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Comparison of Rainfall Products Derived from TRMM Microwave Imager andPrecipitation Radar
HIROHIKO MASUNAGA*
Earth Observation Research Center, National Space Development Agency, Chuo-ku, Tokyo, JapanTOSHIO IGUCHI
Applied Research and Standards Division, Communication Research Laboratory, Koganei, Tokyo, Japan

RIKO OKI
Satellite Program and Planning Department, National Space Development Agency, Minato-ku, Tokyo, JapanMISAKO KACHI
Earth Observation Research Center, National Space Development Agency, Chuo-ku, Tokyo, Japan(Manuscript received 2 November 2001, in final form 18 February 2002)
ABSTRACT
Satellite remote sensing is an indispensable means of measuring and monitoring precipitation on a global scale.
The Tropical Rainfall Measuring Mission (TRMM) is continuing to make significant progress in helping the globalfeatures of precipitation to be understood, particularly with the help of a pair of spaceborne microwave sensors,
the TRMM Microwave Imager (TMI) and precipitation radar (PR). The TRMM version-5 standard products,
however, are known to have a systematic inconsistency in mean monthly rainfall. To clarify the origin of thisinconsistency, the authors investigate the zonal mean precipitation and the regional trends in the hydrometeor
profiles in terms of the precipitation water content (PWC) and the precipitation water path (PWP) derived fromthe TMI profiling algorithm (2A12) and the PR profile (2A25). An excess of PR over TMI in near-surface PWC
is identified in the midlatitudes (especially in winter), whereas PWP exhibits a striking excess of TMI over PR
around the tropical rainfall maximum. It is shown that these inconsistencies arise from TMI underestimating thenear-surface PWC in midlatitude winter and PR underestimating PWP in the Tropics. This conclusion is supportedby the contoured-frequency-by-altitude diagrams as a function of PWC. Correlations between rain rate and PWC/
PWP indicate that the TMI profiling algorithm tends to provide a larger rain rate than the PR profile under a given
PWC or PWP, which exaggerates the excess by TMI and cancels the excess by PR through the conversion fromprecipitation water to rain rate. As a consequence, the disagreement in the rainfall products between TMI and PR
is a combined result of the intrinsic bias originating from the different physical principles between TMI and PR
measurements and the purely algorithmic bias inherent in the conversion from precipitation water to rain rate.

1. Introduction
Satellite remote sensing is an efficient tool for measuring rainfall on a global scale. Techniques for evaluating precipitation from satellites may be divided into
three major categories: those based on visible and/or
infrared measurements, those based on passive-microwave measurements, and those based on radar measurements (Kidder and Vonder Haar 1995). The visible* Current affiliation: Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado.
Corresponding author address: Hirohiko Masunaga, Department
of Atmospheric Science, Colorado State University, Fort Collins, CO
80523.
E-mail: masunaga@atmos.colostate.edu

q 2002 American Meteorological Society

and/or infrared techniques rely on the assumption thata clear correspondence exists between the observed
characteristics at cloud top and rain rates, whereas the
microwave techniques directly detect precipitating hydrometeors in addition to the overlying cloud layer.
Rainfall measurements by spaceborne microwave radiometers have a long history (e.g., Wilheit et al. 1977,
1991; Spencer 1986; Olson 1989; Kummerow and Giglio 1994; Aonashi et al. 1996; Kummerow et al. 1996).
Current widely used sensors for satellite microwave radiometry of precipitation are the Special Sensor Microwave Imager (SSM/I) aboard the Defense Meteorological Satellite Program satellites and the Tropical Rainfall
Measuring Mission (TRMM) Microwave Imager (TMI)
aboard the TRMM satellite. In addition to TMI, theTRMM satellite has the advantage of carrying the pre-

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cipitation radar (PR), which is a unique spaceborne radarused to measure rainfall and is capable of profiling precipitation with a vertical resolution of 250 m. TMI and
PR can independently estimate precipitation. The two
estimations ideally should agree with each other.
The TRMM standard products provided by the National Aeronautics and Space Administration (NASA)
Goddard Space Flight Center (GSFC) support rain rates
near the surface (hereinafter called simply rain rates)
evaluated either from TMI or PR or from their combineduse (Kummerow et al. 2000). Kummerow et al. (2000)
investigated consistency among the TRMM standard
products for precipitation and found a bias of 24% in
the global tropical monthly averages of rain rate in thelatest version (version 5) of the products. The largest
discrepancy lies between the products derived from the
TMI profiling algorithm (2A12) and the PR profile(2A25), where the former provides the maximum rain
rates in the Tropics and the latter the minimum. The
discrepancies in the rainfall products are among the major problems to be resolved to achieve the scientificgoals of TRMM, such as evaluating the latent heat overthe global Tropics (Tao et al. 2001).
There are a number of possible sources of the disagreement in estimated rain rates. First, the disagreement may be attributed to the difference between a radiometer and a radar in the physical principles for sensing rainfall. A radar directly measures the three-dimensional structure of precipitation. In contrast, some model
assumptions in the retrieval algorithm are required toderive the vertical structure from brightness temperatures detected by a radiometer. Radar measurements basically involve only the backscattering and attenuationof microwaves. Radiometric measurements, however,are more complicated because brightness temperatures
can be enhanced by the thermal emissions, can beshielded by the scattering, or there may be a trade-off
between them, depending on the channel frequency andthe phase of hydrometeors (liquid, ice, or their mixture).
TMI has nine channels at five frequencies from 10.65
to 85.5 GHz, with vertical and horizontal polarizations
for each, except for the 21.3-GHz channel. Precipitation
radar, in contrast, is a single-frequency (13.8 GHz) radar.
As a result, PR is insensitive to ice particles unless they
are large enough to be detectable by 2.2-cm wavelength
microwaves. Difference in the footprint size between
the sensors also could produce a disagreement in the
retrievals. TMI retrievals may suffer from the nonuniform beam-filling effect more seriously than PR does
because of the large footprint sizes for the low-frequency channels of TMI (e.g., 63 km in the down-track
direction at 10.65 GHz) as compared with the PR footprint size (4.3 km for nadir).
Second, one may focus on uncertainties that dependon model assumptions involved with individual retrieval
algorithms. A possible source of the uncertainties arises
from the treatment of drop size distributions (DSDs;
Viltard et al. 2000). The TMI profiling algorithm (2A12)

VOLUME 41

is based on the Bayesian approach to derive hydrometeor profiles by comparing the observed brightness
temperatures with a preexisting database (Kummerow
et al. 1996; Olson et al. 1996). In treating DSDs, the2A12 algorithm relies on assumptions in the cloud-resolving models used to construct the database. Uncertainties in the DSD assumptions are not critical in TMI
measurements because TMI brightness temperatures in
low-frequency channels are insensitive to DSD, but
DSD will become important later when the conversion
from precipitation water to rain rate is discussed. In
contrast, the PR 2A25 algorithm employs a globally
averaged DSD as the initial guess to obtain the radarreflectivity–rain rate (Z–R) and specific attenuation–radar reflectivity (k–Z) relations adjusted to be consistent
with the assumed DSD model (Iguchi et al. 2000). The
DSD assumptions more strongly affect PR retrievals
than those from TMI because information on the DSD
enters radar echoes through the sixth moment of the
DSD instead of the third moment. Viltard et al. (2000)
investigated the consistency in observed and synthesized brightness temperatures using TRMM data, where
the synthesized brightness temperatures were simulated
in the use of the PR profiles, to examine the sensitivity
to the assumptions on DSDs. In addition to the ambiguities in treating DSDs, other types of algorithm-dependent error sources include limitation in the universality of model databases and ambiguity in the attenuation correction. These algorithmic problems, in particular the DSD uncertainties, and the differences inmeasurement principle and footprint size are crucial.
They are outside the scope of this paper but should be
investigated in future studies.
In addition to the algorithmic differences, one must
consider the definition of rain rate itself as a candidate
source of the uncertainty. The rain rate is theoretically
proportional toE`y (D)n(D)D 3 dD,(1)0

where y (D) is the fall velocity of a raindrop with diameter D, and n(D) is the DSD. Because neither TMI
nor PR can measure the fall velocity directly, accuracy
in estimating rain rate is limited by the uncertainties iny (D). This point has important implications. In particular, the TMI brightness temperatures do not strongly
depend upon the details of the DSD, surface rainfall,on the other hand, does. We therefore prefer directly
measurable quantities, such as the precipitation watercontent, for comparison between TMI and PR. Correlation between precipitation water content and rain rateis investigated below for each of the TMI and PR products.
In section 2, we describe the data employed in our
analysis. Results are shown and some related discussions are presented in section 3, where results are compared in terms of the zonal-mean precipitation water

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TABLE 1. Coefficients for the Z–W relation in (2) used in our calculations for the water content W (g m23 ) and the radar reflectivity Z(dBZ). The five node points A–E represent typical positions in precipitation profiles and are defined based on the phase and temperature ofhydrometeors and on the rainfall types (stratiform, convective, and others). See Iguchi et al. (2000) for a detailed description of the nodepoints.
Stratiform

