# 1:3.4.3.2 Solar Radiation

The continuity equation relates average daily solar radiation adjusted for wet or dry conditions to the average daily solar radiation for the month:

$$\mu rad\_{mon}\*days\_{tot}=\mu Wrad\_{mon}\*days\_{wet}+\mu Drad\_{mon}\*days\_{dry}$$                                             1:3.4.19

where $$\mu rad\_{mon}$$ is the average daily solar radiation for the month (MJ m$$^{-2}$$), $$days\_{tot}$$ are the total number of days in the month, $$\mu Wrad\_{mon}$$ is the average daily solar radiation of the month on wet days (MJ m$$^{-2}$$), $$days\_{wet}$$ are the number of wet days in the month, $$\mu Drad\_{mon}$$ is the average daily solar radiation of the month on dry days (MJ m$$^{-2}$$), and $$days\_{dry}$$ are the number of dry days in the month.

The wet day average solar radiation is assumed to be less than the dry day average solar radiation by some fraction:

$$\mu Wrad\_{mon}=b\_R\*\mu Drad\_{mon}$$                                                                                                                      1:3.4.20

where $$\mu Wrad\_{mon}$$ is the average daily solar radiation of the month on wet days (MJ m$$^{-2}$$), $$\mu Drad\_{mon}$$ is the average daily solar radiation of the month on dry days (MJ m$$^{-2}$$), and $$b\_R$$ is a scaling factor that controls the degree of deviation in solar radiation caused by the presence or absence of precipitation. The scaling factor, $$b\_R$$, is set to 0.5 in SWAT+.

To calculate the dry day average solar radiation, equations 1:3.4.19 and 1:3.4.20 are combined and solved for $$\mu Drad\_{mon}$$:

$$\mu Drad\_{mon}=\frac{\mu rad\_{mon}*days\_{tot}}{b\_R*days\_{wet}+days\_{dry}}$$                                                                                                                        1:3.4.21

Incorporating the modified values into equation 1:3.4.12, SWAT+ calculated the solar radiation on a wet day using the equation:

$$H\_{day}=\mu Wrad\_{mon}+\chi\_i(3)\*\sigma rad\_{mon}$$                                                                                                    1:3.4.22

and the solar radiation on a dry day using the equation:

$$H\_{day}=\mu Drad\_{mon}+\chi\_i(3)\*\sigma rad\_{mon}$$                                                                                                      1:3.4.23

Table 1:3-4: SWAT+ input variables that pertain to generation of temperature and solar radiation.

| Definition                                                                                    | Source Name | Input Name    | Input File                                                                                    |
| --------------------------------------------------------------------------------------------- | ----------- | ------------- | --------------------------------------------------------------------------------------------- |
| Temperature input: 'sim' for simulated or gage name                                           | tgage       | tmp           | [weather-sta.cli](https://swatplus.gitbook.io/io-docs/introduction-1/climate/weather-sta.cli) |
| Solar radiation input: 'sim' for simulated or gage name                                       | sgage       | slr           | [weather-sta.cli](https://swatplus.gitbook.io/io-docs/introduction-1/climate/weather-sta.cli) |
| $$\mu mx\_{mon}$$: average maximum air temperature for month ($$\degree C$$)                  | tmpmx       | tmp\_max\_ave | [weather-wgn.cli](https://swatplus.gitbook.io/io-docs/introduction-1/climate/weather-wgn.cli) |
| $$\sigma mx\_{mon}$$: standard deviation for maximum air temperature in month ($$\degree C$$) | tmpstdmx    | tmp\_max\_sd  | [weather-wgn.cli](https://swatplus.gitbook.io/io-docs/introduction-1/climate/weather-wgn.cli) |
| $$\mu mn\_{mon}$$: average minimum air temperature for month ($$\degree C$$)                  | tmpmn       | tmp\_min\_ave | [weather-wgn.cli](https://swatplus.gitbook.io/io-docs/introduction-1/climate/weather-wgn.cli) |
| $$\sigma mn\_{mon}$$: standard deviation for minimum air temperature in month ($$\degree C$$) | tmpstdmn    | tmp\_min\_sd  | [weather-wgn.cli](https://swatplus.gitbook.io/io-docs/introduction-1/climate/weather-wgn.cli) |
| $$\mu rad\_{mon}$$: average daily solar radiation for month (MJ m$$^{-2}$$)                   | solarav     | slr\_ave      | [weather-wgn.cli](https://swatplus.gitbook.io/io-docs/introduction-1/climate/weather-wgn.cli) |
| $$days\_{wet}$$: average number of days of precipitation in month                             | pcpd        | pcp\_days     | [weather-wgn.cli](https://swatplus.gitbook.io/io-docs/introduction-1/climate/weather-wgn.cli) |