Journal of the Meteorological Society of Japan, Vol. 87A, pp. 153–164, 2009
DOI:10.2151/jmsj.87A.153

153

Development of Nonuniform Beamfilling Correction Method in Rainfall Retrievals for
Passive Microwave Radiometers over Ocean Using TRMM Observations
Takuji KUBOTA
Earth Observation Research Center, Japan Aerospace and Exploration Agency, Tsukuba, Japan

Shoichi SHIGE
Department of Aerospace Engineering, Osaka Prefecture University, Sakai, Japan

Kazumasa AONASHI
Meteorological Research Institute, Japan Meteorological Agency, Tsukuba, Japanand

Ken'ichi OKAMOTO
Faculty of Environmental and Information Studies, Tottori University of Environmental Studies, Tottori, Japan(Manuscript received 17 June 2008, in final form 28 October 2008)

Abstract
Nonuniform beamfilling (NUBF) is a major error source in physical retrieval algorithms for estimating
rain rates using satellite-borne passive microwave radiometers. The NUBF effects over the ocean within the
beam effective field of view in the 10 GHz channel (FOV10) for the Tropical Rainfall Measuring Mission(TRMM) Microwave Imager (TMI) are investigated from simultaneous measurements made by the TMI
and the Precipitation Radar (PR) aboard the TRMM satellite. They are investigated with respect tovariability of a non-uniform parameter defined by the lognormal assumption from January to December
2000.
The parameter computed using surface rain rates estimated from PR data tends to be small (large) for
stratiform (convective) rainfall in the FOV10. The parameter computed using surface rain rates estimatedfrom brightness temperature (Tb) at 85 GHz is systematically lower in stratiform rainfall than the reference
derived by the PR. Systematic differences are not found for the convective cases. To evaluate the effects onrain retrievals due to the systematic differences of the non-uniform parameters, a simple adjustment isapplied, and rain retrievals from the observed TMI Tb at 10 GHz vertical polarization are performed over
the ocean. Relatively large increases in rain rates retrieved using corrected parameters are found in thetropics, while the increases of the corrected parameters are similar for all latitudes. Effects of the nonuniform parameter differences on the rain retrievals are nonlinear and could be closely related to highbackground values of the non-uniform parameter in the tropics and more frequent high rainfall intensities.

Corresponding author: Takuji Kubota, Earth Obser­
vation Research Center, Japan Aerospace Exploration
Agency, 2-1-1 Sengen, Tsukuba, Ibaraki 305-8505,
Japan
E-mail: kubota@ieee.org©2009, Meteorological Society of Japan

1. Introduction
Nonuniform beamfilling (NUBF) is a major error
source in physical retrieval algorithms for estimating
rain rates using satellite-borne passive microwave
radiometers, as described in previous papers (e.g.,

b

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Journal of the Meteorological Society of Japan
1

2
1 N
2
 N ∑ (Ri − Ravg )  .
σ =  i =1
Ravg

(2)

Here, i represents each pixel of the 85 GHz data within
the FOV area of the low frequency data, and N is thetotal number of pixels in the area. In Eq. (2), Ri is therain rate of the 85 GHz data pixels and Ravg is theaverage in the FOV area of the low frequency data.
Rain rates are retrieved from low frequency Tb datausing the relationship between rainfall and Tbcorrect
for z derived from 85 GHz Tb data. Figure 1 presents
an example of a rain–Tb relation for Tbs at 10-GHz
vertical polarization (Tb10vs) over the mid-latitude
ocean (147.5°E, 32.5°E) on January 1, 2000. Here, z is
R-Tb relation at 10GHz(V)

