Hurricane GPROF: An Optimized Ocean Microwave Rainfall Retrieval for Tropical Cyclones
1. Introduction
Tropical cyclones are a high-impact meteorological event that can have catastrophic impacts, especially if landfall occurs. Tropical ocean environments create the conditions under which tropical storms and tropical cyclones occur, but these environments are difficult to observe using ground-based instrumentation. Consequently, satellite-derived measurements are frequently used to detect and monitor the evolution of tropical cyclones. Space-based microwave radiometers have provided measures of atmospheric moisture since the Special Sensor Microwave Imager (SSM/I) began operating in 1987. Similar instruments are now commonly used to estimate both cyclone features and rain rates (Benedetti et al. 2005; Lau et al. 2008; Jiang et al. 2011), especially with the Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) increasing the number of channels and spatial resolution of SSM/I (Kummerow et al. 2001). TRMM was deployed in 1997 with a Microwave Imager (TMI) and a precipitation radar (PR) on board to provide detailed data on tropical rainfall between 35°N and 35°S, which makes it ideal for studying spatial and temporal rainfall characteristics of tropical cyclones. Similarly, the recent deployment of the Global Precipitation Measurement (GPM) Core Observatory satellite in February 2014 will complement the rainfall products generated from TRMM. The GPM Core Observatory’s Microwave Imager (GMI) and dual-frequency precipitation radar (DPR) provides near-global coverage and improves upon TRMM’s detection of light rain, snow, and the microphysical properties of precipitating particles (Hou et al. 2014).
Over oceans, physical methods that use statistical relationships between brightness temperatures and rain rates/hydrometeors have been developed to retrieve rainfall for TRMM, the GPM Core Observatory, and other satellites (Wilheit et al. 1991; Petty 2001; Hilburn and Wentz 2008; Kummerow et al. 2015), often through Bayesian schemes (Evans et al. 1995; Bauer et al. 2001; Di Michele et al. 2005; Kummerow et al. 2011; Sanò et al. 2013). Bayesian schemes often use a probabilistic approach to match an a priori database of hydrometeor profiles constructed by requiring consistency between hydrometeors and radiometer observations (Marzano et al. 1999; Kummerow et al. 2011; Sanò et al. 2013). Retrievals over land are complicated by surface heterogeneity, affecting emissivities and increasing error in the rainfall estimates (Wang et al. 2009; Petty and Li 2013). Despite these complexities, passive microwave rain products over land show good agreement with other products (Kummerow et al. 2011; 2015), especially as improvements are made to address weaknesses previously identified in the algorithms (Wang et al. 2009; Gopalan et al. 2010; Ferraro et al. 2013).
TRMM’s suitability for monitoring tropical cyclones has led to extensive development and use of databases, such as the tropical cyclone cloud and precipitation feature databases (Liu et al. 2008; Jiang et al. 2011), tropical cyclone track databases (Knapp et al. 2010) and numerous studies of meteorological characteristics of tropical cyclones (Lonfat et al. 2004; Jiang 2012; Ren et al. 2014). However, deficiencies have been shown when comparing estimates from independent radar observations of precipitation and TMI precipitation estimates, with TMI underestimating the inner core and high-rain-rate regions of tropical cyclones (Viltard et al. 2006; Zagrodnik and Jiang 2013a,b). These underestimates are associated with one of the limitations of the Bayesian probability theory applied in the retrieval, which produces a rain-rate estimate based on its likelihood. In the case of tropical cyclones, their hydrometeorological environments and high rain rates are uncommon in the a priori database and are therefore unlikely to be highly weighted by the retrieval’s Bayesian scheme. As TMI has limited information from its observations, it cannot fully distinguish between the Tbs of different rain systems, so identifying these rain systems (e.g., tropical cyclones) using auxillary data adds information to benefit the retrieval.
Creating application-specific versions of the TMI retrieval should result in improvements to the rain-rate estimates for tropical cyclones. In particular, the a priori databases used in the Bayesian scheme of Kummerow et al. (2011) can be populated with data from tropical cyclones. Running a retrieval specifically for tropical cyclones over oceans, based on oceanic tropical cyclone rainfall data alone, should produce better rain-rate estimates than a more generalized global scheme. Adapting the Bayesian retrieval for TMI to improve its performance under oceanic tropical cyclone conditions is the premise of this work. A comparable retrieval over land is also possible, but it was preferable to evaluate the retrieval over oceans where radar data are more robust and the physical relationships between rain and the radar are better understood.
