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# 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.