260

250

240

230

220

M
0.5

210

1

Brightness Temperature (Tb) (K)Wilheit 1986; Chiu et al. 1990; Short and North 1990).
It is necessary to consider nonuniform rainfall within
the field of view (FOV) of the radiometers to quantify
the effects of the NUBF. Turk et al. (1998) examinedthe effects of degraded sensor resolution in passive
microwave radiometers aboard satellites upon retriev­
als of tropical rainfall using fine-scale data derived
from aircraft-based instruments. Kummerow et al.
(2004) discussed the effects of NUBF errors on the
climate variability of rainfall estimated using passive
microwave sensors.
Kummerow and Giglio (1994, hereafter, KG94)
proposed a procedure in which relationships between
rain rates and brightness temperatures (Tbs) derived
from a plane-parallel radiative transfer model (RTM)
are corrected by lognormal distributions estimatedfrom high-resolution 85 GHz Tbs data (Tb85s). They
noted differences between estimations of lognormal
distributions from Tb85s and radars over the Tropical
Ocean Global Atmosphere Coupled Ocean Atmo­
sphere Response Experiment (TOGA COARE)
domain located in the western Pacific. Kummerow(1998) ex­­amined the impact of inhomogeneous rainfall
upon the predicted Tbs using either lognormal or
gamma distri­butions to develop a physically based
error model for microwave precipitation retrievals.
According to KG94, the NUBF correction method
using the lognormal distribution is as follows. Rainfall
is assumed to be distributed lognormally as observedin Biondini (1976), Houze and Cheng (1977), Kedemet al. (1990), and other works. It is then possible that
the RTM-derived Tb–rain relations are modified as afunction of the variability z ,

1.5

200

2

190

Tb

∞

correct( R , ζ )= ∫ Tb(R )
0

180

 −1
2
exp 2 [ln(R )− µ] dR1 170(2π ) 2 ζ R  2ζ1

0∞

correct( R , ζ )= ∫ Tb(R )
0

 −1
2
exp 2 [ln(R )− µ] dR.
1
ζ
2
2

(2π ) ζ R 
1

10

20

30

40

50

Rain Rate (mm/hr)

(1)

2
2
2
2
Here, ζ = ln (σ + 1) , µ = ln ( R ) − 0.5ζ , Tb(R) is
the RTM-derived Tb–rain relation, Tbcorrect is theTb–rain relation corrected by the lognormal distri­bution, R is the rain rate, and <R> is the mean rain
rate of the lognormal distribution. For the FOV of the
low frequency channels, s is defined using rain rates
estimated from Tb85s as

Fig. 1. Example of a rain–Tb relation for Tbs
at 10-GHz vertical polarization over the
mid-latitude ocean (147.5°E, 32.5°N) on
January 1, 2000. The horizontal (vertical)
axis denotes the rain rate (calculated Tb).
The line labeled “M” denotes values
calculated using a plane-parallel RTM;
lines labeled “0.5”, “1”, “1.5”, and “2”denote values calculated with rainfall
inhomogeneity z in the lognormal distri­bution of 0.5, 1, 1.5, and 2, respectively.

60

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T. KUBOTA et al.

regarded as a non-uniform parameter. Similar relations
are found in Fig. 3 of Kummerow (1998) and Fig. 2 ofKubota et al. (2007). In Fig. 1, the line for Tb(R) islabeled as “M”, while lines labeled “0.5”, “1”, “1.5”,
and “2” denote values of Tbcorrect ( R , ζ ) with z of 0.5, 1,
1.5, and 2, respectively. Figure 1 clearly depicts theeffects of NUBF, in that for the same Tb intensity
stronger rain rates are retrieved for larger values of therainfall inhomogeneity z and the relationship between
Tb, rain rate, and a given z is not linear.
Simultaneous rain observations have been per­formed aboard the Tropical Rainfall Measuring
Mission (TRMM) satellite by the TRMM Microwave
Imager (TMI) and Precipitation Radar (PR) (Kum­merow et al. 1998, 2000). By analyzing collo­cated
TMI and PR data, Varma et al. (2004) demon­strated
that a simulation by a plane-parallel RTM significantly
underestimates in convective rainfall events withreference to the averaged relationship be­ween ob­served
Tbs and rain rates at 19 and 37 GHz. Varma and Liu(2006) suggested the parameterization of fractionalrain cover (FRC) and conditional rain-rate probability
density functions (PDFs), based upon three years of
PR data. Their approach is an applica­tion of statisticalparameterization to observed Tbs, while the approachof the KG94 method is an esti­mation of the NUBF
effect from instantaneous satellite observations.
In this study, the method of the lognormal distri­bution based upon the KG94 procedure is investigatedover the ocean within the beam effective FOV in the
10 GHz channel (FOV10) for the TMI (63 km × 37km) using simultaneous measurements made by the
TMI and PR. The simultaneous measurements by thetwo sensors enable us to examine the NUBF effects inthe overall region observed by the TRMM. The overocean algorithm for the microwave radiometers uses
emission signals from low frequency channels suchas the 10 GHz channel in addition to scattering signals
from high frequency channels such as the 85 GHz
channel, while the over-land algorithm uses justscattering signals because of the high and variable
emissivity of the land surface. Thus, we focus on
analyses of the NUBF effects over the ocean.
Values of instantaneous z estimated from TMI
Tb85 and PR data are compared, and then possible
systematic differences are found between them.
Datasets are briefly described in Section 2. The
features of z are documented in Section 3. Section 3
also compares results using TMI Tb85 and PR data.
We try simple corrections for systematic differences
and apply them to the TMI retrievals. A summary is155

