Temperature is one of the most important factors governing plant growth. Each plant has its own temperature range, i.e. its minimum, optimum, and maximum for growth. For any plant, a minimum or base temperature must be reached before any growth will take place. Above the base temperature, the higher the temperature the more rapid the growth rate of the plant. Once the optimum temperature is exceeded the growth rate will begin to slow until a maximum temperature is reached at which growth ceases.

In the 1920s and 1930s, canning factories were searching for ways to time the planting of sweet peas so that there would be a steady flow of peas at the peak of perfection to the factory. Crops planted at weekly intervals in the early spring would sometimes come to maturity with only a 1- or 2-day differential while at other times there was a 6- to 8-day differential (Boswell, 1926; 1929). A heat unit theory was suggested (Boswell, 1926; Magoon and Culpepper, 1932) that was revised and successfully applied (Barnard, 1948; Phillips, 1950) by canning companies to determine when plantings should be made to ensure a steady harvest of peas with no “bunching” or “breaks”.

The heat unit theory postulates that plants have heat requirements that can be quantified and linked to time to maturity. Because a plant will not grow when the mean temperature falls below its base temperature, the only portion of the mean daily temperature that contributes towards the plant’s development is the amount that exceeds the base temperature. To measure the total heat requirements of a plant, the accumulation of daily mean air temperatures above the plant’s base temperature is recorded over the period of the plant’s growth and expressed in terms of heat units. For example, assume sweet peas are growing with a base temperature of 5°C. If the mean temperature on a given day is 20°C, the heat units accumulated on that day are 20 – 5 = 15 heat units. Knowing the planting date, maturity date, base temperature and mean daily temperatures, the total number of heat units required to bring a crop to maturity can be calculated.

The heat index used by SWAT+ is a direct summation index. Each degree of the daily mean temperature above the base temperature is one heat unit. This method assumes that the rate of growth is directly proportional to the increase in temperature. It is important to keep in mind that the heat unit theory without a high temperature cutoff does not account for the impact of harmful high temperatures. SWAT+ assumes that all heat above the base temperature accelerates crop growth and development.

The mean daily temperature during 1992 for Greenfield, Indiana is plotted in Figure 5:1-1 along with the base temperature for corn (8°C). Crop growth will only occur on those days where the mean daily temperature exceeds the base temperature. The heat unit accumulation for a given day is calculated with the equation:

when 5:1.1.1

where is the number of heat units accumulated on a given day (heat units), is the mean daily temperature (°C), and is the plant’s base or minimum temperature for growth (°C). The total number of heat units required for a plant to reach maturity is calculated:

5:1.1.2

where is the total heat units required for plant maturity (heat units), is the number of heat units accumulated on day where on the day of planting and is the number of days required for a plant to reach maturity. is also referred to as potential heat units.

When calculating the potential heat units for a plant, the number of days to reach maturity must be known. For most crops, these numbers have been quantified and are easily accessible. For other plants, such as forest or range, the time that the plants begin to develop buds should be used as the beginning of the growing season and the time that the plant seeds reach maturation is the end of the growing season. For the Greenfield Indiana example, a 120 day corn hybrid was planted on May 15. Summing daily heat unit values, the total heat units required to bring the corn to maturity was 1456.

As the heat unit theory was proven to be a reliable predictor of harvest dates for all types of crops, it was adapted by researchers for prediction of the timing of other plant development stages such as flowering (Cross and Zuber, 1972). The successful adaptation of heat units to predict the timing of plant stages has subsequently led to the use of heat units to schedule management operations.

SWAT+ allows management operations to be scheduled by day or by fraction of potential heat units. For each operation the model checks to see if a month and day has been specified for timing of the operation. If this information is provided, SWAT+ will perform the operation on that month and day. If the month and day are not specified, the model requires a fraction of potential heat units to be specified. As a general rule, if exact dates are available for scheduling operations, these dates should be used.

Scheduling by heat units allows the model to time operations as a function of temperature. This method of timing is useful for several situations. When very large watersheds are being simulated where the climate in one portion of the watershed is different enough from the climate in another section of the watershed to affect timing of operations, heat unit scheduling may be beneficial. By using heat unit scheduling, only one generic management file has to be made for a given land use. This generic set of operations can then be used wherever the land use is found in the watershed. Also, in areas where the climate can vary greatly from year to year, heat unit scheduling will allow the model to adjust the timing of operations to the weather conditions for each year.

For each day of simulation, potential plant growth, i.e. plant growth under ideal growing conditions, is calculated. Ideal growing conditions consist of adequate water and nutrient supply and a favorable climate. Differences in growth between plant species are defined by the parameters contained in the plant growth database.

