Atmospheric Research 163 (2015) 61–73

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Atmospheric Research

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An improved procedure for the validation of satellite-basedprecipitation estimates

Ling Tang a,b,⁎, Yudong Tian a,b, Fang Yan c, Emad Habib c

a Earth System Science Interdisciplinary Center (ESSIC), University of Maryland, College Park, MD, 20740, USAb Code 617, Hydrological Sciences Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, 20771, USAc Department of Civil Engineering, University of Louisiana at Lafayette, P.O. Box 42991, Lafayette, LA, 70504, USA

⁎ Corresponding author at: Hydrological Sciences LaborSpace Flight Center, Greenbelt, MD 20771, USA.

http://dx.doi.org/10.1016/j.atmosres.2014.12.0160169-8095/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 21 March 2014Received in revised form 19 December 2014Accepted 23 December 2014Available online 15 January 2015

Keywords:Satellite-based precipitation estimatesValidation procedureAdditive and multiplicative error modelLogarithmic transformationUncertainty estimation

The objective of this study is to propose and test a new procedure to improve the validation of remote-sensing,high-resolution precipitation estimates. Our recent studies show thatmany conventional validationmeasures donot accurately capture the unique error characteristics in precipitation estimates to better inform both data pro-ducers and users. The proposed new validation procedure has two steps: 1) an error decomposition approach toseparate the total retrieval error into three independent components: hit error, false precipitation and missedprecipitation; and 2) the hit error is further analyzed based on amultiplicative error model. In themultiplicativeerror model, the error features are captured by three model parameters. In this way, the multiplicative errormodel separates systematic and random errors, leading to more accurate quantification of the uncertainties.The proposed procedure is used to quantitatively evaluate the recent two versions (Version 6 and 7) ofTRMM’s Multi-sensor Precipitation Analysis (TMPA) real-time and research product suite (3B42 and 3B42RT)for seven years (2005–2011) over the continental United States (CONUS). The gauge-based National Centersfor Environmental Prediction (NCEP) Climate Prediction Center (CPC) near-real-time daily precipitation analysisis used as the reference. In addition, the radar-basedNCEP Stage IV precipitation data are alsomodel-fitted to ver-ify the effectiveness of themultiplicative errormodel. The results show that winter total bias is dominated by themissed precipitation over the west coastal areas and the Rocky Mountains, and the false precipitation over largeareas in Midwest. The summer total bias is largely coming from the hit bias in Central US. Meanwhile, the newversion (V7) tends to produce more rainfall in the higher rain rates, which moderates the significant underesti-mation exhibited in the previous V6 products. Moreover, the error analysis from the multiplicative error modelprovides a clear and concise picture of the systematic and random errors, with both versions of 3B42RT havehigher errors in varying degrees than their research (post-real-time) counterparts. The new V7 algorithmshows obvious improvements in reducing random errors in both winter and summer seasons, compared to itspredecessors V6. Stage IV, as expected, surpasses the satellite-based datasets in all the metrics over CONUS.Based on the results, we recommend the new procedure be adopted for routine validation of satellite-based pre-cipitation datasets, andweexpect theprocedurewill work effectively for higher resolution data to be produced inthe Global Precipitation Measurement (GPM) era.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Space-borne precipitation products, with their global coverage, highresolution, frequent sampling and easy access, have beenwidely used invarious applications (e.g., natural hazards, hydrology, agricultural fore-casts, and climate studies). However, the errors associated with thesesatellite precipitation products need quantitative evaluation, becauseof the highly nonlinear nature of the physical process to measure pre-cipitation from space. The strengths and limitations of those satelliteprecipitation products need to be understood so they can be interpreted

atory, Code 617, NASA Goddard

correctly between the data-producing community and data users, espe-cially during the Global Precipitation Measurement (GPM) era withlarge volume of higher resolution (~10 km, hourly) precipitation dataexpected to be generated in near future (Huffman et al., 2012).

Quantitative evaluation of satellite precipitation products is critical forboth data producers and external users. On one hand, effective error anal-ysis will yield insight into the sources of errors in the precipitation prod-ucts and possible ways to correct or reduce them. This will lead to theimprovement of next generation data algorithms and enhance theirdata quality. On the other hand, for end users, such evaluation and errorcharacteristics analysis will give better guidance in selecting productsfor their particular applications, and help them assess the impact ofinput errors propagated into their applications (Tian et al., 2009).