The purpose of this paper is to describe the new retrieval methodology for tropical cyclones and to show how it improves estimates of tropical cyclone rain rates over oceans. While this methodology is applied to tropical cyclones here, it can also be applied to other meteorological phenomenon. An overview of the GPROF 2014 retrieval, its use of databases, and their limitations are identified in section 2. Section 2 also describes the new ocean-only database and the adaptations made to the GPROF 2014 rain-rate retrieval for tropical storms and tropical cyclones. Hurricane GPROF is then evaluated in section 3. Section 4 assesses the effect of increasing the error term in the Bayesian retrieval to optimize channel uncertainty in order to account for the incomplete population of tropical storms in the database. Vertical profile retrievals are evaluated in section 5, and then a summary of the new Hurricane GPROF retrieval and conclusions from this work are contained in section 6.
2. TRMM and the GPROF retrieval procedure
a. TRMM instruments
Active and passive microwave instruments are on board the TRMM satellite. The precipitation properties of the PR and the TMI instruments are estimated remotely from the reflectivity and brightness temperatures, respectively. The PR operates at 13.8 GHz, with a surface resolution of 5 km and a 247-km (after boost) swath. The PR 2A25 algorithm (Iguchi et al. 2000) determines rain rates based on the relationship between reflectivity and rain rate, using a drop size distribution model, an attenuation correction, and a nonuniform beamfilling correction. The sensitivity of the PR is roughly 0.7 mm h−1, although it can produce rain rates of as low as approximately 0.3 mm h−1. Consequently, light rain rates, especially those from shallow stratiform rain, are not always detected (Schumacher and Houze 2000, 2003).
TMI is a nine-channel passive microwave radiometer that observes brightness temperatures (Tb) at five different frequencies (10.65, 19.35, 21.3, 37.0, and 85.5 GHz). Vertical and horizontal polarization measurements are taken at all but the 21-GHz (vertical only) channel (Table 1). A spatial resolution of 5.1 km is achieved at 85 GHz and a full swath scan covers 878 km. The overlap between coincident PR and TMI observations is restricted by the much narrower width of the PR swath. A small temporal offset also results from the nadir-oriented PR and the 53° conical scan angle of TMI. It is the overlapping PR and TMI observations from TRMM that provide the basis for obtaining a priori rain structures for GPROF. Ancillary datasets and model output can also be incorporated into retrievals to provide a narrower and therefore more appropriate meteorological context of the precipitating environment.
b. The GPROF 2014 retrieval over oceans
The operational algorithm used to estimate rain rates from TRMM for this study is GPROF 2014 —the newest version of the algorithm (hereafter GPROF). A general overview of GPROF is given here to provide a context for how the new Hurricane GPROF retrieval is developed, as significant changes are made. More detailed descriptions of the GPROF retrieval are contained in Kummerow et al. (2011, 2015).
Over oceans, GPROF is a physically constructed retrieval that uses an a priori database consisting of matched PR rain rates for the 21-GHz footprint (~18 km) and TMI Tb at their native resolution. For raining pixels, the PR profile and cloud-resolving model output are used to construct an initial profile. The PR reflectivity profile is used to select a cloud-resolving model profile of rainwater, cloud water, cloud ice, snow, graupel, and hail hydrometeors that has the most similar vertical reflectivity structure. Brightness temperature simulations through this profile are then compared to simultaneous observations from TMI. The rainfall and ice hydrometeor drop size distribution in the profiles are iteratively adjusted to produce optimal agreement between computed and observed Tb. This process leads to a unique hydrometeor profile that GPROF can use on all other radiometers as well.
The databases that GPROF uses are integral to the performance of the rain-rate retrieval algorithm. The size of the database used in the Bayesian approaches needs to meet a compromise between representativeness and computational efficiency (Viltard et al. 2006). Creating a database from a very long period of PR data creates too many profiles and is computationally very inefficient. To address this compromise, GPROF’s database is stratified by sea surface temperature (SST) and total precipitable water (TPW) to limit the retrieval to meteorologically appropriate regimes and to reduce the computational need for the algorithm. Ancillary datasets provide the SST data, which are especially important when applying GPROF globally.
