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:

$HU=\overline T_{av}-T_{base}$ when $\overline T_{av}>T_{base}$ 5:1.1.1

where $HU$ is the number of heat units accumulated on a given day (heat units), is the mean daily temperature (°C), and $T_{base}$ 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:

$PHU=\sum_{d=1}^m HU$ 5:1.1.2

where $PHU$ is the total heat units required for plant maturity (heat units), $HU$ is the number of heat units accumulated on day $d$ where $d=1$ on the day of planting and $m$ is the number of days required for a plant to reach maturity. $PHU$ 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.

While scheduling by heat units is convenient, there are some negatives to using this type of scheduling that users need to take into consideration. In the real world, applications of fertilizer or pesticide are generally not scheduled on a rainy day. However when applications are scheduled by heat units, the user has no knowledge of whether or not the heat unit fraction that triggers the application will occur on a day with rainfall or not. If they do coincide, there will be a significant amount of the applied material transported with surface runoff (assuming runoff is generated on that day), much higher than if the application took place even one day prior to the rainfall event.

To schedule by heat units, the timing of the operations are expressed as fractions of the potential heat units for the plant or fraction of maturity. Let us use the following example for corn in Indiana.

The number of heat units accumulated for the different operation timings is calculated by summing the heat units for every day starting with the planting date (May 15) and ending with the day the operation takes place. To calculate the fraction of $PHU$ at which the operation takes place, the heat units accumulated is divided by the $PHU$ for the crop (1456).

Note that the fraction of $PHU$ for the harvest operation is 1.16. The fraction is greater than 1.0 because corn is allowed to dry down prior to harvesting. The model will simulate plant growth until the crop reaches maturity (where maturity is defined as $PHU$ = 1456). From that point on, plants will not transpire or take up nutrients and water. They will stand in the HRU until converted to residue or harvested.

While the operations after planting have been scheduled by fraction of $PHU$, operations—including planting—which occur during periods when no crop is growing must still be scheduled. To schedule these operations, SWAT+ keeps track of a second heat index where heat units are summed over the entire year using $T_{base}$ = 0°C. This heat index is solely a function of the climate and is termed the base zero heat index. For the base zero index, the heat units accumulated on a given day are:

$HU_0=\overline T_{av}$ when $\overline T_{av} >$0°C 5:1.1.3

where $HU_0$ is the number of base zero heat units accumulated on a given day (heat units), and $\overline T_{av}$ is the mean daily temperature (°C). The total number of heat units for the year is calculated:

$PHU_0=\sum_{d=1}^{365} HU_0$ 5:1.1.4

where $PHU_0$ is the total base zero heat units (heat units), $HU_0$ is the number of base zero heat units accumulated on day $d$ where $d=1$ on January 1 and 365 on December 31. Unlike the plant $PHU$ which must be provided by the user, $PHU_0$ is the average calculated by SWAT+ using long-term weather data provided in the .wgn file.

For the example watershed in Indiana, $PHU_0$= 4050. The heat unit fractions for the remaining operations are calculated using this value for potential heat units.

As stated previously, SWAT+ always keeps track of base zero heat units. The base zero heat unit scheduling is used any time there are no plants growing in the HRU (before and including the plant operation and after the kill operation). Once plant growth is initiated, the model switches to plant heat unit scheduling until the plant is killed.

The following heat unit fractions have been found to provide reasonable timings for the specified operations:

Table 5:1-1: SWAT+ input variables that pertain to heat units.