Hurricane GPROF: an Optimized Ocean Microwave Rainfall Retrieval for Tropical Cyclones

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Hurricane GPROF: An Optimized Ocean Microwave Rainfall Retrieval for Tropical Cyclones

PAULA J. BROWN,CHRISTIAN D. KUMMEROW, AND DAVID L. RANDEL Department of Atmospheric Science, Colorado State University, Fort Collins, Colorado

(Manuscript received 17 November 2015, in ﬁnal form 18 May 2016)

ABSTRACT

The Goddard profiling algorithm (GPROF) is an operational passive microwave retrieval that uses a Bayesian scheme to estimate rainfall. GPROF 2014 retrieves rainfall and hydrometeor vertical profile information based upon a database of profiles constructed to be simultaneously consistent with Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) and TRMM Microwave Imager (TMI) observations. A small number of tropical cyclones are in the current database constructed from one year of TRMM data, resulting in the retrieval performing relatively poorly for these systems, particularly for the highest rain rates. To address this deficiency, a new database focusing specifically on hurricanes but consisting of 9 years of TRMM data is created. The new database and retrieval procedure for TMI and GMI is called Hurricane GPROF. An initial assessment of seven tropical cyclones shows that Hurricane GPROF provides a better estimate of hurricane rain rates than GPROF 2014. Hurricane GPROF rain-rate errors relative to the PR are reduced by 20% compared to GPROF, with improvements in the lowest and highest rain rates especially. Vertical profile retrievals for four hydrometeors are also enhanced, as error is reduced by 30% compared to the GPROF retrieval, relative to PR estimates. When compared to the full database of tropical cyclones, Hurricane GPROF improves the RMSE and MAE of rain-rate estimates over those from GPROF by about 22% and 27%, respectively. Similar improvements are also seen in the overall rain-rate bias for 2 hurricanes in the database, which is reduced from 0.20 to 20.06 mm h 1.

1. Introduction (TRMM) Microwave Imager (TMI) increasing the number of channels and spatial resolution of SSM/I Tropical cyclones are a high-impact meteorological (Kummerow et al. 2001). TRMM was deployed in 1997 event that can have catastrophic impacts, especially if with a Microwave Imager (TMI) and a precipitation landfall occurs. Tropical ocean environments create the radar (PR) on board to provide detailed data on tropical conditions under which tropical storms and tropical cy- rainfall between 358N and 358S, which makes it ideal for clones occur, but these environments are difﬁcult to studying spatial and temporal rainfall characteristics of observe using ground-based instrumentation. Conse- tropical cyclones. Similarly, the recent deployment of quently, satellite-derived measurements are frequently the Global Precipitation Measurement (GPM) Core used to detect and monitor the evolution of tropical Observatory satellite in February 2014 will complement cyclones. Space-based microwave radiometers have the rainfall products generated from TRMM. The GPM provided measures of atmospheric moisture since the Core Observatory’s Microwave Imager (GMI) and dual- Special Sensor Microwave Imager (SSM/I) began op- frequency precipitation radar (DPR) provides near- erating in 1987. Similar instruments are now commonly global coverage and improves upon TRMM’s detection used to estimate both cyclone features and rain rates of light rain, snow, and the microphysical properties of (Benedetti et al. 2005; Lau et al. 2008; Jiang et al. 2011), precipitating particles (Hou et al. 2014). especially with the Tropical Rainfall Measuring Mission Over oceans, physical methods that use statistical relationships between brightness temperatures and rain rates/hydrometeors have been developed to retrieve Corresponding author address: Paula J. Brown, Department of Atmospheric Science, Colorado State University, 1371 Campus rainfall for TRMM, the GPM Core Observatory, and Delivery, Fort Collins, CO 80523-1371. other satellites (Wilheit et al. 1991; Petty 2001; Hilburn E-mail: [email protected] and Wentz 2008; Kummerow et al. 2015), often through

