growth and water use.

Biomass constraints

The potential biomass predicted with equation 256 is adjusted daily if any of the five plant stress factors is less than 1.0 using the equation [Equation 295] where REG is the crop growth regulating factor (the minimum stress factor).

Equation 295

deltaB = deltaB(p) * REG
added factors for biomassAdjustmentIfLAIDeclining, dayLengthIsAboveThresholdForGrowth
deltaB = PlantIncreaseInBiomass_tPha
deltaB(p) = potentialIncreaseInBiomass_tPha
REG = biomassGrowthConstraint_frn

Water stress factor

The water stress factor is computed by considering supply and demand in the equation [Equation 296] where WS is the water stress factor, u is the water use in layer l, and E(p) is the potential plant water use on day i. This is consistent with the concept that drought stress biomass production is in proportion to transpiration reduction (Hanks, 1983).

Equation 296

WS = (sum with l from 1 to M of) u / E(p)
same (with bounds)
WS = WaterStressFactor_frn
sum of u = totalPlantWaterUse_mm
E(p) = potPlantEvap_mm

Temperature stress factor

The plant temperature stress is estimated with the equation [Equation 297] where TS is the plant temperature stress factor, TG is the average daily soil surface temperature in degrees C, T(b) is the base temperature for crop j, and T(o) is the optimal temperature for crop j. Equation 297 produces symmetrical plant growth stress about the optimal temperature and is driven by average daily soil surface temperature. This approach allows growth of small plants to respond realistically to low soil surface temperature found in temperate regions in the spring. The presence of soil residues can retard simulated soil warming and reduce crop growth. As the crop canopy develops, it shades the soil surface, and simulated average soil surface temperature approaches average air temperature. In addition to the temperature stress imposed by equation 297, plant growth does not occur on days when the average daily temperature exceeds 1.5 * T(o).

Equation 297

if T > 1.5 * T(o) TS = 0
else TS = sin(pi / 2 * (TG - T(b)) / (T(o) - T(b)))
if T < T(b) or T > 1.5 * T(o) TS = 0
else PR = (T - T(b)) / (T(o) - T(b))
if PR > 2 TS = 0
else TS = sin(pi / 2 * PR)
TS = BiomassTempStressFactor_frn
TG = soilSurfaceTemp_degC
T = meanTempForDay_degC
T(b) = baseTemp_degC
T(o) = optimalTemp_degC
PR = proportionOfRange

Nitrogen Stress

The N and P stress factors are based on the ratio of simulated plant N and P contents to the optimal values. The stress factors vary non-linearly from 1.0 at optimal N and P contents to 0.0 when N or P is half the optimal level (Jones, 1983a). In the case of N, the scaling equation is [Equation 298] where SN(s) is a scaling factor for the N stress factor, c(NB) is the optimal N concentration of the crop on day i, B is the accumulated biomass in kg/ha, and UN is the crop N uptake on day k in kg/ha.

Equation 298

SN = 200 * ((sum with k from 1 to i of) UN / (c(NB) * B) - 0.5)
this equation is also used for p stress scaling factor
(note changed later to remove 100 multiplier)
SN(s) = NOrPStressFactorScalingFactor
c(NB) = optimalConc_kgPkg
B = totalPlantBiomassInclRoot_tPha
UN = totalUptake_kgPha

The N stress factor is computed with the equation [Equation 299] where SN is the N stress factor for day i.

Equation 299

SN = SN(s) / (SN(s) + exp(3.52 - 0.026 * SN(s)))
this equation is also used for p stress factor
SN = NOrPStressFactor_frn
SN(s) = stressFactorScalingFactor

Phosphorus stress

The P stress factor, SP, is computed with equations 298 and 299 written in P terms. (Use same functions)

Aeration stress

When soil water content approaches saturation, plants may suffer from aeration stress. The water content of the top 1 m of soil is considered in estimating the degree of stress [Equation 300] and [Equation 301] where SAT is the saturation factor, SW1 is the water content of the top 1 m of soil in mm, PO1 is the porosity of the top 1 m of the soil in mm, CAF is the critical aeration factor for crop j (~~ 0.85 for many crops), and AS is the aeration stress factor.

