266
C. Simmer
Corrected Temperature (PCT) which can be approximated independently of the observing
frequency by:
peT = 1.818Tv - 0.818TH
(11.11)
peT can be interpreted as the radiation temperature of the lower troposphere if it were a
blackbody. Thus in the case of no scatterers peT has an almost constant value close to the
thermodynamic temperature of the top of the lower troposphere, which can be estimated by
climatological means. Scattering reduces peT below these climatological values. The difference
between actual peT and the climatological value can then be used as an index for precipitation.
Petty and Katsaros (1990b) derived from similar principles a scattering index 3, which they
define with the help of the normalized polarization pI by:
3 = P'TV,clear + (1 - Pl)To - Tv
(11.12)
with Tv the measured vertically polarized radiation temperature, TV,clear the clear sky temperature derived from surrounding measurements, and To the hypothetical (unpolarized) radiation
temperature of an opaque boundary layer without rain induced scattering. 3 can be interpreted
approximately as the peT depression caused by scattering (Petty, 1994a) and has to be related
to the rainrate by assumptions about the vertical structure of the hydrometeor profile. Petty
and Katsaros (1990b) used the simple relation RR = 0.25(3 - 10).
Finally, Grody (1991) has derived a scattering index for 85 GHz of similar interpretation by
first predicting the radiation temperature without scatterers using a statistical relation based
on the 19 GHz and 22 GHz channels of SSM/I which are only weakly influenced by scattering.
The relation used by Adler et al. (1993):
RR = (251 - Ts5H)
4.91
(11.13)
can be interpreted as a simplification of this concept by assuming a fixed non-scatter radiation
temperature for 85 GHz. A prerequisite for this algorithm is a screening algorithm which
separates raining from non-raining conditions (see below).
11.6.6 Special problems of microwave-based rainfall determination
over land surfaces
Over land surfaces the surface emittance is much higher (0.80-0.95) than over water surfaces.
Thus the effective radiation temperature of the surface is very similar to the effective temperature of the atmosphere. Also the polarization of rain-free areas is already low. From this
follows that emission and attenuation/polarization methods are difficult to apply, and the less
direct scattering methods must be used.
Since the surface emittance depends on surface structure, vegetation, soil moisture, the surface
signal is very variable and screening algorithms, which differentiate between rain and no-rain
cases, are very important. At present these screening algorithms have decision-tree structure
with partially surface and season dependent thresholds applied to individual radiation temperatures, polarization, spectral gradients, and scattering indices (e.g. Grody, 1991).
11.7 Comparison of algorithm performance
When comparing the performance of satellite-based rain retrieval algorithms commonly three
problems are encountered:
C. Simmer
Corrected Temperature (PCT) which can be approximated independently of the observing
frequency by:
peT = 1.818Tv - 0.818TH
(11.11)
peT can be interpreted as the radiation temperature of the lower troposphere if it were a
blackbody. Thus in the case of no scatterers peT has an almost constant value close to the
thermodynamic temperature of the top of the lower troposphere, which can be estimated by
climatological means. Scattering reduces peT below these climatological values. The difference
between actual peT and the climatological value can then be used as an index for precipitation.
Petty and Katsaros (1990b) derived from similar principles a scattering index 3, which they
define with the help of the normalized polarization pI by:
3 = P'TV,clear + (1 - Pl)To - Tv
(11.12)
with Tv the measured vertically polarized radiation temperature, TV,clear the clear sky temperature derived from surrounding measurements, and To the hypothetical (unpolarized) radiation
temperature of an opaque boundary layer without rain induced scattering. 3 can be interpreted
approximately as the peT depression caused by scattering (Petty, 1994a) and has to be related
to the rainrate by assumptions about the vertical structure of the hydrometeor profile. Petty
and Katsaros (1990b) used the simple relation RR = 0.25(3 - 10).
Finally, Grody (1991) has derived a scattering index for 85 GHz of similar interpretation by
first predicting the radiation temperature without scatterers using a statistical relation based
on the 19 GHz and 22 GHz channels of SSM/I which are only weakly influenced by scattering.
The relation used by Adler et al. (1993):
RR = (251 - Ts5H)
4.91
(11.13)
can be interpreted as a simplification of this concept by assuming a fixed non-scatter radiation
temperature for 85 GHz. A prerequisite for this algorithm is a screening algorithm which
separates raining from non-raining conditions (see below).
11.6.6 Special problems of microwave-based rainfall determination
over land surfaces
Over land surfaces the surface emittance is much higher (0.80-0.95) than over water surfaces.
Thus the effective radiation temperature of the surface is very similar to the effective temperature of the atmosphere. Also the polarization of rain-free areas is already low. From this
follows that emission and attenuation/polarization methods are difficult to apply, and the less
direct scattering methods must be used.
Since the surface emittance depends on surface structure, vegetation, soil moisture, the surface
signal is very variable and screening algorithms, which differentiate between rain and no-rain
cases, are very important. At present these screening algorithms have decision-tree structure
with partially surface and season dependent thresholds applied to individual radiation temperatures, polarization, spectral gradients, and scattering indices (e.g. Grody, 1991).
11.7 Comparison of algorithm performance
When comparing the performance of satellite-based rain retrieval algorithms commonly three
problems are encountered: