atmosphere
ArticleCharacterizing Ice-Scattering Homogeneity in TRMM Microwave
Imagers and Its Influence on Oceanic Rain-Rate Estimation Biasof TRMM Precipitation Radar
Andung Bayu Sekaranom 1,2, *, Emilya Nurjani 1 , Sandy Budi Wibowo 3
1

2
3

4

*

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Citation: Sekaranom, A.B.; Nurjani,
E.; Wibowo, S.B.; Masunaga, H.
Characterizing Ice-Scattering
Homogeneity in TRMM Microwave
Imagers and Its Influence on Oceanic
Rain-Rate Estimation Bias of TRMM
Precipitation Radar. Atmosphere 2021,
12, 1377. https://doi.org/10.3390/
atmos12111377
Academic Editor:
Sergio Fernández-González
Received: 12 September 2021

and Hirohiko Masunaga 4

Department of Environmental Geography, Faculty of Geography, Universitas Gadjah Mada,
Yogyakarta 55281, Indonesia; emilya.nurjani@ugm.ac.id
Center for Disaster Studies, Universitas Gadjah Mada, Yogyakarta 55281, Indonesia
Department of Geographic Information Science, Faculty of Geography, Universitas Gadjah Mada,
Yogyakarta 55281, Indonesia; sandy_budi_wibowo@ugm.ac.id
Institute for Space-Earth Environmental Research, Nagoya University, Furo-cho Chikusa-ku,
Nagoya 464-8601, Japan; masunaga@nagoya-u.jp
Correspondence: andungbayu@geo.ugm.ac.id

Abstract: Precipitation homogeneity is one of the main factors that contribute to the difference in therain-rate estimation from meteorological satellites. Using the Tropical Rainfall Measuring Mission(TRMM) products, this paper aims to characterize the homogeneity of ice-scattering signals from
TRMM Microwave Imagers (TMIs) as related to rain-rate estimation bias with TRMM Precipitation
Radar (PR). Statistical information about the polarization-corrected brightness temperature (PCT)from the TMI 85 GHz band is obtained over the global ocean in the tropics. The characteristics
are the fraction of PCT below a given threshold, the minimum value, and the standard deviationthat are calculated at a 0.25◦ × 0.25◦ grid level. The average values of rain-rate estimation from
TRMM PR and TMI in the same grid position and time are then compared. This result indicatesthat the rain-rate estimation bias is influenced by the homogeneity and organization of precipitation
systems. Using the statistical signature of ice-scattering signals at the grid level, an adjustment
was implemented for TMI rain-rate estimation. The results could produce rain-rate estimations
that conform more to PR, particularly for the inhomogeneous precipitation system mostly affectedby stratiform rain. The characterization of ice-scattering signals as a proxy to the precipitation
homogeneity, as presented in this research, could be implemented in order to improve the accuracyof satellite rain-rate estimation in the future.
Keywords: rain-rate estimation; precipitation homogeneity; Tropical Rainfall Measuring Mission

Accepted: 18 October 2021
Published: 21 October 2021

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1. Introduction
Rainfall analysis based on satellite precipitation estimation has yielded important
information on tropical precipitation systems that are less observable from the ground.
One of the estimation products that makes a significant contribution is the observation of
the Tropical Rainfall Measuring Mission (TRMM). TRMM, launched in 1997, is the firstsatellite that mounts a spaceborne precipitation radar (PR) aimed at identifying raindropsize particles [1]. The results of the TRMM observations have resulted in a more detailed
understanding of precipitation in the tropics. One example is the TRMM PR observation,
which can capture data related to the three-dimensional profile of tropical cyclones and how
they evolve. The three-dimensional profiling ability also has a significant contribution to
the characterization of diurnal rainfall patterns over tropical regions [2–4]. The information
gathered by TRMM also provides a significant contribution to numerical weather prediction
and climate models, particularly in terms of evaluating the physical parameters of clouds
and precipitation [5,6].

4.0/).

Atmosphere 2021, 12, 1377. https://doi.org/10.3390/atmos12111377

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In addition to precipitation radar (PR), TRMM also contains a number of comprehensive sensors, including the TRMM microwave imager (TMI) [7]. Rain-rate estimationfrom TRMM PR and TMI, together with other sensors and satellites, produces a combined
product called TRMM Multisatellite Precipitation Analysis (TMPA) [8]. The two rain-rate
estimation products mentioned above play an important role in producing rainfall estimates for the TMPA and other derivative products. One of the most important points tomention is that PR observations are spatially and temporally coincident with TMIs, which
could produce a calibration reference between active-passive sensors [9,10]. The calibrationreference is useful, not only for TRMM, but also for next-generation satellites.
The PR sensor on the TRMM operates at a radar frequency of 13.8 GHz, where therainfall information (R) is derived from the radar reflectivity (Z) received by the sensor [11].
The rainfall estimation on PR is based on the empirical relationship Z = aRb , which shows
the relationship between radar reflectivity and rain-rate by considering defined constants,
a and b. This relationship is related to the drop size distribution (DSD), where in theRayleigh limit, the radar reflectivity is the sixth moment of the DSD. The assumptions usedin determining the DSD are often one of the causes of differences between the estimatedresults and surface observations [12,13]. PR can also experience significant attenuationin heavy rainfall events, and therefore attenuation needs to be corrected. Correctionof attenuation in PR is carried out using a combination of two approaches. The first
approach is the Hitschfeld-Bordan method, which is not reliable for heavy rainfall but
produces better estimates at low rain-rates. The second approach is surface referencetechnique (SRT) methods, which have opposite characteristics to the Hitschfeld-Bordan
method [14]. The use of a hybrid approach covers the weaknesses of each method. However,
the assumption of attenuation correction of PR is often thought to be one of the sources ofdifferences between rainfall estimates and surface observations [15].
Precipitation estimation in TMI is based on the relationship between the brightness
temperature of several bands and precipitation. The 10, 19, 21, and 37 GHz bands capture
microwave emissions from precipitating particles, while the 85 GHz band captures icescattering signals reflected by cloud tops [16]. The TMI algorithm uses a Bayesian approachto determine the most likely amount of precipitation based on signatures from a set ofsignals captured by those bands, using the hydrometeor profile database as a reference.
One of the disadvantages of TMI is the low spatial resolution of emission bands. Thus,
the TMI may not be very sensitive to small-scale precipitation systems [17,18]. Another
weakness of TMI is that the variation in emission from the land surface results in interference with the signal that is received by the emission bands [19]. Therefore, up to the current
version (version 7), the rainfall estimation algorithm on land is based on ice-scattering
bands. In the ocean, emission and ice-scattering signals can be well received by sensors
and can become the basis for the estimation of precipitation in the ocean [1].
This paper focuses on the estimation products of PR and TMI in the tropical ocean
region to show how the different principles of active and passive sensors can affect theestimation results. One of the important points to be noted from previous studies isthat the differences in the estimation generated from these two sensors are regionallydependent [20]. For example, PR tends to identify higher precipitation than does TMI in
the northern Indian Ocean. In contrast, TMI results in a higher estimate of precipitation
than PR in the eastern Pacific Ocean. Furthermore, previous research shows that the TMI
tends to produce higher estimates of precipitation in organized but shallow precipitation
systems [21]. The above example indicates that precipitation-related processes that compose
the climatological characteristics of each region could affect the estimation [18].
The second important point to note in the rain-rate estimation difference of the two
products is the aspect of microphysical dependence [22,23]. For example, a comparisonof supercells over Oklahoma and shallow rain over Yemen shows that the precipitation
system contains a large ice-water content that is typical during a supercell, and the TMI
detects a larger rain area and estimates a higher rain-rate than PR [10]. However, when the
low ice-water content is low, particularly in a shallow precipitation system, the PR detects