presented in Section 4.

2. Data used in this study
The NUBF effects are investigated with respect to z
from January to December 2000 in this study.
Analyzed cases are restricted to those with fractionalrain cover (FRC) above 50% in the FOV10, because
moderate numbers of pixels for which there is rain arenecessary to establish the lognormal assumption. To
quantitatively estimate the instantaneous NUBF effect,z values are computed from two different datasets,
rain rate estimated from TMI Tb85 (rainTMI85) andrain rate estimated from PR data (rainPR).
2.1 rainTMI85
The rain rate, rainTMI85, is retrieved from theobserved polarization-corrected temperature (PCT,
Spencer et al. 1989) recorded at 85.5 GHz by the TMI
using an RTM calculation, with statistically classified
vertical profiles of precipitation observed by the PR,
and background meteorological variables taken fromthe Japan Meteorological Agency Global Analysis
dataset. This retrieval method is based upon analgorithm developed by the Global Satellite Mappingof Precipitation (GSMaP) Project (Okamoto et al.
2005, 2007); a detailed description is provided by
Aonashi and Liu (2000), Kubota et al. (2007) andAonashi et al. (2009). Rain identification over theocean for rainTMI85 is based on either “rainTMI85 >1 mm h-1” or “observed Tb at 37 GHz (v) (Tb37v) >Tb37v calculated by the RTM for the no-rain condi­tion”, according to the results of Kida et al. (2009). A
four-stream RTM developed by Liu (1998) is used
here. The beam effective FOV for the 85 GHz channel
is 7 km × 5 km. In this study, the analyses are
performed for cases with two or more pixels having
rainTMI85 above 0 mm h-1 in the FOV10. Hereafter,z omputed using rainTMI85 is referred to as “z m85”.
2.2 rainPR
The TRMM PR is the first spaceborne Precipitation
Radar, and its 128-element active phased-array system
operates at 13.8 GHz (Okamoto 2003; Kozu et al.
2001; Iguchi et al. 2000; Okamoto and Shige 2008).
We use estimated surface rain by PR 2A25 Version 6
as rainPR. The horizontal resolution is 4.3 km at nadir.
In this study, the analyses are performed for caseswith two or more pixels having rainPR above 0 mm
h-1 in the FOV10. Hereafter, z computed using rainPR
is referred to as “z rpr”.

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Journal of the Meteorological Society of Japan

2.3 Convective/stratiform rain area and rain ratio
In this paper, a stratiform rain ratio (SRR) over the
FOV10 (63 km × 37 km window) is used for analyses.
The SRR is a ratio of the total rain amount to thestratiform rain amount defined in the following
equation.
N∑( f

SRR = i =1

⋅ Ri )

strat

.

N

∑R
i =1

(3)

i

Here, i represents each pixel within the FOV10 area, N
is the total number of pixels in the area, and Ri is therain rate. fstrat is derived from rain-type classification
algorithms, which differ between the PR and the TMI.
The TRMM PR rain-type classification algorithm uses
two independent methods (Awaka et al. 2007). One isa vertical profile method (Awaka et al. 1998), and theother is a horizontal pattern method (Steiner et al.
1995). Combined results of the two methods classify
rain for a PR pixel as stratiform, convective, or other.
Using PR data, fstrat is a discrete value, and is 0 for
convective rainfall and 1 for stratiform rainfall. For
the TMI algorithm, the method for the TMI Goddard
Profiling Algorithm (GPROF) Version 6 described in
Olson et al. (2001, 2006) is used here. The area
fraction of convective rainfall within the TMI footprint
is computed, combining convective fraction estimatesfrom both TMI polarization signatures and image
texture. Using TMI data, fstrat is a continuous value
between 0 and 1.