Observational databases that constrain the GPROF retrievals are also limited by events that have occurred during the time period from which the database is constructed. The operational algorithm uses a single year of PR and TMI data. The infrequent nature of tropical cyclones reduces the ability of the Bayesian retrieval to reproduce correctly the precipitation associated with them unless the brightness temperatures match exceedingly well.
To improve the ability of GPROF’s retrieval to estimate the rain rates in tropical cyclones, some adjustments need to be made. Using a separate database that contains only information from tropical storm systems should improve the Bayesian rain-rate estimates, when comparable storm systems are present. This is achieved primarily by expanding the number of rain profiles in the meteorological environment of the tropical cyclones, to provide the algorithm with more well-matched profiles. SST and TPW data are not necessary in tropical cyclone environments, as their warm moist ambient conditions are relatively homogeneous compared to those seen globally. More importantly, further stratification of data by SST and TPW would reduce the size of the database, which is already limited by the infrequent nature of hurricanes and the climatologically short duration of the TRMM satellite period. A database that consists of PR rain rates and TMI Tb within tropical storms should improve rain-rate estimates from GPROF.
GPROF was developed for TMI using a database compiled when a single year of data was available, so a database of tropical storms spanning a much longer period will provide enough information to relate the PR rain rates and TMI Tb. Similarly, the reflectivity profile and cloud-resolving model information used to produce GPROF hydrometeor profiles is not required. The database of tropical storms will allow both the rain rates and the hydrometeor profiles to be retrieved using the same Bayesian scheme.
GPROF’s physically constrained methodology is applicable to other radiometers, as it uses a radiative transfer model to construct profile databases that relate observed and simulated Tb for other sensors. In contrast, Hurricane GPROF is constructed only for TMI and GMI, which is sufficiently similar to TMI to use the retrieval without adding too much error. As Hurricane GPROF does not compute Tb to adjust the rain profiles, it cannot produce consistent retrievals from a more diverse set of sensors.
c. Constructing the TRMM hurricane database
To construct a new database for GPROF that contains only PR rain rates and TMI Tb, a large dataset of tropical cyclones is required. The National Hurricane Center’s hurricane database HURDAT2 (Landsea and Franklin 2013) is essentially a subjectively smoothed assessment of tropical cyclone best-track information. It contains the best-track position, minimum pressure, maximum sustained wind, and wind tropical cyclone parameters for storms in the Atlantic and eastern North Pacific Oceans. A limited set of parameters is available prior to 2004, but these early cases did not contain enough information to be included in this work.
Six-hourly track positions (0000, 0600, 1200, and 1800 UTC) and the maximum distance of 34-kt (1 kt = 0.51 m s−1) wind radii were used to determine the spatial extent of the tropical cyclones and tropical storms. Although the 64-kt wind speed radii that differentiate tropical cyclones from weaker systems are included in HURDAT2, this threshold was relaxed due to a desire to capture the entire tropical cyclone structure in the database. HURDAT2 best-track latitude and longitude data are linearly interpolated to estimate the storm’s position at the time of the TRMM PR scan, and its radius is determined from the 34-kt wind radii. The tropical cyclone database was compiled using coincident overpasses of PR rain rates averaged to a TMI footprint, and matching TMI Tb.
PR rain rates were averaged according to the size of the TMI 21-GHz footprint (~18 km) to match the spatial resolution of GPROF. Where the TRMM PR captures some part of the storm, all PR rain rates that fall within the TMI 21-GHz footprint are averaged to calculate the PR rain rate averaged to the TMI footprint. Averages were produced if at least 80% of pixels in the PR swath fell within the TMI footprint. Previous TMI databases used only the center 11 PR pixels to simplify the geometry used to match PR profiles and TMI pixels in three dimensions (Kummerow et al. 2011). That requirement is relaxed here. While PR sensitivity is limited below 0.7 mm h−1, spatial averaging to the TMI footprint produces lower rain rates. Footprints containing land surface pixels are excluded in the ocean-only version of the retrieval. Figure 1 shows the locations and the frequency distribution of the PR averaged rain rates in the new database, rain rates that are dominated by tropical cyclones occurring in the Atlantic Ocean. The rain-rate average is 3.28 mm h−1 and it peaks at 169.42 mm h−1. Despite the large number (~600 000) of rain rates in the hurricane database, the distribution is still heavily skewed toward light rain rates, with relatively few observations in the high end of the rain-rate distribution.
