# 1:3.4.2 Generated Values

The daily generated values are determined by multiplying the residual elements generated with equation 1:3.4.1 by the monthly standard deviation and adding the monthly average value.

$$T\_{mx}=\mu mx\_{mon} + \chi\_i(1)\*\sigma mx\_{mon}$$                                                                                                             1:3.4.10

$$T\_{mn}=\mu mn\_{mon} + \chi\_i(2)\*\sigma mn\_{mon}$$                                                                                                             1:3.4.11

$$H\_{day}=\mu rad\_{mon} + \chi\_i(3)\*\sigma rad\_{mon}$$                                                                                                          1:3.4.12

where $$T\_{mx}$$ is the maximum temperature for the day ($$\degree C$$), $$\mu mx\_{mon}$$ is the average daily maximum temperature for the month ($$\degree C$$), $$\chi\_i(1)$$ is the residual for maximum temperature on the given day, $$\sigma mx\_{mon}$$ is the standard deviation for daily maximum temperature during the month ($$\degree C$$), $$T\_{mn}$$ is the minimum temperature for the day ($$\degree C$$), $$\mu mn\_{mon}$$ is the average daily minimum temperature for the month ($$\degree C$$), $$\chi\_i(2)$$ is the residual for minimum temperature on the given day, $$\sigma mn\_{mon}$$ is the standard deviation for daily minimum temperature during the month ($$\degree C$$), $$H\_{day}$$ is the solar radiation for the day (MJ m$$^{-2}$$), $$\mu rad\_{mon}$$ is the average daily solar radiation for the month (MJ m$$^{-2}$$), $$\chi\_i(3)$$ is the residual for solar radiation on the given day, and $$\sigma rad\_{mon}$$ is the standard deviation for daily solar radiation during the month (MJ m$$^{-2}$$).

The user is required to input standard deviation for maximum and minimum temperature. For solar radiation the standard deviation is estimated as ¼ of the difference between the extreme and mean value for each month.

$$\sigma rad\_{mon}=\frac{H\_{mx}-\mu rad\_{mon}}{4}$$                                                                                                                                    1:3.4.13

where $$\sigma rad\_{mon}$$ is the standard deviation for daily solar radiation during the month (MJ m$$^{-2}$$), $$H\_{mx}$$ is the maximum solar radiation that can reach the earth’s surface on a given day (MJ m$$^{-2}$$), and $$\mu rad\_{mon}$$ is the average daily solar radiation for the month (MJ m$$^{-2}$$).