DOI: 10.1175/JTECH-D-15-0234.1

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Bayesian schemes (Evans et al. 1995; Bauer et al. 2001; also possible, but it was preferable to evaluate the re- Di Michele et al. 2005; Kummerow et al. 2011; Sanò trieval over oceans where radar data are more robust and et al. 2013). Bayesian schemes often use a probabilistic the physical relationships between rain and the radar are approach to match an a priori database of hydrometeor better understood. profiles constructed by requiring consistency between The purpose of this paper is to describe the new re- hydrometeors and radiometer observations (Marzano trieval methodology for tropical cyclones and to show et al. 1999; Kummerow et al. 2011; Sanò et al. 2013). how it improves estimates of tropical cyclone rain rates Retrievals over land are complicated by surface het- over oceans. While this methodology is applied to erogeneity, affecting emissivities and increasing error in tropical cyclones here, it can also be applied to other the rainfall estimates (Wang et al. 2009; Petty and Li meteorological phenomenon. An overview of the GPROF 2013). Despite these complexities, passive microwave 2014 retrieval, its use of databases, and their limitations rain products over land show good agreement with other are identified in section 2. Section 2 also describes the products (Kummerow et al. 2011; 2015), especially as new ocean-only database and the adaptations made to improvements are made to address weaknesses previ- the GPROF 2014 rain-rate retrieval for tropical storms ously identified in the algorithms (Wang et al. 2009; and tropical cyclones. Hurricane GPROF is then eval- Gopalan et al. 2010; Ferraro et al. 2013). uated in section 3. Section 4 assesses the effect of in- TRMM’s suitability for monitoring tropical cyclones creasing the error term in the Bayesian retrieval to has led to extensive development and use of databases, optimize channel uncertainty in order to account for the such as the tropical cyclone cloud and precipitation incomplete population of tropical storms in the data- feature databases (Liu et al. 2008; Jiang et al. 2011), base. Vertical profile retrievals are evaluated in section 5, tropical cyclone track databases (Knapp et al. 2010) and and then a summary of the new Hurricane GPROF re- numerous studies of meteorological characteristics of trieval and conclusions from this work are contained in tropical cyclones (Lonfat et al. 2004; Jiang 2012; Ren section 6. et al. 2014). However, deficiencies have been shown when comparing estimates from independent radar observations of precipitation and TMI precipitation esti- 2. TRMM and the GPROF retrieval procedure mates, with TMI underestimating the inner core and a. TRMM instruments high-rain-rate regions of tropical cyclones (Viltard et al. 2006; Zagrodnik and Jiang 2013a,b). These underesti- Active and passive microwave instruments are on mates are associated with one of the limitations of the board the TRMM satellite. The precipitation properties Bayesian probability theory applied in the retrieval, of the PR and the TMI instruments are estimated re- which produces a rain-rate estimate based on its likeli- motely from the reflectivity and brightness tempera- hood. In the case of tropical cyclones, their hydrome- tures, respectively. The PR operates at 13.8 GHz, with a teorological environments and high rain rates are surface resolution of 5 km and a 247-km (after boost) uncommon in the a priori database and are therefore swath. The PR 2A25 algorithm (Iguchi et al. 2000) de- unlikely to be highly weighted by the retrieval’s Bayes- termines rain rates based on the relationship between ian scheme. As TMI has limited information from its reflectivity and rain rate, using a drop size distribution observations, it cannot fully distinguish between the Tbs model, an attenuation correction, and a nonuniform of different rain systems, so identifying these rain sys- beamfilling correction. The sensitivity of the PR is 2 tems (e.g., tropical cyclones) using auxillary data adds roughly 0.7 mm h 1, although it can produce rain rates of 2 information to benefit the retrieval. as low as approximately 0.3 mm h 1. Consequently, light Creating application-specific versions of the TMI re- rain rates, especially those from shallow stratiform rain, trieval should result in improvements to the rain-rate are not always detected (Schumacher and Houze estimates for tropical cyclones. In particular, the a priori 2000, 2003). databases used in the Bayesian scheme of Kummerow TMI is a nine-channel passive microwave radiometer et al. (2011) can be populated with data from tropical that observes brightness temperatures (Tb) at five dif- cyclones. Running a retrieval specifically for tropical ferent frequencies (10.65, 19.35, 21.3, 37.0, and 85.5 GHz). cyclones over oceans, based on oceanic tropical cyclone Vertical and horizontal polarization measurements rainfall data alone, should produce better rain-rate esti- are taken at all but the 21-GHz (vertical only) channel mates than a more generalized global scheme. Adapting (Table 1). A spatial resolution of 5.1 km is achieved at the Bayesian retrieval for TMI to improve its perfor- 85 GHz and a full swath scan covers 878 km. The overlap mance under oceanic tropical cyclone conditions is the between coincident PR and TMI observations is re- premise of this work. A comparable retrieval over land is stricted by the much narrower width of the PR swath. A

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TABLE 1. Temperature sensitivity of NEDT (K) for the nine TMI channels (Kummerow et al. 1998).

Center frequency (GHZ) 10.65V 10.65H 19.35V 19.35H 21.3V 37.0V 37.0H 85.5V 85.5H Sensitivity, NEDT (K) 0.63 0.54 0.50 0.47 0.71 0.36 0.31 0.52 0.93 small temporal offset also results from the nadir- Ancillary datasets provide the SST data, which are es- oriented PR and the 538 conical scan angle of TMI. pecially important when applying GPROF globally. It is the overlapping PR and TMI observations from Observational databases that constrain the GPROF TRMM that provide the basis for obtaining a priori retrievals are also limited by events that have occurred rain structures for GPROF. Ancillary datasets and during the time period from which the database is con- model output can also be incorporated into retrievals structed. The operational algorithm uses a single year of to provide a narrower and therefore more appro- PR and TMI data. The infrequent nature of tropical priate meteorological context of the precipitating cyclones reduces the ability of the Bayesian retrieval to environment. reproduce correctly the precipitation associated with them unless the brightness temperatures match ex- b. The GPROF 2014 retrieval over oceans ceedingly well. The operational algorithm used to estimate rain rates To improve the ability of GPROF’s retrieval to esti- from TRMM for this study is GPROF 2014 —the newest mate the rain rates in tropical cyclones, some adjust- version of the algorithm (hereafter GPROF). A general ments need to be made. Using a separate database that overview of GPROF is given here to provide a context contains only information from tropical storm systems for how the new Hurricane GPROF retrieval is de- should improve the Bayesian rain-rate estimates, when veloped, as significant changes are made. More detailed comparable storm systems are present. This is achieved descriptions of the GPROF retrieval are contained in primarily by expanding the number of rain profiles in the Kummerow et al. (2011, 2015). meteorological environment of the tropical cyclones, to Over oceans, GPROF is a physically constructed re- provide the algorithm with more well-matched profiles. trieval that uses an a priori database consisting of SST and TPW data are not necessary in tropical cyclone matched PR rain rates for the 21-GHz footprint environments, as their warm moist ambient conditions (;18 km) and TMI Tb at their native resolution. For are relatively homogeneous compared to those seen raining pixels, the PR profile and cloud-resolving model globally. More importantly, further stratification of data output are used to construct an initial profile. The PR by SST and TPW would reduce the size of the database, reflectivity profile is used to select a cloud-resolving which is already limited by the infrequent nature of model profile of rainwater, cloud water, cloud ice, snow, hurricanes and the climatologically short duration of the graupel, and hail hydrometeors that has the most similar TRMM satellite period. A database that consists of PR vertical reflectivity structure. Brightness temperature rain rates and TMI Tb within tropical storms should simulations through this profile are then compared to improve rain-rate estimates from GPROF. simultaneous observations from TMI. The rainfall and GPROF was developed for TMI using a database ice hydrometeor drop size distribution in the profiles are compiled when a single year of data was available, so a iteratively adjusted to produce optimal agreement be- database of tropical storms spanning a much longer tween computed and observed Tb. This process leads period will provide enough information to relate the PR to a unique hydrometeor profile that GPROF can use on rain rates and TMI Tb. Similarly, the reflectivity profile all other radiometers as well. and cloud-resolving model information used to produce The databases that GPROF uses are integral to the GPROF hydrometeor profiles is not required. The data- performance of the rain-rate retrieval algorithm. The base of tropical storms will allow both the rain rates and size of the database used in the Bayesian approaches the hydrometeor profiles to be retrieved using the same needs to meet a compromise between representative- Bayesian scheme. ness and computational efficiency (Viltard et al. 2006). GPROF’s physically constrained methodology is ap- Creating a database from a very long period of PR data plicable to other radiometers, as it uses a radiative creates too many profiles and is computationally very transfer model to construct profile databases that relate inefficient. To address this compromise, GPROF’s observed and simulated Tb for other sensors. In con- database is stratified by sea surface temperature (SST) trast, Hurricane GPROF is constructed only for TMI and total precipitable water (TPW) to limit the re- and GMI, which is sufficiently similar to TMI to use the trieval to meteorologically appropriate regimes and to retrieval without adding too much error. As Hurricane reduce the computational need for the algorithm. GPROF does not compute Tb to adjust the rain profiles,

