The Satterlund equation was developed to achieve better agreement between calculated and measured values of longwave radiation. Two equations for estimating radiation used at the time, Idso and Jackson, 1969 and Brutsaert, 1975, were found to yield large differences in comparison to measured radiation at temperatures below 0°C.

The equation meets 3 physical criteria that were not satisfied by other existing equations at the time of Satterlund's work:

  1. It does not yield a value in excess of ideal black body radiation at any temperature or humidity extreme,
  2. It takes both temperature and humidity into account
  3. It does not yield values lower than those due to the CO2 content of the air.

To ensure the carbon dioxide constraint was met, a variable exponent of vapor pressure was needed in the emissivity, ε, term of the new equation:

\epsilon = 1-e(-e_0^{\frac{T_A}{b}})

where 

e_0 is the screen vapor pressure in millibars,

T_A is the screen air temperature in Kelvin and

b is an empirical constant equal to 2016

This emissivity term is used in the final form of the Satterlund equation for longwave radiation, R_a:

R_a=(\sigma T_A^4)1.08[1-e(-e_0^{\frac{T_A}{b}})]

where 

\sigma is the Stefan-Boltzmann constant, 5.6703728287x10-8 \frac{W}{m^2*K^4}

Required Parameters

Values for a temperature and emissivity coefficient are required for this method. A default value for the temperature coefficient, b, is 2016 Kelvin and is provided for the user. The emissivity coefficient is included for calibration purposes, however the default value of 1.08 is widely used. Temperature, Windspeed, and Dew Point methods must be selected in the Meteorologic Model.