Ground radar rainfall, necessary for satellite rainfall product (e.g., TRMM and GPM) ground validation (GV) studies, is often retrieved using annual or climatological convective/stratiform Z–R relationships. Using the Kwajalein, Republic of the Marshall Islands (RMI), polarimetric S-band weather radar (KPOL) and gauge network during the 2009 and 2011 wet seasons, the robustness of such rain-rate relationships is assessed through comparisons with rainfall retrieved using relationships that vary as a function of precipitation regime, defined as shallow convection, isolated deep convection, and deep organized convection. It is found that the TRMM-GV 2A53 rainfall product underestimated rain gauges by −8.3% in 2009 and −13.1% in 2011, where biases are attributed to rainfall in organized precipitation regimes. To further examine these biases, 2A53 GV rain rates are compared with polarimetrically tuned rain rates, in which GV biases are found to be minimized when rain relationships are developed for each precipitation regime, where, for example, during the 2009 wet-season biases in isolated deep precipitation regimes were reduced from −16.3% to −4.7%. The regime-based improvements also exist when specific convective and stratiform Z–R relationships are developed as a function of precipitation regime, where negative biases in organized convective events (−8.7%) are reduced to −1.6% when a regime-based Z–R is implemented. Negative GV biases during the wet seasons lead to an underestimation in accumulated rainfall when compared with ground gauges, suggesting that satellite-related bias estimates could be underestimated more than originally described. Such results encourage the use of the large-scale precipitation regime along with their respective locally characterized convective or stratiform classes in precipitation validation endeavors and in development of Z–R rainfall relationships.
Much of our knowledge of oceanic rainfall is obtained from microwave precipitation retrievals using spaceborne satellite measurements. To aid in this endeavor, the Tropical Rainfall Measuring Mission (TRMM; Kummerow et al. 1998) monitored precipitation systems in the tropics and subtropics with active and passive microwave sensors from November 1997 until it was decommissioned in 2015. The mission revolutionized precipitation measurements by including the first spaceborne Precipitation Radar (PR) in conjunction with the TRMM Microwave Imager (TMI). The success of the TRMM mission led to the follow-on Global Precipitation Measurement (GPM; Hou et al. 2014) Mission, which builds upon TRMM by adding an active dual-frequency precipitation radar (DPR) and passive GPM Microwave Imager (GMI) providing an extension to TRMM’s long-standing climate record of precipitation measurement while extending spatial coverage to 65°N–S.
Ground validation (GV) of the TRMM and GPM missions has been continuously developed to provide benchmarks for algorithm developers that can be used to tune various assumptions required to retrieve rainfall rates (Kummerow et al. 2000; Bidwell et al. 2004; Wolff et al. 2005). Throughout the TRMM mission there have been numerous efforts to validate surface rain retrievals from TRMM TMI and PR using ground-based measurements (e.g., Wolff and Fisher 2008, 2009; Wang et al. 2014). The launch of the GPM mission embarked a new era of GV measurements focused on land, with improved ground-based instrumentation and field campaigns (Petersen and Krajewski 2013; Barros et al. 2014; Wolff et al. 2015; and others). While these new campaigns will be essential to improve land-based estimates, it is crucial to continue to improve rain-rate validation over the oceans to include quantitative assessment of the techniques and algorithms used in TRMM and GPM retrievals.
To improve oceanic validation, the Kwajalein polarimetric S-band weather radar (KPOL) was installed on the Kwajalein Atoll and is one of the few dual-polarized S-band radars located in an open-ocean tropical regime, making it an invaluable GV site for comparison of rainfall with the TRMM and GPM precipitation radars (e.g., Houze et al. 2004; Chandrasekar et al. 2008). Recently, a major effort has been made toward improving the quality of the GV measurements from the KPOL radar (Marks et al. 2009). The Kwajalein GV site is ideal for observing tropical oceanic convection because of its proximity to the intertropical convergence zone (ITCZ). Seasonal variations in the location of the ITCZ provide observations of a wide variety of convective systems—particularly during the wet seasons occurring from September to December (Schumacher and Houze 2003; Houze et al. 2004). While the location is beneficial for observing a wide variety of precipitating systems, some limitations still need to be considered when evaluating satellite retrievals.