Convective

Others

Nodes

aw

bw

aw

bw

aw

bw

A
B
C
D
E

0.003 836 13
0.003 250 46
0.000 743 01
0.001 998 06
0.002 237 87

0.712 66
0.704 72
0.665 640.613 420.596 58

0.006 208 68
0.003 917 52
0.003 917 52
0.003 917 52
0.004 444 52

0.689 020.578 55
0.578 55
0.578 55
0.562 32

0.006 208 68
0.005 371 14
0.003 917 52
0.003 917 52
0.004 444 52

0.689 020.680 04
0.578 55
0.578 55
0.562 32

contents and precipitation water paths (section 3a) andof the contoured-frequency-by-altitude diagrams (section 3b), followed by a brief examination of their correlation with rain rates (section 3c). The findings are
summarized in section 4.
2. Data
As mentioned in section 1, the 2A12 and 2A25 rain
rates have the largest disagreement among all the
TRMM standard rainfall products (Kummerow et al.
2000). We therefore compare 2A12 and 2A25 in thisstudy. In the 2A12 algorithm, the hydrometeor profiles
are retrieved by relating the observed brightness temperatures to a large number of profiles in a preexisting
database through the Bayesian inversion scheme (Kummerow et al. 1996; Olson et al. 1996). The database iscomputed from cloud-resolving models, such as the
Goddard Cumulus Ensemble Model, that have been tested well for tropical convective systems (Kummerow etal. 1996). The 2A12 data contain the hydrometeor profiles for precipitation water, precipitation ice, cloud liquid water, and cloud ice water, all of which are in unitsof grams per cubic meter, and the latent-heat profile.
The profiled quantities are assigned in 14 layers fromthe surface to 18 km in altitude. The near-surface rain
rate is also included in the 2A12 products. In this paper,
we mainly use the precipitation water and the precipitation ice to study consistency with the PR products andsubsequently investigate the correlation of the watercontents with the near-surface rain rate.
For comparison with the TMI products, we also needto derive the precipitation water and ice from the PRreflectivity, but the 2A25 dataset includes only the rainrate profiles evaluated through the Z–R relations, notthe water/ice contents. We therefore derived the Z–W
relations to connect Z with the water content W, basedon the DSD model consistent with the 2A25 algorithm
in version 5 (Iguchi et al. 2000). [We note that theattenuation-corrected reflectivity, or Z e using the notation in Iguchi et al. (2000), is denoted by the radarreflectivity Z in this paper.] The Z–W relations, like theZ–R relation, are expressed in a power-law relation,
W 5 a w Z bw .

(2)

Coefficients a w and b w depend on the water temperature
for rain and on the fractional abundance of water for asnow–water mixture. They are listed in Table 1 for eachof convective, stratiform, and other rains, according to
the specification for the 2A25 rain-rate profile [see Fig.
4 in Iguchi et al. (2000)].
We chose only the central 21 rays from the 49 rays
within a PR swath because the near-surface quantities
retrieved by PR are liable to be degraded in quality forlarge viewing angles near both ends of a scan line. We
correspondingly omitted TMI footprints that do not
overlap the selected PR beams (i.e., the central 21 rays)from the analysis to reduce errors due to the differencein the sampling swath between TMI and PR.
The 2A12 and 2A25 datasets are then assigned to acommon format of the spatial allocation. The 2A25 data
profiles with 250-m resolution are readjusted, by averaging, to the 14 layers that correspond with the 2A12
profiling format. The 2A12 and 2A25 data at the satellite
footprint level are gridded to 0.5-8 2 resolution by thespatial average inside every grid box. Monthly meandata are obtained after the above-mentioned data processing is performed for every satellite orbit. In thispaper, we present two sets of monthly data (July of 1998
and January of 1999). Neither of these months is affected by the El Niño event that occurred from 1997 toearly 1998 because the event had ceased by July of 1998.
The data are therefore considered to represent the climatological trend, although they may be somewhat influenced by the La Niña event that followed the El Niñoin 1998.
Although it would be interesting to discuss, we do
not include the 2B31 product (i.e., the combined TMI/
PR rainfall) in this study. This is because of the technicalreason that the 2B31 product is not designed to allow
us to estimate the precipitation-water profiles instead of
the rain-rate profiles.
3. Results and discussion
In this section, we present and compare the rainfall
retrievals derived by the TMI (2A12) and PR (2A25)
algorithms. Hereinafter, TMI and PR refer to products/
algorithms specifically of 2A12 and 2A25, respectively,

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FIG. 1. The zonal mean PWC near the surface (in the 0–500-m layer) over (left) ocean and (right) land in (top) Jul 1998 and (bottom)
Jan 1999.

unless otherwise noted. The TMI and PR products arecompared in terms of the precipitation water instead of
the rain rate, which is usually of interest, as noted in
section 1. In section 3a, the precipitation water content(PWC), or the mass density of precipitation water per
unit volume, and the precipitation water path (PWP),
defined as
PWP 5

E

h

PWC(z) dz,

0

where z is the altitude and h 5 18 km is the top altitudeof the highest 2A12 layer, are presented in the zonal
mean. The precipitation water content near the surface
in the 0–500-m layer is called simply PWCns . In section
3b, differences in the statistical trend of the rainfall
profiles between the TMI and PR products are investigated. Correlation between PWCns /PWP and rain rateis examined in section 3c.

a. Zonal mean precipitation water
The zonal mean PWCns and PWP estimated from TMI
and PR are shown in Figs. 1 and 2, where the TMI
retrievals include only the liquid-water component. We
have excluded the precipitation ice to achieve a straightforward comparison with the PR-derived quantities because an appreciable fraction of ice particles is undetectable by PR. Effects of including the precipitation
ice in the TMI products will be demonstrated for reference in the last part of this section (Fig. 3) and insection 3b.
Figure 1 shows excellent agreement in PWCns between TMI and PR over tropical oceans. A systematic
excess of PR-derived PWCns (PR-PWCns ) over TMIderived PWCns (TMI-PWCns ) is observed in the midlatitudes, and more clearly so in the winter hemisphere.
This tendency is most conspicuous at latitudes above
308N in January. Although the data are somewhat noisy,
PWCns over land is similar to that over oceans except

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853

FIG. 2. Same as Fig. 1, but for the zonal mean PWP.

for the region of 208S to 08 in January, in which TMIPWCns is larger than PR-PWCns . It is noted that the land
rainfall is in remarkable agreement despite the limitationof radiometer measurements of continental rainfall. This
result may be because the TMI land algorithm employs
the database constituted of the rainfall profiles that were
carefully selected in comparison with ground measurements (see also section 3b).
Figure 2 illustrates the difference between PWPs derived from TMI and PR (TMI-PWP and PR-PWP),
showing a remarkable contrast to Fig. 1. TMI-PWP and
PR-PWP agree very well in the oceanic environment
except for the region with the maximum PWP in the
Tropics (08 to 108N), in which TMI-PWP exceeds PRPWP by about 20%. Characteristic patterns of PWP overland resemble those of PWCns for TMI and PR, although
the excess of PR in PWCns seen in the midlatitudes has
been reduced in PWP.
In summary, there are two notable differences in the
precipitation water between the TMI and PR products:
1) PR exceeds TMI in PWCns in midlatitude winter and2) TMI exceeds PR in PWP around the tropical rainfall

maximum. In either case, the discrepancy is presumed
to be caused by inconsistencies in the hydrometeor profiles derived by the TMI and PR algorithms. Although
there is no way to determine whether TMI or PR retrieves PWCns and PWP more accurately, we address ahypothetical solution from the viewpoint of the physicalprinciples in radiometric and radar remote sensing.
• PR should be more reliable in retrieving PWCns than
TMI is because PR echoes more directly evaluate thehydrometeor profiles than do TMI brightness temperatures.
• TMI brightness temperature at 10 GHz is preferable
to PR echoes for estimating PWP because the thermal
emissions are less sensitive to the DSD assumptions
and are less damaged by a heavy extinction than isthe scattered radiation. On the other hand, the correlation between PWP and the 10-GHz brightness
temperature would suffer from the poor spatial resolution of the 10-GHz channel. Nevertheless, the TMI
algorithm overcomes this difficulty to some extent
with the help of the high-frequency channels.

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FIG. 3. Same as Fig. 2, but including the precipitation ice for TMI-PWP.

In this context, TMI would underestimate the midlatitude rainfall and PR would underestimate the tropicalmaximum of precipitation. In the next section, we examine characteristic differences in the rainfall profiles
between TMI and PR to validate this hypothesis.
Before closing this section, we demonstrate for reference how much precipitation ice PR misses as compared with TMI in Fig. 3. There is a large differencein the sensitivity to ice particles between TMI and PR.
Sensitivity of PR to hydrometeors depends on the particle-size effect (the backscattering cross section } D 6
in the Rayleigh regime) and on the dielectric propertyof scattering particles. For the dielectric property, liquidwater is about 4 times as large as ice in the Rayleighbackscattering cross section, which accounts for the insensitivity of PR to ice particles in combination withthe particle-size effect. Whereas ice particles are detectable by PR if they are sufficiently large, TMI issensitive to smaller ice hydrometeors as well by virtueof the high-frequency channels. This difference in thedetectability of ice between TMI and PR results in alarge discrepancy in the estimated ice amount.

Figure 3 is the same as Fig. 2, but the precipitation
ice is included in the TMI retrieval. Addition of the icecomponent leads to a drastic increase in global TMIPWP except for the subtropics over lands in the dry
season. Adding precipitation ice does not cause any apparent change in TMI-PWCns (not shown), because thecontribution of snow is negligible near the surface
throughout the latitude range observable from the
TRMM satellite.
b. Vertical profiles of precipitation water
The results obtained in the previous section motivate
us to examine characteristics in the vertical profiles ofhydrometeors retrieved by TMI and PR. In this section,
we investigate statistical trends in the vertical profilesof PWC using contoured-frequency-by-altitude diagrams (CFADs). The abscissa conventionally represents
the radar reflectivity in a CFAD, but radar reflectivity
is replaced by PWC in this work.
Figures 4–7 present CFADs for some representative
sites listed in Table 2. Each figure consists of threeAUGUST 2002

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TABLE 2. Area coverages for the four representative sites adopted
in section 3b.
Sites

