Temperature influences a number of physical, chemical and biological processes. Plant production is strongly temperature dependent, as are organic matter decomposition and mineralization. Daily air temperature may be input to the model or generated from average monthly values. Soil and water temperatures are derived from air temperature.

Soil temperature will fluctuate due to seasonal and diurnal variations in temperature at the surface. Figure 1:1-2 plots air temperature and soil temperature at 5 cm and 300 cm below bare soil at College Station, Texas. Figure 1:1-2: Four-year average air and soil temperature at College Station, Texas.

This figure illustrates several important attributes of temperature variation in the soil. First, the annual variation in soil temperature follows a sinusoidal function. Second, the fluctuation in temperature during the year (the amplitude of the sine wave) decreases with depth until, at some depth in the soil, the temperature remains constant throughout the year. Finally, the timing of maximum and minimum temperatures varies with depth. Note in the above graph that there is a three month difference between the recording of the minimum temperature at the surface (January) and the minimum temperature at 300 cm (March).

Carslaw and Jaeger (1959) developed an equation to quantify the seasonal variation in temperature:

In order to calculate values for some of the variables in this equation, the heat capacity and thermal conductivity of the soil must be known. These are properties not commonly measured in soils and attempts at estimating values from other soil properties have not proven very effective. Consequently, an equation has been adopted in SWAT+ that calculates the temperature in the soil as a function of the previous day’s soil temperature, the average annual air temperature, the current day’s soil surface temperature, and the depth in the profile.

The equation used to calculate daily average soil temperature at the center of each layer is:

1:1.3.3

The depth factor is calculated using the equation:

The equation used to calculate the soil surface temperature is:

SWAT+ input variables that directly impact soil temperature calculations are listed in Table 1:1-7. There are several other variables that initialize residue and snow cover in the subbasins or HRUs (SNO_SUB and SNOEB in .sub; RSDIN in .hru). The influence of these variables will be limited to the first few months of simulation. Finally, the timing of management operations in the .mgt file will affect ground cover and consequently soil temperature.

Table 1:1-7: SWAT+ input variables that pertain to soil temperature.

Daily Air Temperature SWAT+ requires daily maximum and minimum air temperature. This data may be read from an input file or generated by the model. The user is strongly recommended to obtain measured daily temperature records from gages in or near the watershed if at all possible. The accuracy of model results is significantly improved by the use of measured temperature data.

The variable TMPSIM in the master watershed (file.cio) file identifies the method used to obtain air temperature data. To read in daily maximum and minimum air temperature data, the variable is set to 1 and the name of the temperature data file(s) and the number of temperature records stored in the file are set. To generate daily air temperature values, TMPSIM is set to 2. The equations used to generate air temperature data in SWAT+ are reviewed in Chapter 1:3. SWAT+ input variables that pertain to air temperature are summarized in Table 1:1-5.

Table 1:1-5: SWAT+ input variables that pertain to daily air temperature.

See description of .tmp file in the User’s Manual for input and format requirements if measured temperature data is being used.

Water temperature is required to model in-stream biological and water quality processes. SWAT+ uses an equation developed by Stefan and Preud’homme (1993) to calculate average daily water temperature for a well-mixed stream:

$T_{water}=5.0+0.75\overline T_{av}$ 1:1.3.13

where $T_{water}$ is the water temperature for the day (C), and $^{\overline T_{av}}$is the average air temperature on the day (C).

Due to thermal inertia of the water, the response of water temperature to a change in air temperature is dampened and delayed. When water and air temperature are plotted for a stream or river, the peaks in the water temperature plots usually lag 3-7 hours behind the peaks in air temperature. As the depth of the river increases, the lag time can increase beyond this typical interval. For very large rivers, the lag time can extend up to a week. Equation 1:1.3.13 assumes that the lag time between air and water temperatures is less than 1 day.

In addition to air temperature, water temperature is influenced by solar radiation, relative humidity, wind speed, water depth, ground water inflow, artificial heat inputs, thermal conductivity of the sediments and the presence of impoundments along the stream network. SWAT+ assumes that the impact of these other variables on water temperature is not significant.

Table 1:1-8: SWAT+ input variables that pertain to water temperature.

Air temperature data are usually provided in the form of daily maximum and minimum temperature. A reasonable approximation for converting these to hourly temperatures is to assume a sinusoidal interpolation function between the minimum and maximum daily temperatures. The maximum daily temperature is assumed to occur at 1500 hours and the minimum daily temperature at 300 hours (Campbell, 1985). The temperature for the hour is then calculated with the equation:

$T_{hr} = \overline T_{av} + \frac{T_{mx}-T_{mn}}2 *cos(0.2618*(hr-15))$ 1:1.3.1

where $T_{hr}$ is the air temperature during hour $hr$of the day (C), $\overline T_{av}$is the average temperature on the day (C), $T_{mx}$ is the daily maximum temperature (C), and $T_{mn}$ is the daily minimum temperature (C).

Table 1:1-6: SWAT+ input variables that pertain to hourly air temperature.