The TRMM-era KPOL operational radar-derived rain rate is obtained using the radar reflectivity–rain rate (Z–R) relationship derived from the window probability matching method (WPMM; Rosenfeld et al. 1994). The Kwajalein Atoll contains six rain gauge sites that can be implemented in the derivation of radar–rain relationships. This sparse rain gauge network limits the derivation of WPMM relationships to an annual basis (Wolff et al. 2005; Wolff and Fisher 2008). Because the WPMM Z–R relationships at Kwajalein can only be reconstructed each year, it is possible that seasonal changes in Z–R relationships are not captured by the annual WPMM Z–R, and individual events can still deviate from an annually derived mean rain-rate relationship. TRMM studies have demonstrated how shifts in meteorological regime result in variations in cloud morphology (Schumacher et al. 2004; Masunaga et al. 2005), and if ground-based retrievals are unable to capture this convective variability, pinpointing biases between GV and satellite estimates becomes more difficult to assess.
The high temporal resolution of ground validation observations provides sufficient sampling to study precipitation evolution and create a climatological representation of precipitation in the rainfall retrievals. TRMM and GPM retrievals are limited regionally to 15–20 satellite overpasses per month with only occasional overpasses containing significant rainfall (Schumacher and Houze 2000). To be consistent with the climatological rainfall relationships, previous work quantified local biases in microwave precipitation retrievals at annual and multiannual time scales; however, the origins of the biases remain speculative and biases are highly variable when calculated month-to-month or shorter time scales (Wolff and Fisher 2008; Wang and Wolff 2010). To aid this endeavor, a validation procedure involving regime-based comparisons could help pinpoint sources of error at overpass time scales; connecting validation statistics to systems with similar physical properties, which can vary with monthly–seasonal shifts in meteorological regime (Berg et al. 2002, 2006). To do this we must first take steps to evaluate the performance of GV retrieval methodologies in a manner that can be linked to GV–satellite comparisons.
As a result of infrequent sampling, observing regional convective variability from satellite measurements can be difficult as they provide an instantaneous snapshot of precipitation characteristics. To aid temporal limitations, cloud and precipitating systems are commonly grouped into similar convective states (e.g., Rossow et al. 2005; Nesbitt et al. 2000; Liu et al. 2008; Elsaesser et al. 2010; Houze et al. 2007; Duncan et al. 2014). Implementation of such classifications has assisted evaluation of TRMM precipitation characteristics beyond convective and stratiform partitioning alone (e.g., Elsaesser and Kummerow 2013; Masunaga 2012; Yokoyama et al. 2014; Barnes et al. 2015; Rassmusen et al. 2013). Recently, Elsaesser et al. (2010) illustrated that clusters of convective precipitation from various organizational states were found to be self-similar and repeating over all tropical ocean basins. The work motivates the incorporation of precipitation regimes into the precipitation evaluation process as they provide validation statistics segregated by the precipitation regime in which they are developing. If precipitation regimes are used to assess the sensitivity of the GV products to convective variability, it provides a definitive pathway to apply results to satellite overpass comparisons.
This study aims to assess the impact of convective variability for common precipitation retrievals used in ground validation studies: WPMM, used in the operational TRMM GV products (Wolff et al. 2005); convective and stratiform partitioning; and a polarimetrically tuned Z–R approach. Specific convective and stratiform rainfall relationships can increase information content but may not be able to fully capture physical properties between different rain events (Bringi et al. 2004). Finally, it is advantageous to use the Kwajalein KPOL polarimetric data to infer precipitation microphysics to assist retrieval assessment (Chandrasekar et al. 2008). Applying a polarimetrically tuned Z–R relationship is beneficial as it is continually adjusted for each pixel as drop size distributions (DSD) evolve in time. By implementing the methodology described by Elsaesser et al. (2010), we test if convective types influence validation statistics between radar-derived rainfall and ground gauge measurements and identify how predominant precipitation regimes influence rain-rate relationships.
The procedures and data used within this analysis are provided in the following sections. Section 2 of this manuscript describes the standard TRMM products used in deriving the WPMM relationships, as well as describing the polarized-tuned rain retrieval and radar-based precipitation classification methodology. Section 3 presents the results of the retrieval evaluations, and concluding remarks and discussion can be found in section 4.