Atmosphere 2021, 12, 1377

3 of 15a larger rain area and estimates a higher rain-rate than the TMI [21]. The TMI rain-rate
estimation is also known to have a strong relationship with the ice-water content [24].
Ice-scattering signals detected by the 85 GHz channel in the TMI peaked when the cloudheight was at a maximum. The maximum rainfall is often estimated in the TMI algorithm
under the above conditions [25]. However, there are a number of events where PR detects
maximum rainfall where ice particles are lower than those identified by the TMI [13].
The above conditions could presumably occur when intense collision and coalescenceprocesses occur [6,26].
The third important point is that the PR and TMI rain estimation difference is related to the spatial homogeneity of the precipitation. PR has a higher spatial resolution(approximately 4 km preboost and up to 5 km postboost) than TMI [27]. The TMI hasvaried resolution depending on its bands. The highest resolution is from the 85 GHz band
(5 km × 7 km in preboost/6 km × 8 km in postboost), while the lowest is from the 10 GHz
band (approximately 60 km in width during preboost and up to 70 km during postboost).
As mentioned earlier, one of the weaknesses of TMI is in detecting small-scale precipitation
systems [21]. For example, TMI shows the contribution of shallow organized precipitation
but shows a lower contribution than the PR for deep precipitation systems [21]. When thetwo products are compared statistically at the grid scale level, the PR shows higher rain-rate
variation than the TMI [13]. This means that the TMI is less sensitive to high precipitation
variability at the grid scale.
The above discussion highlights how the PR and TMI estimations could be biased,because each region has different precipitation characteristics. The main objective of thisresearch is to find whether spatial homogeneity information could be useful in explaining
the precipitation estimation difference between the two products. In this research, we use
the ice-scattering signatures obtained by the TMI 85 GHz channel as a proxy for the scaleof homogeneity. The TMI 85 GHz channels are used as a proxy for ice particles near theupper part of clouds that can vary on different scales of precipitation. The following
section explains the detailed TRMM products and the processing methods used in thisresearch. The results section is intended to explain how understanding the homogeneityand properties of the ice-scattering signature could be related to the rain-rate estimationdifference between the PR and TMI. The discussion section explains this in a more general
way and the manner in which the above information could be useful in future algorithm
development is summarized in the last section.
2. Materials and Methods
The focus of this section is to explain the type of TRMM data used to characterize
the PR and TMI rain-rate estimation differences, particularly using ice-scattering characteristics at the grid level. The TRMM version 7 data after postboost were used for the
analysis, starting from 1 January 2002 to 31 December 2006 (orbit number 23,559 to 52,014).
We intended to evaluate precipitation estimation differences over the ocean, where all TMI
channels were used as the basis of the estimation inside the TMI algorithm over the ocean.
The focus is the tropical ocean, between 15◦ north and 15◦ south over the global tropics.
The main product to be compared is the level 2 products, particularly near surface rain-rate
estimation from PR2A25 and surface rain-rate estimation from TMI 2A12. The TMI 85
GHz ice-scattering signals were obtained from TMI 1B11. In addition to the above products, convective/stratiform information was obtained from PR2A23. We limit the data togrids where the average rain-rates are higher than 1 mm/h from PR2A25 and TMI2A12.
This threshold was selected because it is higher than the minimum detection from PR and
TMI [1]. Therefore, we avoid false signals of rain/no-rain conditions that are often foundat lower rain-rates [28].
The comparison of the data is conducted at the grid level to populate a set of data
inside the grid where PR and TMI observe the same location at almost the same time.
We use a 0.25◦ × 0.25◦ grid where the precipitation estimation and other related data at theoriginal resolution were stored. The 0.25◦ × 0.25◦ spatial resolution is selected because it
contains a considerable amount of original pixel data from PR and TMI. The above spatial

Atmosphere 2021, 12, 1377

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resolution is also the same as the TMPA product, so the adjustment presented in this paper
can be useful for operational purposes. In this research, the average rain-rates from PR and
TMI inside the 0.25◦ grid are calculated, and the difference is represented in terms of thegridded rain-rate from PR minus the gridded rain-rate from TMI. The convective/stratiform
classification of each grid is determined by the most dominant type, as populated from
PR2A23. The TMI ice-scattering channel (85 GHz) brightness temperature data from 1B11
are also populated at the same grid. The vertical and horizontal polarizations (TBV and
TBH , respectively) from the TMI 85 GHz channel are utilized to calculate the polarizationcorrected brightness temperature (PCT) [29], where:
PCT = 1.818 TBV − 0.818TBH(1)

