Retrieval of Precipitation from Satellites
265
Emission methods
A typical emission algorithm has been derived by Prabhakara et al. (1992):
RR = [exp{,B(W) (T37H - T*)}!.7 - l],(W)
(11.9)
with B, , and T* empirical functions of the total water vapour content W. The latter can
be derived quite accurately by microwave measurements. According to (11.9) the rain rate
increases monotonically but in a nonlinear fashion with increasing radiation temperature of the
37 GHz channel measurements. The threshold for the occurrance of rain T* on the 37 GHz
radiation temperature is assumed to be dependent on the state of the atmosphere itself, which
is parameterized by the amount of total water vapour in the atmospheric column.
Attenuation/polarization methods
The microwave radiation emanating from the ocean surface is radiatively cold and highly polarized. When the atmosphere becomes optically thick due to a raining cloud the signal becomes
less an less polarized. Thus the polarization difference at a fixed frequency,
P=Tv-TH
(11.10)
often simply called polarization, is an index for the transmittance of the atmosphere and thus
for the amount of hydrometeor extinction. It has the following properties:
• For the usual observation angle around 50° P is at least over water surface maximum for
an optically thin i.e. cloud-free atmosphere.
• P decreases both with increasing optical thickness of the atmosphere and with the area
covered by an optically thick cloud.
• P does not depend on scattering, because both polarizations are affected in the same way.
• The effect of near-surface wind and of the gas atmosphere on P can be reduced by
normalizing with the value of Pc/ear for the cloud-free environment obtained from nearby
observations: pI = P / Pc/ear.
• It can be shown that (e.g. Petty and Katsaros, 1990aj Petty, 1994a ) that pI ~ TO with
a between 1.5 and 2.
The higher the frequency the more the relation between the normalized polarization and the
rainrate will depend on the areal extend of the raining cell and not so much on the rainrate itself.
Thus the transformation of R' into a rainrate will also depend on the type of precipitation.
Scattering methods
Scattering algorithms are based on the assumption that precipitation is always produced with
the help of the ice phase via the Bergeron-Findeisen process. The precipitation-size ice particles
in the upper part of the raining cloud cause scattering of microwave radiation which leads to a
radiation temperature depression (Fig. 11.8), which is assumed to be a monotonic function of
the rain itensity. To derive the scattering-based depression the radiation temperatures without
precipitation size ice particles must be estimated. This idea has been put forward first by
Spencer (1986) and refined by Spencer et al. (1989) who derived the so-called Polarization
265
Emission methods
A typical emission algorithm has been derived by Prabhakara et al. (1992):
RR = [exp{,B(W) (T37H - T*)}!.7 - l],(W)
(11.9)
with B, , and T* empirical functions of the total water vapour content W. The latter can
be derived quite accurately by microwave measurements. According to (11.9) the rain rate
increases monotonically but in a nonlinear fashion with increasing radiation temperature of the
37 GHz channel measurements. The threshold for the occurrance of rain T* on the 37 GHz
radiation temperature is assumed to be dependent on the state of the atmosphere itself, which
is parameterized by the amount of total water vapour in the atmospheric column.
Attenuation/polarization methods
The microwave radiation emanating from the ocean surface is radiatively cold and highly polarized. When the atmosphere becomes optically thick due to a raining cloud the signal becomes
less an less polarized. Thus the polarization difference at a fixed frequency,
P=Tv-TH
(11.10)
often simply called polarization, is an index for the transmittance of the atmosphere and thus
for the amount of hydrometeor extinction. It has the following properties:
• For the usual observation angle around 50° P is at least over water surface maximum for
an optically thin i.e. cloud-free atmosphere.
• P decreases both with increasing optical thickness of the atmosphere and with the area
covered by an optically thick cloud.
• P does not depend on scattering, because both polarizations are affected in the same way.
• The effect of near-surface wind and of the gas atmosphere on P can be reduced by
normalizing with the value of Pc/ear for the cloud-free environment obtained from nearby
observations: pI = P / Pc/ear.
• It can be shown that (e.g. Petty and Katsaros, 1990aj Petty, 1994a ) that pI ~ TO with
a between 1.5 and 2.
The higher the frequency the more the relation between the normalized polarization and the
rainrate will depend on the areal extend of the raining cell and not so much on the rainrate itself.
Thus the transformation of R' into a rainrate will also depend on the type of precipitation.
Scattering methods
Scattering algorithms are based on the assumption that precipitation is always produced with
the help of the ice phase via the Bergeron-Findeisen process. The precipitation-size ice particles
in the upper part of the raining cloud cause scattering of microwave radiation which leads to a
radiation temperature depression (Fig. 11.8), which is assumed to be a monotonic function of
the rain itensity. To derive the scattering-based depression the radiation temperatures without
precipitation size ice particles must be estimated. This idea has been put forward first by
Spencer (1986) and refined by Spencer et al. (1989) who derived the so-called Polarization