2. Data sources and analysis
a. GV products
The Kwajalein GV site provides continuous radar information from the KPOL radar in conjunction with a network of ground rain gauges (Fig. 1). The radar measurements arise from the dual-polarized S-band KPOL radar located on the southern edge of the Kwajalein Atoll. The version-7 TRMM 2A53, 2A54, and 2A55 products for Kwajalein are utilized for this study over two wet-season periods of September–November 2009 and September–November 2011—periods where the radar is considered well calibrated within ±0.5 dB (Silberstein et al. 2008; Marks et al. 2009). Each product has a gridded horizontal resolution of 2 km × 2 km that extends 150 km from the KPOL radar site. The 2A53, 2A54, and 2A55 products provide instantaneous rain rates, classification of convective or stratiform precipitation type using the methods of Steiner et al. (1995), and 3D reflectivity fields, respectively. The 2A55 reflectivity product provides three-dimensional gridded data with a horizontal resolution of 2 km × 2 km and vertical resolution of 1.5 km.
Surface rainfall measurements are collected through a series of rain gauges distributed around the atoll. The rain gauges are automated tipping-bucket style and record at 0.254-mm intervals. The TRMM 2A56 rain gauge product is produced by interpolating the gauge surface rain-rate-measured tips into 1-min intervals using a cubic-spline-based algorithm (Wang et al. 2008). The Kwajalein gauge network consists of seven rain gauge locations on the atoll, only six located outside the radar “cone of silence,” and each location contains at least two gauges to assist with quality control (QC). For this work, if more than one gauge contains a valid rainfall estimate, the gauge with the higher rain rate is used to reduce error that may occur if a gauge stops recording resulting in a reduced number of tips (D. Marks 2015, personal communication). Three levels of quality-control procedures are implemented on a monthly basis by assessing the 1-min interpolated rain rates (Wang et al. 2008) and insuring valid radar observations (Marks et al. 2011), and through comparison with collocated radar–reflectivity data (Amitai 2000). Monthly rain gauge observations for each gauge location that do not meet the quality-control standards are not included in the analysis.
The Z–R relationships implemented in the 2A53 product are derived using the WPMM using the 1.5-km constant-altitude plan position indicator (CAPPI) level reflectivities and 7-min rain gauge averages. The WPMM statistically matches quality-controlled reflectivities extracted from radar volume scans to gauge-estimated rain rates such that the probability distribution of the radar rain rates above the gauge is equal to that of the gauge rain rates at an annual level. The derived 2A53 instantaneous rain-rate maps are available approximately every 10 min, corresponding to the volume scan interval of the KPOL radar. Comparisons of radar and rain gauge data are only implemented if quality-controlled data from both sources are valid. Data gaps associated with missing radar data are therefore not used in this study; however, more than 90% of radar data were available during these time periods.
b. Radar-derived products
1) Polarimetric data and rain-rate estimates
Dual-polarimetric data allow the direct estimation of drop sizes used to improve rain-rate retrieval accuracy (e.g., Gorgucci et al. 2000, 2001; Bringi et al. 2004, 2012). In this work, we make use of the dual-polarized Kwajalein S-pol radar to provide increased information on drop microphysics and to retrieve rain rates tuned to polarimetric parameters. The Kwajalein S-Pol radar completes a volume scan, created from 18 plan position indicator (PPI) scans, approximately every 10 min. We utilize horizontal reflectivity Zh (for notational simplicity we let Z = Zh), differential reflectivity Zdr, and the differential propagation phase Kdp to aid in the precipitation retrieval and to infer information on precipitation characteristics. Detailed descriptions of the radar and improved data quality-control procedures for the polarimetric data can be found in Marks et al. (2009, 2011).
This work makes use of the polarimetrically tuned Z–R relation derived by Bringi et al. (2004). The retrieval continuously varies in space and time as storm microphysics evolves without the need to preclassify rain type. This procedure is based on retrieving the DSD parameters of a normalized Gamma model using polarimetric observations of Zh, Zdr, and Kdp. They begin with the assumption of a first-guess Z–R relationship of the form
and adjust the coefficient a in Eq. (1) as the DSD evolves in space and time for each radar pixel. Rain rates are derived using the lowest radar PPI elevation scan and interpolated to 0.5 km. The technique has resulted in noticeably improved correlations with rain gauges while not requiring gauge data for calibration (Marks et al. 2009).
