254
C. Simmer
11.3.1 Solar and thermal infrared
From Fig. 11.2 we see that scattering processes at all atmospheric hydrometeors is important
in the solar and thermal IR, and that we have to apply Mie-theory in any case. Although the
extinction coefficients of clouds in the visible are not very different from those in the thermal
infrared (Fig. 11.3), clouds are more opaque in the infrared. In the visible the imaginary part
of the index of refraction mil is very low (Tab. 11.1) giving rise to a single scattering albedo
Wo (fraction of the extinction coefficient caused by scattering) close to unity. In the IR mil is
much higher causing Wo to decrease down to values of 0.5. Thus, after only a few scattering
events any infrared photon will be absorbed by the cloud particles while there are still high
chances for a visible photon to escape the cloud. The opacity of clouds in the IR enables the
quite accurate determination of its top temperature in the thermal infrared window.
But from the above it is obvious that it is impossible to sense rain from satellites directly in
the visible or thermal infrared regions. The rain generating cloud will almost always shield
very effectively the rain it produces from the satellite view. But the rain producing cloud will
be detectable against the cloud-free atmosphere due to its much higher optical depth. Thus
rain intensity must always be completely indirectly inferred from the cloud parameters we are
able to sense, like its reflectivity in the solar spectral range, which is dependent on the cloud
liquid water and on the cloud drop radius (clouds with smaller droplets are brighter because
small droplets scatter visible radiation more effectively), and its top temperature, which can
be measured in the thermal infrared because of their high opacity.
11.3.2 Microwaves
In the microwaves both clouds and rain have optical depths much lower than clouds in the
visible and thermal infrared (Fig. 11.3). It follows that except for very high rain intensities
cloudy and rain-bearing areas will not be deliniated in satellite images as sharply as clouds are
in the visible and thermal infrared. The signal reaching the satellite sensor will be influenced
also by the interior of the raining cloud, which is a desirable effect if we want to retrieve
precipiation.
Scattering in clouds is small in most of the microwave region (Fig. 11.2) and can often be
neglected without large errors. For frequencies up to about 50 GHz scattering at raindrops
can be adequately described by Rayleigh scattering characterized by a phase function which
is symmetric in the forward and backward directions (Fig. l1.4a,b). At higher frequencies
forward scattering increases (Fig. ll.4c,d), and Mie-theory must be applied. For ice particles,
but also for large raindrops, the particles differ from ideal spheres and become complicated
computationally. Ray-tracing methods which are used in the visible where the hydrometeors
are much larger than the wavelength cannot be used in the Mie-regime.
Over large parts of the microwave region the refractive index of water increases with decreasing
temperature. This leads to an increasing mass absorption coefficient with cloud height (Fig.
11.5). This behaviour counteracts the effect of decreasing thermal emission caused by the
temperature decrease with height. Thus radiances at frequencies below 50 GHz measured
above non-raining clouds are largely independent of the vertical distribution of cloud water and
enable the retrieval of integrated cloud water content in this spectral region (e.g. Karstens et
al., 1994). Emission by cirrus clouds is very small (Fig. 11.5) and can be neglected in most
cases.
Compared to the non-raining clouds rain droplet spectra lead to much higher mass extinction
coefficients than non-raining clouds and a drastic increase of the scattering coefficient (Fig.
C. Simmer
11.3.1 Solar and thermal infrared
From Fig. 11.2 we see that scattering processes at all atmospheric hydrometeors is important
in the solar and thermal IR, and that we have to apply Mie-theory in any case. Although the
extinction coefficients of clouds in the visible are not very different from those in the thermal
infrared (Fig. 11.3), clouds are more opaque in the infrared. In the visible the imaginary part
of the index of refraction mil is very low (Tab. 11.1) giving rise to a single scattering albedo
Wo (fraction of the extinction coefficient caused by scattering) close to unity. In the IR mil is
much higher causing Wo to decrease down to values of 0.5. Thus, after only a few scattering
events any infrared photon will be absorbed by the cloud particles while there are still high
chances for a visible photon to escape the cloud. The opacity of clouds in the IR enables the
quite accurate determination of its top temperature in the thermal infrared window.
But from the above it is obvious that it is impossible to sense rain from satellites directly in
the visible or thermal infrared regions. The rain generating cloud will almost always shield
very effectively the rain it produces from the satellite view. But the rain producing cloud will
be detectable against the cloud-free atmosphere due to its much higher optical depth. Thus
rain intensity must always be completely indirectly inferred from the cloud parameters we are
able to sense, like its reflectivity in the solar spectral range, which is dependent on the cloud
liquid water and on the cloud drop radius (clouds with smaller droplets are brighter because
small droplets scatter visible radiation more effectively), and its top temperature, which can
be measured in the thermal infrared because of their high opacity.
11.3.2 Microwaves
In the microwaves both clouds and rain have optical depths much lower than clouds in the
visible and thermal infrared (Fig. 11.3). It follows that except for very high rain intensities
cloudy and rain-bearing areas will not be deliniated in satellite images as sharply as clouds are
in the visible and thermal infrared. The signal reaching the satellite sensor will be influenced
also by the interior of the raining cloud, which is a desirable effect if we want to retrieve
precipiation.
Scattering in clouds is small in most of the microwave region (Fig. 11.2) and can often be
neglected without large errors. For frequencies up to about 50 GHz scattering at raindrops
can be adequately described by Rayleigh scattering characterized by a phase function which
is symmetric in the forward and backward directions (Fig. l1.4a,b). At higher frequencies
forward scattering increases (Fig. ll.4c,d), and Mie-theory must be applied. For ice particles,
but also for large raindrops, the particles differ from ideal spheres and become complicated
computationally. Ray-tracing methods which are used in the visible where the hydrometeors
are much larger than the wavelength cannot be used in the Mie-regime.
Over large parts of the microwave region the refractive index of water increases with decreasing
temperature. This leads to an increasing mass absorption coefficient with cloud height (Fig.
11.5). This behaviour counteracts the effect of decreasing thermal emission caused by the
temperature decrease with height. Thus radiances at frequencies below 50 GHz measured
above non-raining clouds are largely independent of the vertical distribution of cloud water and
enable the retrieval of integrated cloud water content in this spectral region (e.g. Karstens et
al., 1994). Emission by cirrus clouds is very small (Fig. 11.5) and can be neglected in most
cases.
Compared to the non-raining clouds rain droplet spectra lead to much higher mass extinction
coefficients than non-raining clouds and a drastic increase of the scattering coefficient (Fig.