Equation 300, 301

SAT = 100 * (SW1 / PO1 - CAF) / (1 - CAF)
AS = 1.0 - SAT / (SAT + exp(5.1 - 0.082 * SAT))
(note later changed SAT so it is not * 100 because changed X portion of scurve to get rid of multiplier)
AS = AerationStressFactor_frn
SAT = saturationFactor
SW1 = top1MWaterContent_mm
PO1 = top1mPorosity_mm
CAF = criticalAerationFactor

Finally, the value of REG is determined as the lowest of the stress factors, WS, TS, SN, SP, and AS.

Root Growth Constraints

As described in equation 265, root growth is proportional to water use. Water use from a soil layer is estimated as a function of soil depth, water content, and a compensation factor according to equations 273 and 274. Soil strength, temperature, and aluminum toxicity stress factors are calculated from soil properties. The lowest of these three stress factors constrains root growth by governing the water use compensation factor (UC).

Temperature stress on root growth

Cold soil temperatures may limit root growth, especially when subsoil layers warm slowly in the spring (Taylor, 1983). The temperature stress for each soil layer is computed by substituting soil temperature at the center of the layer for soil surface temperature in equation 297.
there is not a separate root temp stress equation written in the publication
RS = sin(pi/2 * ST / OT)
RS = RootTempStressFactorForLayer_frn
ST = soilTemp_degC
OT = optimalTemp_degC

Soil strength stress on root growth

Numerous studies have shown that root growth is affected by soil strength. Three important strength determinants are bulk density, texture, and water content (Eavis, 1972. Monteith and Bonath, 1965. Taylor et al., 1966). All three variables are considered in estimating the EPIC soil strength stress factor by using the following equation [Equation 302] where SS is the soil strength factor in layer l, BD is the bulk density in t/m3 adjusted for water content, and bt(1) and bt(2) are parameters dependent upon soil texture.

Equation 302

SS = BD / (BD + exp(bt(1) + bt(2) + BD))
(the + before the last BD must be a typo, should be a *)
code adds adjustment based on rock content
SS = SoilStrengthFactor_frn
BD = bulkDensityAdjForWaterContentForLayer_tPm3
bt(1) = soilTextureParams[0
bt(2) = soilTextureParams[1

The values of bt(1) and bt(2) are obtained from a simultaneous solution of equation 302 by substituting boundary conditions for stress. The lower boundary, where essentially no stress ocurrs, is given by the equation (Jones, 1983b) [Equation 303] where BDL is the bulk density near the lower boundary (SS = 1.0) for a particular percentage of sand, SAN.

Equation 303

BDL = 1.15 + 0.00445 * SAN
same (rootGrowthRestrictionInSandySoilParam = 1.15)
However, in the file PARM3090.DAT this parameter is listed as 1.5. Am using 1.5.
BDL = BulkDensityForLowStress_tPm3
SAN = soilSandContent_pct

The upper boundary is given by the equation (Jones, 1983b) [Equation 304] where BDU is the bulk density near the upper boundary (SS ~~ 0.2) for a particular percentage of sand, SAN.

Equation 304

BDU = 1.5 + 0.005 * SAN
same (rootGrowthRestrictionInSandySoilParam = 1.15, 1.15 + 0.35 = 1.5)
However, in the file PARM3090.DAT this parameter is listed as 1.5. Am using 1.5.
BDU = BulkDensityForHighStress_tPm3
SAN = soilSandContent_pct

The equations for estimating bt(1) and bt(2) are [Equation 305] and [Equation 306]. Equations 305 and 306 assure that equation 302 gives SS values of 1.0 and 0.2 for BD = BDL and BD = BDU.

