Biases in the standard rain rate product by the TRMM
microwave radiometer over land
Shinta Seto, Shinsuke Satoh, Nobuhiro Takahashi, and Toshio Iguchi
Applied Research and Standards Department
National Institute of Information and Communications Technology
Tokyo, Japan
Abstract— This study investigates the causes of biases in the rain
rate estimates by the TMI standard algorithm. Retrieval error isseparated from rain/no-rain classification error. As it is wellknown, the retrieval error is sensitive to storm height. It isinteresting that the observed brightness temperature at 85GHz
shows clear diurnal variation for given storm height and surface
rain rate. It can be explained by the diurnal variation of the land
surface brightness temperature (related with the land surface
physical temperature) under inhomogeneous rainfall or the
diurnal variation of the freezing height (related with the airtemperature).
Keywords-TRMM; TMI; storm height; diurnal variationI.

INTRODUCTION

Rain rate estimates by TRMM Microwave Imager (TMI)
can be quantitatively validated by comparing with the estimatesby Precipitation Radar (PR) which is on the same platform.
The observation and rain rate estimation technique of PR arecompletely different from those of TMI. Over land, it is
widely acknowledged that the estimates by PR (denoted as
R_PR) is much more reliable than the estimates by TMI(denoted as R_TMI). In this study, the rain rate estimates by
PR using the standard algorithm version 6 is assumed to be
perfect, then the error of the rain rate estimates by TMI using
the standard algorithm version 6 can be calculated by∆R=R_TMI-R_PR. The purpose of this study is to statisticallyanalyze ∆R and to examine causes of the error.
II.

DATA

A. The TMI Standard Algorithm
While there are many precipitation retrieval algorithms for
TMI, this study goes with the latest version of TMI standard
algorithm, which is developed by Kummerow et al [1]. Thisalgorithm, one of the Goddard profiling algorithm (GPROF),
applies statistical technique to retrieve rain rate. Below, we
briefly introduce the land part of this algorithm. It consists of
two steps: rain/no-rain classification (RNC, in short) andretrieval. RNC judges whether a TMI pixel has the rainfall
signature (rain) or not (no-rain). Retrieval is done only for the“rain” pixels and is not applied for “no-rain” pixels, whose
R_TMI becomes zero.

Characteristic precipitation profiles simulated by cloud
resolving models with the calculated brightness temperaturesare summarized as database. Retrieval process referred the
databases to find the profiles to have brightness temperatures
similar to the observed brightness temperatures. Over land,
only one channel 85GHz Vertical (85V) is used, because lower
frequency channels generally do not have much valid
information of the precipitation. Two databases, one forconvective precipitation and another for stratiform
precipitation, are referred to give the estimates R_TMI_C and
R_TMI_S, respectively. To merge the two estimates, CSI(Convective / Stratiform ratio Index) is calculated as explained
below. Like as over-ocean algorithm, polarization method andtexture method are used to judge convective or stratiform. CSI
is calculated by the next equation (1).
CSI=0.062+0.00887*{1.11*TB(10V)-1.24*TB(37V)+0.45*TB(85V)-1.25*(POL)+0.22*(NPOL)+1.24*(STDEV)+0.14*(PIWD)-84.3}(1)
POL and NPOL are indices used in the polarization method
and STDEV and PIWD are indices used in the texture method.
Among other terms, TB(37V) and TB(85V) have some
information to be related with the precipitation, however,
TB(10V) is generally not related with precipitation over land.
The indices and channels are selected to statistically match CSI
with the classification by PR efficiently. The reason why
TB(10V) is selected is explained as “convection occurs more
over warmed surfaces” in McCollum and Ferraro [2]. The
final estimates R_TMI are calculated by equation (2)R_TMI=(1-CSI)*R_TMI_S+CSI*R_TMI_C(2)

If CSI is unavailable, the third (mixed) database is referred
to get the rain rate estimates R_TMI_M, then R_TMI_M istreated as the final estimates R_TMI. This database has both
stratiform and convective precipitation profiles.
This study will examine not only apparent but potential
characteristic of the rain rate estimates by the standard
algorithm. For that, the standard algorithm with two minor
modification (A) and (B) as below are applied for three years,
January 1998 to December 2000.
(A)

R_TMI is always derived over land even if the
RNC is “no-rain”.

(B)

R_TMI_M is always calculated with R_TMI.

