Temperature stress is a function of the daily average air temperature and the optimal temperature for plant growth. Near the optimal temperature the plant will not experience temperature stress. However as the air temperature diverges from the optimal the plant will begin to experience stress. The equations used to determine temperature stress are:

$tstrs=1$ when $\overline T_{av} \le T_{base}$ 5:3.1.2

$tstrs=1-exp[\frac{-0.1054*(T_{opt}-\overline T_{av})^2}{(\overline T_{av}-T_{base})^2}]$ when $T_{base}<\overline T_{av} \le T_{opt}$ 5:3.1.3

$tstrs=1-exp[\frac{-0.1054*(T_{opt}-\overline T_{av})^2}{(2*T_{opt}-\overline T_{av}-T_{base})^2}]$ when $T_{opt}<\overline T_{av}\le 2*T_{opt}-T_{base}$ 5:3.1.4

$tstrs=1$ when $\overline T_{av} > 2*T_{opt}-T_{base}$ 5:3.1.5

where $tstrs$ is the temperature stress for a given day expressed as a fraction of optimal plant growth,$\overline T_{av}$is the mean air temperature for day (°C), $T_{base}$ is the plant’s base or minimum temperature for growth (°C), and $T_{opt}$ is the plant’s optimal temperature for growth (°C). Figure 5:3-1 illustrates the impact of mean daily air temperature on plant growth for a plant with a base temperature of 0°C and an optimal temperature of 15°C.

Actual growth varies from potential growth due to extreme temperatures, water deficiencies and nutrient deficiencies. This chapter reviews growth constraints as well as overrides that the user may implement to ignore growth constraints.

Nitrogen stress is calculated only for non-legumes. SWAT+ never allows legumes to experience nitrogen stress.

Nitrogen stress is quantified by comparing actual and optimal plant nitrogen levels. Nitrogen stress varies non-linearly between 0.0 at optimal nitrogen content and 1.0 when the nitrogen content of the plant is 50% or less of the optimal value. Nitrogen stress is computed with the equation:

$nstrs=1-\frac{\phi _n}{\phi_n +exp[3.535-0.02597*\phi _n]}$ 5:3.1.6

where $nstrs$ is the nitrogen stress for a given day, and $\phi_n$ is a scaling factor for nitrogen stress. The scaling factor is calculated:

$\phi_n=200*(\frac{bio_N}{bio_{N,opt}}-0.5)$ 5:3.1.7

where $bio_{N,opt}$ is the optimal mass of nitrogen stored in plant material for the current growth stage (kg N/ha) and $bio_N$ is the actual mass of nitrogen stored in plant material (kg N/ha).

Water stress is 0.0 under optimal water conditions and approaches 1.0 as the soil water conditions vary from the optimal. Water stress is simulated by comparing actual and potential plant transpiration:

$wstrs=1-\frac{E_{t,act}}{E_t}=1-\frac{w_{actualup}}{E_t}$ 5:3.1.1

where $wstrs$ is the water stress for a given day, $E_t$ is the maximum plant transpiration on a given day (mm H$_2$O), $E_{t,act}$ is the actual amount of transpiration on a given day (mm H$_2$O) and $w_{actualup}$ is the total plant water uptake for the day (mm H$_2$O). The calculation of maximum transpiration is reviewed in Chapter 2:2 and the determination of actual plant water uptake/transpiration is reviewed in Chapter 5:2.

As with nitrogen, phosphorus stress is quantified by comparing actual and optimal plant phosphorus levels. Phosphorus stress varies non-linearly between 0.0 at optimal phosphorus content and 1.0 when the phosphorus content of the plant is 50% or less of the optimal value. Phosphorus stress is computed with the equation:

$pstrs=1-\frac{\phi_p}{\phi_p +exp[3.535-0.02597*\phi_p]}$ 5:3.1.8

where $pstrs$ is the phosphorus stress for a given day, and $\phi_p$ is a scaling factor for phosphorus stress. The scaling factor is calculated:

$\phi_p=200*(\frac{bio_P}{bio_{P,opt}}-0.5)$ 5:3.1.9

where $bio_{P,opt}$ is the optimal mass of phosphorus stored in plant material for the current growth stage (kg N/ha) and $bio_P$ is the actual mass of phosphorus stored in plant material (kg N/ha).

Table 5:3-1: SWAT+ input variables that pertain to stress on plant growth.

Plant growth may be reduced due to extreme temperatures, and insufficient water, nitrogen or phosphorus. The amount of stress for each of these four parameters is calculated on a daily basis using the equations summarized in the following sections.

The harvest index predicted with equation 5:2.4.1 is affected by water deficit using the relationship:

$HI_{act}=(HI-HI_{min})*\frac{\gamma _{wu}}{\gamma _{wu}+exp[6.13-0.883*\gamma _{wu}]}+HI_{min}$ 5:3.3.1

where $HI_{act}$ is the actual harvest index, $HI$ is the potential harvest index on the day of harvest calculated with equation 5:2.4.1, $HI_{min}$ is the harvest index for the plant in drought conditions and represents the minimum harvest index allowed for the plant, and $\gamma _{wu}$ is the water deficiency factor. The water deficiency factor is calculated:

$\gamma_{wu}=100*\frac{\sum^m_{i=1} E_a}{\sum ^m_{i=1} E_o}$ 5:3.3.2

where $E_a$ is the actual evapotranspiration on a given day, $E_o$ is the potential evapotranspiration on a given day, $i$ is a day in the plant growing season, and $m$ is the day of harvest if the plant is harvested before it reaches maturity or the last day of the growing season if the plant is harvested after it reaches maturity.