2) Classification of precipitating systems
This study will separate GV precipitation from individual radar scans into self-similar convective states following the architecture described by Elsaesser et al. (2010). Their work defined three distinct convective systems (akin to Johnson et al. 1999) through a k-means clustering methodology. The clusters were separated using TRMM PR–derived echo-top heights (ETH) in convective rainfall, mean rain rate of convective-only precipitation, and the ratio of mean convective precipitation to the total contained in 1° × 1° boxes within the TRMM PR swath. The methodology yields three tropical oceanic convective clusters further explored and interpreted in Elsaesser and Kummerow (2013) as 1) shallow, typically warm rain, congestus clouds with echo tops commonly below 5 km; 2) deep unorganized convection; and 3) deep organized convection containing substantial amounts of deep stratiform rainfall. The algorithm provides instantaneous classification of precipitation systems, which were found to be consistent in vertical structure, rainfall, and diabatic heating across meteorological regimes. This is significant, as the results from the precipitation regimes should remain consistent even for regions influenced by different synoptic conditions—providing results that can be exportable throughout the tropics.
Kwajalein KPOL GV data contain the necessary information to apply the clustering classification from a ground radar perspective. The application of the classification introduces a novel way to identify oceanic raining systems in order to evaluate ground-based retrievals segregated by distinct precipitation regimes. Following the method described in Elsaesser et al. (2010), radar echo-top heights for convective grid boxes and surface rainfall within a 1° × 1° region surrounding the radar and gauge locations (shown in Fig. 1) are input into the k-means clustering algorithm. To obtain a closer match to TRMM classification procedure, the horizontal reflectivity is averaged to a 4 km × 4 km and the vertical resolution was reprocessed from 1.5 km to 750 m. Surface rain rates and precipitation identification are taken from the TRMM 2A53 and 2A54 products, respectively. All KPOL radar scans with valid QC for the two wet seasons described above are input into the k-means clustering algorithm, yielding nearly 17 000 radar volume scans containing raining cases.
In the forthcoming sections we discuss the performance of the WPMM, polarimetrically tuned Z–R relationships, and convective- and stratiform-partitioned rainfall estimates and how the application of precipitation regimes can aid their evaluation. We first evaluate the rain estimates based on pairs of concurrent radar–gauge observations following the methods used in Wang and Wolff (2010), who compare TRMM 2A53 products with gauges at multiple time scales in Melbourne, Florida. For this work, gauges are integrated to 10-min intervals matched to the radar scan times for the precipitation regimes described above. The statistics are computed using the mean gauge rain rate from all locations and collocated radar products where both radar and gauge report nonzero rainfall. It should be noted that the rain gauges used in the comparison are not independent of 2A53 as the rain gauge data assist in creating the yearly WPMM Z–R. Dependent validation, however, is useful to assess inconsistencies in the rain-rate relationship and the gauges provide a consistent reference when evaluating the rain retrievals.
Kwajalein rain gauge observations from the September–November months of the 2009 and 2011 wet seasons are used to evaluate the radar-derived rainfall products. Characteristics of the precipitation regimes and their associated gauge measurements used to derive Z–R relationships are shown in Table 1. The rain gauge accumulation is defined as the cumulative rainfall from all valid rain gauges over each wet-season period. The wet seasons provide a subset of precipitating systems compared to what is observed annually, where intense convective systems occur more frequently. Shallow and deep convection are the most prominent precipitation types over the two seasons; however, because of the sparse nature of shallow convection, fewer cases are captured by the rain gauges. Organized systems account for the majority of accumulated rainfall measured by the gauges, with higher accumulation in the 2009 wet season associated with increased frequency in precipitation during an El Niño event. Mean rain rates and convective fractions, main drivers in the k-means cluster classification, are consistent with Elsaesser et al. (2010) mean characteristics over the tropical oceans; however, the convective fractions are slightly higher for organized rainfall regimes. The higher fraction likely corresponds to a higher frequency of embedded convective rain identified from the Kwajalein radar algorithms in stratiform areas (Schumacher and Houze 2003).