Area definitions

Western PacificEastern PacificSouth America
Midlatitude Pacific58–208N, 1308–1658E over ocean
158S–158N, 1308–908W over ocean
358S–108N, 808–458W over land
208–358N, 1208–1658E over ocean

panels showing PR-PWC (left), TMI-PWC without ice(middle), and TMI-PWC including the precipitation ice(right). All data are based on monthly statistics in January of 1999.
Figure 4 represents a heavily precipitating region
close to the western Pacific warm pool. In the TMIPWC profiles, the freezing level is clearly identified at
an altitude of about 4 km, above which PWC in theliquid phase decreases rapidly with increasing heightand disappears completely at 9 km in altitude (Fig. 4,
middle), as an appreciable amount of the precipitation
ice takes its place up to (or beyond) the tropopause (Fig.
4, right). The PR-PWC profiles, in contrast, show thatPWC gradually and monotonically decreases with increasing height without discontinuity at the freezing layer as identified by TMI (Fig. 4, left). A straightforward
comparison between the TMI- and PR-derived profiles
is therefore not easy because of the difference in thedetectability of pure ice particles between TMI and PR
as mentioned at the end of the previous section, and the
PR-derived profile is expected to correspond to an intermediate profile between extremes as shown by the
middle and right panels in Fig. 4. However, comparison
is meaningful for the domain where hydrometeors are855

all melted, or below a typical freezing level of 4–5 km
in the Tropics. PR echoes detected far above the freezing
levels are attributed to a small but finite fraction of verylarge frozen hydrometeors.
Figure 5 presents a CFAD for an eastern Pacific region containing the ITCZ. As expected, both the left
and right panels indicate that average heights of rainfall
tend to be relatively lower than in the western Pacific(Fig. 4), whereas the freezing level appears to show nosubstantial difference between the western and eastern
Pacific regions (middle panel).
In Figs. 4 and 5, PWC tends to be systematicallylarger 3–4 km above the surface for TMI than for PR
while the frequency distributions of PWC are similar
near the surface. This behavior explains the tropicalcharacteristics in the zonal mean precipitation water, thatis, the excellent agreement in PWCns and the large excess of TMI-PWP over PR-PWP around the tropicalrainfall maximum (cf. section 3a).
PWC profiles over the South American continent are
illustrated in Fig. 6. The PR and TMI (with ice) profiles
consistently indicate that precipitation is often developed at higher altitudes than oceanic rainfall is (Figs.
4 and 5), as expected for continental precipitation. The
liquid precipitation water cuts off more sharply above
4 km in the TMI profiles than in the tropical oceaniccases. It is reasonable that the continental rainfall profiles are still more homogeneous than the oceanic rainfalls in the TMI products because the TMI land algorithm employs a limited number of profiles in the database that were carefully selected so that the satelliteretrieved rain rate by the scattering scheme (i.e., using

FIG. 4. CFAD for PWC, as abscissa, at the western Pacific site (cf. Table 2) in Jan 1999: (left) PR-PWC profile, (middle) TMI-PWC
profile without ice, and (right) TMI-PWC profile including the precipitation ice.

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FIG. 5. Same as Fig. 4, but at the eastern Pacific site (cf. Table 2).

the 85-GHz brightness temperature) should be consistent with ground-radar measurements.
Figure 7 illustrates the northern midlatitude Pacificprecipitation. The PWC profile acquired by PR exhibits
very different characteristics from those shown above(Figs. 4–6). This is reasonable in the context of thevariance in the precipitation mechanisms between tropical convection systems and midlatitude storms. A peakat 1 km above the surface in the CFAD by PR is presumed to result from significantly lower heights of rainfall than in the tropical Pacific and South Americancases. In contrast, TMI shows much less variety in the
PWC profiles, except for the double peaks in the precipitation ice profile at 2–4 and 12 km in height seenin Fig. 7. The freezing level at 1 km in height cannot
be reproduced by the TMI algorithm because the TMI

FIG. 6. Same as Fig. 4, but at the South American site (cf. Table 2).

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857

FIG. 7. Same as Fig. 4, but at the midlatitude Pacific site (cf. Table 2).