0-7803-9051-2/05/$20.00 (C) 2005 IEEE

B. Match up with PR Data
As R_PR, near surface rain rate derived by the latest
version of PR standard algorithm [3] is used. PR can notobserve several ranges near surface because of the groundclutter, however, in version 6, Z profiles are extrapolated andrain rate are estimated at the surface level (stored as“e_SurfRain” in the product 2A25). Convective / Stratiform
classification and the storm height (SH) derived by the PR
standard algorithm are also used for the analysis.
Single or multiple (usually two) PR pixels within a TMI
footprint for 85GHz (7.2km along track x 4.6km cross track)
are matched up with the TMI pixel. As a result, following
variables become available for each TMI pixel.
•

RNC by TMI; T (rain) or t (no-rain)•

R_TMI (rain rate estimates by TMI using convective
and stratiform databases); according to (A), R_TMI isalways calculated•

R_TMI_M (rain rate estimates by TMI using mixed
database); according to (B), R_TMI_M is always
calculated•

RNC by PR; P (rain) or p (no-rain). If the “rain” and“no-rain” coexist within a footprint, it is treated as P
(rain).

•

R_PR (near surface rain rate estimates by PR); If themultiple PR pixels exist, R_PR is calculated as an
unconditional average.

•

SH (storm height); If the multiple PR pixels exist, SH
is calculated as a conditional average of rain pixels.

•

Convective / Stratiform classification by PR; If“stratiform” and “convective” pixels coexist, it istreated as “convective”.

As a matter of convenience, RNC’s by PR and TMI are
denoted in combination. If the RNC by PR is P and RNC by
TMI is t, for example, they are combined as Pt. The PR rain
rate for Pt is, for example, denoted as R_PR[Pt]. It is obviousthat R_TMI and R_PR are given as equation (3).

III.

R_TMI=R_TMI[PT]+R_TMI[pT](3-1)

R_PR=R_PR[PT]+R_PR[Pt](3-2)

RNC ERROR AND RETRIEVAL ERROR

A. Definition
The total error ∆R is decomposed to be two terms: the error
caused by inaccurate RNC and the error caused by inaccurate
retrieval. The former is named as “RNC error” and denoted as∆R_RNC and the latter is named as “retrieval error” anddenoted as ∆R_RET. They are calculated by equation (4).

∆R_RNC=R_TMI[pT]-R_TMI[Pt](4-1)∆R_RET=R_TMI[PT]+R_TMI[Pt]-R_PR[PT]-R_PR[Pt] (4-2)

Figure 1. Zonal mean of ∆R, ∆R_RET, and ∆R_RNC [mm/month] forthe 3-year data from Jan. 1998 to Dec. 2000.

Figure 2. Same as Fig. 1, but for diurnal variation.

R_TMI[Pt] is originally not calculated, but calculated forthis study as written above.

∆R_RNC is the difference between the false rain rate when
it is actually not raining and the missed rain rate when it isactually raining. If the RNC by TMI is perfect (perfectly
agreed with the RNC by PR), ∆R_RNC is zero. While the
RNC by TMI is not perfect, if the false rain rate and the missed
rain rate is equally balanced, ∆R_RNC also becomes zero.
When the RNC by TMI is not perfect, ∆R_RNC is dependent
on the retrieval algorithm.
∆R_RET is the difference of R_TMI and R_PR for all theraining cases. ∆R_RET is not dependent on RNC methods.
This independence is the benefit by using the term R_TMI[Pt]in the definition.
If R_TMI[Pt] is not used, the RNC error and the retrieval
error are defined as equation (5)∆R_RNC=R_TMI[pT]-R_PR[Pt](5-1)∆R_RET=R_TMI[PT]-R_PR[PT](5-2)

With this definition, ∆R_RET is dependent on the RNC
method, because ∆R_RET evaluates the difference between
R_TMI and R_PR only for PT case. Therefore, the former
definition by equation (4) is adopted in this study.

Figure 3. Statistics for storm height (SH) x surface rain (R_PR) categories, (a) the histogram of occurrence, (b) TB (85V), (c) R_TMI, and (d) for ∆R_RET.

B. Zonal Mean and Diurnal Variation
3-years PR and TMI data from Jan. 1998 to Dec. 2000 areused to calculate ∆R_RNC and ∆R_RET [mm/month]. Fig. 1
shows their zonal mean and Fig. 2 shows their diurnal
variation.
Generally, ∆R_RNC is negative (indicates
underestimation of R_TMI) and ∆R_RET is positive (indicatesoverestimation of R_TMI). The absolute value of ∆R_RET ismuch larger than ∆R_RNC, then ∆R becomes positive. It
should be noted that ∆R_RET which is calculated as an
unconditional average tends to be larger when R_TMI and
R_PR are larger. More detailed analysis for ∆R_RET is shownin the next section.
IV.

