Incoming longwave radiation

Incoming longwave radiation is given by:

\[ LWR_{in} = \varepsilon \sigma T^4 \; , \]

wherein \( \varepsilon, \sigma, T \) refer to the emissivity, the Stefan-Boltzmann constant and air temperature, respectively.

The emissivity \( \varepsilon \) has two components , i.e., emissivity under clear ( \( \varepsilon_{cl} \)) and clouded sky ( \( \varepsilon_{cl} \)):

\[ \varepsilon = (1 - f_{cl}) \varepsilon_{cs} + f_{cl} \varepsilon_{cl} \]

The partitioning coefficient \( f_{cl} \) refers to the cloud fracion. For \( \varepsilon_{cl} \), a constant value of 0.976 is used [20].

Clear sky atmospheric emissivity
Emissivity of incoming longwave radiation under clear sky conditions is calculated based on vapour pressure \( vp \) [7] :

\[ \varepsilon_{cs} = B_c + B_d \sqrt{vp} \]

The parameters \( B_c \) and \( B_d \) are set to 0.53 and 0.212, respectively [58].

Cloudiness
Cloudiness is derived from global radiation using the Angstrom formular:

\[ f_{cl} = \frac{\frac{SWR}{SWR^{\ast}} - A}{B} \]

using the Angstrom parameters \( A = 0.29 \) and \( B = 0.52 \) [58].

Table of Contents

Incoming longwave radiation