====== Incoming short-wave radiation ======

The incoming short wave radiation can be estimated based on several formulae. If the [[en:hydro:extraterrestrial-radiation|solar radiation at the exterior of the atmosphere]] $I_o$ is known, the incoming short wave radiation can be estimated based on an empirical formula of Black et al 1954:

$$ Q_s = I_o*(0.803-0.340*C-0.458*C^2)$$

where $C$ is the mean monthly cloudiness as decimal fraction and $I_o$ is the [[en:hydro:extraterrestrial-radiation|extraterrestrial-radiation]] for the whole month in cal/cm²/day.

Another method of estimating $Q_s$ is by means of the equation:

$$ Q_s = I_o * \left (a+b* \frac{n } {N }  \right )$$

where $a,b$ are empirical constants, $n$ are observed duration of sunshine hours per day and $N$ are maximum possible duration of sunshine hours.

^ Location         ^ a                        ^ b                           ^ Source                  ^
| World             | 0.23                   | 0.48                     | Black et al. 1954 |
| World             | 0.23*cos $\lambda$  | 0.52         | Glover and McCulloch 1958 |
| S.E. England  | 0.18                   | 0.55                     | Penman 1948 |
| Virgina U.S.A | 0.22                   | 0.54                     | in Penman 1948 |
| Canberra Australia | 0.25         | 0.54                     | in Penman 1948 |
| Brisbane Australia | 0.23 to 0.35 | 0.38 to 0.54   | Cartledge 1973 |
| West Africa     | -0.12 to 0.26   | 0.99 to 0.50       | Davies 1966 |