62 L. Tang et al. / Atmospheric Research 163 (2015) 61–73

The Algorithm Inter-comparison Projects (AIP) of the Global Precip-itation Climatology Project (GPCP) (e.g., Arkin andXie, 1994; Ebert et al.,1996), the Precipitation Inter-comparison Projects (PIP) (e.g., Smithet al., 1998; Adler et al., 2001), and a comprehensive validation studyat global scale called the Pilot Evaluation of High Resolution Precipita-tion Products (PEHRPP) (Arkin and Turk, 2006) are examples of majorpast inter-comparison studies. The International Precipitation WorkingGroup (IPWG, online at www.isac.cnr/it~ipwg/), builds upon the earlierevaluation experiences, has established a validation program to provideboth the data producers and external userswith up-to-date informationon the quality of the precipitation estimates from virtually all the oper-ational satellite algorithms (Ebert et al., 2007). Meanwhile, a number ofnew multi-sensor precipitation algorithms have been developed to ex-ploit the complementary strengths of three different types of precipita-tion measuring sensors: Infrared (IR), Passive Microwave (PMW)Radiometers, and Precipitation Radar (PR) (e.g., Sorooshian et al.,2000; Joyce et al., 2004; Huffman et al., 2007). Some multi-sensor pre-cipitation products also incorporate ground-based precipitation mea-surements, such as rain gauge data. A considerable number ofevaluation studies have been devoted to the error analysis and uncer-tainty quantification for satellite-based precipitation products(e.g., McCollum et al., 2002; Gottschalck et al., 2005; Ebert et al., 2007;Hossain and Huffman, 2008; Lin and Hou, 2008; Tian andPeters-Lidard, 2007; Tian et al., 2007, 2009; Sapiano and Arkin, 2009;Kubota et al., 2009; Habib et al., 2009a; Tian and Peters-Lidard, 2010;Tian et al., 2010; Kirstetter et al., 2012; Tian et al., 2013; Chen et al.,2013a,b; Maggioni et al., 2014; Tang et al., 2014). Most of these re-searches used conventional error metrics to quantify the uncertainties(e.g. bias, root mean square error). For instance, Ebert et al. (2007) eval-uated several operational satellite and numerical weather prediction(NWP) precipitation products, against gauge-based data sets over thecontinental US, Australia, and Europe, using several conventional errormetrics (e.g., correlation, bias ratio, probability of detection and falsealarm ratio, etc.). They found that satellite precipitation estimates aremore accurate during summer and at lower latitudes. Meanwhile,Hossain and Huffman (2008) proposed a conceptual framework for de-veloping error metrics in three general dimensions: 1) spatial (howdoes the error vary in space?); 2) retrieval (how “off” is each precipita-tion estimate from the true value?); and 3) temporal (how does theerror vary in time?). They employed formulations for error metrics spe-cific to each dimension, in addition to the conventional error metrics.They applied the error framework on four satellite precipitation prod-ucts and found that this error framework can identify seasonal and re-gional differences in uncertainties of data sets more clearly than theconventional error metrics.

Some recent validation studies focused on the performance of thenewest version (V7) of Tropical Rainfall Measurement Mission(TRMM) Multi-sensor Precipitation Analysis (TMPA). Yong et al.(2013) compared the performance of TMPA real-time and post-processed products 3B42RT and 3B42 Version 7 (V7) with the previousVersion 6 (V6) over two river basins in China, and found that V7 algo-rithm significantly reduced systematic bias in the low-latitude riverbasin, while it was ineffective in the high-latitude river basin. Y. Chenet al. (2013) evaluated 3B42 V7 precipitation estimates for tropical cy-clone rainfall on two terrain types: low-lying atoll sites (considered asopen ocean), and coastal and island sites (land). The results show that3B42V7 tends to overestimate heavy rain frequency on atoll sites, andunderestimate heavy rain frequency on coastal and island sites. Chenet al. (2013a,b) gave comprehensive evaluations of TMPA V7 productsover China and continental US against the daily gauge analysis, andfound that relative bias and RMSE significantly decreasedwhile correla-tion increases from V6 to V7. Generally most studies agree that forheavy rainfall, significant underestimation observed in 3B42 V6 is re-duced in 3B42 V7 (e.g., Li et al., 2013; Xue et al., 2013; Y. Chen et al.,2013; Chen et al., 2013a,b). The underestimation in heavy rainfall ismost severe over higher terrain (e.g., Y. Chen et al., 2013).

The errors in satellite-based precipitation estimates are from twomajor sources: sampling error and retrieval errors. The former resultsfrom estimation the precipitation amount for a continuous spatial andtemporal domain with measurements at discrete space and time inter-vals, such as estimating the daily or monthly total precipitation from in-stantaneous observations at 3-hour intervals. The sampling error hasbeen studied extensively, and its relationship with rain-rate and spatial/temporal resolution has beenwell established both empirically and theo-retically (e.g., Laughlin, 1981;Huffman, 1997; Bell andKundu, 1996, 2000,2003; Bell et al., 2001; Steiner et al., 2003;Nijssen and Lettenmaier, 2004).As well, this part of the errors is beyond the scope of this paper.

