# WEM | Water Engineering

Applied Ecohydrology

# 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.