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21 FIG. 1. PR averaged to TMI FOV rain rates (mm h ) in the database and their histogram (inset). it cannot produce consistent retrievals from a more di- spatial resolution of GPROF. Where the TRMM PR verse set of sensors. captures some part of the storm, all PR rain rates that fall within the TMI 21-GHz footprint are averaged to c. Constructing the TRMM hurricane database calculate the PR rain rate averaged to the TMI foot- To construct a new database for GPROF that contains print. Averages were produced if at least 80% of pixels only PR rain rates and TMI Tb, a large dataset of in the PR swath fell within the TMI footprint. Previous tropical cyclones is required. The National Hurricane TMI databases used only the center 11 PR pixels to Center’s hurricane database HURDAT2 (Landsea and simplify the geometry used to match PR profiles and Franklin 2013) is essentially a subjectively smoothed TMI pixels in three dimensions (Kummerow et al. 2011). assessment of tropical cyclone best-track information. It That requirement is relaxed here. While PR sensitivity is 2 contains the best-track position, minimum pressure, limited below 0.7 mm h 1, spatial averaging to the TMI maximum sustained wind, and wind tropical cyclone footprint produces lower rain rates. Footprints containing parameters for storms in the Atlantic and eastern North land surface pixels are excluded in the ocean-only version Pacific Oceans. A limited set of parameters is available of the retrieval. Figure 1 shows the locations and the prior to 2004, but these early cases did not contain frequency distribution of the PR averaged rain rates in enough information to be included in this work. the new database, rain rates that are dominated by Six-hourly track positions (0000, 0600, 1200, and tropical cyclones occurring in the Atlantic Ocean. The 2 1800 UTC) and the maximum distance of 34-kt (1 kt 5 rain-rate average is 3.28 mm h 1 and it peaks at 2 2 0.51 m s 1) wind radii were used to determine the spatial 169.42 mm h 1. Despite the large number (;600 000) extent of the tropical cyclones and tropical storms. Al- of rain rates in the hurricane database, the distribution though the 64-kt wind speed radii that differentiate tropical is still heavily skewed toward light rain rates, with cyclones from weaker systems are included in HURDAT2, relatively few observations in the high end of the rain- this threshold was relaxed due to a desire to capture rate distribution. the entire tropical cyclone structure in the database. Hydrometeor profile information is also contained in HURDAT2 best-track latitude and longitude data are the database. The PR 2A25, version 7, algorithm pro- linearly interpolated to estimate the storm’s position at the duces liquid and ice water content vertical profiles on 80 time of the TRMM PR scan, and its radius is determined layers with 250-m vertical resolution. Starting with a from the 34-kt wind radii. The tropical cyclone database convective/stratiform classification technique, the PR was compiled using coincident overpasses of PR rain rates algorithm assigns a different drop size distribution based averaged to a TMI footprint, and matching TMI Tb. upon a five-node vertical structure. For stratiform rain, a PR rain rates were averaged according to the size of mix of liquid and frozen hydrometeors is assumed in the the TMI 21-GHz footprint (;18 km) to match the 500 m above and below the freezing level, and this range