The retrieval error arises from the remote-sensing procedures in-volved to convert satellite observations (brightness temperature) torain rate. This error type is more complex, because of its dependencieson many factors, including sensor type (conical vs. cross-track, activevs. passive microwave), sensor resolution and viewing geometry, pre-cipitation type, surface type, atmospheric condition, cloud microphys-ics, and retrieval algorithm itself (e.g., Arkin and Xie, 1994; Sorooshianet al., 2000; Adler et al., 2001; McCollum et al., 2002; McCollum andFerraro, 2003; Gottschalck et al., 2005; Hossain and Anagnostou, 2006;Ebert et al., 2007; Tian et al., 2007; Tian and Peters-Lidard, 2010; Tianet al., 2010; Kirstetter et al., 2012; Tian et al., 2013; Chen et al., 2013a,b; Maggioni et al., 2014; Tang et al., 2014).

For the retrieval error, it can be further decomposed into systematicand random errors. The systematic errors reflect predictable, consistenterror behaviors often associated with instrument or algorithm charac-teristics (e.g., miss calibration). This can be further decomposed intomissed, false, and hit errors (Hossain and Anagnostou, 2006; Tianet al., 2009; Habib et al., 2009b; Maggioni et al., 2014). Assessment ofsources of the systematic error helps to gain additional insight into per-formance accuracy of those satellite-based precipitation estimates(Gebregiorgis et al., 2012; Habib et al., 2012).Meanwhile, it was also re-vealed that the amplitudes of the three components were often largerthan the systematic error, because different error components can can-cel each other (Tian et al., 2009). Therefore, it is not enough to evaluatethe performance of one satellite precipitation product solely based onits total retrieval error as most existing studies do. The random erroris the stochastic component whose magnitude directly determines theuncertainty. Therefore correct error analysis and modeling to separatethe different error components are essential to the quantification of un-certainty, which is also the major purpose of this paper.

Meanwhile, most conventional error metrics (e.g., correlation coeffi-cients) are based on the assumption of additive, Gaussian errors. Howev-er, this proves to be unrealistic for precipitation estimates which have anon-Gaussian distribution. Habib et al. (2001) demonstrated that the es-timation of linear correlation coefficients in precipitation is not accuratedue to departures from the normal distribution assumption, and isskewed by extreme precipitation rates. In addition, it has been suggestedthat some transformation be applied to precipitation prior to computingerrors, e.g., Stephenson et al. (1999) used the square root transformationon the extreme daily precipitation events to improve the predictability ofensemble forecasts of the mean Indian rainfall. Tian et al. (2013) demon-strated that the conventional additive error model is not applicable tohigh-resolution precipitation data, and error evaluation should be basedon amultiplicative error model. In this multiplicative error model, a loga-rithmic transformation was applied to the precipitation estimates. Theerror model was then evaluated at precipitation logarithmic space.

Considering these new developments and the deficiencies in theconventional approaches, this study systematically proposes and testsa new procedure for the validation of the satellite-based high-resolution precipitation estimates. The new validation procedure hastwo steps: 1) we employ the error decomposition scheme of Tianet al. (2009) to separate the total error into three independent compo-nents: hit error, missed precipitation, and false precipitation; and2) the hit error is further analyzed based on a multiplicative errormodel provided by Tian et al. (2013). In the multiplicative error

63L. Tang et al. / Atmospheric Research 163 (2015) 61–73

model, the error features are captured by three model parameters, witheach describing a unique aspect of the systematic and random errors.These three parameters can largely replace the variety of conventionalerrormetrics, and producemore accurate quantification of both system-atic and random errors.

To demonstrate the effectiveness of the proposed new procedure, weapplied it to quantitatively evaluate the recent two versions (Version 6and 7) of TMPA real-time and post-real-time product suite (3B42RT and3B42) for six years (2005–2010) over the continental U.S. (CONUS). Thegauge-based National Centers for Environmental Prediction (NCEP) Cli-mate Prediction Center (CPC) near-real-time daily precipitation analysisat 0.25° was used as the reference (Chen et al., 2008). This data set usessolely rain gauge measurements from the dense gauge network overCONUS. In addition, the radar-based NCEP Stage IV precipitation data(Lin and Mitchell, 2005; Kitzmiller et al., 2013) were also evaluatedwith the same procedure as a reference, as we already understand itserror characteristics fairly well (e.g., Tian et al., 2007).

The approach used for error decomposition is introduced inSection 2. The multiplicative error model and its three parameters arediscussed in Section 3. Section 4 describes the four TMPA data sets, aswell as the reference data. Section 5 presents the results on error com-ponents, and evaluations of the three parameters in the multiplicativeerror model. Finally, the results are summarized in Section 6, with rec-ommendations for future improvement of next version TMPA algorithmbased on the findings in this paper.