algorithm outside the Tropics is represented by a discrete
set of raining profiles that have freezing levels at 3.5,
2.9, and 2.3 km, which probably account for the lower
TMI peak (2–4 km). The other TMI peak, at a heightof 12 km, seems unrealistic for precipitation in midlatitude winter, and reminds us of tropical convective precipitation rather than a midlatitude storm. In the middle
panel of Fig. 7, the freezing level is frequently identified
at a height of 4 km, which also reminds us of tropicalrainfall.
We now revisit the hypothesis addressed in section
3a. It implies that the tropical rainfall maximum shouldbe estimated more accurately by TMI and underestimated by PR and that the midlatitude rainfall should bederived more precisely by PR and underestimated by
TMI. This hypothesis is consistent with the fact that thepreexisting database in the TMI profiling algorithm(2A12) is based on the cloud-resolving models focusing
mainly on the tropical rainfall system (Kummerow etal. 1996). The PWC profiles by TMI are acceptable fortropical precipitation (Figs. 4 and 5). Examination ofFig. 7 reveals that PWC is reasonably concentrated near
the surface in the PR-derived profile but that TMI redistributes the precipitation water into a more verticallyhomogeneous profile, although the vertically integrated
PWC (or PWP) agrees well in this region according to
Fig. 2. The discrepancy in PWC is inferred to result
from failure in the profiling by TMI. This may be because the model database in the TMI algorithm does
not completely cover the actual variation in precipitation
profiles, particularly for precipitation types differingfrom those typical in the Tropics.
Furthermore, the hypothesis above does not contra-

dict the tendency that PR measurements are subject touncertainties in the attenuation correction, especially forthe heavy precipitation typical in the Tropics, which
could increase errors in estimating PWC and PWP by
PR. If the radar reflectivity is damaged by a heavy extinction, it would lead to a notable disagreement in the
retrieved rainfall between TMI and PR in the Tropics
as observed in PWP (Fig. 2). In contrast, PWCns shows
an excellent agreement in the Tropics (Fig. 2). In fact,
the near-surface quantities would be less seriously degraded in accuracy than the off-surface quantities byvirtue of the surface reference technique used for theattenuation correction. In the surface reference technique, the path-integrated attenuation (PIA) is estimatedby comparing the surface echoes in the precipitatingarea with those in a rain-free area (Meneghini et al.
2000). Under a given constraint on PIA, PWCns is evaluated more precisely than off-surface PWCs, for which
the attenuation correction would be less accurate because of the uncertainty in the vertical extinction profile.
The PR algorithm (2A25) depends on the surface reference technique to avoid numerical difficulties encountered when solving the Hitschfeld–Bordan equation
for the attenuation correction in heavy-precipitation regions (Iguchi et al. 2000).
As a result, it is plausible that the TMI algorithm
tends to underestimate PWC in the midlatitudes (especially in the winter hemisphere) and that the PR algorithm tends to underestimate PWP in the tropical rainfall maximum, as predicted by the hypothesis raised in
section 3a. Our next step is to investigate how the rain
rate relates with PWC and PWP, which is the subjectof the subsequent section.

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FIG. 8. Same as Fig. 1, but for the zonal mean rain rate near the surface.

c. Correlation between rain rate and precipitationwater
A major concern of meteorologists and hydrologists
engaged in precipitation studies is the rain rate rather
than PWC and PWP. In this section, we examine thecorrelation between rain rate and precipitation water todiscuss the influences of the results obtained in the preceding sections.
Figure 8 shows the zonal mean monthly rain rates
derived from the TMI and PR products. One can immediately find a considerable excess of the TMI rain
rate over the PR rain rate around the tropical maximum, which obviously reflects the tendency in PWP(Fig. 2). A small excess of PR is identified in thenorthern midlatitude in January of 1999 in accordancewith the trend in PWCns (Fig. 1), although the discrepancy is less pronounced in rain rate than in
PWCns . This excess of PR disappears, or is inverted,
in July, and hence the discrepancy in the midlatitude
rain rates is almost canceled in the annual average.
The overall features in Fig. 8 are consistent with Kum-merow et al. (2000), who found that the disagreementin the tropical-mean monthly rain rates over oceansin 1998 is 24% among the TRMM standard algorithms
in version 5 (Fig. 4 of Kummerow et al. 2000). As
compared with Fig. 8, the region with a large difference in rain rate extends over a broad region overtropical oceans in Kummerow et al. (2000), which isdeemed to be affected by the anomaly in tropical precipitation due to the El Niño event.
The excess of TMI in rain rate over PR around thetropical rainfall maximum seems to be reasonably interpreted to result from a similar feature in PWP (Fig.
2). However, it is still curious why PWCns , which should
be more closely related with near-surface rain rate than
PWP, shows no sign for such excess in the Tropics (Fig.
1). This result implies the presence of an algorithmic
bias in the conversion from precipitation water to rain
rate in addition to the intrinsic bias inherent in PWP
and PWCns .
Some differences in the assumptions underlying boththe algorithms could produce a bias in the conversion

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FIG. 9. Scatter diagrams for (top) rain rate vs PWCns and (bottom) rain rate vs PWP for the (left) TMI profiling algorithm and (right) PR
profile.

from precipitation water to rain rate. First, the TMI and
PR algorithms are based on different DSD assumptions.
The PR algorithm assumes a gamma distribution for the
DSD model to derive the Z–R relations for each rain
type (i.e., stratiform, convective, and others). In contrast, the TMI algorithm adopts the Marshall–Palmer
distribution for the DSD. Second, the definitions of precipitation water and rain rate are based on different
physical backgrounds between TMI and PR. The retrievals are ‘‘physical’’ outputs given by model simulations in the TMI rainfall products, whereas rainfall
quantities are directly connected with the radar reflectivity through the Z–R and Z–W relations in the PR
algorithm.
Figure 9 demonstrates the correlation between therain rate and the precipitation water over the globe for
the TMI (without ice) and PR products. The best-fit
linear functions for the scatter plots, delineated in Fig.
9, are found to be