In short, each grid contains the average rain-rate for PR and TMI, statistical information about TMI 85 GHz PCT, and convective/stratiform precipitation.
The gridded TMI 85 GHz PCT data are the focus in explaining the difference between
rain-rate estimations of the two products. Figure 1 shows a comparison between the two
precipitation systems inside the 0.25◦ grid (red color bounding box). The images in the
top indicate a shallow precipitation system where the TMI 85 GHz PCT is warmer thanthe bottom images (later classified as a deep precipitation system). The first image in the
top left shows the PR rain-rate estimation value in its original footprint, while the secondin the middle is for TMI rain-rate estimation. Note that the average rain-rates inside thegrid are 5.9 mm/h and 3.7 mm/h for PR and TMI, respectively. The difference between
the gridded rain-rate from the two products is not as high as that in the bottom images.
The first image in the bottom left shows the PR rain-rate estimation value, where the grid
average is 16.2 mm/h. The TMI gridded rain-rate estimation value is only 5.7 mm/h.
The interesting point is TMI 85 GHz data in the right part of the figure. The standard
deviation for TMI 85 GHz PCT inside the grid is lower for the top images than for the bottom
images. The TMI 85 GHz standard deviation may reflect the variation in precipitationin each 0.25◦ grid. For example, a low standard deviation might be associated with ahomogeneous precipitation system, while high variation in a grid is likely to be associatedwith a specialization system that is less homogeneous.
In addition to the standard deviation, the difference in shallow/deep precipitation
systems could be an important source to address. Therefore, we calculate the minimum
TMI 85 GHz PCT (denoted as min TMI_PCT ) inside each grid. A brightness temperaturethreshold of 240 K is used to classify shallow or deep precipitation systems [30]. When theminimum TMI 85 GHz PCT inside a grid is less than 240 K, it is classified as a deep
precipitation system, and vice versa for a shallow precipitation system. To further analyze
the homogeneity inside the 0.25◦ grid, we use the fraction of TMI 85 GHz PCT pixels
that are lower than 240 K for deep precipitation grids. For shallow precipitation grids(characterized by warmer PCT than the deep precipitation system), we use the fraction of
TMI 85 GHz PCT pixels containing brightness temperatures of less than 273 K.
Information about homogeneity is not considered by the original TMI ocean algorithm,
since the estimations are estimated based on each pixel. However, it could be considered ina larger scope/area (using 0.25◦ × 0.25◦ spatial resolution in this research). The question
is to what degree can it influence the rain-rate estimation bias between PR and TMI.
As suggested in the above paragraph, the grid-scale homogeneity is characterized bystandard deviations of ice-scattering signals inside the 0.25◦ grid (σTMI_PCT ) and fractionsof ice-scattering signals ( f TMI_PCT ) lower than the threshold (240 K and 273 K for deepand shallow precipitation, respectively). To measure the degree to which both parameters
can influence the rain-rate estimation, an adjustment was conducted to derive the most
likely gridded rain-rate estimated by PR (R PR ) using a set of data derived from TMI as
the correction factor (TB85 CF). TB85 CF consists of four parameters, namely, the estimatedgridded rain-rate from TMI (R TMI ), minimum gridded TMI 85 GHz PCT (min TMI_PCT ),σTMI_PCT , and f TMI_PCT .

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FigureFigure1.1.Example
Exampleofof(a)(a)PRPRrain-rate
rain-rateestimation,
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GHzPCT
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than the 2nd example (d–f) at the bottom (indicating a deep precipitation system).
the 2nd example (d–f) at the bottom (indicating a deep precipitation system).

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PR data were considered the true value only to compare the degree to which they could
R adj = ∑ R PR · P( R PR | TB85 CF )(2)
match the TMI. A rain information
database was developed using the five years of observationThepreviously
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andbecausethe two periods
aretion
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each
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andknown to have different characteristics in terms of precipitation organization [31]. It is
itsalsocorresponding
𝐶𝐹. Convective/stratiform
were
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rectionfactor (𝑇 and𝐶𝐹), the probabilityof PR gridded
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wasrateevaluated(Figurewas obtained
matchedwith the (𝑃)database.
The adjusted
rain
was calculated
based on a set of rain-rate probabilities that correspond to any given TB85 CF as shown inphere 2021, 12, x FOR PEER REVIEW
Atmosphere 2021, 12, 1377

6 of 16
6 of 15

2). The adjusted rain-rate (𝑅 ) was calculated based on the sum of each possible rainrate in the databasethat(2).
weighted(multiplied)by wasits corresponding
probability,
where: TMI rain-rate
Equation
The adjusted
rain-ratethen comparedwith the original(before adjustment) and PR rain-rate at the same grid. The differences were explained=
𝑅 . 𝑃(𝑅|𝑇 Root
𝐶𝐹)Mean Square Error (RMSE).
𝑅(2)
using joint histogram,correlation(r), andFigure 2.ofIllustrationof thecontainuniquebinnedvalues offactor
correction
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contain thatuniquebinnedvaluesof correction
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corresponding probability of PR gridded rain-rate.

