The incoming short wave radiation can be estimated based on several formulae. If the 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 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 |