RR 5

5

20.0053 1 20.0PWCns
20.0033 1 14.5PWCns

for TMIfor PRandfor TMIfor PRand(3)

for PWCns (g m 23 ) andRR 5

520.0084 1 0.004 42PWP
0.0001 1 0.003 58PWP(4)for PWP (g m 22 ), where RR is the rain rate (mm h 21 ).
In both (3) and (4), TMI tends to have a larger inclination of the best-fit line than PR does, and the offset
is negligibly small in every case. In other words, TMI
tends to yield a higher rain rate than PR in response toa given PWCns or PWP, and the difference increases as
the precipitation becomes heavier, as demonstrated bytaking the difference between TMI and PR in (3) and
(4):

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JOURNAL OF APPLIED METEOROLOGYVOLUME 41

FIG. 10. Similar to Fig. 9, but each shown separately for (left) oceanic and (right) continental rainfalls for the TMI profiling algorithm.

DRR(TMI 2 PR)
5520.0020 1 5.5PWCns
20.0085 1 0.000 84PWP

for PWCns
for PWP.

and(5)

As a consequence, the excess of TMI over PR in
precipitation water would be expanded in rain rate andvice versa, although these trends would not be notablein low-precipitation regions. This accounts for thetrend found in Fig. 8, where the excess of TMI overPR around the tropical rainfall maximum, which originated from the feature appearing in PWP (Fig. 2), is
exaggerated in rain rate while the midlatitude excessof PR over TMI in PWCns is suppressed in rain rate.
We thus conclude that the large excess of TMI overPR in tropical rainfall results from a combined effectof the intrinsic retrieval bias in PWP and an algorithmic
bias in the conversion from PWP to rain rate. Excessof PR in midlatitude PWCns , in contrast, appears to becompensated by an opposite bias in the rain rate–
PWCns relation. The coincidence in rain rate between
TMI and PR in the midlatitudes thus seems to be afortunate artifact rather than a successful agreement
between the algorithms.
One might wonder if the correlation between rain rate
and precipitation water depends on the surface condition(i.e., ocean or land) for TMI measurements because of
the difference in algorithmic strategies, where retrieval
techniques exclusively depend on the depression ofbrightness temperatures by scattering by ice particles
for radiometric measurements of rainfall over land. To
examine this point, we further divide the scatter diagrams for TMI in Fig. 9 into oceanic and continental
rainfalls. Figure 10 shows separate diagrams for eachtype of TMI-derived rainfall over ocean and land areas.
The correlation between rain rate and precipitation wateris excellent in an oceanic environment, whereas scatterplots are much more widely dispersed over land areas.
The best-fit lines for Fig. 10 are

AUGUST 2002

MASUNAGA ET AL.
20.0032 1 20.3PWCns

 for TMI (over ocean) and
RR 5 
1 19.5PWC
20.0020
for TMI (over land)

(6)

ns



for PWCns and20.0064 1 0.004 21PWP

for TMI (over ocean) and
RR 5 
20.0019 1 0.004 77PWP
 for TMI (over land)(7)

for PWP. Comparison of (6) and (7) with (3) and (4)reveals that the dependence on the surface condition(ocean or land) in TMI measurements is very small incomparison with the difference from PR measurements.
Hence, the overall conclusions derived from Fig. 9 with
(3) and (4) are unchanged for oceanic and continental
rainfalls.
4. Summary and conclusions
In this paper, we compare TRMM standard rainfall
products derived by the TMI (2A12) and PR (2A25)
profiling algorithms to clarify the origins of the disagreement among the products pointed out by Kummerow et al. (2000). In our strategy, we focus on the
precipitation water content and the precipitation water
path, given by the vertical integration of PWC, for comparison instead of the rain rate that is usually of interest.
This approach enables us to separate the intrinsic problems involved in the physical principles of remote sensing from the uncertainties resulting from the conversion
from precipitation water to rain rate. We adopted two
sets of monthly data (July of 1998 and January of 1999)
for the analysis.
PWP and near-surface PWC, or PWCns , in the zonal
mean generally show good agreement between the TMI
and PR products except in midlatitude winter for PWC,
where PR-PWCns exceeds TMI-PWCns (Fig. 1), andaround the tropical rainfall maximum for PWP, where
TMI-PWP exceeds PR-PWP (Fig. 2). These discrepancies are attributed to characteristic differences in thehydrometeor profiles retrieved by the TMI and PR algorithms, which are examined in terms of CFADs as afunction of PWC (instead of the conventional definitionof the radar reflectivity). Direct comparison between the
PR- and TMI-derived PWC profiles is justified below
the freezing level because of the insensitivity of PR topure ice particles.
As a general trend, TMI shows very little variety in
the PWC profiles in comparison with PR, which presents
significant variations in the profiles corresponding to awide range of precipitation characteristics from tropicalconvective rainfall to midlatitude storms. This invariability in the TMI-retrieved rainfall may be responsible
for the underestimation of TMI-PWP in midlatitudes,

