FAO 56 Longwave Radiation

The FAO56 Method implements the algorithm detailed by Allen, Pereira, Raes, and Smith (1998). The algorithm calculates the solar declination and solar angle for each time interval of the simulation, using the coordinates of the subbasin, Julian day of the year, and time at the middle of the interval. The solar values are used to compute the clear sky radiation for each subbasin. The computed shortwave radiation is then divided by the calculated clear sky radiation to estimate the fraction of shortwave radiation reaching the ground. Finally, the fraction of shortwave radiation reaching the ground is combined with the vapor pressure to calculate a reduction to the downwelling longwave radiation based on the Stefan-Boltzmann equation. Shortwave radiation calculation details can be found here: FAO56 Shortwave Radiation

Longwave radiation emission is proportional to the absolute temperature raised to the fourth power. The relationship between temperature and net longwave radiation relies on the Stefan-Boltzmann law, however net energy  flux is decreased by absorption in the atmosphere by water vapor, clouds and carbon dioxide. Therefore, the Stefan-Boltzmann law is corrected by accounting for humidity and cloudiness with equation 39 in Food and Agriculture Organization Irrigation and Drainage Paper no. 56 for net longwave radiation, $//<![CDATA[ \begin{array}{l}R_n_l\end{array} //]]>$:

where

$//<![CDATA[ \begin{array}{l}\sigma\end{array} //]]>$ is the Stefan Boltzmann constant, 5.6703728287x10^-8 $//<![CDATA[ \begin{array}{l}\frac{W}{m^2*K^4}\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}T_m_a_x_,_K\end{array} //]]>$ is maximum absolute temperature during the 24-hour period

$//<![CDATA[ \begin{array}{l}T_m_i_n_,_K\end{array} //]]>$ is minimum absolute temperature during the 24-hour period

$//<![CDATA[ \begin{array}{l}e_a\end{array} //]]>$ is actual vapor pressure in kPa 

$//<![CDATA[ \begin{array}{l}R_s\end{array} //]]>$ measured or calculated solar radiation $//<![CDATA[ \begin{array}{l}W/m^2\end{array} //]]>$

$//<![CDATA[ \begin{array}{l}R_S_O\end{array} //]]>$ calculated clear-sky radiation $//<![CDATA[ \begin{array}{l}W/m^2\end{array} //]]>$

The $//<![CDATA[ \begin{array}{l}\frac{R_s}{R_s_o}\end{array} //]]>$ term must be less than or equal to 1.

Required Parameters

Temperature (or Dew Point Temperature) and a Windspeed methods must be selected in the Meteorologic Model. It is required to input the central meridian of the local time zone of the basin model area. There is currently no specification for the time zone so the meridian must be specified manually.  Meridians west of zero longitude should be specified as negative while meridians east of zero longitude should be specified as positive. A representative elevation for each subbasin is also required.