3.

Fig. 2. Seasonally averaged values of nonuniform parameter z in the TMI 10 GHz
FOV computed using PR surface rain.
Values of z are averaged in 2.5 × 2.5ºlatitude/longitude boxes and a) fromJanuary to March 2000 or b) from July to
September 2000. Cases are selected for
FRCs above 50%. Darker colors represent
larger values; white indicates missing
values.

Non-uniform parameter z and its influence
on rain retrievals

3.1 Features of z determined from PR data
In this section, features of z rpr are noted forcomparison between z rpr and z m85. Figure 2 plots
horizontal distributions of z rpr averaged from January
to March or July to September 2000. Cases with FRC
above 50% in the FOV10 are analyzed here. In both
periods, z rpr values are smaller than 0.9 over the
winter mid-latitude ocean, while they exceed 1.1 overthe subtropical ocean. Stratiform rainfall dominates at
mid latitude (Schumacher and Houze 2003). Thus,
variances are relatively small, and z rpr values, which
are related to variances divided by averages, are small.
However, isolated convections dominate in the sub­tropics (Short and Nakamura 2000; Schumacher andHouze 2003) and z rpr values are large. In contrast, theFig. 3. Probability density function (PDF) ofz rpr for all cases (solid circles), convec­
tive cases (open triangles), and stratiform
cases (open circles) from January to
December 2000. The bin width of thehorizontal axis is 0.1.

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T. KUBOTA et al.

values of z rpr are moderate over the South Pacificconvergence zone (SPCZ) during the boreal winterand the intertropical convergence zone (ITCZ) during
the boreal summer, although the rainfall amounts arelarge in those areas. This is because precipitation
systems, which are organized by convective and strat­iform regions, contribute to the large rainfall
amount. Houze (1977) indicated that stratiform rain­
fall ac­­counted for 40% of the total for a tropical squallline system observed during the Global AtmosphericResearch Program (GARP) Atlantic Tropical Ex­­
periment (GATE). Using the TRMM PR data, Schu­macher and Houze (2003) demonstrated that the ITCZ
has more moderate stratiform rain fractions and ismore clearly delineated from regions outside of the
ITCZ. Thus, organized systems as seen in the ITCZ
are quite different from isolated convections as seen in
the subtropics.
The z rpr distributions are analyzed in terms of therain-type classification. Figure 3 presents the prob­
ability density functions (PDFs) of z rpr in all cases,
convective cases, and stratiform cases from January to
December 2000. Here, convective (stratiform) cases
have SRRs below 10% (above 90%) over the FOV10
based on PR data. There was a total of 4918045, of which
46622 were convective and 2444648 were stratiform.
In this definition, the number of the convective cases
is much smaller than the number of the stratiform

Fig. 4. Seasonally averaged differences be­­tween z m85 and z rpr . Values are averaged
in 2.5 × 2.5º latitude/longitude boxes anda) from January to March 2000 or b) from
July to September 2000. Darker colors
represent smaller values; white indicatesmissing values.

157

cases, because an organized convective system is notincluded in the “convective” cases, and a relatively
large amount of rainfall is observed in the stratiform
region of the system. Considering all cases, a peak isfound around 0.95, while a peak is found around 0.85
(1.15) for stratiform (convective) cases. In the strat­iform cases, 85% of z rpr values are below 1.0, while
83% of z rpr values are above 1.0 in the convective
cases. Thus, z rpr tends to be small (large) for stratiform(convective) rain defined by the rainPR in the FOV10.
3.2 Comparison of z values determined using TMI
and PR data
This section compares z m85 with the reference z rpr
from January to December 2000. Analyzed cases are
restricted to FRC above 50% using rainPR in theprevious section. In this section, the cases are
restricted using both rainPR and rainTMI85 to elim­

Fig. 5. Zonally averaged z m85, z rpr , anddifferences between z m85 and z rpr . Values
are averaged a) from January to March
2000 or b) from July to September 2000.
Solid (open) circles denote z m85 (z rpr). A
dashed line indicates differences (i.e.,z m85 minus z m85).