The distribution of reflectivity profiles for each of the three precipitation regimes, separated into convective (Fig. 2, top) and stratiform (Fig. 2, bottom) rainfall types, is illustrated in Fig. 2 using contoured frequency by altitude diagrams (CFADs). The overall mean reflectivity profile for each rain type is included to provide a visual reference when comparing the precipitation regimes. The CFADs of convective precipitation show a monotonic increase in the maximum occurrence of near-surface reflectivity as well as an increase in the maximum height attained as a function of organization. Further, similar to the Elsaesser et al. (2010) results, shallow and deep precipitation regimes contain a higher frequency of shallow light-rain convection near 17 dBZ below 5 km in altitude. The stratiform CFADs also exhibit the monotonic increase in near-surface reflectivity. While deep and organized precipitation regimes contain similar maximum heights and occurrences, the organized regimes exhibit evidence of a stronger brightband signature. It is interesting to note that stratiform rainfall occurring in the shallow precipitation regime also contains a brightband signature, albeit occurring at much lower radar reflectivities.
a. Integrating precipitation regimes into WPMM Z–R relationships
Comparisons of rain gauge rain rates and radar-derived rain rates, segregated by the precipitation regimes, from the 2A53 product are displayed in Fig. 3. Included in each panel are percent bias, root-mean-square error, and correlation between the rain gauge rain estimate and the concurrent radar retrieved rain rate. For this work the percent bias is defined as
where, Ri and Gi are the radar and integrated gauge-derived rain rates, respectively. A large amount of scatter exists for all precipitating systems, which is expected when comparing rainfall measurements at the instantaneous time scale. In general, the relationships between radar and gauge rain rates between 2009 and 2011 are fairly consistent. While annual comparisons of radar and gauges are largely unbiased, the radar-derived rain rates are negatively biased overall for the wet seasons analyzed here. This is particularly noticeable during the 2011 wet-season bias because of a higher frequency of heavy rainfall underestimated associated with organized convection. Biases between gauge and radar estimates are worst for organized convective events during the 2009 and 2011 wet seasons and are negatively biased by 11.8% and 18.1%, respectively. Shallow convection biases are typically largely negative; however, the rain rates are lower compared to the deep convective and organized precipitation regimes. Deep convection and organized convection contain nearly equal cases above and below the one-to-one line, but positively biased rain-rate comparisons occur at much lower rain rates. Negative biases for deep and organized precipitation regimes are driven by underestimation at higher rain rates. Above 10 mm h−1 (~76% of cases) nearly 80% of radar estimates are underestimated with biases of −28% for deep convection and −35% for organized convection. This is significant as the majority of rainfall accumulation is accounted for by these two regimes.
Rao et al. (2001) relate the overestimation of lighter rainfall and underestimation by more intense rainfall derived from a single Z–R relationship directly to stratiform and convective rainfall. To examine this, all precipitation regimes in 2009 and 2011 are separated into convective or stratiform components using the TRMM 2A54 classification (Fig. 4). We first examine biases using a conventional Z–R relationship of Z = 175R1.5 derived from the Kwajalein Atoll Field Experiment (KWAJEX; Fiorino 2002). Clear separation in biases in stratiform (+12.9%) and convective rainfall (−22.4%) is observed. These biases are larger in magnitude compared to the WPMM, which was designed to better capture climatological rain rates; however, similar separations in biases still exist as well for convective (−10.1%) and stratiform (+9.9%) rainfall, demonstrating that WPMM relationships do not contain the information required to fully capture the DSD variability between the different precipitating types. While convection is negatively biased overall, large scatter exists largely from isolated deep convective comparisons. When comparing convective rain rates < 30 mm h−1 for deep isolated precipitation regimes, the radar-derived rainfall overestimate gauges by 6.2%. This lighter rainfall is typical during the dry-season months and may provide explanation for the unbiased result on the annual level.
The overall negative biases observed for both wet seasons seem to be weighted by the underestimation of convective precipitation in organized convective systems. The differences in rainfall products are regulated in terms of frequency of occurrence by the convective events. The biases are a direct result of the increased occurrence of intense rainfall during the wet-season time period that cannot be captured by the WPMM relationship and is a pattern that should be consistently observed for a given wet-season period at the Kwajalein site. This effect of sampling on a subannual time scale could be even further amplified when GV and satellite measurements are compared on a sampling scale closer to satellites. When reducing the temporal scale to 12–48 h (not shown), we found the bias estimates to be variable dependent on the occurrence of the individual precipitating regimes. This temporal aspect is not the only concern, as the sparse rain gauge distribution can complicate error statistics as well (e.g., Habib and Krajewski 2002). To better understand the impact the precipitation regimes impart on rain-rate estimates, a spatially and temporally matched comparison is ideal. The dual-polarization availability from the KPOL radar provides spatially and temporally matched data—offering further insight into how much the WPMM estimates may miss in the shorter term because of convective variability.