2. Error decomposition

In the first step, we decomposed the total error into three differentcomponents using the error decomposition approach derived in Tianet al. (2009) and Habib et al. (2009b). During the retrieval process, thetotal error (E) in the estimate can be from three possible causes:1) the sensor detects the precipitation event, but the estimated precip-itation amount is different from the truth. This difference is defined ashit bias (H) – the event is detected but the amount is biased, and itcan be either negative or positive; 2) a precipitation event is not detect-ed by the sensor at all. This leads tomissed precipitation (−M), which isobviously always negative; and 3) the sensor detects some false signa-ture of rain (e.g., Tian and Peters-Lidard, 2007) while there is no precip-itation in reality, and the mistakenly measured amount is called falseprecipitation (F), and is always positive. It is easy to prove (Tian et al.,2009) that the total error can be decomposed as:

E ¼ H–M þ F ð1Þ

The three components can have substantial magnitudes with largespatial and temporal variations. Sometimes, the amplitude of the indi-vidual components is larger than that of the total error, simply becausethe three components may cancel one another. Thus this approach re-veals much more of the error characteristics.

3. Analysis of hit errors

In the second step, a multiplicative error model (Tian et al., 2013) isapplied to evaluate the hit errors derived from the error decompositionin the first step. Compared with the conventional additive error model,this multiplicative error model can better separate the systematic andrandom errors (Tian et al., 2013).

Normally, the additive error model of is defined as:

Yi ¼ aþ bXi þ εi ð1Þ

where i is the index of the datum, in this paper, it refers to a single pre-cipitation measurement at a certain grid box; Xi is the “truth” referencedata, indicates CPC data; Yi represents a certain satellite estimate, refersto TMPA products. a is the offset; b is a scale parameter to represent the

different dynamic range of measurements with the reference data. εirepresents random error which has zero mean and variance σ2. There-fore, the error model is defined by three independent parameters,namely, a, b and σ, where a and b jointly specify the systematic errorand the random error in the measurements Yi is quantified by σ (Tianet al., 2013).

The multiplicative error model is usually defined as

Yi ¼ aXbi e

εi ð2Þ

In the multiplicative error model, the systematic error (defined by aand b) is now a non-linear function of the reference data. The randomerror eεi is a multiplicative factor, with zero mean and variance σ2.Note here the values of σ in Eqs. (1) and (2) will be different, indicatingthat the uncertainty definition depends on the errormodel formulation.

After a logarithmic transformation in Eq. (2), the multiplicativemodel becomes:

ln Yið Þ ¼ α þ β ln Xið Þ þ εi ð3Þ

where alphaα= ln a, beta β= b, this equation is a simple linear regres-sion in the transformed domain, and the three parameters (α, β and σ)can be easily estimated with the ordinary least squares (OLS) method.

The effect of the three error model parameters is illustrated in Fig. 1.The PDFs of the true rainfall (Xi), the true rainfall corrupted with sys-tematic error only (Y0i =aXi

b), and the one corrupted with both system-

atic and random errors Yi ¼ aXbi e

εi� �

, are shown in log-linear scale, for

two different sets of parameter values extracted from Table 1 (yearly3B42V7 and Stage IV). The offset parameter α, simply shifts the PDF ofXi to the left (α b0) or right (α N0) in the logarithmic scale of Xi (forboth 3B42V7 and Stage IV, shifting the PDF to the right); while thescale parameter β expands (β N1) or shrinks (β b 1) the PDF of Xi (forboth 3B42V7 and Stage IV, shrinking the PDFs). The addition of the ran-dom error given by σ, uniformly broadens the resultant PDF. Thereforeα and β capture the systematic differences in the position (offset) andwidth (scale) of the probability distribution within the respectiverange of Xi and Yi. This is more representative than simply using “bias”to quantify the systematic error in the additive model.

4. Data

We focused specifically on two TMPA three-hourly microwave-IRmerged estimates (Huffman et al., 2007, 2010) – the real-time productknown as 3B42RT and the post-real-time with gauge adjustmentknown as 3B42. Our new validation procedure was applied to on boththe previous version (V6) and the newest version (V7) of the two prod-ucts. Hereafter, we name them 3B42RT-V6 and 3B42RT-V7 (for 3B42RTVersion 6 and 7), 3B42V6 and 3B42V7 (for 3B42 Version 6 and 7). Thenear-real-time production of 3B42RT requires several simplificationscompared to 3B42. The main focus of 3B42RT data is timeliness, while3B42 is strongly recommended for any research work not specificallyfocused on real-time applications (ftp://precip.gsfc.nasa.gov/pub/trmmdocs/3B42_3B43_doc.pdf). Since TMPA V6 was ended on 30 June2011 (superseded by version 7 after then), we selected a common peri-od of seven years (2005–2011) for this study. Each of the original TMPAdata sets is available at spatial and temporal resolution of 3 hourly and0.25°. We aggregated them into daily resolution, to match the referencedata CPC gauge analysis.