Unauthenticated | Downloaded 10/09/21 05:54 AM UTC JULY 2016 B R O W N E T A L . 1543 is expanded to 750 m for convective rain. These bands of TABLE 2. Descriptions of the seven storms selected and their liquid and frozen hydrometeors in the vertical profiles matching TMI orbits. are classified as mixed in the database, with those above TMI orbit No. Date Storm name and below these bands being classified as ice- and liquid- 67041 22 Aug 2009 Tropical Strom Danny phase hydrometeors, respectively. 67115 27 Aug 2009 Hurricane Bill To match the vertical resolution of GPROF, the 80 72808 27 Aug 2010 Hurricane Danielle PR profile layers of the rain-, mixed-, and ice-phase 73102 15 Sep 2010 Hurricane Igor hydrometeors are averaged into 20 layers of 500 m for 78490 26 Aug 2011 Hurricane Irene the first 10 km, and 8 layers of 1 km above 10 km. Al- 78592 02 Sep 2011 Hurricane Katia 84154 24 Aug 2012 Tropical Storm Isaac though cloud water is not detected by the PR, it can be estimated from models. As a specific user required cloud water profile information from the retrieval, a crude observed and database Tb. The expected rain rate is method was developed using a cloud-resolving model. similarly defined as Average nonraining, convective, and stratiform cloud " # water content profiles are generated from a cloud- R 1 5 å k å 2 : 2 2 resolving model simulation of a hurricane. The profiles R exp 0 5 2(Tbl,Obs Tbl,k) , 5 w 5 s are averaged into the TMI footprint based on the rain k 1,Dbase l 1,9 l type classification of the PR pixels. The resultant rain (2) (liquid), cloud, ice, and mixed water content profiles for 28 vertical layers that are averaged into the TMI foot- where Rk is the rain rate of the kth entry in the database. print. A database of hydrometeor profiles can be Seven tropical cyclones identified from HURDAT2, matched to TMI Tb, using a comparable method to that and well captured by TRMM PR overpasses, were for rain rates. Section 5 elaborates on how this in- chosen as representative case studies (Table 2). To formation is used in the retrieval. generate independent rain rates for each tropical cyclone scene, the database entries associated with the d. Hurricane GPROF orbit being processed were excluded from the retrieval. To use the TRMM hurricane database with the GPROF The Hurricane GPROF retrieval using instrument un- retrieval, some minor changes to the operational algo- certainties (NEDT) error was run for these seven trop- rithm were required. In particular, the changes affect ical cyclones to assess its performance. how channel uncertainties are incorporated into the Because the Hurricane GPROF database is con- retrieval. Table 1 lists the channel temperature sensi- structed for tropical storm/cyclone pixels where the tivity [noise-equivalent differential temperature (NEDT)] wind speed exceeds 34 kt, the retrieval is applied only to associated with the measurement errors of the nine TMI such pixels. Determining whether the tropical storm and channels. In GPROF, the Bayesian procedure uses the high wind conditions are present can be determined instrument uncertainties in addition to forward model from reanalyses and observations. If this methodology errors estimated from the residual differences between was used operationally, observations of tropical storms observed and simulated Tb differences. Forward model and cyclones could be used to identify where to apply errors associated with these residual uncertainties the Hurricane GPROF retrieval. If these tropical storm result from the PR/TMI matching procedure used in and wind conditions are not met, the GPROF retrieval is GPROF and are not pertinent when using an obser- used as the best method for estimating rain rates from vational database. Therefore, channel uncertainties TMI. Therefore, the two retrievals work in tandem, with consist solely of the instrument noise (temperature Hurricane GPROF effectively replacing the rain-rate sensitivity) in Hurricane GPROF. The resultant re- and hydrometeor estimates of raining TMI pixels pro- trieval algorithm follows that described in Kummerow duced by GPROF near tropical storms. et al. (1996, 2001)andViltard et al. (2006). Bayesian weights (w) are defined as " # 3. Evaluating hurricane GPROF

1 2 Differences between the TMI averaged PR rain rates w 5 å exp å 2 0:5 (Tb 2 Tb ) , (1) s2 l,Obs l,k k51,Dbase l51,9 l for the two GPROF retrieval estimates are summarized in Table 3, for the seven orbits previously selected. Four where database entries (k) are used in conjunction with different measures for evaluating the estimated rain the relationship between the TMI channel’s (l) tem- rates are presented. Root-mean-square error (RMSE), perature sensitivity (s) and the difference between mean absolute error (MAE), and the mean bias are

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TABLE 3. Retrieval evaluation statistics of the GPROF and HGPROF retrievals compared to the TMI footprint averaged PR rain rates for seven orbits. The proportion of PR rain rates that fall within two terciles of the mean in the Bayesian weighted rain-rate distribution 2 2 2 generated from the database (two terciles), RMSE (mm h 1), MAE (mm h 1), and mean bias (mm h 1) are listed.