CAUSES OF RETRIEVAL ERROR

A. Precipitation Characteristics
For the further analysis of the retrieval error, precipitation
systems are characterized with the storm height (SH) and therain rate (R_PR). Precipitation can be classified into one of
144 categories = 16 categories for SH (2km to 10km, each
500m bin) x 9 categories for R_PR (0, 0.01-0.2, 0.2-0.5, 0.5-1,
1-2, 2-5, 5-10, 10-20, 20-50 [mm/h]). Fig. 3 shows the results.
The abscissa of each small figure is R_PR and the ordinate is
SH. Fig. 3 (a) shows the histogram of occurrence. Positive
correlation between SH and R_PR is seen with the exception ofrelatively high occurrence of high SH and zero R_PR
precipitation systems. Fig. 3 (b) shows TB (85V). Generally,
higher SH decreases TB (85V) much. In addition to the strong
sensitivity to SH, TB (85V) is somewhat sensitive to R_PR.
This relation is clear when SH is high. The direct relationshipbetween R_PR and TB (85V) should be weak, because theeffect of liquid rain rate on TB (85V) is easily saturated up to
weak rain rate (~1mm/h). We hypothesize that the near surface

rain rate and the rain rate above the freezing level are positively
correlated. If so, the positive correlation between R_PR and
TB (85V) can be explained.
Fig. 3 (c) shows R_TMI [mm/h]. In this figure, R_TMI iscalculated as a conditional average. Similar with Fig. 3 (b),R_TMI shows sensitivity both with SH and with R_PR. It isnatural because R_TMI is derived mainly from TB (85V). Fig.
3 (d) shows ∆R_RET [mm/h]. It is unavoidable that ∆R_RET
have the sensitivity to SH for the fixed R_PR. The sensitivity
to R_PR is not simple. When SH is low, ∆R_RET is positive
for weak rain, but negative for strong rain. When SH is large,∆R_RET is the largest around 1 [mm/h] of R_PR.
B. Diurnal Variation
As shown in Fig. 3 (a), 7 categories of (SH, R_PR) werechosen. For these categories, diurnal variation is examined.
Fig. 4 (a) shows the number of occurrence for each one-hour
local time bin. Low precipitation (such as category 1) appears
in the early afternoon (around 12-15 LCT), but highprecipitation (such as category 7) appears in the evening(around 18 LCT). Fig. 4 (b) shows TB (85V). It is interestingthat diurnal variation is clearly seen even though each category
has fixed SH and R_PR. TB (85V) takes the maximum in theearly afternoon (around 12 -15 LCT) except for category 7.
Black dotted line in Fig. 4 (b) indicates the TB (85V) under norain conditions. The width of diurnal variation is more than 10[K] under no-rain conditions. Under rain conditions, the widthof diurnal variation is smaller for lower or weaker rainfall andlarger for higher or stronger rainfall. Category 6 shows
approximately 10 [K] of diurnal variation. Category 7 shows
no distinct diurnal variation.
It is clear that the reason of diurnal variation under no-rain
condition is the diurnal variation of land surface brightness
temperature which is mainly determined by land surface

physical temperature.

What is the reason of the diurnal

variation under rain condition? The difference of the land
surface brightness temperature does not reflect on the observedbrightness temperature, if the liquid rainfall covers the land
surface. The exception is the non-uniform rain within afootprint. In this case, the land surface information can affectthe observed brightness temperature. Another possibility to
explain the diurnal variation under rain conditions is the changeof freezing height. In the daytime, the freezing height moves tohigh altitude, then the solid precipitation layer becomes thin forthe same SH.
Fig. 4 (c) shows the diurnal variation of R_TMI [mm/h]. It
seems strange that the diurnal variation of R_TMI is not agreed
with the diurnal variation of TB (85V). Fig. 4 (d) shows thediurnal variation of R_TMI_M [mm/h], which is rather agreed
with the diurnal variation of TB (85V). Every category except
for category 7 takes the minimum R_TMI_M around 12-15
LCT same as TB (85V). The difference between R_TMI and
R_TMI_M is the usage of CSI or not. CSI becomes higher inthe daytime because of the TB (10V). This artificial diurnal
variation of CSI can compensate the diurnal variation of TB(85V). Consequently, R_TMI for the fixed SH and R_PR does
not clearly decrease in the daytime.
V.

SUMMARY

The main source of ∆R_RET is storm height as Furuzawa
and Nakamura [4] pointed out. This study finds that TB(85V)
under rain conditions shows clear diurnal variation even if thestorm height and surface rain rate are fixed. The phase of thediurnal variation is similar between under rain conditions andunder no-rain conditions. The diurnal variation of land surface
brightness temperature or freezing level are possible causes ofthe diurnal variation under rain conditions. The reason why
TB (10V) is used to calculate CSI is thought to compensate thediurnal variation of TB (85V) under rain conditions.
ACKNOWLEDGMENT
This study is part of “production of a high-precision, highresolution global precipitation map using satellite data
(GSMaP)” supported by JST/CREST.
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Figure 4. Diurnal variation of (a) the number of occurrence, (b) TB(85V), (c) R_TMI, (d) R_TMI_M for the seven categories, which isshown in Fig.3 (a). Number on the solid line denotes the number ofcategory. Black dotted line in (b) is the statistics for “no-rain” case.

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