The CPC unified gauge analysis was used as the reference data. Toverify the effectiveness of the multiplicative error model mentioned inSection 3, we also used the NOAA Next Generation Weather Radar(NEXRAD) Stage IV data (Lin and Mitchell, 2005; Kitzmiller et al.,2013) as another reference (see Section 5.2 on how it works). Notehere, the Stage IV data wasmodel-fitted using the CPC data as the refer-ence, to verify the effectiveness of the multiplicative error model we

Fig. 1. Illustration of the effects of the three multiplicative error model parameters (alpha, beta and sigma) on the PDF of the 3B42V7 (top panel) and Stage IV (bottom panel). Alpha andbeta define the systematic errors (in y0), with the offset parameter (alpha) shifting themeasurements PDF (dashed line) to the left (alpha b0) or right (alpha N 0) relative to the referencePDF (x, solid line),while the scale parameter (beta) shrinking (beta b 1)or expanding (beta N 1) themeasurements PDF.When randomerror defined by sigma is included (y, dotted line), itonly broadens the PDF (dotted line).

64 L. Tang et al. / Atmospheric Research 163 (2015) 61–73

used. No satellite estimates were validated against Stage IV data in thispaper. Based on previous research (Tian et al., 2010), over the easternCONUS, the differences between the two reference datasets are small,because of the high density of gauge stations and relatively flat terrain.The uncertainties of the CPC and Stage IV data are one order of magni-tude lower than the satellite-based precipitation datasets, which willnot affect the uncertainty quantification in TMPA datasets. However,over the west CONUS, because of the complex terrain and relatively

Table 1Area-averaged values of the three error model parameters (α, β, and σ) over CONUS forthe four TMPAproducts, for year-around,winter and summer, respectively. Theparametervalues for Stage IV data are also shown for comparison (last row).

Parameters Years Winters Summers

Data α β σ α β σ α β σ

3B42RT-V6 1.12 0.40 0.95 1.09 0.31 0.88 1.25 0.41 0.953B42RT-V7 1.08 0.42 0.9 1.16 0.35 0.87 1.15 0.4 0.883B42V6 0.93 0.42 0.86 0.96 0.38 0.85 0.97 0.39 0.823B42V7 1.02 0.47 0.88 1.08 0.43 0.87 1.05 0.44 0.83Stage IV 0.37 0.74 0.57 0.30 0.75 0.48 0.45 0.71 0.60

sparse radar coverage, the uncertainties in Stage IV data are expectedto bemuch larger than the CPC unified guage analysis, especially inwin-ter (December - February) (Tian et al., 2010). Stage IV data severely un-derestimate precipitation than the CPC unified gauge analysis, whichwill result in the discrepancywhenmodel-fittedwith ourmultiplicativeerror model (Section 3).

5. Results

Fig. 2 shows an example of daily mean precipitations in winter 2006and summer 2005 for the four TMPA data sets, compared with theground reference Stage IV and CPC data during the same periods. Inwinter, the mean precipitation of the real-time products 3B42RT-V6 or3B42RT-V7 shows obvious overestimation over the Midwest, especiallyfor 3B42RT-V7. Error decomposition analysis (see Section 5 and Fig. 3)indicates this overestimation is dominated by false precipitation (F).After gauge correction, the overestimation is well removed from3B42V6 and 3B42V7. Meanwhile, all the four TMPA data sets show dif-ferent levels of underestimation along the coastal area in theNorthwest,largely due to the challenging in detecting warm, coastal precipitation.

Fig. 2. Sample mean daily precipitation in four datasets (left): 3B42RT-V6, 3B42RT-V7, 3B42V6, and 3B42V7, over CONUS during winter (DJF 2006) and summer (JJA 2005). For compar-isons, daily precipitation analysis fromStage IV and CPC data (right) are also shown for the sameperiod. Thenewest version (V7) TMPA3B42data show closer rain distribution as the StageIV and CPC data, for both real-time and research products, during both summer and winter (units: mm/day).

65L. Tang et al. / Atmospheric Research 163 (2015) 61–73

Among the four TMPA data sets, only 3B42RT-V6 could not capture theprecipitation pattern in the Southeast. It is consistent with earlier find-ings (e.g., Yong et al., 2013; Chen et al., 2013a) that V6 products (espe-cially for the real-time products) exhibit significant underestimation ofmoderate to high rain rates for winter.

In summer, both 3B42RT-V6 and 3B42RT-V7 show obvious overesti-mation over the Midwest. This is well corrected in the research versiondata sets 3B42V6 and 3B42V7, which have very similar spatial patternsof precipitation as the Stage IV and CPC data. Not much difference is ob-served in 3B42V6 and 3B42V7, except that 3B42V7 has slightly higherprecipitation in the Southeast, which is in accordance with the groundreference.