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Journal of the Meteorological Society of Japan

Fig. 6. a) Differences between z m85 and z rpr
with respect to intensity of z m85 fromJanuary to December 2000. Analyzed
data numbers are displayed in b).

inate rain identification problems.
Figure 4 plots seasonally averaged differences
defined as “z m85 minus z rpr”. Values of z m85 are 0.3
lower than those of z rpr over the winter mid-latitude
ocean, while differences are relatively small over thesubtropical ocean. As illustrated in Fig. 2, z rpr issmaller in the winter mid-latitude ocean than in otherregions and the differences between z rpr and z m85 arelarger in this region. Figure 5 depicts zonally averagedz m85, z rpr , and differences between z m85 and z rpr .
Values of z tend to be about 0.2 smaller in the midlatitudes, in particular, in the winter hemisphere, thanin the tropics. In contrast the differences between z m85
and z rpr are 0.1 larger in mid-latitudes.
Differences of z m85 and z rpr are quantitatively
analyzed in Figs. 6 and 7 with respect to the intensityof z m85 and averaged rainTMI85. In Fig. 6a, z m85 islower than z rpr when z m85 is smaller than 1.2, and ishigher when z rpr is larger than 1.2. However, there are

Fig. 7. Same as Fig. 6, but with respect to
FOV10-averaged rainTMI85.

many more cases of z m85 below 1.2 than there areabove 1.2 (Fig. 6b). Values of z m85 are about 0.4 lower
than those of z rpr when z m85 is 0.2 to 0.3. Figure 7aillustrates the relationship between the differences
and rainTMI85 averaged in the FOV10, showing thatz m85 is systematically lower than z rpr when the
averaged rainTMI85 is less than 1 mm h-1 . Thissuggests that the poor sensitivity of rainTMI85 toweak rain rates causes large differences because Tbs
at 85 GHz is sensitive to scattering of ice particles.
Furthermore, the differences between z m85 and z rpr
are analyzed in terms of the rain-type classification.
Figure 8 presents the differences with respect to theintensity of the SRR, which is derived from the PR or
the TMI. For both SRR values, differences of z arelarger for high SRR values than for low values. Figure
8b shows that there are many more cases of high SRR
values than low values. Figure 9 plots two-dimensional
PDFs in terms of z m85 and z rpr for stratiform cases
from January to December 2000. The definition of astratiform case is the same as that used in Fig. 3.
Figure 9 indicates that z rpr is about 0.3 higher thanMarch 2009

T. KUBOTA et al.

159

Fig. 9. Two-dimensional PDFs in terms ofz m85 (horizontal axis) and z rpr (verticalaxis) for stratiform cases from January to
Decem­ber 2000. Contours show labeledvalues. Cases are selected for FRCs above
50%.

Fig. 8. Differences between z m85 and z rpr
from January to December 2000 analyzed
with respect to intensity of SRR. Solidcircles denote results of SRR from the PR,
and open circles denote results of SRR
from the TMI. Analyzed data numbers
are displayed in b).

z m85 in stratiform cases and that the variations in z m85
correspond well to those in z rpr . The correlation
coefficient between z m85 and z rpr is 0.70, and 2362625
stratiform cases were analyzed. Figure 10 presents theresults for convective cases; no systematic differences
are found for the convective cases. The correlation
coefficient between z m85 and z rpr is 0.53, and 45733
convective cases were analyzed.
3.3 Actual effects on rain retrievals using differential
z values
Differences of z values determined using TMI and
PR data are large in stratiform rainfall. To evaluate
the effects of the systematic differences on rain
retrievals, we adopt the following simple correction
for z m85,

ζ m* 85 = ζ m85 + Cdiff (SRR).

(4)

Fig. 10. Same as Fig. 9, except for convective
cases.