b. KPOL polarimetric estimates
Retrieving rain rates using the dual-polarized KPOL data is advantageous as the retrievals are fully independent of the rain gauges and do not require convective and stratiform separation. For this reason, the TRMM-GPM GV office has recommended increased use of dual-polarimetric rainfall retrievals in precipitation validation (Petersen et al. 2013). Therefore, it is essential to also assess polarimetrically tuned rain-rate estimates with ground gauges to understand where uncertainties may occur and how they may relate to the WPMM results. Further, dual-polarimetric measurements from the KPOL radar can be used to understand microphysical differences in precipitation regimes as well as reveal precipitation variability that may be missed by the annually derived WPMM for each precipitation regime. The polarimetrically tuned rain rates are compared with the ground gauges, in a similar manner as the above section, for each precipitation regime and wet season (Fig. 5). The dual-polarimetrically tuned rain rates are manipulated by DSD parameters on a gate-by-gate instantaneous manner providing improved validation statistics with the ground gauge measurements compared to the annual WPMM-derived rain rates. Bias, RMSE, and correlations (0.89 in organized convection) with gauges are improved for each case during both wet seasons; however, significant outliers do exist in the comparisons. With the exception of organized convection in 2011, biases from the polarimetrically tuned rain rates are below 10%, demonstrating overall improvement. The reduced RMSE, particularly in 2011, validates that DSD variation is likely driving the large amount of scatter found in the WPMM comparisons. For example, in higher rates, the rain-rate retrieval incorporates Kdp to help differentiate DSDs and seems to be an important factor in improving comparisons with the gauges. Negative biases for the organized regimes are caused by a few extreme rainfall events but still show improvement compared to the annual WPMM estimates. Removal of these events yields bias estimates similar to the 2009 wet period; however, it is difficult to differentiate if the large negative bias are noise related to outliers. Slight underestimations of rain rates exist in deep isolated precipitation regimes with biases reduced to −0.8% in 2009 and −3.7% in 2011. Overall, the retrieval demonstrates the ability to capture rainfall variability from the regimes and is beneficial as the methods are independent of rain gauges and precipitation-type partitioning. The retrieval described by Bringi et al. (2004) is one of many ways of deriving rainfall from dual-polarimetric data; however, the improved error statistics found in these comparisons provide a strong foundation in how the DSD information content is useful when evaluating the retrieved rainfall.
The polarimetrically tuned rain-rate retrieval provides rain estimates for each grid box throughout the 1° × 1° classification region. The increased spatial sampling is beneficial to examine regime-based precipitation variability that may be missed by the WPMM relationships through the use of the matched radar reflectivity–rain rate pairs. To observe precipitation variability that may be missed by WPMM, rain rate–reflectivity relationships are examined for all wet-season data using 2D histograms colored by frequency of occurrence for each regime (Fig. 6). To aid in this visualization, convective and stratiform power-law relationships (described in Thompson et al. 2015) and the TRMM 2A53 annual WPMM Z–R relationships are also plotted to help illustrate the scale of variability occurring when evaluating each regime. In general, the large amount of variability throughout each radar reflectivity bin indicates the range of rain rates the annual WPMM relationships are unable to capture during the wet seasons. The radar–rain pairs in Fig. 6 provide additional evidence that the annual Z–R WPMM relationships generally overestimate stratiform precipitation (Fig. 6, bottom) and underestimate convective rainfall (Fig. 6, top), most notably in the deep isolated and organized regimes. In stratiform rainfall, radar–rain pairs are generally located to the left of the annual WPMM relationship, whereas convective rainfall radar–rain pairs are generally located to the right of the annual WPMM relationship, particularly at higher rain rates. Unique characteristics emerge for the predominant areas of occurrence within each regime. In stratiform rainfall there is a clear shift in occurrence and variance in the radar rain pairs for each precipitation regime. Radar–rain pairs within the organized regimes contain increased occurrence of heavier raining stratiform precipitation where points lie to the left of the WPMM relationship line for Z < 35 dBZ. For convective rainfall, the majority of radar–rain pairs in deep isolated regimes lie to the right of the WPMM relationship line for Z ~ 40 dBZ, indicating higher rain rates for a similar reflectivity. Similarly, radar–rain pairs within the organized regimes lie to the right of the WPMM relationship; however, the highly occurring points extend toward 50 dBZ where the radar–rain pairs begin to converge toward the WPMM relationship.