These initial comparisons reveal that the newest TMPA V7 researchversion shows substantial improvements, while the real-time versionsees mixed performance gain and degradation. We present results oferror analysis of the four TMPA products, using the new validation pro-cedure described above. In Section 5.1, we discuss the spatial character-istics of the error components for each TMPA product for winter andsummer seasons, respectively, as well as the distributions of error

components as a function of precipitation intensity for both seasons.In Section 5.2, we present results using the multiplicative error model,and studied the spatial, seasonal and probability distribution of themodel parameters. The physical meanings of the model parametersare also illustrated.

5.1. Error decomposition

Wedecomposed the total error of daily data over the CONUS into thethree error components described above. Figs. 3 and 4 show the spatialdistributions of total error and its three components for winter andsummer seasons, respectively. The seasonal sum of the total bias (E)and its three error components: hit bias (H), missed precipitation(−M), false precipitation (F) have the relationship as: E = H-M + F.This relationship still holds after averaging over the seasons.

Inwinter, four TMPAdata sets showdifferent spatial patterns of totalerror and three error components (Fig. 3). For real-time product3B42RT, both V6 and V7 products show obvious overestimation overthe Midwest. The overestimation is largely dominated by the false

Fig. 3. Error components of the four datasets for thewinter average (sixwinters, fromDJF 2006 to DJF 2011): total bias (E), hit bias (H), missed precipitation (−M), and false precipitation(F). The relationship between the components is E = H−M + F.

66 L. Tang et al. / Atmospheric Research 163 (2015) 61–73

precipitation, probably due to themore complex land surface conditionsduring winter (inaccurate snow-cover mask, frozen soil, etc.). Aftergauge-correction, false precipitation is well reduced from 3B42V6 and3B42V7 over the Midwest.

Another significant difference is the underestimation along thewest coastal areas and the Rockies. The underestimation is primarilyfrom the missed precipitation, and second from the negative hit bias.Missed precipitation is either the consequence of snow cover on theground at high latitudes or over the Rockies, or the lack of capabilityto capture the warm rain process and convective rainfall at low lati-tudes with passive microwave radiometers (PMW) (Tian et al.,2009). Obviously, the V7 products do not overcome this issue. Thenegative hit bias also contributes to the underestimation, but isonly confined to the west coast.

The large variations of hit bias and missed precipitation over theNortheast and the Southeast, are probably caused by the shortfalls ofthe inter-calibrated TMPA algorithm. The positive hit bias over thesoutheast US is an example of the overcompensation in newest TMPAalgorithm observed on the V7 products. Meanwhile, the 3B42 productwas corrected using the TMPA monthly satellite-gauge product 3B43,this particular gauge-correctly strategy could not make up the missedprecipitation over the Northeast.

In summer, the spatial patterns of total errors and error compo-nents for all data sets are quite different comparing to its wintercounterpart (Fig. 4). Real-time products show quite significant over-estimation over the central US. Different from its winter counterpart(overestimation is from false precipitation), the overestimation

observed in summer is primarily from the hit bias. The gauge-corrected scheme improves the quality of 3B42 products over thisregion, especially for 3B42V7. For 3B42V6, however, excessive re-duction of precipitation causes negative hit bias around the GreatLakes and the East US.

Both missed precipitation and false precipitation are not very pro-nounced in summer for all four data sets. Most missed precipitationtakes place along the Atlantic, Gulf coast and Florida, which is probablycaused by the under-sampling of convective thunderstorms. V7 per-forms slightly better than V6 for both real-time and post-real-timeproducts.

Fig. 5 shows the distributions of total precipitation and error com-ponents as the function of precipitation intensities. In Fig. 5a, distri-butions of total precipitation show difference among four TMPA datasets for both winter and summer seasons. In winter, when precipita-tion intensity is less than 10 mm/day, the total precipitation of3B42RT-V6 and 3B42RT-V7 are close to the reference data. Over10 mm/day, they go towards the opposite directions, with 3B42RT-V6 underestimates the total precipitation and 3B42RT-V7 overesti-mates. On the contrary, Gauge-corrected product 3B42V6 constantlyunderestimates precipitation till around 50 mm/day, while matcheswell with the reference data for extreme precipitation (N50 mm/day). 3B42V7 underestimates when rain intensity is less than around25mm/day but turns out to overestimate afterwards. In summer, thedistribution of total precipitation in 3B42V7 aligns the closest to thereference data. Three data sets (3B42RT-V6, 3B42RT-V7, and3B42V7) are well overlapped with the distribution of the reference

Fig. 4. Same as Fig. 3, except for the summer seasons.