3. adjustment
Results
The above
was calculated based on a five-year period (2002 to 2006) andneeds to be validated
using
observationofdata
outside that range.
In this andpaper,
the valida3.1. General
Characteristics
the Ice-Scattering
Homogeneity
Its Influenceon PR-TMItion period isRain-Ratetaken by Estimation
contrastingBias
El Niño and La Niña events, because the two periods
are known to haveThe
different
characteristics
in terms
of precipitation[31]. It estimation
first partof this section
is intended
to explainorganization
the PR-TMI rain-rateis also important
to identify
whether
the algorithm
wellinonly
a specifictime
differenceby using
examplesfrom Elperformed
Niño events
2007inand
La Niña
events in 2009
forElcomparison.
The Thecomparison
considersa condition
where thePR1 estimation isperiod (during
Niño/La Niña).
El Niño also
validation
periodwas conductedfrom
higher
TMI andvice
versa.
generalexplanation
presented
December 2007,
to 28thanFebruary
2008,
while
the TheLa Niña
validation
periodwas fromin1 thisDe- subsection is
to introduce
inside inthebothdatabase,which
explained in the
cember 2009, intended
to 28 February
2010. theFordifference
any rain event
periods,
the is𝑇 further
𝐶𝐹 wassection.
obtained and next
matchedwith the database. The adjusted rain rate was calculated based on
As mentioned
the previous
the 𝑇rain-rate
a set of rain-rate probabilities
thatincorrespondtosection,
any given
𝐶𝐹 asestimation
shown in difference
Equation between thetwoproducts
isapparent
between
El
Niño
and
La
Niña
[30].
The
TMI
rain-rate(2). The adjusted rain-rate was then compared with the original TMI rain-rate (before
ad- estimation
often
higheratduring
El Niño
thandifferencesthat of PR.were
Previous
research
results
justment) andisPR
rain-rate
the samegrid. The
explained
using
joint also indicatethat the overestimation
comesfrom Error
organized
precipitation over the East Pacific Ocean,histogram, correlation(r), and Root Mean
Square(RMSE).
particularly during El Niño [21]. The organized precipitation appears to be shallow, and the
PR therefore estimates a lower rain-rate than TMI. To explain the difference, PR and TMI
3. Results
rain-rate contributions
between Homogeneity
the two events
fraction of specific PCT
3.1. General Characteristicsof the Ice-Scattering
andareItscompared.
Influence onThe
PR-TMI
values below a given threshold ( f TMI_PCT ) is used to represent the difference. The 273 K
Rain-Rate Estimation Bias
threshold ( f TMI_PCT273 ) is used for shallow precipitation systems, while the 240 K threshold
The first(partof this)section
is intended
todeepexplainthe PR-TMI
rain-rate estimationf TMI_PCT
thresholdis used for
precipitation
systems.
240
difference by usingFigure
examples
from
El
Niño
events
in
2007
and
La
Niña
eventsforin shallow
2009 for precipitation
3 shows the comparison of rain-rate contributions
comparison. The
comparison
also
considersacondition
where
the
PR
estimationishighersystems between PR and TMI gridded precipitation during El Niño in2007 and La Niña
than TMI andin
viceversa.
The
generalexplanation
presented
in
this
subsectionisintended2009. The fraction ( f TMI_PCT273 ) is classified into three classes based on its possible
to introduce thedifference
inside the database,whichis further
in theminimum
to maximum
range. A low
fraction(lessexplained
than or equal
tonext0.33)secmight be assocition.
ated with less organized precipitation, while a higher fraction indicates more organized
As mentioned
in the previous
section,the rain-rate
estimationdifference
precipitation(classified
as mediumif falls between
0.33–0.67
andbetween
higher ifthemore than 0.67).
two productsThe
is apparent
between
El
Niño
and
La
Niña
[30].
The
TMI
rain-rateestimation
results show that the PR rain-rate contribution is lower than the TMI when the PCT
is often higherfraction
during is
Elhigher,Niño thanthat of PR.
resultsThealsodifferenceindicate thatparticularly
forPrevious
shallow researchprecipitation.
is higher during

in 2009. The fraction (𝑓 _) is classified into three classes based on its possible minimum to maximum range. A low fraction (less than or equal to 0.33) might be associatedwith less organized precipitation, while a higher fraction indicates more organized precipitation (classified as medium if falls between 0.33–0.67 and higher if more than 0.67).
Atmosphere 2021, 12, 1377
7 of 15
The results show that the PR rain-rate contribution is lower than the TMI when the PCT
fraction is higher, particularly for shallow precipitation. The difference is higher during
El Niño since the rain-rate contribution is the lowest for PR. In contrast, the TMI rain-rate
contributionsEl
arehigher,the valuecontributionis almost equal
forlowest
differentof fractions.
Niño
sincesince
the rain-rateis thefor classes
PR. In contrast,
the TMI rain-rate
contributions are higher, since the value is almost equal for different classes of fractions.

Figure 3. Comparisonof contribution
PR rain-rate contribution(a) and TMI
rain-rate contribution(b)precipitation
for shallow systems
Figure 3. Comparisonof PR rain-rate(a) and TMI rain-rate
contribution(b) for shallow
precipitation
systems
duringNiñoineventsin 2007and LatropicalNiña events
2009 overglobalduring El Niño
events in 2007
and LaNiña Elevents2009 overthe global
ocean. in(Source:data theprocessing).
tropical ocean. (Source: data processing).

Figure 4 shows the comparison of rain-rate contributions between PR and TMI in
terms
ofthe
deep
precipitation
products indicate
higherFigure 4 shows
comparisonof systems.
rain-rateBoth
contributions
betweena PR
andrain-rate
TMI in contribution
the deep precipitation
systemduring
La Niña
compared
to Elcontribution
Niño. The two products
terms of deepof
precipitation
systems. Bothproducts
indicatea higherrain-rate
also conform to the higher contribution of precipitation from the shallow precipitationof the deep precipitation system during La Niña compared to El Niño. The two products
system during El Niño. However, it is clear that the PR shows a higher contribution ofalso conform to the higher contribution of precipitation from the shallow precipitation
the deep precipitation that contains a low PCT fraction compared to the TMI. The PR
system during El Niño. However, it is clear that the PR shows a higher contribution of thealso estimates a higher contribution from precipitation with a medium
PCT
here 2021, 12, x FOR PEER REVIEW
8 of
16 fraction thandeep precipitation that contains a low PCT fraction compared to the TMI. The PR also
from precipitation with a high PCT fraction. The rain contribution difference between theestimates a higher contribution from precipitation with a medium PCT fraction than frommedium and high PCT fractions from the TMI is less significant than that from the PR.
precipitation with a high PCT fraction. The rain contribution difference between the medium and high PCT fractions from the TMI is less significant than that from the PR.

Figure 4. Comparisonof PR
rain-rate contribution
and TMIrain-rate contribution
for deep systems
Figure 4. Comparisonof PR rain-rate
contribution(a) and TMI(a)rain-rate
contribution(b) for deep(b)precipitation
precipitation
systems
duringEl
Niño
events
in
2007
and
La
Niña
events
in
2009
over
the
globalduring El Niño events in 2007 and La Niña events in 2009 over the global tropical ocean. (Source: data processing).
tropical ocean. (Source: data processing).