Here, an SRR value is computed from the TMI
defined in Eq. (3). Cdiff is the value of the averaged
differences defined as “z rpr minus z m85” (in otherwords, the differences depicted by open circles of Fig.
8a multiplied by –1) and is a function of the intensityof SRR derived from the TMI. Thus, if we use the*same analysis for z m85
as that used in Fig. 8a with the160

Journal of the Meteorological Society of Japan

Fig. 11.
RMSEs of z m85 and z rpr fromJanuary to December 2000 with respect
to intensity of SRR from the TMI. Solidcircles represent uncorrected results; open
circles, corrected results.

*

Fig. 12. Zonally averaged z m85, z m85, and*differences between z m85 and z m85.
Values over the ocean are averaged a)from January to March 2000 or b) from
July to September 2000. Solid (open)*
circles denote z m85 (z m85). Dashed line*
minus z m85).
indicates differences (i.e., z m85

Fig. 13. Normalized differences “R diff ” bet­
ween R10_LA and R10_L, averaged a)from January to March or b) from July to
September 2000. The differences are per­centages. The horizontal resolution is 2.5
× 2.5º latitude/longitude. Darker colors
represent larger values.

SRR from the TMI, there will be no differences. On
the other hand, small root mean square errors(RMSEs) are not guaranteed and the RMSEs for z m85*
and z m85
are compared in Fig. 11. In Fig. 11, data arebinned according to SRR values. Figure 11 shows that*
RMSEs are significantly less using z m85. Average*
values of RMSE for z m85 and z m85 are 0.33 and 0.21,
respectively, showing that RMSEs decrease by anaverage of 64% when using the z adjustment. Figure*
12 depicts zonally averaged z m85, z m85, and differences*
between z m85 and z m85. The differences are similar for
all latitudes, while slight increases are found at midlatitudes. Comparison with Fig. 12 and Fig. 5 for the*z m85 reveals that z m85
derived by the current simple
method is over-corrected less than 0.1 in zonal
averages in the tropics.
To examine the effects of the above z adjustment,*
we retrieved rain rates using z m85 and z m85
fromobserved TMI Tb10vs. The retrieval method is based
upon the RTM calculation and is the same as that
described in Section 2.1 for rainTMI85. In this exper­
iment design, the NUBF correction method using thelognormal distribution is applied to FRC above 50% in*
the FOV10. Rain retrievals using z m85 (z m85) arereferred to as “R10_L” (“R10_LA”). Figure 13 depicts
the difference, that is, “R10_LA minus R10_L”,
divided by R10_LA, which is defined as “Rdiff ”. In the*adjustment method, z m85
is larger than z m85 for all
values of SRR. The Tb relations with rainfall forMarch 2009

T. KUBOTA et al.

Fig. 14. Zonally averaged differences bet­
ween surface rain rates of R10_LA and
R10_L. Solid (open) circles denote values
averaged from January to March 2000
(July to September 2000). Panel a showsdifferences (mm month -1); Panel b, nor­malized differences (%).

Fig. 15. Histogram showing the sum rainfall
for different rain rates over the ocean
from January to December 2000. Solid(dashed) lines indicate rain rates of R10_L(R10_LA). This analysis is for daily 0.5 ×
0.5º boxes. The width of the histogram
bin is 0.02 mm h-1.

