Available Energy: Net Radiation and Soil Heat Flux - Transport in the Atmosphere-Vegetation-Soil Continuum - page 39

where e a is the water vapour pressure in hPa, and c 1 and c 2 are empirical constants
with standard values of 0.52 and 0.065 hPa 1/2 (but having ranges of 0.34-0.71 and
0.023-0.110, depending on location and season (Jiménez et al., 1987 )). In combina-
tion with Eq. ( 2.24 ) the expression for ε a,clear yields a model for the clear-sky long-
wave radiation L 0 .
For conditions with clouds, the total incoming longwave radiation can be param-
eterized as an interpolation between the clear sky emissivity and the emissivity of
clouds (equal to one):

ε = + − f ( 1 f ) ε (2.26)

a cloud cloud a,clear

where f cloud is the cloud fraction (Crawford and Duchon, 1999 ). It should be noted that
it depends on the height of the cloud base to which extent the air temperature at screen
level (as used in Eq. ( 2.24 )) is actually representative for the cloud temperature.

Question 2.12: Ozone and oxygen in the atmosphere absorb radiation mainly in the
shortwave region (see Figure 2.2 ). At what wavelengths is the absorbed energy emitted
again?

Question 2.13: Of the total radiation emitted by clouds, only the part inside the atmo-
spheric window reaches the ground. Consider Figure 2.14a .
a) If we assume that around 9 UTC the temperature of the lower atmosphere is iden-
tical on May 22 and May23, then how large is the contribution of the clouds to the
longwave incoming radiation?
b) At a temperature representative of the temperature of the lower atmosphere, a black
body emits roughly 35% of its radiation in the wavelength range of the atmospheric
window. What is the temperature of clouds on May 22?

Question 2.14: Consider the observations of downwelling longwave radiation in
Figure 2.14a . On May 22 and 23, the air temperatures at screen level at 12 UTC were 19.0 °C
and 19.5 °C. At those moments the relative humidity was 88% and 49%, respectively.
a) Compute the atmospheric emissivity for both days at 12 UTC.
b) Estimate the atmospheric emissivity for both days based on Eqs. ( 2.25 ) and ( 2.26 ).
c) Evaluate the error due to the use of the empirical emissivity of answer (b) in both
downwelling longwave radiation and the net longwave radiation (upwelling long-
wave radiation is given in Figure 2.14b ).

2.2.5 Emitted (and Relected) Longwave Radiation
In good approximation Earth's surface behaves as a grey-body in the longwave part
of the spectrum. Consequently, the longwave radiation emitted by the surface can by
approximated as

↑ ≈ εσ 4

(2.27)

L T

e s s

in which ε s is the broadband emissivity of the surface in the longwave wavelength
region and T s is the surface temperature (in K).