Table 1 shows a significant difference when considering the fraction of the PCT threshold fora shallow
precipitationin general, notin relation
to the comparison
Table 1 shows
significant
differencesystems
when considering
the only
fractionof the PCT
between
El Niño andsystems
La Niña
is explained
difference
threshold for shallow
precipitation
inwhichgeneral,not only inabove.
relationTheto thecompar-is separated bywhether
theLa
PRNiñarain-rate
is above.
higher The
thandifference
the TMI is(PRison between El
Niño and
whichestimation
is explained
separated
RR > TMIRR ) and viceby whether the PR rain-rate estimation is higher than the TMI (PRRR > TMIRR) and viceversa (PRRR < TMIRR). The difference is characterized by the average value of the standard
deviation ( 𝜎 _ ) , convective fraction ( 𝑓 _), and the minimum PCT value(𝑀𝑖𝑛𝑇𝑀𝐼_𝑃𝐶𝑇 ). The convective fraction obtained from the ratio of convective pixels to theAtmosphere 2021, 12, 1377

8 of 15versa (PRRR < TMIRR ). The difference is characterized by the average value of the standard deviation (σTMI_PCT ), convective fraction ( f PR_conv ), and the minimum PCT value( Min TMI_PCT ). The convective fraction obtained from the ratio of convective pixels to thesum of convective and stratiform pixels from TRMM PR2A23. The result shows that ahigher estimation achieved by PR (compared to TMI) is associated with a large variation in
PCT captured by the TMI 85 GHz channel (higher standard deviation). The TMI could also
estimate a higher rain-rate than PR but was associated with a lower variation in PCT thanwhen PR estimated a higher rain-rate than TMI. A comparison of the f PR_conv from the PRrain type product at the same grid position indicates that the convective fraction is lower
for a condition where PR identifies a higher rain-rate than TMI, compared to when the TMI
estimates a higher rain-rate than PR. There is also a difference in Min TMI_PCT when PR
estimates a higher rain-rate than TMI and vice versa. The higher rain-rate estimation from
PR is also associated with a lower value of Min TMI_PCT , compared to when TMI estimatesa higher rain-rate. The above differences are found from precipitation with low to highPCT fractions. The above properties are similar for deep precipitation systems (Table 2),
although the difference is higher in terms of σTMI_PCT and Min TMI_PCT .
Table 1. Difference in the statistical characteristics of gridded TMI 85 GHz PCT standard deviation, PR convective fraction,and minimum TMI 85 GHz PCT for shallow precipitation system based on fraction of number of TMI 85 GHz PCT below
273 K threshold (Source: data processing).
fTMI_PCT273 ≤ 0.33

0.33 < fTMI_PCT273 ≤ 0.67

0.67 < fTMI_PCT273

0.25◦ × 0.25◦
Grid

PRRR > TMIRRPRRR < TMIRRPRRR > TMIRRPRRR < TMIRRPRRR > TMIRRPRRR < TMIRRσTMI_PCTf PR_conv
Min TMI_PCT

5.63
0.47
259.354.44
0.77
262.376.98
0.64
253.375.87
0.87
256.356.26
0.90
249.365.85
0.96
250.48

Table 2. Difference in the statistical characteristics of gridded TMI 85 GHz PCT standard deviation, PR convective fraction,and minimum TMI 85 GHz PCT for deep precipitation system based on fraction of number of TMI 85 GHz PCT below 273
K threshold (Source: data processing).
fTMI_PCT240 ≤ 0.33

0.33 < fTMI_PCT240 ≤ 0.67

0.67 < fTMI_PCT240

0.25◦ × 0.25◦
Grid

PRRR > TMIRRPRRR < TMIRRPRRR > TMIRRPRRR < TMIRRPRRR > TMIRRPRRR < TMIRRσTMI_PCTf PR_conv
Min TMI_PCT

10.86
0.62
212.977.47
0.87
221.8015.02
0.68
197.899.19
0.90
214.1215.98
0.71
186.689.81
0.90
204.463.2. The PR-TMI Rain-Rate Estimation Difference as Related to the TMI 85 GHz PCT Minimum
Value and Standard Deviation
This subsection focuses on two significant points to be noted in the rain-rate database,namely, the minimum value TMI 85 GHz PCT inside each grid and its deviation. As suggested in the previous section, there are differences in the rain-rate estimation between thetwo products, which are influenced by precipitation inhomogeneity. The difference in theminimum TMI 85 GHz PCT value ( Min TMI_PCT ) and its standard deviation (σTMI_PCT )are explained in this section using information obtained from the database. The first resultin Figure 5 shows the joint frequency histogram of the rain-rate difference in terms of gridscale, regarding. Min TMI_PCT . In this subsection, the differences are separated between
convective and stratiform precipitation based on dominant rain type pixels inside the grid.
The result shows that the difference in convective precipitation is not symmetrical between
the negative and positive values. For convective rain grids, the frequency is higher for thenegative value (PR estimate less rain-rate than TMI) for PCT ranges from approximately
220 K to 260 K. The positive bias is higher in lower PCT (PR estimate higher rain-rate than
TMI) ranges from 100 K to 220 K. For the stratiform cases, it is clear that the positive bias is
more dominant from the lowest PCT range at 100 K to 270 K.

Atmosphere 2021, 12, 1377

The result shows that the difference in convective precipitation is not symmetrical between the negative and positive values. For convective rain grids, the frequency is higher
for the negative value (PR estimate less rain-rate than TMI) for PCT ranges from approximately 220 K to 260 K. The positive bias is higher in lower PCT (PR estimate higher rainrate than TMI) ranges from 100 K to 220 K. For the stratiform cases, it is clear that9 theof 15
positive bias is more dominant from the lowest PCT range at 100 K to 270 K.

Figure 5. Joint frequency histogram of the gridded rain-rate estimation difference between PR and TMI regarding the

Figure2021,
5. Jointx FOR
frequency
histogram of the gridded rain-rate estimation difference between PR and TMI regarding the10 of 16
Atmosphere
PEERPCTREVIEW
minimum 12,
TMI 85 GHz
value at the same grids for (a) convective precipitation and (b) stratiform precipitation. (Source:
minimum TMI 85 GHz PCT value at the same grids for (a) convective precipitation and (b) stratiform precipitation.
data processing).
(Source: data processing).

