3.3 Potential Modification
As indicated above, there are no provisions for handling inversions and optically thin
clouds. With this in mind, it is feasible to recast the formulation of the cloud radiance and
the attenuation of the cloud-emitted radiance in terms of parameters that would be readily
available. It should be remembered that the proposed approach is only a surrogate for a
more complete representation of cloud and atmospheric processes that account for the
downwelling radiance at the surface. To accurately model these more complicated
processes, it is necessary to have atmospheric profiles of temperature and moisture plus
profiles of the cloud optical properties, parameters that are not readily available. The
proposed model is based on the following assumptions:
1. Low and middle clouds are optically thick. This implies the cloud emissivity is one,
while the cloud reflection and transmission are zero. It also implies that clouds radiate
at the cloud base temperature. This assumption is not true for ice clouds and some of
the thinner stratus type clouds found over ocean areas. Ice clouds, because of their
relatively cold temperatures, do not contribute significant amounts of downwelling
radiance. For high clouds (ice clouds), an emissivity of less than one would be used.
2. The lower atmosphere contributes the greatest amount of clear sky radiance and
causes the greatest amount of attenuation of the cloud-emitted radiance. This implies
that an effective atmospheric emissivity can be computed from the ambient relative
humidity (or vapor pressure).
3. Cloud overlap, for multi-layered cloud systems, is governed by the principle of
random overlap. In reality the dynamic atmospheric processes most likely govern the
overlap. If the dynamic processes are synoptic scale in nature, they influence the
atmosphere from the surface to the tropopause and above. In this case, the multi-
layered clouds are most likely correlated.
The general equation for the downwelling radiation can be given as
Iir↓ = ε aσ Ta + (1 - ε a )clσ Tcl + (1 - ε a )ceff σ Tcm + (1 - ε a )ceff σ Tch .
m
h
(3.13)
The effective atmospheric emissivity and effective middle and high cloud cover are
calculated as indicated above. The cloud radiating temperature is calculated as follows:
Tc(l ,m,h) = Ta + Γ(lat, season, z)Z
(3.14)
where Γ(lat, season, z) is the integrated atmospheric lapse rate and is a function of
station location (latitude), season, and cloud base altitude. The lapse rate can be obtained
from the Geophysics Laboratory model atmospheres or from the Atmospheric Circulation
Statistics model atmospheres of Oort and Rasmusson (1971). The Geophysics Laboratory
model atmospheres is stratified into three latitude zones and two seasons, while the
Atmospheric Circulation Statistics model atmospheres is stratified by month and five
degree latitude bands. For each latitude zone and each time period, the integrated lapse
rate could be computed for the altitude range 01 km, 02 km, 03 km, and 010 km. In
addition, the atmospheric profile could be adjusted in the lower levels of the atmosphere
to be consistent with the observed ambient temperature and humidity. The cloud height,
if not available from observations, can be specified in a physically consistent manner
with the model vertical temperature profiles.
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