PR averaged to TMI FOV rain rates (mm h−1) in the database and their histogram (inset).
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
Hydrometeor profile information is also contained in the database. The PR 2A25, version 7, algorithm produces liquid and ice water content vertical profiles on 80 layers with 250-m vertical resolution. Starting with a convective/stratiform classification technique, the PR algorithm assigns a different drop size distribution based upon a five-node vertical structure. For stratiform rain, a mix of liquid and frozen hydrometeors is assumed in the 500 m above and below the freezing level, and this range is expanded to 750 m for convective rain. These bands of liquid and frozen hydrometeors in the vertical profiles are classified as mixed in the database, with those above and below these bands being classified as ice- and liquid-phase hydrometeors, respectively.
To match the vertical resolution of GPROF, the 80 PR profile layers of the rain-, mixed-, and ice-phase hydrometeors are averaged into 20 layers of 500 m for the first 10 km, and 8 layers of 1 km above 10 km. Although 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 method was developed using a cloud-resolving model. Average nonraining, convective, and stratiform cloud water content profiles are generated from a cloud-resolving model simulation of a hurricane. The profiles are averaged into the TMI footprint based on the rain type classification of the PR pixels. The resultant rain (liquid), cloud, ice, and mixed water content profiles for 28 vertical layers that are averaged into the TMI footprint. A database of hydrometeor profiles can be matched to TMI Tb, using a comparable method to that for rain rates. Section 5 elaborates on how this information is used in the retrieval.
d. Hurricane GPROF
Seven tropical cyclones identified from HURDAT2, and well captured by TRMM PR overpasses, were chosen as representative case studies (Table 2). To generate independent rain rates for each tropical cyclone scene, the database entries associated with the orbit being processed were excluded from the retrieval. The Hurricane GPROF retrieval using instrument uncertainties (NEDT) error was run for these seven tropical cyclones to assess its performance.
Descriptions of the seven storms selected and their matching TMI orbits.
Because the Hurricane GPROF database is constructed for tropical storm/cyclone pixels where the wind speed exceeds 34 kt, the retrieval is applied only to such pixels. Determining whether the tropical storm and high wind conditions are present can be determined from reanalyses and observations. If this methodology was used operationally, observations of tropical storms and cyclones could be used to identify where to apply the Hurricane GPROF retrieval. If these tropical storm and wind conditions are not met, the GPROF retrieval is used as the best method for estimating rain rates from TMI. Therefore, the two retrievals work in tandem, with Hurricane GPROF effectively replacing the rain-rate and hydrometeor estimates of raining TMI pixels produced by GPROF near tropical storms.
3. Evaluating hurricane GPROF
Differences between the TMI averaged PR rain rates for the two GPROF retrieval estimates are summarized in Table 3, for the seven orbits previously selected. Four different measures for evaluating the estimated rain rates are presented. Root-mean-square error (RMSE), mean absolute error (MAE), and the mean bias are three statistics used to describe skill. The fourth measure uses the fraction of PR rain rates that fall within two terciles of the mean Bayesian weighted rain-rate distribution. Because PR rain is used in the a priori database as truth, the probability distribution function described in Eq. (2) should contain the true answer within one standard deviation on either side of the mean about 67% or two-thirds of the time. Terciles are used here to account for the fact that the PDF is not Gaussian, but lognormal. The measure nonetheless is intended to quantify how well the PDF captures the true answer. Therefore, the best representation of the PR rain rates is achieved when the retrieval produces approximately two-thirds of the PR rain rates within two terciles of the rain-rate estimates. This equates to PR rain rates being within the Bayesian weighted rain-rate database distribution 67% of the time.
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 generated from the database (two terciles), RMSE (mm h−1), MAE (mm h−1), and mean bias (mm h−1) are listed.
