of the earth-atmosphere is normally less than unity, so
there is significant reflection and a significant surface component to the radiance
measured at the satellite. Variations in surface emissivity must be taken into account in
using microwave radiances to derive soundings. However, as noted earlier, the fact that
clouds are largely transparent to microwave radiation means that microwave sensors, both
active and passive, provide an all-weather remote sounding capability. The Rayleigh-Jeans approximation
due to long microwave wavelengths holds in the
microwave so that the Planck function may be approximated by a linear function of
temperature:
Noting that emissivity is defined as the ratio of emitted radiance to that from an ideal blackbody then
Therefore a brightness temperature may be defined in terms of emissivity and blackbody temperature T, as follows:
The brightness temperature is the blackbody temperature corresponding to the radiance
.Emissivity (and hence reflectivity) is a complicated function of the dielectric constant of a substance, and also depends on surface roughness and the angle of incident radiation.
A natural consequence of microwave emission from rain, and the difference in microwave emissivity between rain (
~ 0.9) and oceans (~ 0.5), is that passive microwave measurements from
satellites can be used to estimate rainfall rates, especially over oceans. The success of
these techniques relies on the different microwave electromagnetic signature of rain
compared to the background radiation from land or ocean. Observed brightness temperatures
from the ocean appear relatively cold, whereas the brightness temperature over a rain area
is much higher. As a practical example, note that although in the 10 to 50 GHz region microwave emission can emanate from rain, surrounding non-raining clouds are largely transparent to this radiation. Microwave remote sensing therefore provides the potential of a more direct measurement of rainfall by satellite as distinct from the use of visible and infrared techniques which rely on indirect relationships between rainfall and cloud top height, for example.
The important area of microwave remote sensing estimation of precipitation is covered further in later lectures, and by Murphy et al (1987), Barrett and Martin (1981), and in references cited therein.