Two terciles RMSE MAE Bias Orbit GPROF HGPROF GPROF HGPROF GPROF HGPROF GPROF HGPROF 67041 0.39 0.21 3.9 3.6 1.8 1.76 20.08 20.08 67115 0.71 0.21 7.38 6.63 2.6 2.39 21.79 21.08 72808 0.32 0.2 5.39 5.59 2.22 2.3 0.28 0.21 73102 0.4 0.19 5.68 6.04 2.75 2.7 0.84 0.9 78490 0.34 0.12 4.3 3.26 2.49 1.72 1.38 0.34 78592 0.42 0.16 9.21 9.21 4.14 3.92 21.18 21.91 84154 0.59 0.15 7.35 8.87 3.53 3.98 21.06 1.23 three statistics used to describe skill. The fourth measure not improve rain-rate estimates over GPROF estimates, uses the fraction of PR rain rates that fall within two neither fraction is consistently close to the expected terciles of the mean Bayesian weighted rain-rate distri- value of two-thirds. bution. Because PR rain is used in the a priori database After combining the seven scenes presented in Table as truth, the probability distribution function described 3, the PR rain rates were separated into quintiles to in Eq. (2) should contain the true answer within one evaluate how the GPROF and Hurricane GPROF re- standard deviation on either side of the mean about 67% trievals perform at different rain rates. The differences or two-thirds of the time. Terciles are used here to ac- between GPROF and Hurricane GPROF rain-rate es- count for the fact that the PDF is not Gaussian, but timates, presented in Table 4, are clear. Hurricane lognormal. The measure nonetheless is intended to GPROF generally improves RMSE, MAE, and bias quantify how well the PDF captures the true answer. for the low and medium rain-rate quintiles, only. How- Therefore, the best representation of the PR rain rates is ever, the two terciles indicate that few PR rain rates fall achieved when the retrieval produces approximately within the expected Bayesian probability distribution two-thirds of the PR rain rates within two terciles of the value of two-thirds for Hurricane GPROF. rain-rate estimates. This equates to PR rain rates being Figure 2 shows the seven storm’s rain-rate distributions within the Bayesian weighted rain-rate database distri- of the PR, GPROF, and Hurricane GPROF (HGPROF), bution 67% of the time. and it is apparent that Hurricane GPROF produces a Bias between the PR- and TMI-estimated rain rates is better ﬁt to the PR data. GPROF displays a different reduced by approximately 17% on average using Hur- shaped distribution to the PR for these seven tropical cy- ricane GPROF compared to GPROF 2014, as bias im- clones, generating too little light and heavy rain, while proves at only three of the seven selected scenes (Table overestimating medium rain rates. In contrast, Hurricane 3). Little change is seen between the RMSE and MAE GPROF tends to match high rain rates quite well, while statistics of the retrievals, with Hurricane GPROF ac- slightly underestimating light rain. Comparable differences tually increasing these numbers for two of the tropical between the distribution of PR and retrieval estimates also cyclone scenes. While the smaller proportion of PR rain exist when looking at the seven cases individually. rates falling within two terciles of the Bayesian proba- TMI ﬁeld-of-view (FOV) averaged PR, GPROF, and bility distribution indicates that Hurricane GPROF did Hurricane GPROF rain rates for three hurricanes are

TABLE 4. Retrieval evaluation statistics of the GPROF and HGPROF retrievals compared to the TMI footprint averaged PR rain rates for the PR quintiles of the seven orbits combined. The proportion of PR rain rates that fall within two terciles of the mean in the Bayesian 2 2 2 weighted rain-rate distribution generated from the database (two terciles), RMSE (mm h 1), MAE (mm h 1), and mean bias (mm h 1) are listed.

Two terciles RMSE MAE Bias Quintiles GPROF HGPROF GPROF HGPROF GPROF HGPROF GPROF HGPROF 0.00–0.11 0.17 0.22 1.04 0.79 0.55 0.31 0.54 0.29 0.11–0.51 0.40 0.19 1.71 1.36 0.89 0.69 0.74 0.40 0.51–1.58 0.44 0.18 2.77 2.17 1.64 1.30 1.21 0.59 1.58–4.60 0.49 0.18 4.66 4.65 2.92 2.70 1.75 1.06 4.60–169.42 0.68 0.16 11.24 12.31 7.79 8.28 24.61 22.00

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discerns finer detail in some of the rainbands. Higher rain rates seen in the PR data are not generated by GPROF 2014 but are in some of the Hurricane GPROF data. While the Hurricane GPROF retrieval generally resembles the PR observations, it also shows some features that are not very spatially coherent. The noise in the Hurricane GPROF retrieval in some parts of the tropical cyclones indicates that the retrieval is producing highly variable estimates in the high rain-rate regions. Such variability is not present in the PR rain rates averaged over the TMI FOV, nor is it in the GPROF rainfall estimates, and it suggests a problem with the Tb uncertainties specified in the Hurricane GPROF retrieval. This was also evident in FIG. 2. Histogram of PR averaged to TMI FOV (PR), GPROF, and the terciles, which indicate the retrieval is applying high 21 HGPROF rain rates (mm h ) for the seven selected retrievals. weights to a narrow PDF of rain rates in the database. shown in Fig. 3. These three storms show similar results 4. Assessment of error to those obtained from all seven selected cases. Both GPROF and Hurricane GPROF reproduce the main rain The small uncertainty specified by instrument NEDT features of the tropical cyclone, but Hurricane GPROF results in a very narrow weighting function w that tends

21 FIG. 3. Rain rates (mm h ) from TRMM PR, PR averaged to the TMI FOV, GPROF, and HGPROF for three orbits (72808, 73102, and 84154).

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FIG. 4. Average change in rain rate (%) for randomly resampled proportions of TMI Hdb compared to the complete TMI Hdb. Rain-rate quintiles are the lowest rain rates in quintile 1 and the highest rain rate in quintile 5. to select a single proﬁle from the a priori database the size of the database, the effect of these reductions on (generally with a low weight) rather than a smooth PDF. the rain rates can be determined and the database un- Higher rain rates are affected the most, as the number of certainty can then be inferred. The Hurricane GPROF database entries decreases as rain rates increase (Fig. 1). retrieval was repeatedly run, while randomly removing Kummerow et al. (2006) noted that incomplete data- greater proportions of the tropical cyclone database, for bases contribute considerable uncertainty to rainfall the seven orbits previously selected. Retrievals were run 5 retrievals. Nine years of data populate the TMI hurri- times for each orbit, removing 25%, 33%, 50%, and 75% cane database (Hdb), but this cannot be considered to of the entries to indicate how sensitive rain-rate estimates be a completely representative database of all tropical are to database size, and to allow one to extrapolate the cyclones, given their infrequent nature. Consequently, effect of this reduced database. the incomplete database contributes to uncertainty in Channel uncertainty was also evaluated by incre- the retrieval, particularly when viewed with the low mentally increasing NEDT while examining the width of uncertainty values of ;0.5 K in each of the TMI chan- the PDF and the ideal result that the truth will lie within nels. Therefore, it was concluded that NEDT was not two-thirds of the PDF two-thirds of the time. Care must sufﬁcient to account for additional error associated with be taken when increasing NEDT as high values can the uncertainties and limitations of the tropical cyclone oversmooth rain rates in the tropical cyclones. Re- database. The low incidence of the PR rain rates falling trievals were also separated into rain-rate quintiles, as within the expected Bayesian probability distribution Fig. 2 suggests that the limitations of the tropical cyclone value of two-thirds for Hurricane GPROF (i.e., the two database would affect high and low rain rates differ- terciles column in Tables 3 and 4) further suggests the ently. The changes in database size, rain-rate quintile, uncertainties are too low, as they cause the Bayesian and NEDT are assessed through their effect on percent distribution to be too narrow. change in rain rate and bias. The sensitivity of rain rates It is not possible to calculate how much error is intro- to the completeness of the database is intrinsically reduced by using a limited hurricane database, compared lated to the channel uncertainty (or detail) in the to a truly complete one. However, the sensitivity of the retrieval. rain-rate estimates to the database can be assessed Different approaches to increasing the uncertainties through a randomized resampling procedure. By reducing were assessed. These included increasing NEDT by