With annuals and perennials, the plants are able to reach full maturity within a single calendar year. With trees, a number of years are needed for a plant to transition from a seedling to a sapling to a fully-developed tree. The parameters in the plant growth database related to radiation-use efficiency represent the annual growth for a fully-developed tree. The heat units to maturity input in the management file is also used to simulate growth within a single year, defining for trees and perennials the period within a year bounded by the development of buds at the beginning of the annual growing season and the maturation of plant seeds at the end of the growing season.

To simulate the smaller amount of biomass accumulation seen in seedlings/saplings, tree growth within a single year is limited to a fixed amount determined by the age of the tree relative to the number of years for the tree species to reach full development. Parameters in the plant growth database define the total number of years for trees to reach full development as well as the biomass of a fully-developed tree. Until the trees in an HRU reach full development, the amount of biomass they can accumulate in a single year is limited to:

$bio_{annual}=1000*(\frac{yr_{cur}}{yr_{fulldev}})*bio_{fulldev}$ 5:2.1.9

where $bio_{annual}$ is the amount of biomass a tree can accumulate in a single year (kg/ha), is the current age of the tree (years), is the number of years for the tree species to reach full development (years), is the biomass of a fully developed tree stand for the specific tree species (metric tons/ha), and 1000 is a conversion factor.

Once the total growth in biomass in a year, , reaches the annual limit, , no more growth occurs until the next year when a new annual limit is calculated. When a tree stand has reached its biomass limit in a year, the increase in plant biomass for a day,, is set to 0.

The change in canopy height and leaf area for annuals and perennials through the growing season as modeled by SWAT+ is illustrated using parameters for Alamo Switchgrass in Figures 5:2-1 and 5:2-2.

In the initial period of plant growth, canopy height and leaf area development are controlled by the optimal leaf area development curve:

$fr_{LAImx}=\frac{fr_{PHU}}{fr_{PHU}+exp(\Box_1 - \Box_2 * fr_{PHU})}$ 5:2.1.10

where $fr_{LAImx}$ is the fraction of the plant’s maximum leaf area index corresponding to a given fraction of potential heat units for the plant, $fr_{PHU}$ is the fraction of potential heat units accumulated for the plant on a given day in the growing season, and $\Box_1$and $\Box_2$ are shape coefficients. The fraction of potential heat units accumulated by a given date is calculated:

5:2.1.11

where is the fraction of potential heat units accumulated for the plant on day d in the growing season, is the heat units accumulated on day (heat units), and is the total potential heat units for the plant (heat units).

The shape coefficients are calculated by solving equation 5:2.1.10 using two known points (,) and (,):

5:2.1.12

5:2.1.13

where is the first shape coefficient, is the second shape coefficient, is the fraction of the growing season (i.e. fraction of total potential heat units) corresponding to the 1st point on the optimal leaf area development curve, is the fraction of the maximum plant leaf area index (i.e. fraction of ) corresponding to the 1st point on the optimal leaf area development curve, is the fraction of the growing season corresponding to the 2nd point on the optimal leaf area development curve, and is the fraction of the maximum plant leaf area index corresponding to the 2nd point on the optimal leaf area development curve.

The canopy height on a given day is calculated:

5:2.1.14

where is the canopy height for a given day (m), is the plant’s maximum canopy height (m), and is the fraction of the plant’s maximum leaf area index corresponding to a given fraction of potential heat units for the plant. As can be seen from Figure 5:2-1, once the maximum canopy height is reached, will remain constant until the plant is killed.

For tree stands, the canopy height varies from year to year rather than day to day:

5:2.1.15

where is the canopy height for a given day (m), is the plant’s maximum canopy height (m), is the age of the tree (years), and is the number of years for the tree species to reach full development (years).

The amount of canopy cover is expressed as the leaf area index. For annuals and perennials, the leaf area added on day is calculated:

5:2.1.16

while for trees, the leaf area added on day is calculated:

5:2.1.17

The total leaf area index is calculated:

5:2.1.18

where is the leaf area added on day , and are the leaf area indices for day and respectively, and are the fraction of the plant’s maximum leaf area index calculated with equation 5:2.1.10 for day and , is the maximum leaf area index for the plant, is the age of the tree (years), and is the number of years for the tree species to reach full development (years).

