Net radiation requires the determination of both incoming and reflected short-wave radiation and net long-wave or thermal radiation. Expressing net radiation in terms of the net short-wave and long-wave components gives:
1:1.2.11
or
1:1.2.12
where is the net radiation (), is the short-wave solar radiation reaching the ground (), is the short-wave reflectance or albedo, is the long-wave radiation (), is the net incoming long-wave radiation () and the arrows indicate the direction of the radiation flux.
Net short-wave radiation is defined as . SWAT+ calculates a daily value for albedo as a function of the soil type, plant cover, and snow cover. When the snow water equivalent is greater than 0.5 mm,
1:1.2.13
When the snow water equivalent is less than 0.5 mm and no plants are growing in the HRU,
1:1.2.14
where is the soil albedo. When plants are growing and the snow water equivalent is less than 0.5 mm,
1:1.2.15
where is the plant albedo (set at 0.23), and is the soil cover index. The soil cover index is calculated
1:1.2.16
where is the aboveground biomass and residue ().
Long-wave radiation is emitted from an object according to the radiation law:
Table 1:1-3: Experimental coefficients for net long-wave radiation equations (from Jensen et al., 1990).
Table 1:1-4: SWAT+ input variables used in net radiation calculations.
1:1.2.17
where is the radiant energy (, is the emissivity, is the Stefan-Boltzmann constant (, and is the mean air temperature in Kelvin (273.15 + C). Net long-wave radiation is calculated using a modified form of equation 1:1.2.17 (Jensen et al., 1990):
1:1.2.18
where is the net long-wave radiation (), is a factor to adjust for cloud cover, a is the atmospheric emittance, and vs is the vegetative or soil emittance.
Wright and Jensen (1972) developed the following expression for the cloud cover adjustment factor, :
1:1.2.19
where a and b are constants, is the solar radiation reaching the ground surface on a given day (), and is the maximum possible solar radiation to reach the ground surface on a given day (). The two emittances in equation 1:1.2.18 may be combined into a single term, the net emittance . The net emittance is calculated using an equation developed by Brunt (1932):
1:1.2.20
where and are constants and is the vapor pressure on a given day (kPa). The calculation of e is given in Chapter 1:2. Combining equations 1:1.2.18, 1:1.2.19, and 1:1.2.20 results in a general equation for net long-wave radiation:
1:1.2.21
Experimental values for the coefficients and are presented in Table 1:1.3. The default equation in SWAT+ uses coefficient values proposed by Doorenbos and Pruitt (1977):
1:1.2.22
Region | (a, | b) | (a1, | b1) |
---|---|---|---|---|
Variable Name | Definition | File Name |
---|---|---|
Davis, California
(1.35,
-0.35)
(0.35,
-0.145)
Southern Idaho
(1.22,
-0.18)
(0.325,
-0.139)
England
not available
not available
(0.47,
-0.206)
England
not available
not available
(0.44,
-0.253)
Australia
not available
not available
(0.35,
-0.133)
General
(1.2
-0.2)
(0.39,
-0.158)
General-humid areas
(1.0
0.0)
General-semihumid areas
(1.1
-0.1)
SOL_ALB
: moist soil albedo
.sol
MAX TEMP
: Daily maximum temperature (C)
.tmp
MIN TEMP
: Daily minimum temperature (C)
.tmp
SOL_RAD
: Daily solar radiation reaching the earth’s surface (MJ m-2 d-1)
.slr