21 FIG. 5. Average bias (mm h ) of randomly resampled proportions of TMI Hdb compared to the complete TMI Hdb. Rain rates were separated into ﬁve quintiles that increase with the lowest rain rates in quintile 1 and the highest rain rates in quintile 5.

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FIG. 6. The NEDT multiplier of between 1 and 10 that produces the best retrieval evaluation statistic, 2 2 2 using the two terciles, RMSE (mm h 1), MAE (mm h 1), and mean bias (mm h 1) measures.

adding a fixed Tb increment, exponentially, as a pro- inferred that a complete database with NEDT33ora portion of Tb range and as a proportion of Tb variability. somewhat smaller one with a NEDT34 or NEDT35 It was determined that increasing NEDT using a mul- would be appropriate. However, this premise also relies tiplier produced a better representation of rain rates upon the assumption that two-thirds of the truth also lies than the other approaches. Similarly, as NEDT is related within two-thirds of the PDF, with low rain rates prop- to channel sensitivity (Table 1) and Tb, the effect of the erly accounted for or explained. database incompleteness is a reasonable approximation To complement the assessment of changing NEDT of the additional error. This NEDT multiplier method made from Figs. 4 and 5, the effects of systematically was then further investigated using the evaluation mea- increasing NEDT on the seven selected orbits’ retrieval sures described above. evaluation statistics are also assessed. The NEDT mul- Figure 4 shows the percent change in rain-rate quin- tiplier that maximizes the tercile, RMSE, MAE, and bias tiles associated with randomly removing different pro- evaluation measures, for both the seven orbits individu- portions of the TMI hurricane database while increasing ally and combined orbit quintiles, are summarized in NEDT. Only the results restricting the database by 25% Fig. 6. A lot of variability is displayed in the best-fitting and 75% are shown, as the 33% and 50% databases NEDT multiplier from the four evaluation statistics, show very similar changes that differ only in magni- when looking at the seven orbits individually. More sys- tude. Database size has a large impact on rain-rate tematic changes are occurring when the orbits are com- estimates. When 75% of the database is randomly bined and then assessed according to rain-rate quintiles. removed, rain rates change by up to 76% when only Overall, bias is generally optimized using a low NEDT instrument noise is allowed. As the size of the data- multiplier between one and three, but RMSE, MAE, and base increases, the percent change in rain rate de- the terciles are optimized with an NEDT multiplier be- creases, and the differences between quintile 1 and tween three and five. quintile 5 rain rates also decrease. The differences be- The effect of increasing NEDT was also assessed vi- tween each quintile and database size converge when sually. Figures 7 and 8 show how the rain rates in two NEDT is multiplied by between three and four, suggesting different tropical environments become more coherent that the size of the database is no longer contributing to as NEDT is increased. Subjectively, the NEDT of be- the rain-rate uncertainties. tween three and five appear optimal, as these rain rates A comparable plot to Fig. 4, but showing rain-rate are most similar to the PR. Increasing NEDT propor- biases, is presented in Fig. 5. Bias shows a similar re- tionally increases the error term (s) for each channel in sponse to percent change in rain rate, with a decreasing Eqs. (1) and (2), allowing more weight to be applied to relationship, relative to increases in database size. rain rates with similar Tb. This is because increasing Multiplying NEDT by between three and four produces NEDT increases the weights applied to rain rates in the the greatest reduction in bias, as bias drops to less than Bayesian scheme. Consequently, rain-rate estimates 2 0.1 mm h 1 for each subsampled database. It can be are produced using a greater range of database rain