Leaf area index is defined as the area of green leaf per unit area of land (Watson, 1947). As shown in Figure 5:2-2, once the maximum leaf area index is reached, will remain constant until leaf senescence begins to exceed leaf growth. Once leaf senescence becomes the dominant growth process, the leaf area index for annuals and perrenials is calculated:

5:2.1.19

while for trees, the calculation is

5:2.1.20

where is the leaf area index for a given day, is the maximum leaf area index, is the fraction of potential heat units accumulated for the plant on a given day in the growing season, is the fraction of growing season () at which senescence becomes the dominant growth process, is the number of years of development the tree has accrued (years), and is the number of years for the tree species to reach full development (years).

The amount of daily solar radiation intercepted by the leaf area of the plant is calculated using Beer’s law (Monsi and Saeki, 1953):

$H_{phosyn}=0.5*H_{day}*(1-exp(-k_{\Box}*LAI))$ 5:2.1.1

where $H_{phosyn}$ is the amount of intercepted photosynthetically active radiation on a given day (MJ m$^{-2}$), $H_{day}$ is the incident total solar (MJ m$^{-2}$), $0.5*H_{day}$ is the incident photosynthetically active radiation (MJ m$^{-2}$), $k_{\Box}$ is the light extinction coefficient, and $LAI$ is the leaf area index.

Photosynthetically active radiation is radiation with a wavelength between 400 and 700 mm (McCree, 1972). Direct solar beam radiation contains roughly 45% photosynthetically active radiation while diffuse radiation contains around 60% photosynthetically active radiation (Monteith, 1972; Ross, 1975). The fraction of photosynthetically active radiation will vary from day to day with variation in overcast conditions but studies in Europe and Israel indicate that 50% is a representative mean value (Monteith, 1972; Szeicz, 1974; Stanhill and Fuchs, 1977).

Radiation-use efficiency is the amount of dry biomass produced per unit intercepted solar radiation. The radiation-use efficiency is defined in the plant growth database and is assumed to be independent of the plant’s growth stage. The maximum increase in biomass on a given day that will result from the intercepted photosynthetically active radiation is estimated (Monteith, 1977):

5:2.1.2

where is the potential increase in total plant biomass on a given day (kg/ha), is the radiation-use efficiency of the plant (kg/ha⋅(MJ/m) or 10 g/MJ), and is the amount of intercepted photosynthetically active radiation on a given day (MJ m). Equation 5:2.1.2 assumes that the photosynthetic rate of a canopy is a linear function of radiant energy.

The total biomass on a given day, , is calculated as:

5:2.1.3

where is the total plant biomass on a given day (kg ha), and is the increase in total plant biomass on day (kg/ha).

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.

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.

Radiation-use efficiency is sensitive to variations in atmospheric $CO_2$ concentrations and equations have been incorporated into SWAT+ to modify the default radiation-use efficiency values in the plant database for climate change studies. The relationship used to adjust the radiation-use efficiency for effects of elevated $CO_2$ is (Stockle et al., 1992):

$RUE=\frac{100*CO_2}{CO_2+exp(r_1-r_2*CO_2)}$ 5:2.1.4

where $RUE$ is the radiation-use efficiency of the plant (kg/ha⋅(MJ/m$^2$)$^{-1}$ or 10$^{-1}$ g/MJ), $CO_2$ is the concentration of carbon dioxide in the atmosphere (ppmv), and $r_1$ and $r_2$ are shape coefficients.

The shape coefficients are calculated by solving equation 5:2.1.4 using two known points ($RUE_{amb}$, $CO_{2amb}$) and (, ):

5:2.1.5

5:2.1.6

where is the first shape coefficient, is the second shape coefficient, is the ambient atmospheric concentration (ppmv), is the radiation-use efficiency of the plant at ambient atmospheric concentration (kg/ha⋅(MJ/m) or 10 g/MJ), is an elevated atmospheric concentration (ppmv), is the radiation-use efficiency of the plant at the elevated atmospheric concentration, , (kg/ha⋅(MJ/m) or 10 g/MJ). Equation 5:2.1.4 was developed when the ambient atmospheric concentration was 330 ppmv and is valid for carbon dioxide concentrations in the range 330-660 ppmv. Even though the ambient atmospheric concentration of carbon dioxide is now higher than 330 ppmv, this value is still used in the calculation. If the concentration used in the simulation is less than 330 ppmv, the model defines RUE = .

