Environmental Engineering Reference
In-Depth Information
where
R
E
is the estimated rain rate, [
R
] is the true rain rate within the FOV, and
T
0
and
T
00
are slope and curvature of
T-R
relation (Eq.
15.1
), and [
x
] represents area
averaging. The first term on the right-hand side (
T
00
/2
T
0
) depends only on the
atmospheric and radiative transfer model, the sensor response, and the orbital
parameters of the satellite. The second part, [(
R
[
R
])
2
], depends solely on the
structure of the rain field. It is the coupling of these effects that comprise the
beamfilling effect. Since the slope of the
T-R
relation is positive and the curvature
negative, and the rain rate variance is always positive, the right-hand side of (
15.5
)
is negative, i.e., a negative bias is incurred.
Ha and North (
1995
) examined different theoretical rain rate distributions and
concluded that a climatological correction for the beamfilling error is appropriate.
From theoretical considerations, Wang (
1997
) proposed a FL-dependent BFC. Cho
et al. (
2004
) examined data collected by the TRMM Precipitation Radar and
showed that both the gamma and lognormal distributions provide good fits to the
observed data. However, the gamma (lognormal) distribution tends to better fit the
observed distribution for wet (dry) conditions.
Kummerow (
1998
) provide a methodology to examine the BFC structure and
Kummerow et al. (
2004
) showed the sensitivity of the slant path and rain rate
inhomogeneity within the FOV on the BFC based on TRMM data. Methods to
correct for the BFC have been investigated (Kubota et al.
2009
; Lafont and
Guillemet
2004
).
15.3 Data Product
15.3.1 Data Processing
The processing of the data begins with the computation of the brightness tempera-
ture (
T
b
) histograms and the determination of the FL using the top one percentile of
the vertically polarized
T
b
at 22 GHz (
T
b 22V
) and vertically polarized
T
b
(
T
b 19V
).
This choice is an attempt to exclude non-raining pixel in the FL calculations. The
method of moments is used. The mean of the combination channel (
T ¼
2
T
b 19V
T
b 22V
) of the non-raining pixels and the first, second, and third moments of the
T
histogram are calculated. These moments of the
T
histogram are matched iteratively
to the parameters of a mixed lognormal distribution via the
T-R
relation. The output
parameters are RE,
T
0
,
σ
0
,
p
,
μ
,
σ
, and FL, where RE is the estimated rain rate,
T
0
and
σ
0
the mean and variance of the non-raining portion of the
T
b
histogram,
p
the
rain fraction, and
are the estimated mean and variance of the logarithm of
the rain rate. After the computation of the RE, a BFC is applied to get the BFC
corrected rain rate (see Wilheit et al.
1991
).
The METH technique has been applied to all SSM/I data on the DMSP satellites
(F8, F10, F11, F13, F14, F15) and SSMIS on board F17 satellites. The data are
available via the Global Precipitation Climatology Project-Polar Satellite Precipi-
tation Data Center
μ
and
σ
(GPCP-PSPDC) website
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