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21 FIG. 7. Retrieval estimated rain rates (mm h ) using increasing values of NEDT that range from 1 to 10 for TMI orbit 73102. rates through the higher weights, which decreases the all the PR rain rates in the database (Fig. 1) and the variability of rain-rate estimates. Similar relationships Hurricane GPROF and GPROF rain rates retrieved is between the NEDT adjusted retrieval and PR rain rates shown in Table 5 and Fig. 11. Overall, Hurricane were also seen in the other five cases. GPROF outperforms GPROF, although Hurricane Given the consistency of the results in this assessment GPROF cannot reproduce the very lowest PR rain rates of uncertainties, the NEDT term in Eqs. (1) and (2) was (Fig. 11). Despite this overestimation of low rain rates, increased by a factor of 4 over the value of NEDT alone. improvements over GPROF are seen in all four of The resultant rain-rate estimates produced by Hurri- Hurricane GPROF’s rain-rate quintile evaluation sta- cane GPROF for the seven cases investigated are tistics (Table 5). Hurricane GPROF reduces the average presented in Fig. 9. Hurricane GPROF produces a RMSE and MAE by ;25%, and bias decreases from 2 reasonable representation of tropical cyclone rainfall, 0.20 to 20.06 mm h 1, over GPROF estimates. A check when compared to the more direct measurement of the of the assumption that stratifying the database by SST TRMM PR, even though the highest rain rates are not and TPW is not necessary was also made by evaluating reproduced. More importantly, Hurricane GPROF tropical cyclones in the database that occurred north of produces a better rain-rate retrieval than GPROF 308N. Hurricane GPROF produced better estimates of (Fig. 3), particularly for heavy rainband features in the PR rain rates than GPROF for these northern storms inner and outer cores of the systems. A direct compar- (not shown), to confirm that SST and TPW were not ison of the rain rates for orbits 72808 and 78490 in Fig. 10 essential for the hurricane retrieval. indicates Hurricane GPROF produces a closer relationship with the PR rain rates than GPROF. Over- 5. Profile retrieval estimation of low rainfall amounts and underestimation of high rainfall amounts is still present in Hurricane The Hurricane GPROF rain-rate retrieval procedure GPROF due to the Bayesian approach. is also applicable for estimating hydrometeor profiles, On the strength of the results obtained from the seven using the profiles in the database described in section 2. selected orbits, Hurricane GPROF was run for all of the Even more benefits may be realized in the vertical orbits in the hurricane database. A comparison between profiles since the retrieval now is limited to profiles

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FIG.8.AsinFig. 7, but for TMI orbit 84154. associated only with hurricanes instead of all possible phases. The IWP estimates from GPROF are larger storm types. Using the NEDT34 multiplier, as the than the sum of MWP and IWP from PR by between 2 profile retrievals are subject to the same types of errors 0.14 and 0.82 kg m 2. as surface rain rates, TMI estimates of rain water con- RMSE, MAE, and bias evaluation measures for rain, tent (RWC), cloud water content (CWC), mixed water cloud, mixed, and ice water paths are listed in Table 6. content (MWC), and ice water content (IWC) are pro- Overall, Hurricane GPROF reduces the GPROF error duced. Estimates of the profiles and mixed water path by ;38% on average when compared to the PR, with the (MWP) from GPROF are not available in the current RWP showing the greatest improvements in the three version of GPROF 2014 and are therefore not compared measures of error. For RWP, bias is greatly reduced by here. Hurricane GPROF average rain, cloud, mixed, Hurricane GPROF, although RMSE and MAE are also and ice water content profiles compare well to the shape lowered by an average of between 53% and 80% over and magnitude of PR profiles averaged to the TMI FOV estimates from GPROF. CWP is generally well esti- (Fig. 12). Differences between the PR average and the mated by both retrievals. Estimates of IWP from 2 retrieval profiles average less than 0.05 g m 3 for RWC GPROF are again shown to considerably overestimate 2 and less than 0.02 g m 3 for CWC, MWC, and IWC. ice in the atmosphere, which inflates all three measures Figure 13 shows the seven orbits’ column-integrated of error. However, the hydrometeors in GPROF differ water path variables for the four hydrometeor phases, in density from those based on the PR as the profiles are from the PR, GPROF, and Hurricane GPROF. Hurri- adjusted, so such comparisons are not completely valid. cane GPROF produces the most similar rain water path In contrast, Hurricane GPROF shows little error or bias (RWP), cloud water path (CWP), mixed water path for MWP and IWP. (MWP), and ice water path (IWP) retrieval to the PR, The spatial features of a tropical cyclone’s surface while GPROF generally overestimates the amount of rainbands are also present in the water path variables, as water in these tropical storms by 60% on average. At- shown for orbit 78490 in Figs. 9 and 14. As noted with the mospheric water content is dominated by RWP, which surface rain rate, the GPROF retrieval produces larger 2 averages 0.78 kg m 2 from the PR, and is comparable bands of moisture in the storms than are present in the the total water content of the three other hydrometeor PR. For RWP, CWP, and IWP, GPROF generally

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21 FIG. 9. Rain rates (mm h ) for the PR averaged to the TMI FOV, the ﬁnal version of the HGPROF retrieval, and their differences for the seven selected orbits.

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FIG. 10. Density plots of GPROF and HGPROF rain-rate estimates compared to the PR averaged to the TMI FOV rain rates for orbits 72808 and 78490. The mean of GPROF (dashed line), HGPROF (dotted line), and 1:1 line (solid) are also depicted in each plot. overestimates all but the highest column-integrated path environments. The key to this retrieval is the creation of values, creating less spatially distinct hydrometeor fea- an a priori database derived from the HURDAT2 hur- tures in the tropical cyclones. Although Hurricane ricane database, describing storm locations and sizes. GPROF produces similar estimates to the PR hydro- The Hurricane GPROF retrieval has been shown to meteors, it fails to replicate the lowest and highest water improve rain rates for tropical storms, over those pro- path amounts of the tropical cyclones as a result of the duced by the globally applied algorithm, GPROF. Bayesian scheme. Measures of error indicate that on average a 25% improvement in rain rates is achieved and bias is reduced. PR-based rain rates near the eyewall and in the sur- 6. Summary and conclusions rounding rainbands are more clearly delineated by An adapted version of the GPROF retrieval called Hurricane GPROF than by GPROF. These features are Hurricane GPROF has been produced for TMI and deﬁned more clearly due to better estimates of low and GMI, but unlike GPROF it cannot be used for other high rain rates in the tropical systems. One GPROF microwave sensors. Hurricane GPROF is an ocean-only weakness previously identiﬁed (Viltard et al. 2006; rainfall retrieval that is applicable to tropical cyclone Zagrodnik and Jiang 2013a,b) is its inability to recreate

TABLE 5. Retrieval evaluation statistics of the GPROF and HGPROF retrievals compared to the TMI footprint averaged PR rain rates for the PR quintiles of the entire hurricane database. The proportion of PR rain rates that fall within two terciles of the mean in the 2 2 Bayesian weighted rain-rate distribution generated from the database (two terciles), RMSE (mm h 1), MAE (mm h 1), and mean bias 2 (mm h 1) are listed. The percentage change in RMSE, MAE, and bias for GPROF compared to HGROF are also listed.

