1:1.2.5 Daily Net Radiation

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:

$H_{net}=H_{day}\downarrow-\alpha*H_{day}\uparrow+H_L\downarrow-H_L\uparrow$ 1:1.2.11

or

$H_{net} = (1-\alpha) H_{day} + H_b$ 1:1.2.12

where $H_{net}$ is the net radiation ($MJ m^{-2} d^{-1}$), $H_{day}$ is the short-wave solar radiation reaching the ground ($MJ m^{-2} d^{-1}$), is the short-wave reflectance or albedo, $H_L$ is the long-wave radiation ($MJ m^{-2} d^{-1}$), is the net incoming long-wave radiation () and the arrows indicate the direction of the radiation flux.

1:1.2.5.1 Net Short-Wave Radiation

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 ().

1:1.2.5.2 Net Long-Wave Radiation

Long-wave radiation is emitted from an object according to the radiation law:

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 + ). 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, is the atmospheric emittance, and 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 and 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 (). The calculation of 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

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.