Proceedings - C-SRNWP Project

aerosols was neglected, i.e. cloud free parts of layers were completely transparent. In solar
band, both diffuse fluxes and direct solar flux took part, but there was no emission. There
isn’t any direct flux in thermal band, where on the other hand emission takes place. Thermal
computations assumed isothermal profile with reference temperature.
In idealized simulations, cloud was illuminated from one side by direct flux (solar band) or
diffuse flux (thermal band) and radiative transfer was computed wavelength by wavelength.
Resulting monochromatic fluxes were then summed up to get reference broadband values.
Next step was to find such broadband values k abs , k scat , which would give the same broadband
fluxes as the reference monochromatic computations. In special case of single homogeneous
cloud layer (and cosine of solar zenithal µ 0 = 0.5), inversion of outgoing broadband fluxes to
saturated coefficients k abs , k scat could be done analytically. Having both saturated and
unsaturated values of absorptions and scattering coefficients, it was possible to determine
saturation factors c abs , c scat defined as their ratios (c abs = k abs / k abs 0 , c scat = k scat /k scat 0 ).
In the heart of the new parameterization there is expressing the saturation factors c abs , c scat as
functions of unsaturated cloud optical depth. These dependencies were fitted on sample of 1-
layer homogeneous clouds. Results for solar band are shown on figures 1. They were obtained
for 5 values of solar zenithal angle θ 0 (with cos(θ 0 )=µ 0 =0.1,0.3,0.5,0.7,0.9) It can be seen that
dependency is quite sharp in wide range of cloud optical depths and can be fitted with simple
function (blue line on the plots). Moreover, dependency on solar zenithal angle is rather weak
and it does not cause too much extra spread. In thermal band dependency becomes much less
sharp for bigger optical depths (not shown), but this does not pose a serious problem since in
such situation fluxes are close to blackbody radiation.
Figure 1: Dependency of saturation factors c abs (left) and c scat (right) on unsaturated optical depth in solar band.
Sample of homogeneous clouds, solar band, 5 solar zenithal angles. Red dots -liquid clouds, blue dots - ice
clouds, black dots - mixed cloud, blue lines -fitted dependencies.
Afterwards, dependency of saturation factors c abs , c scat obtained on sample of 1-layer
homogeneous clouds was tested in more complex environment, using samples of multi-layer
inhomogeneous clouds and multi-layer clouds with nontrivial geometry (in this case concept
of cloud optical depth had to be generalized, in order to account for cloud geometry).
Broadband fluxes leaving the cloud in parameterized version were compared against their
reference values computed wavelength by wavelength. This approach enables avoiding the
inversion of broadband fluxes to saturated coefficients k abs , k scat in multi-layer case, which
would have to be done numerically and becomes extremely costly. Performance of the old and
new schemes is compared on figures 2, showing parameterized versus reference total cloud
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