# 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.

&#x20;                       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+.

&#x20;               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.

| Variable Name | Definition                                                                        | File Name |
| ------------- | --------------------------------------------------------------------------------- | --------- |
| TMPSIM        | Temperature input code: 1-measured, 2-generated                                   | file.cio  |
| SLRSIM        | Solar radiation input code: 1-measured, 2-generated                               | file.cio  |
| TMPMX(mon)    | $$\mu mx_{mon}$$: average maximum air temperature for month (°C)                  | .wgn      |
| TMPSTDMX(mon) | $$\sigma mx_{mon}$$: standard deviation for maximum air temperature in month (°C) | .wgn      |
| TMPMN(mon)    | $$\mu mn_{mon}$$: average minimum air temperature for month (°C)                  | .wgn      |
| TMPSTDMN(mon) | $$\sigma mn_{mon}$$: standard deviation for minimum air temperature in month (°C) | .wgn      |
| SOLARAV(mon)  | $$\mu rad_{mon}$$: average daily solar radiation for month (MJ m$$^{-2}$$)        | .wgn      |
| PCPD(mon)     | $$days_{wet}$$: average number of days of precipitation in month                  | .wgn      |