Bias between the PR- and TMI-estimated rain rates is reduced by approximately 17% on average using Hurricane GPROF compared to GPROF 2014, as bias improves at only three of the seven selected scenes (Table 3). Little change is seen between the RMSE and MAE statistics of the retrievals, with Hurricane GPROF actually increasing these numbers for two of the tropical cyclone scenes. While the smaller proportion of PR rain rates falling within two terciles of the Bayesian probability distribution indicates that Hurricane GPROF did not improve rain-rate estimates over GPROF estimates, neither fraction is consistently close to the expected value of two-thirds.
After combining the seven scenes presented in Table 3, the PR rain rates were separated into quintiles to evaluate how the GPROF and Hurricane GPROF retrievals perform at different rain rates. The differences between GPROF and Hurricane GPROF rain-rate estimates, presented in Table 4, are clear. Hurricane GPROF generally improves RMSE, MAE, and bias for the low and medium rain-rate quintiles, only. However, the two terciles indicate that few PR rain rates fall within the expected Bayesian probability distribution value of two-thirds for Hurricane GPROF.
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 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.
Figure 2 shows the seven storm’s rain-rate distributions of the PR, GPROF, and Hurricane GPROF (HGPROF), and it is apparent that Hurricane GPROF produces a better fit to the PR data. GPROF displays a different shaped distribution to the PR for these seven tropical cyclones, generating too little light and heavy rain, while overestimating medium rain rates. In contrast, Hurricane GPROF tends to match high rain rates quite well, while slightly underestimating light rain. Comparable differences between the distribution of PR and retrieval estimates also exist when looking at the seven cases individually.
Histogram of PR averaged to TMI FOV (PR), GPROF, and HGPROF rain rates (mm h−1) for the seven selected retrievals.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
TMI field-of-view (FOV) averaged PR, GPROF, and Hurricane GPROF rain rates for three hurricanes are shown in Fig. 3. These three storms show similar results to those obtained from all seven selected cases. Both GPROF and Hurricane GPROF reproduce the main rain features of the tropical cyclone, but Hurricane GPROF 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 the terciles, which indicate the retrieval is applying high weights to a narrow PDF of rain rates in the database.
Rain rates (mm h−1) from TRMM PR, PR averaged to the TMI FOV, GPROF, and HGPROF for three orbits (72808, 73102, and 84154).
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
4. Assessment of error
The small uncertainty specified by instrument NEDT results in a very narrow weighting function w that tends to select a single profile from the a priori database (generally with a low weight) rather than a smooth PDF. Higher rain rates are affected the most, as the number of database entries decreases as rain rates increase (Fig. 1). Kummerow et al. (2006) noted that incomplete databases contribute considerable uncertainty to rainfall retrievals. Nine years of data populate the TMI hurricane database (Hdb), but this cannot be considered to be a completely representative database of all tropical cyclones, given their infrequent nature. Consequently, the incomplete database contributes to uncertainty in the retrieval, particularly when viewed with the low uncertainty values of ~0.5 K in each of the TMI channels. Therefore, it was concluded that NEDT was not sufficient to account for additional error associated with the uncertainties and limitations of the tropical cyclone database. The low incidence of the PR rain rates falling within the expected Bayesian probability distribution value of two-thirds for Hurricane GPROF (i.e., the two terciles column in Tables 3 and 4) further suggests the uncertainties are too low, as they cause the Bayesian distribution to be too narrow.
It is not possible to calculate how much error is introduced by using a limited hurricane database, compared to a truly complete one. However, the sensitivity of the rain-rate estimates to the database can be assessed through a randomized resampling procedure. By reducing the size of the database, the effect of these reductions on the rain rates can be determined and the database uncertainty can then be inferred. The Hurricane GPROF retrieval was repeatedly run, while randomly removing greater proportions of the tropical cyclone database, for the seven orbits previously selected. Retrievals were run 5 times for each orbit, removing 25%, 33%, 50%, and 75% of the entries to indicate how sensitive rain-rate estimates are to database size, and to allow one to extrapolate the effect of this reduced database.