861

implying a limitation of the preexisting database incorporated in the current TMI profiling algorithm. The PR
measurements are liable to suffer from ambiguity in theattenuation correction in heavy precipitation around thetropical rainfall maximum, which is presumed to be thecause of the underestimation of near-surface PWC by
PR in the Tropics.
It is meaningful to demonstrate how the discrepancies
in PWC and PWP influence the rain rate in response tometeorological and hydrological interests. Scatter diagrams for PWCns and PWP versus rain rate indicate that
TMI tends to yield a larger rain rate than PR does fora given PWCns or PWP, which is more significant for
heavier precipitation. As a consequence, an excess of
TMI in precipitation water over PR would be increasedin terms of rain rate and vice versa. This bias accounts
for the characteristics in the zonal mean monthly rain
rate (Fig. 8), where the TMI products show a large
excess in the tropical rain rate over the PR products but
the discrepancy is reduced in the midlatitudes, consistent with Kummerow et al. (2000). Summarizing all theabove findings, we conclude that the disagreement in
the rainfall products between TMI and PR is a combined
result of the intrinsic bias originating from the different
physical principles between TMI and PR measurements
and the purely algorithmic bias inherent in the conversion from precipitation water to rain rate.
This paper is a starting point toward development of
an ultimate rainfall algorithm by combined use of a radar
and a radiometer. There are unresolved issues such as
the DSD uncertainty problem addressed in section 1.
Furthermore, in contrast to this work, which is basedon monthly averages, instantaneous matching of TMI
and PR data would provide a greater insight into theorigins of the disagreement in the retrievals. Althoughthese topics are left to future studies, we have some
implications from the current study that may be usefulfor future development of rainfall algorithms using either a microwave radiometer or a radar, or their combination.
As one may expect, difficulties in determining thevertical profiles from radiometric measurements and uncertainties in the attenuation correction for radar measurements are crucial obstacles to precise estimation of
rainfall. The Bayesian approach based on a preexisting
database as adopted in the TMI profiling algorithm(2A12) could be greatly improved by enriching the database to cover a wider variety in possible rainfall profiles. A combined algorithm using radiometric brightness temperatures at low frequencies to constrain the
total attenuation in radar measurements (Haddad et al.
1997) would also be an efficient way to overcome theproblems. More formidable problems are involved in
ambiguities in the conversion from precipitation waterto rain rate because a DSD and y (D), required to evaluate (1), and their regional variations are uncertain. Nevertheless, the achievement of reasonable agreement in

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JOURNAL OF APPLIED METEOROLOGY

rain rate requires significant reduction of the discrepancy in the conversion from precipitation water to rain
rate among the algorithms.
A consistency study for rainfall products between radiometric and radar measurements will also be helpful
in algorithm development for the TRMM follow-on project, currently being planned, in which a spaceborne
dual-frequency precipitation radar with an additional
channel at 35 GHz is being examined along with a successor of TMI. The addition of a higher-frequency radar
channel would require a more precise correction of attenuation but would provide information about the DSD.
This would eliminate many of the ambiguities that remain in PWP, PWC, and the surface rainfall. The Global
Precipitation Measurement (GPM) mission is being
planned in which a constellation of eight satellites carrying microwave radiometers is to be organized alongwith the TRMM follow-on satellite described above asa core satellite. It is required for GPM to develop aradiometer algorithm for the constellation satellites thattakes advantage of the dual-frequency radar aboard thecore satellite for improving accuracy of the retrieval. A
possible solution is to update the current TMI (2A12)
algorithm by incorporating radar-retrieved rainfall profiles in some way into the database. Efforts to sophisticate rainfall algorithms using spaceborne radar andradiometer are now being started with a view toward
use in future projects in planning, such as GPM.
Acknowledgments. The authors greatly appreciate theassistance of S. Harada [Remote Sensing Technology
Center of Japan (RESTEC)], who made a great effort
to prepare and to reprocess the data products. They arealso grateful to T. Kozu (Shimane University) and T.
Higashiuwatoko (RESTEC) for preparing the lookup table for deriving the Z–W relations. They appreciate comments and suggestions provided by the anonymous reviewers, which were helpful for improving the paper.
They thank H. Hanado (Communication Research Laboratory), S. Shige (NASDA/EORC), and T. Nomaki(RESTEC) for their discussions. TMI (2A12) and PR(2A25) data were provided by NASA GSFC.

VOLUME 41

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