> For the complete documentation index, see [llms.txt](https://swatplus.gitbook.io/io-docs/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://swatplus.gitbook.io/io-docs/~/changes/GiVD5ID0WVyRIAumaMy2/theoretical-documentation/untitled/solar-radiation/daily-net-radiation.md). # 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 $$(1-\alpha)\*H\_{day}$$ . 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: $$H\_R=\varepsilon\*\sigma\*T\_K^{4}$$ 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$$ 1:1.2.22 Table 1:1-3: Experimental coefficients for net long-wave radiation equations (from Jensen et al., 1990).
Region(a,b)(a1,b1)
Davis, California(1.35,-0.35)(0.35,-0.145)
Southern Idaho(1.22,-0.18)(0.325,-0.139)
Englandnot availablenot available(0.47,-0.206)
Englandnot availablenot available(0.44,-0.253)
Australianot availablenot available(0.35,-0.133)
General(1.2-0.2)(0.39,-0.158)
General-humid areas(1.00.0)
General-semihumid areas(1.1-0.1)
Table 1:1-4: SWAT+ input variables used in net radiation calculations. | Variable Name | Definition | File Name | | ------------- | ----------------------------------------------------------------------------- | --------- | | SOL\_ALB | $$\_{soil}$$: moist soil albedo | .sol | | MAX TEMP | $$T\_{mx}$$: Daily maximum temperature (C) | .tmp | | MIN TEMP | $$T\_{mn}$$: Daily minimum temperature (C) | .tmp | | SOL\_RAD | $$H\_{day}$$: Daily solar radiation reaching the earth’s surface (MJ m-2 d-1) | .slr |