In the harvest only operation (.mgt), the model allows the user to specify a harvest efficiency. The harvest efficiency defines the fraction of yield biomass removed by the harvesting equipment. The remainder of the yield biomass is converted to residue and added to the residue pool in the top 10 mm of soil. If the harvest efficiency is not set or a 0.00 is entered, the model assumes the user wants to ignore harvest efficiency and sets the fraction to 1.00 so that the entire yield is removed from the HRU.

$yld_{act}=yld*harv_{eff}$ 5:3.3.4

where $yld_{act}$ is the actual yield (kg ha$^{-1}$), $yld$ is the crop yield calculated with equation 5:2.4.2 or 5:2.4.3 (kg ha$^{-1}$), and $harv_{eff}$ is the efficiency of the harvest operation (0.01-1.00). The remainder of the yield biomass is converted to residue:

$\Delta rsd=yld*(1-harv_{eff})$ 5:3.3.5

$rsd_{surf,i}=rsd_{surf,i-1}+\Delta rsd$ 5:3.3.6

where $\Delta rsd$ is the biomass added to the residue pool on a given day (kg ha$^{-1}$), $yld$ is the crop yield calculated with equation 5:2.4.2 or 5:2.4.3 (kg ha$^{-1}$) and $harv_{eff}$ is the efficiency of the harvest operation (0.01-1.00) $rsd_{surf,i}$ is the material in the residue pool for the top 10 mm of soil on day $i$ (kg ha$^{-1}$), and $rsd_{surf,i-1}$ is the material in the residue pool for the top 10 mm of soil on day $i-1$ (kg ha$^{-1}$).

Table 5:3-3: SWAT+ input variables that pertain to actual plant yield.

In the plant and harvest only operations (.mgt), the model allows the user to specify a target harvest index. The target harvest index set in a plant operation is used when the yield is removed using a harvest/kill operation. The target harvest index set in a harvest only operation is used only when that particular harvest only operation is executed.

When a harvest index override is defined, the override value is used in place of the harvest index calculated by the model in the yield calculations. Adjustments for growth stage and water deficiency are not made.

$HI_{act}=HI_{trg}$ 5:3.3.3

where $HI_{act}$ is the actual harvest index and $HI_{trg}$ is the target harvest index.

The plant growth factor quantifies the fraction of potential growth achieved on a given day and is calculated:

$\gamma_{reg}=1-max(wstrs,tstrs,nstrs,pstrs)$ 5:3.2.3

where $\gamma_{reg}$ is the plant growth factor (0.0-1.0), $wstrs$ is the water stress for a given day, $tstrs$ is the temperature stress for a given day expressed as a fraction of optimal plant growth, $nstrs$ is the nitrogen stress for a given day, and $pstrs$ is the phosphorus stress for a given day.

The potential biomass predicted with equation 5:2.1.2 is adjusted daily if one of the four plant stress factors is greater than 0.0 using the equation:

$\Delta bio_{act}=\Delta bio*\gamma_{reg}$ 5:3.2.1

where $\Delta bio_{act}$ is the actual increase in total plant biomass on a given day (kg/ha), $\Delta bio$ is the potential increase in total plant biomass on a given day (kg/ha), and $\gamma_{reg}$ is the plant growth factor (0.0-1.0).

The potential leaf area added on a given day is also adjusted daily for plant stress:

$\Delta LAI _{act,i}=\Delta LAI_i*\sqrt{\gamma _{reg}}$ 5:3.2.2

where $\Delta LAI _{act,i}$ is the actual leaf area added on day $i, \Delta LAI_i$ is the potential leaf area added on day $i$ that is calculated with equation 5:2.1.16 or 5:2.1.17, and $\gamma _{reg}$ is the plant growth factor (0.0-1.0).

The model allows the user to specify a total biomass that the plant will produce each year. When the biomass override is set in the plant operation (.mgt), the impact of variation in growing conditions from year to year is ignored, i.e. $\gamma_{reg}$ is always set to 1.00 when biomass override is activated in an HRU.

When a value is defined for the biomass override, the change in biomass is calculated:

$\Delta bio_{act} = \Delta bio_i*\frac{(bio_{trg}-bio_{i-1})}{bio_{trg}}$ 5:3.2.4

where $\Delta bio_{act}$ is the actual increase in total plant biomass on day $i$ (kg/ha), $\Delta bio_i$ is the potential increase in total plant biomass on day $i$ calculated with equation 5:2.1.2 (kg/ha), $bio_{trg}$ is the target biomass specified by the user (kg/ha), and $bio_{i-1}$ is the total plant biomass accumulated on day $i-1$ (kg/ha).

Table 5:3-2: SWAT+ input variables that pertain to actual plant growth.