Channel uncertainty was also evaluated by incrementally increasing NEDT while examining the width of the PDF and the ideal result that the truth will lie within two-thirds of the PDF two-thirds of the time. Care must be taken when increasing NEDT as high values can oversmooth rain rates in the tropical cyclones. Retrievals were also separated into rain-rate quintiles, as Fig. 2 suggests that the limitations of the tropical cyclone database would affect high and low rain rates differently. The changes in database size, rain-rate quintile, and NEDT are assessed through their effect on percent change in rain rate and bias. The sensitivity of rain rates to the completeness of the database is intrinsically related to the channel uncertainty (or detail) in the retrieval.
Different approaches to increasing the uncertainties were assessed. These included increasing NEDT by adding a fixed Tb increment, exponentially, as a proportion of Tb range and as a proportion of Tb variability. It was determined that increasing NEDT using a multiplier produced a better representation of rain rates than the other approaches. Similarly, as NEDT is related to channel sensitivity (Table 1) and Tb, the effect of the database incompleteness is a reasonable approximation of the additional error. This NEDT multiplier method was then further investigated using the evaluation measures described above.
Figure 4 shows the percent change in rain-rate quintiles associated with randomly removing different proportions of the TMI hurricane database while increasing NEDT. Only the results restricting the database by 25% and 75% are shown, as the 33% and 50% databases show very similar changes that differ only in magnitude. Database size has a large impact on rain-rate estimates. When 75% of the database is randomly removed, rain rates change by up to 76% when only instrument noise is allowed. As the size of the database increases, the percent change in rain rate decreases, and the differences between quintile 1 and quintile 5 rain rates also decrease. The differences between each quintile and database size converge when NEDT is multiplied by between three and four, suggesting that the size of the database is no longer contributing to the rain-rate uncertainties.
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.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
A comparable plot to Fig. 4, but showing rain-rate biases, is presented in Fig. 5. Bias shows a similar response to percent change in rain rate, with a decreasing relationship, relative to increases in database size. Multiplying NEDT by between three and four produces the greatest reduction in bias, as bias drops to less than 0.1 mm h−1 for each subsampled database. It can be inferred that a complete database with NEDT×3 or a somewhat smaller one with a NEDT×4 or NEDT×5 would be appropriate. However, this premise also relies upon the assumption that two-thirds of the truth also lies within two-thirds of the PDF, with low rain rates properly accounted for or explained.
Average bias (mm h−1) 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.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
To complement the assessment of changing NEDT made from Figs. 4 and 5, the effects of systematically increasing NEDT on the seven selected orbits’ retrieval evaluation statistics are also assessed. The NEDT multiplier that maximizes the tercile, RMSE, MAE, and bias evaluation measures, for both the seven orbits individually and combined orbit quintiles, are summarized in Fig. 6. A lot of variability is displayed in the best-fitting NEDT multiplier from the four evaluation statistics, when looking at the seven orbits individually. More systematic changes are occurring when the orbits are combined and then assessed according to rain-rate quintiles. Overall, bias is generally optimized using a low NEDT multiplier between one and three, but RMSE, MAE, and the terciles are optimized with an NEDT multiplier between three and five.
The NEDT multiplier of between 1 and 10 that produces the best retrieval evaluation statistic, using the two terciles, RMSE (mm h−1), MAE (mm h−1), and mean bias (mm h−1) measures.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
The effect of increasing NEDT was also assessed visually. Figures 7 and 8 show how the rain rates in two different tropical environments become more coherent as NEDT is increased. Subjectively, the NEDT of between three and five appear optimal, as these rain rates are most similar to the PR. Increasing NEDT proportionally increases the error term (σ) for each channel in Eqs. (1) and (2), allowing more weight to be applied to rain rates with similar Tb. This is because increasing NEDT increases the weights applied to rain rates in the Bayesian scheme. Consequently, rain-rate estimates are produced using a greater range of database rain rates through the higher weights, which decreases the variability of rain-rate estimates. Similar relationships between the NEDT adjusted retrieval and PR rain rates were also seen in the other five cases.
