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 ($MJ m^{-2} d^{-1}$), $H_b$is the net incoming long-wave radiation ($MJ m^{-2} d^{-1}$) and the arrows indicate the direction of the radiation flux.

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 ().

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 + 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

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.