Stockle and Kiniry (1990) have shown that a plant’s radiation-use efficiency is affected by vapor pressure deficit. For a plant, a threshold vapor pressure deficit is defined at which the plant’s radiation-use efficiency begins to drop in response to the vapor pressure deficit. The adjusted radiation-use efficiency is calculated:

if 5:2.1.7

if 5:2.1.8

where is the radiation-use efficiency adjusted for vapor pressure deficit (kg/ha⋅(MJ/m) or 10 g/MJ), is the radiation-use efficiency for the plant at a vapor pressure deficit of 1 kPa (kg/ha⋅(MJ/m) or 10 g/MJ), is the rate of decline in radiation-use efficiency per unit increase in vapor pressure deficit (kg/ha⋅(MJ/m)⋅kPa or (10 g/MJ)⋅kPa), is the vapor pressure deficit (kPa), and is the threshold vapor pressure deficit above which a plant will exhibit reduced radiation-use efficiency (kPa). The radiation-use efficiency value reported for the plant in the plant growth database, , or adjusted for elevated carbon dioxide levels (equation 5:2.1.4) is the value used for . The threshold vapor pressure deficit for reduced radiation-use efficiency is assumed to be 1.0 kPa for all plants ().

The radiation-use efficiency is never allowed to fall below 27% of . This minimum value was based on field observations (Kiniry, personal communication, 2001).

The amount of total plant biomass partitioned to the root system is 30-50% in seedlings and decreases to 5-20% in mature plants (Jones, 1985). SWAT+ varies the fraction of total biomass in roots from 0.40 at emergence to 0.20 at maturity. The daily root biomass fraction is calculated with the equation:

$fr_{root}=0.40-0.20*fr_{PHU}$ 5:2.1.21

where $fr_{root}$ is the fraction of total biomass partitioned to roots on a given day in the growing season, and $fr_{PHU}$ is the fraction of potential heat units accumulated for the plant on a given day in the growing season.

Calculation of root depth varies according to plant type. SWAT+ assumes perennials and trees have roots down to the maximum rooting depth defined for the soil throughout the growing season:

$z_{root}=z_{root,mx}$ 5:2.1.22

where is the depth of root development in the soil on a given day (mm), and is the maximum depth for root development in the soil (mm). The simulated root depth for annuals varies linearly from 10.0 mm at the beginning of the growing season to the maximum rooting depth at = 0.40 using the equation:

if 5:2.1.23

if 5:2.1.24

where is the depth of root development in the soil on a given day (mm), is the fraction of potential heat units accumulated for the plant on a given day in the growing season, and is the maximum depth for root development in the soil (mm). The maximum rooting depth is defined by comparing the maximum potential rooting depth for the plant from the plant growth database (RDMX in crop.dat), and the maximum potential rooting depth for the soil from the soil input file (SOL_ZMX in .sol—if no value is provided for this variable the model will set it to the deepest depth specified for the soil profile). The shallower of these two depths is the value used for .

If upper layers in the soil profile do not contain enough water to meet the potential water uptake calculated with equation 5:2.2.2, users may allow lower layers to compensate. The equation used to calculate the adjusted potential water uptake is:

$w'_{up,ly}=w_{up,ly}+w_{demand}*epco$ 5:2.2.3

where $w'_{up,ly}$is the adjusted potential water uptake for layer $ly$ (mm H$_2$O), $w_{up,ly}$ is the potential water uptake for layer $ly$ calculated with equation 5:2.2.2 (mm H$_2$O), $w_{demand}$ is the water uptake demand not met by overlying soil layers (mm H$_2$O), and $epco$ is the plant uptake compensation factor. The plant uptake compensation factor can range from 0.01 to 1.00 and is set by the user. As $epco$ approaches 1.0, the model allows more of the water uptake demand to be met by lower layers in the soil. As $epco$ approaches 0.0, the model allows less variation from the depth distribution described by equation 5:2.2.1 to take place.

As the water content of the soil decreases, the water in the soil is held more and more tightly by the soil particles and it becomes increasingly difficult for the plant to extract water from the soil. To reflect the decrease in the efficiency of the plant in extracting water from dryer soils, the potential water uptake is modified using the following equations:

when 5:2.2.4

when 5:2.2.5

where is the potential water uptake adjusted for initial soil water content(mm HO), is the adjusted potential water uptake for layer (mm HO), is the amount of water in the soil layer on a given day (mm HO), and is the available water capacity for layer (mm HO). The available water capacity is calculated:

5:2.2.6

where is the available water capacity for layer (mm HO), is the water content of layer at field capacity (mm HO), and is the water content of layer at wilting point (mm HO).