Retrieval estimated rain rates (mm h−1) using increasing values of NEDT that range from 1 to 10 for TMI orbit 73102.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
As in Fig. 7, but for TMI orbit 84154.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
Given the consistency of the results in this assessment of uncertainties, the NEDT term in Eqs. (1) and (2) was increased by a factor of 4 over the value of NEDT alone. The resultant rain-rate estimates produced by Hurricane GPROF for the seven cases investigated are presented in Fig. 9. Hurricane GPROF produces a reasonable representation of tropical cyclone rainfall, when compared to the more direct measurement of the TRMM PR, even though the highest rain rates are not reproduced. More importantly, Hurricane GPROF produces a better rain-rate retrieval than GPROF (Fig. 3), particularly for heavy rainband features in the inner and outer cores of the systems. A direct comparison of the rain rates for orbits 72808 and 78490 in Fig. 10 indicates Hurricane GPROF produces a closer relationship with the PR rain rates than GPROF. Overestimation of low rainfall amounts and underestimation of high rainfall amounts is still present in Hurricane GPROF due to the Bayesian approach.
Rain rates (mm h−1) for the PR averaged to the TMI FOV, the final version of the HGPROF retrieval, and their differences for the seven selected orbits.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
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.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
On the strength of the results obtained from the seven selected orbits, Hurricane GPROF was run for all of the orbits in the hurricane database. A comparison between all the PR rain rates in the database (Fig. 1) and the Hurricane GPROF and GPROF rain rates retrieved is shown in Table 5 and Fig. 11. Overall, Hurricane GPROF outperforms GPROF, although Hurricane GPROF cannot reproduce the very lowest PR rain rates (Fig. 11). Despite this overestimation of low rain rates, improvements over GPROF are seen in all four of Hurricane GPROF’s rain-rate quintile evaluation statistics (Table 5). Hurricane GPROF reduces the average RMSE and MAE by ~25%, and bias decreases from 0.20 to −0.06 mm h−1, over GPROF estimates. A check of the assumption that stratifying the database by SST and TPW is not necessary was also made by evaluating tropical cyclones in the database that occurred north of 30°N. Hurricane GPROF produced better estimates of PR rain rates than GPROF for these northern storms (not shown), to confirm that SST and TPW were not essential for the hurricane retrieval.
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 Bayesian 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. The percentage change in RMSE, MAE, and bias for GPROF compared to HGROF are also listed.
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.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
5. Profile retrieval
The Hurricane GPROF rain-rate retrieval procedure is also applicable for estimating hydrometeor profiles, using the profiles in the database described in section 2. Even more benefits may be realized in the vertical profiles since the retrieval now is limited to profiles associated only with hurricanes instead of all possible storm types. Using the NEDT×4 multiplier, as the profile retrievals are subject to the same types of errors as surface rain rates, TMI estimates of rain water content (RWC), cloud water content (CWC), mixed water content (MWC), and ice water content (IWC) are produced. Estimates of the profiles and mixed water path (MWP) from GPROF are not available in the current version of GPROF 2014 and are therefore not compared here. Hurricane GPROF average rain, cloud, mixed, and ice water content profiles compare well to the shape and magnitude of PR profiles averaged to the TMI FOV (Fig. 12). Differences between the PR average and the retrieval profiles average less than 0.05 g m−3 for RWC and less than 0.02 g m−3 for CWC, MWC, and IWC.
Average TMI RWC, CWC, MWC, and IWC profiles of orbits 72808 and 78490, from the PR averaged to the TMI FOV and HGPROF.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
Figure 13 shows the seven orbits’ column-integrated water path variables for the four hydrometeor phases, from the PR, GPROF, and Hurricane GPROF. Hurricane GPROF produces the most similar rain water path (RWP), cloud water path (CWP), mixed water path (MWP), and ice water path (IWP) retrieval to the PR, while GPROF generally overestimates the amount of water in these tropical storms by 60% on average. Atmospheric water content is dominated by RWP, which averages 0.78 kg m−2 from the PR, and is comparable the total water content of the three other hydrometeor phases. The IWP estimates from GPROF are larger than the sum of MWP and IWP from PR by between 0.14 and 0.82 kg m−2.
