====== Net longwave radiation ======

Net long wave radiation can be estimated using the Brunt equation:

$$Q_{lw} = \sigma * \left [ {T_s}^4-(c+d*\sqrt[2]{e_2})*{T_2}^4 \right ]*(1-a*C)$$

where $\sigma$ is the Boltzmann constant that equals $1.17 * 10^{-7} cal/cm^2/K^4/day$, $T_s$ is the temperature of the surface in Kelvin, $T_2$ is the temperature at the 2 m level, $e_2$ is the vapor pressure of the air at the 2 m level (mb), $c,d$ are empirical coefficients, $C$ is the cloudiness (decimal fraction of the sky covered) and $a$ is a constant depending upon cloud type, 0.25, 0.6 and 0.9 for high, medium and low clouds, respectively.

The constants $c$ and $d$ have been compiled:

^ Location         ^ c                        ^ d                           ^
| Sweden          | 0.43                   | 0.082                   |
| Washington   | 0.44                   | 0.061                   |
|Austria            | 0.47                    | 0.063                   | 
|Algeria            | 0.48                    | 0.058                   | 
|California       | 0.50                    | 0.032                   | 
|England          | 0.53                    | 0.065                   | 
|France            | 0.60                    |0.042                    | 
|India               | 0.62                    |0.029                    | 
|Oklahoma     | 0.68                     |0.036                    | 

If data on cloud type are not available, the last term of the equation $(1-aC)$ can be replaced by $(0.10+0.9*C)$ or by $\left ( 0.10+0.9*\frac{n}{N} \right )$, where the ratio $n/N$ corresponds to the ratio of actual to potential sunshine hours per day.

There is an alternative equation that does not require surface temperature:

$$Q_{lw} = \sigma*{T_2}^4* \left ( 0.56-0.08*\sqrt[2]{e_2} \right ) * \left ( 1-a*C \right ) $$

where $T_2$ is in Kelvin and $e_2$ is in mb.