# 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 ($$MJ m^{-2} d^{-1}$$), $$H\_b$$ is the net incoming long-wave radiation ($$MJ m^{-2} d^{-1}$$) 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 $$(1-\alpha) H\_{day}$$. 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 $$\alpha\_{soil}$$ 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 $$\alpha\_{plant}$$ 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 ($$kg ha^{-1}$$).
### 1:1.2.5.2 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 ($$MJ m^{-2} d^{-1})$$, $$\varepsilon$$ is the emissivity, $$\sigma$$ 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 + $$\degree C$$). 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, $$\varepsilon\_a$$ is the atmospheric emittance, and $$\varepsilon\_{vs}$$ 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 $$\varepsilon'$$. 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$$ 1:1.2.22
Table 1:1-3: Experimental coefficients for net long-wave radiation equations (from Jensen et al., 1990).
| Region | (a, | b) | (a1, | b1) |
|---|
| Davis, California | (1.35, | -0.35) | (0.35, | -0.145) |
| Southern Idaho | (1.22, | -0.18) | (0.325, | -0.139) |
| England | not available | not available | (0.47, | -0.206) |
| England | not available | not available | (0.44, | -0.253) |
| Australia | not available | not available | (0.35, | -0.133) |
| General | (1.2 | -0.2) | (0.39, | -0.158) |
| General-humid areas | (1.0 | 0.0) | | |
| General-semihumid areas | (1.1 | -0.1) | | |
Table 1:1-4: SWAT+ input variables used in net radiation calculations.
| Definition | Source Name | Input Name | Input File |
| -------------------------------------------------------------------------------------- | ----------- | ---------- | --------------------------------------------------------------------------------- |
| $$\alpha\_{soil}$$: moist soil albedo | alb | alb | [soils.sol](/io-docs/introduction-1/soils/soils.sol.md) |
| $$T\_{mx}$$: Daily maximum temperature ($$\degree C$$) | max temp | tmpmax | [.tmp](/io-docs/introduction-1/climate/tmp.cli-and-temperature-data-files.md) |
| $$T\_{mn}$$: Daily minimum temperature ($$\degree C$$) | min temp | tmpmin | [.tmp](/io-docs/introduction-1/climate/tmp.cli-and-temperature-data-files.md) |
| $$H\_{day}$$: Daily solar radiation reaching the earth’s surface ($$MJ m^{-2}d^{-1}$$) | solrad | slr | [.slr](/io-docs/introduction-1/climate/slr.cli-and-solar-radiation-data-files.md) |
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