Figures 6 and 7 show the frequency histogram of the rain-rate difference between theseparated
betweenanddeep precipitation
systemsbaseddifferenceonthe minimum
PCT
twoFigures
products
at thegrid thescale
regarding
σTMI_PCTofin
therain-rate
rain-rate
database.
The results
6 and
7 shallow
show
frequency
histogramthebetweenthevalue.
The
differencesintheshallow
precipitation
systemsarefurther
separated
intoconareseparated
betweenshallowanddeep
precipitation
systems
based
on
the
minimumtwo products at the grid scale regarding 𝜎 _ in the rain-rate database. The results are
vectiveand Thestratiform
systems,
is similar
to the systems
previousare
result.
Forseparated
shallow conPCT value.
differencesin thewhichshallow
precipitation
further
into
vectiverain,PRestimatesalower
rain-rate
than
TMI
when
the
standard
deviationislowconvective and stratiform systems, which is similar to the previous result. For shallow
(the
left
of
Figure6).
Forshallowstratiform
rain
(the
right
of
Figure
6),
PR
tends
to
esticonvective rain, PR estimates a lower rain-rate than TMI when the standard deviation ismatea higherthanparticularly
whenthestandardlow (theleft ofrain-rate
Figure 6).
ForTMI,
shallowstratiform
rain
(the
right ofdeviations
Figure 6),arePR high.
tends toestimate a higher rain-rate than TMI, particularly when the standard deviations are high.

Figure 6. Joint frequency histogram of the gridded rain-rate estimation difference between PR and TMI regarding the
Figure 6. Joint frequency histogram of the gridded rain-rate estimation difference between PR and TMI regarding thestandard deviation of TMI 85 GHz PCT at the same grids for (a) shallow convective precipitation and (b) shallow stratiform
standard deviation of TMI 85 GHz PCT at the same grids for (a) shallow convective precipitation and (b) shallow stratiprecipitation. (Source: data processing).
form precipitation. (Source: data processing).

Figure 7 shows a histogram like the previous figure, but for the deep precipitation
system. For deep convective rain, the difference is found particularly when the standard
deviation is low. The PR tends to estimate a lower rain-rate than TMI when the precipitation is homogeneous, as indicated by several events at the bottom part of the left figure.

Atmosphere 2021, 12, x FOR PEER REVIEW
Atmosphere 2021, 12, 1377

11 of 16
10 of 15

Figure 7. Joint frequency histogram of the gridded rain-rate estimation difference between PR and TMI regarding the
Figure 7. Joint frequency histogram of the gridded rain-rate estimation difference between PR and TMI regarding thestandard deviation of TMI 85 GHz PCT at the same grids for (a) deep convective precipitation and (b) deep stratiform
standard deviation of TMI 85 GHz PCT at the same grids for (a) deep convective precipitation and (b) deep stratiform
precipitation. (Source: data processing).
precipitation. (Source: data processing).

Figure 7 shows a histogram like the previous figure, but for the deep precipitation
3.3. Implementationof the TMIrain,
Rain-Rate
Estimation
system.
For deep convective
the difference
is Adjustment
found particularly when the standard
deviation
low. The PR
tends
estimatea lowerrain-rate
than
TMI
when
the precipitaThis issubsection
shows
thetoresultof theadjustmentin the
grid
level
based
on the aption
is homogeneous,as indicatedby several
eventsareat thebottom partof theleft
proachexplained in themethodology.
The results
represented
in theform
offigure.
a joint
However,thedistribution
of
the
bias
for
the
higherstandard
deviationshowsasimilarfrequency histogram between the rain-rate difference and the grid minimum TMI 85 GHz
frequency
betweenthe positive
and negativevalues. For
deepstratiformand
rain,stratiform
it is clear that). The result
is also separated
into
convectiverain,
PCT value(𝑀𝑖𝑛𝑇𝑀𝐼_𝑃𝐶𝑇
PR
mostlyestimatesahigherrain-rate
than
TMI
in
all
rangesofdeviation.
The
standard
which is similar to the previous subsection and is referring to the original data andadjustdeviationof deep
stratiform andrain stratiform
is also higher
than thatconvective
rain. The
ment result.
The convective
fractions
fromofPR
are not included
in higher
the adstandard
in theice-scattering
stratiform part
mightbecomesindicate thea gridthatofisthis
inhomogeneous.
justmentdeviation
since the TMI
channelfocus
analysis.
The comparison
beforeand after adjustment
conducted for the El Niño event at the3.3. Implementationof theTMI Rain-Rate
Estimation Adjustment
end of 2007 is shown in Figure 8. The original data for convective rain (top left) are slightly
This subsection shows the result of the adjustment in the grid level based on thebiased to the right. This means that TMI tends to estimate a lower rain-rate than PR whenapproach explained in the methodology. The results are represented in the form of athere are strong ice-scattering signals. The difference is larger for the stratiform rain origjoint frequency histogram between the rain-rate difference and the grid minimum TMI 85
inal data, where PR tends to estimate higher rain-rates than TMI except for the bottom
GHz PCT value ( Min TMI_PCT ). The result is also separated into convective and stratiform
part (shallow precipitation). The result of the adjustment for convective rain is shown inrain, which is similar to the previous subsection and is referring to the original data andthe bottom left of Figure 8. Although the result shows that the correlation between theadjustment result. The convective and stratiform fractions from PR are not included in thetwo products
is thehigherthe differencein termsof RMSEis lower,
the distribution
adjustment
since
TMIandice-scatteringchannelbecomesthe focusof this analysis.
changesslightly
to
the
left.
Therefore,
at
a
lower
PCT,
the
adjustment
appears
to at
bethe
too
The comparison before and after adjustment conducted for the El Niño event
high
for
the
original
TMIrain-rate.
The
stratiform
rain-rateadjustment
is
shown
in
the
end of 2007 is shown in Figure 8. The original data for convective rain (top left) are slightly
bottomtorightof Figure8. Thethatchangesappearbe better
thanrain-rate
the convective
asbiasedthe right.
This means
TMI tends
to toestimatea lowerthan PRpart,when
indicatedbytheimprovementinthecorrelation
value
and
lower
RMSE.
The
histogram
there are strong ice-scattering signals. The difference is larger for the stratiform rain originalalso showsin the distributionof the bias
be centeredat thezerobottomlines. part
data,
where improvement
PR tends to estimate
higher rain-rates
thantoTMI
except for(shallow precipitation). The result of the adjustment for convective rain is shown in thebottom left of Figure 8. Although the result shows that the correlation between the two
products is higher and the difference in terms of RMSE is lower, the distribution changes
slightly to the left. Therefore, at a lower PCT, the adjustment appears to be too high forthe original TMI rain-rate. The stratiform rain-rate adjustment is shown in the bottom
right of Figure 8. The changes appear to be better than the convective part, as indicatedby the improvement in the correlation value and lower RMSE. The histogram also shows
improvement in the distribution of the bias to be centered at zero lines.