TMI RWP, CWP, MWP, and IWP estimates from the PR averaged to the TMI FOV, GPROF, and HGPROF, for seven selected orbits.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
RMSE, MAE, and bias evaluation measures for rain, cloud, mixed, and ice water paths are listed in Table 6. Overall, Hurricane GPROF reduces the GPROF error by ~38% on average when compared to the PR, with the RWP showing the greatest improvements in the three measures of error. For RWP, bias is greatly reduced by Hurricane GPROF, although RMSE and MAE are also lowered by an average of between 53% and 80% over estimates from GPROF. CWP is generally well estimated by both retrievals. Estimates of IWP from GPROF are again shown to considerably overestimate ice in the atmosphere, which inflates all three measures of error. However, the hydrometeors in GPROF differ in density from those based on the PR as the profiles are adjusted, so such comparisons are not completely valid. In contrast, Hurricane GPROF shows little error or bias for MWP and IWP.
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 generated from the database RMSE (mm h−1), MAE (mm h−1), and mean bias (mm h−1) are listed.
The spatial features of a tropical cyclone’s surface rainbands are also present in the water path variables, as shown for orbit 78490 in Figs. 9 and 14. As noted with the surface rain rate, the GPROF retrieval produces larger bands of moisture in the storms than are present in the PR. For RWP, CWP, and IWP, GPROF generally overestimates all but the highest column-integrated path values, creating less spatially distinct hydrometeor features in the tropical cyclones. Although Hurricane GPROF produces similar estimates to the PR hydrometeors, it fails to replicate the lowest and highest water path amounts of the tropical cyclones as a result of the Bayesian scheme.
TMI RWP, CWP, MWP, and IWP estimates for orbit 78490, from the PR, GPROF, and HGPROF.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
6. Summary and conclusions
An adapted version of the GPROF retrieval called Hurricane GPROF has been produced for TMI and GMI, but unlike GPROF it cannot be used for other microwave sensors. Hurricane GPROF is an ocean-only rainfall retrieval that is applicable to tropical cyclone environments. The key to this retrieval is the creation of an a priori database derived from the HURDAT2 hurricane database, describing storm locations and sizes. The Hurricane GPROF retrieval has been shown to improve rain rates for tropical storms, over those produced by the globally applied algorithm, GPROF. 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 surrounding rainbands are more clearly delineated by Hurricane GPROF than by GPROF. These features are defined more clearly due to better estimates of low and high rain rates in the tropical systems. One GPROF weakness previously identified (Viltard et al. 2006; Zagrodnik and Jiang 2013a,b) is its inability to recreate rain-rate estimates in the most intense rainfall regions of tropical cyclones. This deficiency has only been partially addressed in Hurricane GPROF. Despite the improvements in the rain-rate retrieval, it still overestimates the lowest rain rates and underestimates the highest rain rates. This effect is largely unavoidable when using a Bayesian technique to estimate values at the upper and lower limits of their distribution.
The water content profile estimates of the Hurricane GPROF hydrometeors reflect similar deficiencies as those seen in surface rain rates, when compared to the PR. Still, Hurricane GPROF rain, cloud, mixed, and ice water path estimates reduce the average bias from the PR to 9%, compared to 28% using GPROF. Such a reduction constitutes a considerable improvement in the hydrometeor estimates.
GMI has now superseded TMI, and while Hurricane GPROF is not optimized for this sensor, they are similar enough that the retrieval can be applied, as noted in section 2b. The additional error determined from the TMI hurricane database is also used for GMI. Figure 15 shows an example of the GPM Core Observatory Ku-band PR rain rates and Hurricane GPROF rain rates from GMI for Hurricane Gonzalo. This type of retrieval could also be included in future implementations of the GPM algorithm. However, at this time there is not enough data to construct a multiyear database from the dual-frequency precipitation radar.
Rain rates (mm h−1) from GPM Core Observatory Ku-band PR and HGPROF for Hurricane Gonzalo on 16 Oct 2014.
Citation: Journal of Atmospheric and Oceanic Technology 33, 7; 10.1175/JTECH-D-15-0234.1
The use of a condition-specific database to improve retrievals for tropical cyclones indicates that such a methodology could also be applied to other rare meteorological situations. Other examples of rare meteorological situations where the GPROF rain-rate retrieval could be improved upon by using condition-specific databases are severe convection in the U.S. plains and the Río de la Plata basin storms. As with Hurricane GPROF, TRMM can be used to create such databases. Alternatively, the GPM Core Observatory could also be used in the future, when enough observations are available to construct condition-specific databases.
Acknowledgments
This project was funded under NOAA’s Sandy Supplemental Award NA14OAR4830122.
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