Equation 305

bt(2) = (log(0.0112 * BDL) - log(8.0 * BDU)) / (BDL - BDU)
bt(2) = SoilTextureParam2
BDL = bulkDensityForLowStress_tPm3
BDU = bulkDensityForHighStress_tPm3

Equation 306

bt(1) = log(0.0112 * BDL) - bt(2) * BDL
bt(1) = SoilTextureParam1
bt(2) = SoilTextureParam2
BDL = bulkDensityForLowStress_tPm3

The water-content-adjusted bulk density is estimated with Grossman's equation (Grossman et al., 1985) [Equation307] where BD is the water- content-adjusted bulk density of day i, BD3 is the bulk density of 33 kPa water content BDD is the bulk density of the oven dry soil, FC is the field capacity, WP is the wilting point, and SW is the soil water content for layer l on day i.

Equation 307

BD = BD3 + (BDD - BD3) * (FC - SW)
/ (FC - WP * (4.083 - 3.33 * pow(BDD, 1/3)))
code uses current bulk density as BD3
BD = BD3 + (BDD - BD3 * BDD / BDS) * (FC - SW)
/ (FC - WP * (4.083 - 3.33 * pow(BDD / BDS, 1/3)))
BD = BulkDensityAdjForWaterContentForLayer_tPm3
BD3 = bulkDensity_tPm3
BDD = bulkDensityOvenDry_tPm3
BDS = settledBulkDensity_tPm3
FC = fieldCapacity_mm
SW = waterContent_mm
WP = wiltingPoint_mm

Aluminum toxicity stress factor

Aluminum (Al) toxicity can limit root growth in some acid soil layers, and Al saturation is a widely used index of its effects (Abruna et al., 1982. Brenes and Pearson, 1973. Pavan et al., 1982). Because crops and cultivars differ in sensitivity to Al toxicity (Foy et al., 1974. Mugwira et al. 1980), EPIC expresses Al toxicity as a function of this sensitivity. The Al toxicity stress factor associated with root growth is estimated with the equations [Equation 308] and [Equation 309] where ATS is the Al toxicity stress factor (0-1) for soil layer l, ALS is the Al saturation in percent, and ALO is the maximum ALS value crop j can tolerate without stress in percent.

Equation 308, 309

if ALS > ALO, ATS = (100 - ALS) / (100 - ALO)
else ATS = 1.0
ATS = AluminumToxicityStressFactorForLayer_frn
ALS = aluminumSaturation_pct
ALO = maxAlSaturationForCrop_pct

Crop specific values of ALO are determined from the equation [Equation 310] where ALT is the Al tolerance index number for crop j. Values of ALT range from 1 to 5 (1 is sensitive, 5 is tolerant) for various crops.

Equation 310

ALO = 10 + 20 * (ALT - 1)
ALO = MaxAlSaturationForCrop_pct
ALT = alToxicitySensitivityForCrop_1to5

Finally, the root growth constraint, RGF, is the lowest of the stress factors, SS, ATS, and TS.
(no equation in publication)

How root water use is affected by the stress factors (UC)

Plant water is governed by the root growth stress factor and the water deficit compensation factor of equation 273 (UC). Recall that the water deficit compensation factor, UC, allows total compensation if the value is 1.0 and no compensation at 0.0. The value of UC for any layer is estimated as the product of the root growth stress factors for the layer and all the layers above [Equation 311]. Thus a low RGF(k) greatly reduces water compensation for layer k and all layers below k.

Equation 311

UC = (product from k = 1 to (layer) of) RGF
UC = PlantWaterDeficitCompensFactorForLayer_frn
RGF = rootGrowthConstraint_frn

Home ... News ... Products ... Download ... Order ... Support ... Consulting ... Company
Updated: March 10, 1999. Questions/comments on site to
Copyright © 1998, 1999 Paul D. Fernhout & Cynthia F. Kurtz.