The potential water uptake from the soil surface to any depth in the root zone is estimated with the function:

5:2.2.1

where is the potential water uptake from the soil surface to a specified depth, , on a given day (mm HO), is the maximum plant transpiration on a given day (mm HO), is the water-use distribution parameter, is the depth from the soil surface (mm), and is the depth of root development in the soil (mm). The potential water uptake from any soil layer can be calculated by solving equation 5:2.2.1 for the depth at the top and bottom of the soil layer and taking the difference.

5:2.2.2

Plant maturity is reached when the fraction of potential heat units accumulated, , is equal to 1.00. Once maturity is reached, the plant ceases to transpire and take up water and nutrients. Simulated plant biomass remains stable until the plant is harvested or killed via a management operation.

Table 5:2-1: SWAT+ input variables that pertain to optimal plant growth.

Once the potential water uptake has been modified for soil water conditions, the actual amount of water uptake from the soil layer is calculated:

5:2.2.7

where is the actual water uptake for layer (mm HO), is the amount of water in the soil layer on a given day (mm HO), and is the water content of layer at wilting point (mm HO). The total water uptake for the day is calculated:

5:2.2.8

If nitrate levels in the root zone are insufficient to meet the demand of a legume, SWAT+ allows the plant to obtain additional nitrogen through nitrogen fixation. Nitrogen fixation is calculated as a function of soil water, soil nitrate content and growth stage of the plant.

5:2.3.9

where is the amount of nitrogen added to the plant biomass by fixation (kg N/ha), is the plant nitrogen demand not met by uptake from the soil (kg N/ha), is the growth stage factor (0.0-1.0), is the soil water factor (0.0-1.0), and is the soil nitrate factor (0.0-1.0). The maximum amount of nitrogen that can be fixed by the plant on a given day is .

Growth stage exerts the greatest impact on the ability of the plant to fix nitrogen. The growth stage factor is calculated:

When a harvest or harvest/kill operation is performed, a portion of the plant biomass is removed from the HRU as yield. The nutrients and plant material contained in the yield are assumed to be lost from the system (i.e. the watershed) and will not be added to residue and organic nutrient pools in the soil with the remainder of the plant material. In contrast, a kill operation converts all biomass to residue.

The fraction of the above-ground plant dry biomass removed as dry economic yield is called the harvest index. For the majority of crops, the harvest index will be between 0.0 and 1.0. However, plants whose roots are harvested, such as sweet potatoes, may have a harvest index greater than 1.0.

The economic yield of most commercial crops is the reproductive portion of the plant. Decades of crop breeding have lead to cultivars and hybrids having maximized harvest indices. Often, the harvest index is relatively stable across a range of environmental conditions.

SWAT+ calculates harvest index each day of the plant’s growing season using the relationship:

Plant phosphorus uptake is controlled by the plant phosphorus equation. The plant phosphorus equation calculates the fraction of phosphorus in the plant biomass as a function of growth stage given optimal growing conditions.

5:2.3.19

where is the fraction of phosphorus in the plant biomass on a given day, is the normal fraction of phosphorus in the plant biomass at emergence, is the normal fraction of phosphorus in the plant biomass at maturity, is the fraction of potential heat units accumulated for the plant on a given day in the growing season, and and are shape coefficients.

The shape coefficients are calculated by solving equation 5:2.3.19 using two known points () and ():

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:

5:3.1.1

where is the water stress for a given day, is the maximum plant transpiration on a given day (mm HO), is the actual amount of transpiration on a given day (mm HO) and is the total plant water uptake for the day (mm HO). 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.

Plant nitrogen uptake is controlled by the plant nitrogen equation. The plant nitrogen equation calculates the fraction of nitrogen in the plant biomass as a function of growth stage given optimal growing conditions.

5:2.3.1

where is the fraction of nitrogen in the plant biomass on a given day, is the normal fraction of nitrogen in the plant biomass at emergence, is the normal fraction of nitrogen in the plant biomass at maturity, is the fraction of potential heat units accumulated for the plant on a given day in the growing season, and and are shape coefficients.

The shape coefficients are calculated by solving equation 5:2.3.1 using two known points (, ) and (, ):

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:

when 5:3.1.2

when 5:3.1.3

when 5:3.1.4

when

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 growth cycle of a plant is controlled by plant attributes summarized in the plant growth database and by the timing of operations listed in the management file. This chapter reviews the heat unit theory used to regulate the growth cycle of plants. Chapter 6:1 focuses on the impact of user inputs in management operations on the growth and development of plants.

Plant growth is modeled by simulating leaf area development, light interception and conversion of intercepted light into biomass assuming a plant species-specific radiation-use efficiency.

SWAT+ monitors plant uptake of nitrogen and phosphorus.