Two terciles RMSE MAE Bias Quintile GPROF HGPROF GPROF HGPROF GPROF HGPROF GPROF HGPROF 0.00–0.11 0.20 0.74 0.78 0.37 0.40 0.24 0.39 0.24 0.11–0.51 0.40 0.79 1.18 0.57 0.59 0.33 0.52 0.26 0.51–1.58 0.50 0.65 1.98 1.01 1.08 0.66 0.77 0.31 1.58–4.60 0.54 0.63 3.49 2.03 2.11 1.44 1.15 0.49 4.60–169.42 0.68 0.57 8.62 6.83 5.91 4.66 21.80 21.63 Average 0.47 0.68 3.21 2.16 2.02 1.47 0.20 20.06

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FIG. 11. Density plots of GPROF and HGPROF rain-rate estimates compared to all the PR values averaged to the TMI FOV rain rates in the Hdb. The mean of GPROF (dashed line), HGPROF (dotted line), and 1:1 line (solid) are also depicted in each plot. rain-rate estimates in the most intense rainfall regions of lowest rain rates and underestimates the highest rain tropical cyclones. This deﬁciency has only been partially rates. This effect is largely unavoidable when using a addressed in Hurricane GPROF. Despite the improve- Bayesian technique to estimate values at the upper and ments in the rain-rate retrieval, it still overestimates the lower limits of their distribution.

FIG. 12. Average TMI RWC, CWC, MWC, and IWC proﬁles of orbits 72808 and 78490, from the PR averaged to the TMI FOV and HGPROF.

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FIG. 13. TMI RWP, CWP, MWP, and IWP estimates from the PR averaged to the TMI FOV, GPROF, and HGPROF, for seven selected orbits.

The water content profile estimates of the Hurricane water path estimates reduce the average bias from the GPROF hydrometeors reflect similar deficiencies as PR to 9%, compared to 28% using GPROF. Such a those seen in surface rain rates, when compared to the reduction constitutes a considerable improvement in the PR. Still, Hurricane GPROF rain, cloud, mixed, and ice hydrometeor estimates.

TABLE 6. Retrieval evaluation statistics of the GPROF and HGPROF retrievals compared to the TMI footprint averaged PR rain rates for seven orbits. The proportion of PR rain rates that fall within two terciles of the mean in the Bayesian weighted rain-rate distribution 2 2 2 generated from the database RMSE (mm h 1), MAE (mm h 1), and mean bias (mm h 1) are listed.

RMSE MAE Bias Orbit GPROF HGPROF GPROF HGPROF GPROF HGPROF RWP 67041 0.77 0.55 0.50 0.26 0.30 20.01 67115 1.10 0.99 0.41 0.33 20.06 20.14 72808 0.94 0.74 0.62 0.32 0.44 0.05 73102 1.18 0.73 0.74 0.35 0.54 0.10 78490 0.83 0.48 0.58 0.23 0.46 0.02 78592 1.47 1.37 0.81 0.57 0.20 20.31 84154 1.35 1.31 0.72 0.60 0.18 0.19 CWP 67041 0.24 0.15 0.20 0.10 0.14 0.00 67115 0.24 0.18 0.17 0.12 0.03 20.04 72808 0.27 0.15 0.23 0.11 0.18 0.03 73102 0.38 0.14 0.29 0.10 0.27 0.03 78490 0.28 0.18 0.23 0.12 0.18 0.01 78592 0.27 0.24 0.22 0.16 0.10 20.06 84154 0.29 0.19 0.21 0.12 0.14 20.02 MWP 67041 N/A 0.11 N/A 0.06 N/A 0.01 67115 N/A 0.17 N/A 0.06 N/A 20.02 72808 N/A 0.26 N/A 0.07 N/A 20.01 73102 N/A 0.16 N/A 0.08 N/A 0.00 78490 N/A 0.09 N/A 0.05 N/A 0.02 78592 N/A 0.18 N/A 0.10 N/A 20.01 84154 N/A 0.38 N/A 0.16 N/A 0.03 IWP 67041 0.90 0.07 0.61 0.04 0.61 0.02 67115 0.85 0.12 0.46 0.06 0.45 20.03 72808 0.79 0.13 0.63 0.05 0.62 20.01 73102 0.83 0.13 0.61 0.07 0.61 20.02 78490 0.40 0.08 0.27 0.04 0.26 0.00 78592 1.42 0.14 1.13 0.08 1.13 0.01 84154 0.91 0.17 0.61 0.10 0.60 0.01

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10.0 ) −2

1.0 Water content (kg.m

0.1

FIG. 14. TMI RWP, CWP, MWP, and IWP estimates for orbit 78490, from the PR, GPROF, and HGPROF.

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21 FIG. 15. Rain rates (mm h ) from GPM Core Observatory Ku-band PR and HGPROF for Hurricane Gonzalo on 16 Oct 2014.

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