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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

$H_{net} = (1-\alpha)*H_{day} + H_b$ 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 $(1-\alpha)*H_{day}$ . 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,

$\alpha=0.8$ 1:1.2.13

When the snow water equivalent is less than 0.5 mm and no plants are growing in the HRU,

$\alpha=\alpha_{soil}$ 1:1.2.14

where $_{soil}$ is the soil albedo. When plants are growing and the snow water equivalent is less than 0.5 mm,

$\alpha=\alpha_{plant}*(1-cov_{sol})+\alpha_{soil}*cov_{sol}$ 1:1.2.15

where $_{plant}$ is the plant albedo (set at 0.23), and $cov_{sol}$ is the soil cover index. The soil cover index is calculated

$cov_{sol}=exp(-5.0X10^{-5}*CV)$ 1:1.2.16

where $CV$ is the aboveground biomass and residue ( $kg ha^{-1}$ ).

Net Long-Wave Radiation

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.

1:1.2.5 Daily Net Radiation

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

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

Net Short-Wave Radiation

$\alpha=0.8$ 1:1.2.13

When the snow water equivalent is less than 0.5 mm and no plants are growing in the HRU,

$\alpha=\alpha_{soil}$ 1:1.2.14

where $_{soil}$ is the soil albedo. When plants are growing and the snow water equivalent is less than 0.5 mm,

$\alpha=\alpha_{plant}*(1-cov_{sol})+\alpha_{soil}*cov_{sol}$ 1:1.2.15

where $_{plant}$ is the plant albedo (set at 0.23), and $cov_{sol}$ is the soil cover index. The soil cover index is calculated

$cov_{sol}=exp(-5.0X10^{-5}*CV)$ 1:1.2.16

where $CV$ is the aboveground biomass and residue ( $kg ha^{-1}$ ).

Net Long-Wave Radiation

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

$H_R=\varepsilon*\sigma*T_K^{4}$ 1:1.2.17

where $H_R$ is the radiant energy ( $MJ m^{-2} d^{-1})$ , is the emissivity, is the Stefan-Boltzmann constant ( $4.903 10^{-9} MJ m^{-2} K^{-4} d^{-1})$ , and $T_K$ 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):

$H_b=f_{cld}*(\varepsilon_a -\varepsilon_{vs})*\sigma*T_K^{4}$ 1:1.2.18

where $H_b$ is the net long-wave radiation ( $MJ m^{-2} d^{-1}$ ), $f_{cld}$ 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, $f_{cld}$ :

$f_{cld}=a*\frac{H_{day}}{H_{MX}}-b$ 1:1.2.19

where $a$ and $b$ are constants, $H_{day}$ is the solar radiation reaching the ground surface on a given day ( $MJ m^{-2}d^{-1}$ ), and $H_{MX}$ is the maximum possible solar radiation to reach the ground surface on a given day ( $MJ m^{-2}d^{-1}$ ). 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):

$\varepsilon'=\varepsilon_a-\varepsilon_{vs}=-(a_1+b_1*\sqrt(e))$ 1:1.2.20

where $a_1$ and $b_1$ are constants and $e$ 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:

$H_b=-[a*\frac{H_{day}}{H_{MX}}-b]*[a_1+b_1*\sqrt(e)]*\sigma*T_k^4$ 1:1.2.21

Experimental values for the coefficients $a,b,a_1$ and $b_1$ are presented in Table 1:1.3. The default equation in SWAT+ uses coefficient values proposed by Doorenbos and Pruitt (1977):

$H_b=-[0.9*\frac{H_{day}}{H_{MX}}+0.1]*[0.34-0.139\sqrt(e)]*\sigma*T_k^4$ 1:1.2.22

Table 1:1-3: Experimental coefficients for net long-wave radiation equations (from Jensen et al., 1990).

Region

(a,

(a1,

b1)

Table 1:1-4: SWAT+ input variables used in net radiation calculations.

Variable Name

Definition

File Name