Atmosphere 2021, 12, 1377
Atmosphere 2021, 12, x FOR PEER REVIEW

11 of 15
12 of 16

Figure8. Comparisonof theresultduringthetheEl El
Niño
the adjustment
adjustmentwas
wasimplemented
implemented for
Figure8. Comparisonof adjustment
the adjustment
resultduringNiñoevent
eventinin2007.
2007.(a)(a) Before
Before theconvective precipitation, (b) after the adjustment was implemented for convective precipitation, (c) before the adjustment was imfor convective precipitation, (b) after the adjustment was implemented for convective precipitation, (c) before the adjustment
plemented for stratiform precipitation, and (d) after the adjustment was implemented for stratiform precipitation (source: data prowas implemented for stratiform precipitation, and (d) after the adjustment was implemented for stratiform precipitation
cessing).
(source: data processing).

Figure 99 shows
shows the comparison
comparison before and after adjustment, similar to the previous
Figureresult,
but
for
the
La
Niña
event at the end of 2009. The
The result
result isis similar
similar to the comparison
result,of El Niño events, where the adjustment is better for stratiform rain than for convectiveofrain. However,
However, it should
should be noted
noted that there is no clear
clear difference
difference between El Niño and La
rain.
Niña inin terms
terms ofof distribution
distribution regarding
regarding thethe PCT.
PCT. This means
means that thethe relationshiprelationship between
Niña
PR
and
TMI
rain
estimation
bias
regarding
PCT
does
not
changeovertime.
However,
PR and TMI rain estimation bias regarding PCT does not change over time.
However,thethechangesinthefrequency
of
the
scale
of
precipitation
organizationasaffectedby ENSO
ENSO
changes in the frequency of the scale of precipitation organization as affected bycould generate
generate temporal
temporal variation,
variation, where
where PR/TMI
PR/TMIestimatesestimateshigher
higherrain-rates.
rain-rates.
couldAtmosphere2021,
12,12,
1377
Atmosphere2021,
x FOR PEER REVIEW

1213
of of
1516

Figure9. 9.
Comparisonof theadjustment
resultduringthe LaNiña
in 2009.
Beforeadjustment
was implemented
FigureComparisonof theadjustment
resultduringtheLa event
Niña event
in(a)
2009.
(a) the
Beforethe adjustment
was implemented
forconvective
precipitation,
(b)
after
the
adjustment
wasimplemented
forconvective
precipitation,
before thefor convective precipitation, (b) after the adjustment was implemented for convective precipitation, (c) before the (c)adjustment
adjustment
wasimplemented
forstratiform
precipitation,
and
(d)
after
the
adjustment
wasimplemented
forstratiform
was implemented for stratiform precipitation, and (d) after the adjustment was implemented for stratiform precipitation
precipitation(source:
dataprocessing).
(source: data processing).

4.4.Discussion
Discussion
This
Thissection
sectiondiscusses
discussesthe
thePR-TMI
PR-TMIfundamental
fundamentaldifference
differenceininrain-rate
rain-rateestimation
estimation
based
GHz
ice-scattering
shown
inin
basedononinformation
informationobtained
obtainedfrom
fromthetheTMI
TMI8585GHz
ice-scatteringsignals,
signals,asas
shown
the
previous
section.
Beforetheresultsarediscussed,itisimportanttoreviewtheconcept
the previous section. Before the results are discussed, it is important to review the conceptbehindtheice-scattering
signalsreceived
by bythetheTMITMI85 GHZ
channel.
Strongice-scatteringbehindtheice-scattering
signalsreceived
85 GHZ
channel.
Strongice-scattersignals
indicatethat there
large
of ice particles
at the top
part
ofpartprecipitating
ing signals
indicatethat arethere
are amounts
large amountsof ice particles
at thetopof precipiclouds
This
usually
happenshappens
when strong
clouds exist
at exista considerable
tating[32].
clouds[32].
This usuallywhenconvective
strong convective
cloudsat a considheighttheabovefreezing[26].level
Strongconvective
clouds areclouds
also often
associatedwitherableabove
heightthe level
freezing[26].
Strong convective
are also
often associheavy
rainfallnear
thesurface.
Therefore,
strongerice
scatteringcanbeinterpretedtohaveated with heavy rainfall near the surface. Therefore, stronger ice scattering can be intera preted
larger amount
ice particles,
highertops,higher
and heavier
precipitation.
to have ofa largeramountof icecloudparticles,
cloud tops,
and heavier precipitaWhen
there
are
cloudsthat
containa
specificamountoficeparticleswith no significant
tion.
differencefromits
surroundings
over
a
large
area
(e.g.,
atthe
gridscale,as shown
thisWhen there are clouds that contain a specific amount of ice particles
with noinsignifiresearch),theprecipitation
will
appeartobehomogeneous.
In
contrast,
when
there
arein
cant difference from its surroundings over a large area (e.g., at the grid scale, as shown
large
in theamount ofwill
ice particles,
might be a large
variationwhen
in terms
this differences
research), theprecipitation
appear tothere
be homogeneous.
In contrast,
there
ofare
cloud
heights
andprecipitation.
For
example,inthisstudy,
oneoftheparameterslarge differences in the amount of ice particles, there might be a large variationtoin