67L. Tang et al. / Atmospheric Research 163 (2015) 61–73

when the precipitation intensity is less than 16 mm/day. When over16 mm/day, the overestimates behave as 3B42RT-V6 N 3B42RT-V7 N 3B42V7. 3B42V6 consistently underestimates moderate precip-itation (around 8 ~ 40 mm/day) while well following the referencedata on two sides (b8 mm/day and N40 mm/day). Overall, 3B42V7performs better than the other three products in total precipitationin winter. Due to the spatial average process, this trend is not as ob-vious in summer. 3B42V6 constantly underestimates and 3B4RT-V7constantly overestimates total precipitation in both summer andwinter. Hit precipitation (Fig. 5b) shows similar distributions as thetotal precipitation (Fig. 5a), except that all the TMPA data sets under-estimate hit precipitation from the low-end of the precipitation in-tensity. This is reasonable because the satellite-based passivemicrowave radiometers are less sensitive to the light rain than theground measurements. There is not much difference in the missedprecipitation for the four data sets in both winter and summer(Fig. 5c). In winter, the distributions of false precipitation are slightlyseparated to two groups with more false precipitation in the real-time products 3B42RT-V6 and 3B42RT-V7 for both winter and sum-mer (Fig. 5d).

The study on spatial distributions of the total bias and three errorcomponents shows distinguished error patterns in winter and summer.The winter total bias is dominated by the missed precipitation over thewest coastal area and the Rockies, and the false precipitation over largeareas in Midwest. The summer total bias is largely from the hit bias inCentral US. The study on precipitation intensity distribution demon-strates the improvement of TMPA V7 algorithm. The new versiontends to producemore rainfall in the higher rain rates,whichmoderatesthe significant underestimation exhibited in the V6 products.

5.2. The multiplicative error model

In this section, the multiplicative error model is used to furtherquantify the hit bias. The three parameters of the multiplicative errormodel (Eq. (3) in Section 3) were evaluated for the four TMPA datasets in both winter and summer. The parameters were estimated foronly the hit rain events with a threshold of 0.25 mm/day, as the lighterrain events are statistically unreliable for either gauge data or satellitemeasurements.

Spatial distribution of α is shown for four TMPA data sets in winterand summer, respectively (Fig. 6).The closer α is to zero, the better.From Fig. 6,α is positive across the CONUS for bothwinter and summer.This is consistent with the results shown in Fig. 5b, from which all theprecipitation intensity distributions shift towards the right (larger pre-cipitation intensity) in both winter and summer. For winter, α is in-creased in V7 products in the Midwest, which is probably caused bythe overcompensation of hit precipitation in V7 algorithm (for signifi-cant underestimation in V6 algorithm). For summer, large hit biasesover the Central US in 3B42RT-V6 and 3B42RT-V7 (shown in Fig. 3)are also observed here (with α N1.6). The V7 algorithm shows effecton decreasing α in 3B42RTV7. After gauge-correction, the values of αare significantly reduced for both 3B42V6 and 3B42V7. We alsomodel-fitted the Stage IV data using the CPC data as the reference, toverify the effectiveness of the multiplicative error model we used.Stage IV data have much smaller α (average 0.30 in winters and 0.45in summers), compared to larger than 1 in winters and summers forTMPA data sets (Table 1). This is consistent with reality. Note here thegridded Stage IV data behave a bit smoother than the gauge analysis,which also results in the values of model parameters α, β and σ.

Fig. 5. Precipitation intensity distributions of total precipitation and hit precipitation for four TMPA data sets aswell as the ground reference (CPC) are shown in Fig. 5a and b. Distributionsof missed precipitation and false precipitation for four TMPA data sets are shown in Fig. 5c and d. Left column is for winter (DJF 2006–2011), and right for summer (JJA 2005–2010).

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Similar to Fig. 6, Fig. 7 presents results on the spatial distributionof shape parameter β for the four TMPA data sets for winter and sum-mer, respectively. The perfect situation, beta equals to 1, means anidentical dynamic range for the TMPA data sets and the referencedata. Generally, four TMPA data sets show very similar spatial pat-terns of β in both winter and summer. For winter, β is relatively larg-er cross the East and in West coastal area, with the largest over theSoutheast. This is reasonable as southeast regions share the most

various climate patterns with extreme rain events throughout theyear. On the contrary, Midwest and the Rocky mountain areasshare the lowest β values, where liquid precipitation is seldomformed in winter. Dynamic ranges of satellite estimates are small inboth regions. For summer, spatial distributions of β are quite similaramong all the TMPA data sets, with relatively large values in the Eastand Central US, and small values in the West. For Stage IV data, mostareas show a much larger β (closer to 1), with average β equals to

Fig. 6. Spatial distributions of the scale parameterα in the error model. Results are compared for winters (DJF 2006–2011) and summers (JJA 2005–2010) for TMPA data sets and Stage IVdata.the values of α closer to zero means smaller offset errors.

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0.75 for winter and 0.71 for summer, compared to around 0.4 forwinter and summer for the TMPA data sets (Table 1). This is also con-sistent with reality.

