Chapter 3
Longwave (IR) Radiation Model
3.0 Introduction
The net longwave radiation at the surface is an important component of any surface
energy budget model. Unfortunately, measurements of the net longwave radiation
(upwelling longwave radiation and downwelling longwave radiation) are not readily
available. Therefore, it is necessary to use parameters that are available and simple
models to calculate the upwelling and downwelling longwave radiation at the surface.
The net longwave radiation is a function of atmospheric conditions, especially cloud
conditions, and the surface optical and physical properties.
3.1 Downwelling Longwave Radiation
One of the major components to the downwelling radiation at the surface is the
atmosphere. Most of the downwelling atmospheric radiation originates in the lower
atmosphere (below altitudes of several kilometers) where the absolute humidity is
relatively high. The component ( Iicrl↓ ) for a clear sky is calculated from
r
Iicrl↓ = ε aσ Ta
4
r
(3.1)
and σ (5.669 108 W/m2⋅ K4) is the Stefan-Boltzmann constant. The effective
atmospheric emissivity is calculated from Crawford et al. (1999)
(1 7)
ε a = 1.24 * ( ea / Ta ) .
(3.2)
ea is the vapor pressure in millibars and can be found from
e
RH ≈ 100 a
(3.3)
eas
where RH is the relative humidity in percent and
⎡ l ⎛ 1 1 ⎞⎤
eas = eso exp ⎢ ⎜ - ⎟⎥
(3.4)
⎣ Rv ⎝ To Ta ⎠⎦
is the saturated vapor pressure. eso is the saturated vapor pressure at standard conditions
( ≈ 6.11 mbars), l is the temperature-dependent latent heat of condensation (sublimation),
Rv is the gas constant for water vapor, and T0.is the standard temperature (273.15 C).
For cloudy skies the downwelling flux ( Iicrl↓ ) is given as
d
Iicrl↓ = cl χ l + ceff χ m + ceff χ h
d
m
h
(3.5)
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