161

various z values of the lognormal distribution, as
shown in Fig. 1, suggest increases in retrieved rain
rates with increases in z . The rain rates increase when*using z m85
instead of z m85 over global rainfall areas.
R diff averaged over the ocean from 40°S to 40°N fromJanuary to December 2000 is 5.5%.
In Fig. 13, more large differences are seen in thetropics than in the mid-latitudes. Figure 14 presents
zonally averaged differences between surface rain
rates of R10_LA and R10_L. Figure 14 compares
differences, in addition to normalized differences.
Figure 14 also demonstrates that differences between
R10_LA and R10_L are relatively large in the tropics.
In contrast, increases of z are similar for all latitudes(Fig. 12). There are two possible reasons. First is the
background intensity of z. As indicated in Figs. 5 and12, values of z are larger in the tropics than in the
mid-latitudes. The relationship between Tb and rain
rate is more sensitive to the intensity of z when theintensity of z is larger. For example, Fig. 1 showsdifferences between rain rates retrieved for z = 1 andz = 1.5 from the same Tbs are larger than thoseretrieved for z = 0.5 and z = 1. Thus, more increasesof rain rates derived from the z adjustment in thetropics can be related to the high background valuesof z there.
The second reason is that there are more frequent
high rain rates in the tropics. Figure 1 also suggests
increases in retrieved rain rates are larger whenintensities of rain are stronger for the same positive
increment of z. For example, rain rates of z = 0.5 andz = 1 for Tb=200 (K) are 10.3 and 12.6 mm h-1 andthose for Tb=210 (K) are 15.0 and 20.0 mm h-1,
respectively (Fig. 1). This implies that there are large
increases in rain rates retrieved in the tropics wherestrong rainfall intensities and high Tb10vs due to them
are more frequently observed. Figure 15 is a histogram
showing the sum rainfall for different rain rates over
the ocean from January to December 2000, indicating
the contribution of specific rain intensities to the total
rainfall amount. This analysis is done for daily 0.5 ×
0.5º boxes. Figure 15 demonstrates clear increases(slight decreases) in the summation of rainfall above*(below) 2.0 mm h-1 using z m85. Thus, the z adjustmentof z m85 can result in more frequent high rainfall
intensities.

4. Summary
The NUBF effects over the ocean within the FOV10
for TMI were investigated from simultaneous mea­
surements made by TMI and PR aboard the TRMM

162

Journal of the Meteorological Society of Japansatellite. They are examined in overall regions
observed by the TRMM with respect to z of thelognormal distribution for cases with FRC above 50%
in the FOV10 from January to December 2000. z rpr,
which is z determined from rainPR, is less than 0.9
over the mid-latitude ocean and exceeds 1.1 over thesubtropical ocean. z rpr tends to be small (large) for
stratiform (convective) rain in the FOV10. Here,convective (stratiform) rain cases have SRRs, which
are ratios of the total rain amount to the stratiform
rain amount using 2A25 rain-type classification,
below 10% (above 90%) over the FOV10.
z m85, which is z determined from rainTMI85, iscompared with z rpr from January to December 2000.
z m85 is systematically lower than z rpr over the wintermid-latitude ocean, while differences are relatively
small over the subtropical ocean. z m85 is systemat­
ically lower than z rpr for stratiform rainfall, with thevariations in z m85 corresponding well to those of z rpr.
Large differences are found when rain rates of therainTMI85 averaged over the FOV10 are less than 1
mm h-1. No systematic difference is found for theconvective cases. To evaluate the effects of thesystematic differences of z on rain retrievals, a simple
adjustment is applied to z m85. The adjustment of z
leads to an average 5.5% increase in rain retrievalsfrom the observed TMI Tb10v over the ocean. The
effects of the non-uniform parameter differences on
the rain retrievals are nonlinear, and relatively large
increases in retrieved rain rates are found in thetropics, while the increases of z are similar for all
latitudes. It is suggested that this can be closely related
to high background values of z in the tropics and more
frequent high rainfall intensities.
In this paper, the NUBF effects are analyzed forcases of FRC above 50%. This threshold is usedbecause a certain number of rain pixels is necessary toestablish the lognormal assumption. For small rain
area cases, parameterization based upon PR data canbe effective, as demonstrated by Varma and Liu(2006).

Acknowledgements
This study was partly supported by “Production ofa High-Precision, High-Resolution Global Precipitation
Map Using Satellite Data” (the GSMaP project) underthe “Core Research for Evolutional Science andTechnology” (CREST) program of the Japan Scienceand Technology Agency (JST), and partly by the Fifth
TRMM Japanese Research Announcement of theJapan Aerospace Exploration Agency (JAXA). The

authors would like to thank the members of the
GSMaP Project for many valuable comments. Theyuse a part of 2A12 source programs for detection of
convective/nonconvective rain area. We thank Prof. C.
D. Kummerow (Colorado State University) for
providing 2A12 programs and valuable suggestions.
They would also like to thank Dr. G. Liu (Florida
State University) for the RTM code. Figures weredrawn using the Grid Analysis and Display System
and GFD-DENNOU Library.

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