The standard deviation of the random error (Fig. 8) σ is shown forwinter and summer, respectively. For winter, real-time products3B42RT-V6 and 3B42RT-V7 exhibit fairly random errors over theMidwest. Although the random error is obviously reduced in

3B42V6, the precipitation compensation process in V7 algorithmseems to add more random error into 3B42V7 over this region. TheGauge-correction in 3B42V6 and 3B42V7 adds more random errorover theWest coastal area. Another interesting finding is the randomerror is smaller along the Rocky Mountain region. This region is cov-ered with snow during the winter, and less variance is observed forliquid precipitation. For summer, the difference in random errors is

Fig. 7. Same as Fig. 6, except for the shape parameter β in the error model. The closer the value of β to 1, the lower the shape error.

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very marked for real-time products and gauge-corrected products.3B42RT-V6 exhibits significant random error over the Central USand East coastal area. Random error is effectively reduced in3B42RT-V7. After gauge-correction, random error is notably reducedin 3B42V6 and 3B42V7 over the central US. Stage IV data showsmuch smaller random error over the CONUS, compared to theTMPA data sets. The average σ for Stage IV is 0.48 for winters and

0.60 for summers, while TMPA data sets have an average σ around0.87 for both winter and summer (Table 1).

From our results, it is apparent that the multiplicative errormodel effectively captured the error characteristics in both thesatellite-based and ground radar-based datasets, and their errorcharacteristics are succinctly summarized in the three modelparameters.

Fig. 8. Same as Fig. 6, except for the random error parameter sigma, which represents the standard deviation of the random error (unit: mm/day).

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6. Conclusions and discussions

In this paper, we proposed a new procedure for the quantitativevalidation of high-resolution satellite-based precipitation estimates.To test the procedure, a comprehensive error analysis was per-formed for the newest version 7 TMPA products and its predecessorversion 6 products using daily 0.25° CPC data over the CONUS as the

reference for a period of six years (2005–2011). The new procedurewas separated into two steps: first, an error decomposition process(Tian et al., 2009; Habib et al., 2009b) to decompose the total errorinto three difference error components, hit bias, missed precipita-tion and false precipitation; then a multiplicative error model(Tian et al., 2013) is employed to further analyze the hit error. Theeffectiveness of the new procedure is verified by applying it to the

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well-understood radar-based Stage IV data. The major findings aresummarized as follows:

(1) The new procedure proposed in this paper is effective in quanti-fying both the systematic errors and random errors. It overcomesmany of the deficiencies in the conventional approaches(e.g., cancellation among error components, skewed error met-rics from Gaussian error assumption, etc.), and results in moreaccurate description, separation and quantification of the errorcomponents, and of the systematic and random errors. Thisleads to more accurate assessment of the uncertainty in thedata. Therefore, we recommend the new procedure be adoptedfor routine validation of satellite-based precipitation data sets.

(2) With the new procedure, we performed analysis of spatial distri-butions of the total bias and three error components (Figs. 3 and4) and examined their error patterns in winter and summer forfour TMPA data sets. The winter total bias is dominated by themissed precipitation over the west coastal area and the RockyMountains, and the false precipitation over the large areas inMidwest. The summer total bias is largely from the hit bias incentral United States.

(3) Analysis of precipitation intensity distribution (Fig. 5) demon-strates the improvement of TMPA V7 algorithm. The new versiontends to produce more rainfall in the higher rain rates, whichmoderates the significant underestimation exhibited in the pre-vious V6 products.

(4) All the three parameters in the multiplicative error model, worktogether, are effective in evaluating both the systematic and ran-dom error in the hit error in the four studied TMPA products.

As mentioned earlier, TMPA V7 products are still quite recent, andnot many investigations have been conducted to evaluate their system-atic and random error characteristics compared to their V6 predeces-sors, especially for potential use in various hydrological applications.In this paper, we presented a comprehensive error analysis on Version7 TMPA real-time and post-real-time products 3B42 and 3B42RT, in aneffort to draw a consistent conclusion on the advancement of TMPAV7 algorithm. Meanwhile, this analysis provides input to the generationof the next version TMPA algorithm by constructing the characteristicsof both the systematic and random errors.

The same validation procedure can be applied to other areas, withother satellite-based datasets, such as CMORPH (Joyce et al., 2004),or the upcoming IMERG [http://pmm.nasa.gov/sites/default/files/document_files/IMERG_ATBD_V4.1.pdf]. Moreover, the proposedvalidation procedure can also be used on quantitative precipitationforecasted from models.

Acknowledgements

This researchwas supported by theNASAEarth SystemDataRecordsUncertainty Analysis Program (Martha E. Maiden) under solicitationNNH10ZDA001N-ESDRERR. Computing resources were provided bythe NASA Center for Climates Simulation. We appreciate the very help-ful suggestions from two anonymous reviewers.

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