Atmosphere 2021, 12, 1377

13 of 15

measure is whether the fraction of TMI 85 GHz PCT is lower than 240 K ( f TMI_PCT240 ).
The larger number of PCT pixels that are lower than the above threshold, which also
have no significant deviation, indicates deep convective clouds that contain a significant
amount of rain over a large area. In contrast, a smaller number of PCT pixels lower than
the threshold, which is also associated with high deviation, might be interpreted as deep
convective clouds surrounded by much lower stratiform clouds.
The TMI is known to underestimate the rain-rate from isolated precipitation systems,
which is possibly related to the large TMI footprint for emission channels [21]. In accordance with previous research, the TMI tends to estimate a lower rain-rate than PR for lessorganized systems, as shown in Figures 3 and 4. The characteristics of TMI estimationin Figure 5 show that it often estimates higher rain-rates than PR for shallow convective
precipitation that is heavily organized. In contrast, PR often estimates a higher rain-rate
than TMI when there is large variation in the precipitating clouds. Previous research
indicates that a higher PR estimation might be associated with less organized precipitation [30]. In addition to the previous research results, this research shows that the higher
PR estimation is attributed to precipitating stratiform clouds that contain large variationsin ice particles (Figures 6 and 7). The variation in ice particles also means that there arevariations in terms of cloud heights and precipitation. The strong ice-scattering signals
and their large variation indicate that they might be associated with a small-deep convective system surrounded by stratiform rain, as previously explained. Since the convective
part is much less than the stratiform part, in this research, it is classified as stratiform
precipitation. It should be noted that TMI estimation also depends on emission channels
that have a large footprint. The analysis is conducted at a 0.25◦ × 0.25◦ grid resolution(approximately 27.75 km × 27.75 km near the equator), while the largest TMI emission
footprint is 72 km × 43 km (at 10 GHz). This kind of characteristic is not observable fromTMI emission channels. As a result, TMI estimates a lower rain-rate than PR.
The TMI rain-rate adjustment explained above indicates that the characteristics related
to precipitation homogeneity can influence the rain-rate estimation bias between PR and
TMI. Figures 8 and 9 show that the adjustment produces rain-rate estimations from TMI
that conform more to PR rain estimation than the original product. However, there arestill large variations in the rain-rate estimation bias from the two products, particularly forconvective precipitation. The TMI does not have information related to the type of precipitation and therefore is not included in the adjustment. As a result, the method developedin this research does not differentiate convective and stratiform precipitation. Since theestimation bias for stratiform precipitation is relatively linear compared to convective precipitation, the algorithm works well in terms of increasing correlation and lower difference.
The adjustment produces a higher rain-rate estimation compared to the original estimation
for stratiform precipitation. Therefore, the adjustment could produce rain-rate estimations
that conform more closely with PR. However, when a similar adjustment is implemented
to convective precipitation, it becomes higher than PR, and the joint histogram is slightly
biased to the left.
5. Conclusions
In summary, this paper highlights the PR-TMI rain-rate estimation differences that are
influenced by precipitation organization and homogeneity. The TMI estimates a higher
rain-rate than PR when it detects precipitation from heavily organized precipitation that has
homogeneous characteristics. However, it estimates a lower rain-rate than PR when there
is deep but less organized precipitation that has inhomogeneous characteristics. The above
difference might be associated with TMI emission channels that have a relatively large footprint compared to PR. At the grid level, the information about precipitation organizationand homogeneity obtained from the TMI 85 GHz ice-scattering signature could produce
adjustments, so TMI rain-rate estimation becomes more consistent with PR to a certain
degree. This is particularly applicable for inhomogeneous rain that shows large variationsin precipitating clouds and is dominated by stratiform precipitation. The TMI-based ad-

Atmosphere 2021, 12, 1377

14 of 15

justment for convective precipitation, although slightly improved, is also influenced bystratiform precipitation that is not differentiated in the rain-rate database.
The differentiation of convective-stratiform precipitation in the adjustment algorithm
might produce a better result than that presented in this research. Information about theconvective-stratiform fraction might be obtained from PR rain-type products (in PR2A23)
and included in the database. However, since the TMI swath is three times larger than
the PR swath, the PR rain-type product will only be applicable when the PR and TMI
data overlap. In other words, it will not be useful when the only available information isfrom passive microwave data and therefore is not included in the analysis. Improvementof the footprint size in the future of TRMM satellites, such as GPM, might also reduce
the estimation difference. However, the largest footprint for the GPM Microwave Imager
is 32 km × 19 km (at 10.65 GHz) [33]. Compared to the GPM dual precipitation radar,which has a 5 km × 5 km footprint, the GPM footprint is still larger. Therefore, bias due todifferent precipitation organizations and homogeneity is predicted to exist.
This research not only contributes to the improvement of satellite rain-rate estimation
products but also gives an insight into how the precipitation process at a small scale (subgrid level) could affect the higher scale (grid level). For example, inhomogeneous rainfall
generated by deep isolated precipitation systems could produce a considerable rain-rate at
the local scale but is often underestimated at the grid level [13]. In relation to precipitation
downscaling, estimating rain-rates at the sub-grid level in the above case often becomesproblematic [34]. However, characterization of the ice-scattering signatures as presented
in this study also could be considered in the precipitation downscaling process to obtain
more reliable results.
Author Contributions: Conceptualization, H.M. and A.B.S.; methodology, A.B.S.; validation, A.B.S.
and S.B.W.; formal analysis, A.B.S. and E.N.; investigation, A.B.S.; resources, H.M. and E.N.; writing—original draft preparation, A.B.S.; visualization, S.B.W.; supervision, H. M; project administration,
E.N. and S.B.W.; funding acquisition, A.B.S. and E.N. All authors have read and agreed to the
published version of the manuscript.
Funding: This research was funded by a Grant of “Penelitian Dasar Perguruan Tinggi (PDUPT)—SIMLITABMAS” from the Indonesian Ministry of Education and Culture in 2021 with Dr. Andung
Bayu Sekaranom as the principal investigator (Contract number: 1632/UN1/DITLIT/DIT-LIT/2021).
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: TRMM PR (2A25) and TMI (2A12), and other TRMM datasets (TMI1B11,
PR2A23) analyzed in this work are available online from the NASA Precipitation Measurement
Mission (PMM) archives (https://pmm.nasa.gov/data-access/downloads/TRMM) accessed in 30
September 2018.
Conflicts of Interest: The authors declare no conflict of interest.

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2.
3.
4.
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