The polarimetric variables can also be used to further explore differences in convective and stratiform precipitation characteristics related to these regimes. We utilize reflectivity Z (dBZ) and Zdr (dB) from the lowest interpolated level to infer differences in the median drop size between the precipitating systems in the 2009 wet season [in a manner that is similar to that of Bringi et al. (2012)]. Figure 7 shows the frequency of occurrence of Zdr for a given Z for raining pixels occurring in deep isolated and organized regimes. The solid line indicates mean Zdr for reflectivity bins of 0.5-dBZ widths and the mean Zdr for deep isolated regimes are repeated in the organized regime panels to aid visual comparison (dashed line in Figs. 7b,d). For convective rainfall, light rainfall (Z < 20 dBZ) has a high occurrence near 0 dB in Zdr, indicating these cases are likely drizzle or light rainfall associated with shallow convection with smaller spherical drops. For both stratiform and convective rain, there are small differences in Zdr between the regimes from 20 dBZ < Z < 30 dBZ. This suggests that differences found in the rainfall relationship in this reflectivity are not largely attributable to mean drop diameter but rather to the number concentration (Steiner and Smith 2004; visualized in Fig. 19 of Thompson et al. 2015). Differences in convective rainfall occurring in deep isolated regimes and in organized regimes seem to be attributable to an increase in median drop size, as indicated by higher Zdr, for Z > 35 dBZ. This is illustrated by the divergence of mean Zdr values in Fig. 7d, where, beginning at 35 dBZ, mean Zdr values for the organized regime (solid line) continually diverge from the Zdr values associated with rainfall occurring in deep isolated regimes (dashed). This disparity in median drop size indicated by the regimes may be useful in the validation of satellite-based rainfall as DSD variability has been demonstrated as a source of uncertainty in rain-rate retrievals (Munchak et al. 2012).
c. Regime-based relationships
Over the oceans, biases found between satellite-derived rainfall products have been directly related to discrepancies in the characteristics in raining systems and variability in the synoptic meteorological conditions (Berg et al. 2002, 2006). To relate precipitating systems across regions, validation efforts commonly group precipitating systems by their physical characteristics, such as size or rainfall intensity, or by segregating rain-rate comparisons into convective and stratiform components; however, WPMM methodologies and convective and stratiform partitioning may need to be redefined regionally across the tropics. Therefore, understanding rain-rate relationship sensitivity to the individual precipitation regimes is an important factor.
Regime-based rain-rate relationships are derived specifically for the WPMM and convective–stratiform Z–R relationships to assess how sampling of the individual regimes influences rain-rate relationships. The above section demonstrated that polarimetric data prove to be a useful tool for understanding the variability missed by the WPMM relationships. In the following sections, rain-rate relationships will now be compared to the spatially and temporally matched polarimetrically tuned rain-rate estimates. Because the self-similar regimes are represented in terms of their distribution of clouds and precipitation within a 1° × 1° region, the polarimetrically tuned rain rates allow an independent assessment using all raining pixels in the 1° × 1° region—providing a comparison that is representative of the precipitation characteristics associated within each precipitation regime. Statistics between the rainfall estimates will be presented as before, with the polarimetrically tuned results used as reference.
1) Regime-derived WPMM relationships
The results thus far have demonstrated the issue of applying an annual WPMM Z–R to instantaneous data. For a given radar-derived rain rate, a multitude of solutions exist from the gauges as well as the polarimetrically tuned estimates (as shown in Fig. 3 and 5). The results show that regime occurrence may help to regulate overall biases, but they do not fully demonstrate the direct impact each regime has on the WPMM rain-rate relationships. This can be further examined through derivation of rain relationships for individual precipitation regimes; demonstrating the error that may occur in GV comparisons if only a single precipitation regime is sampled. By rederiving the WPMM relationships for each precipitation regime, we can get a sense of the error that may occur in the GV product at the instantaneous level.
The Z–R relationships are created for each convective state using the WPMM using combined data from the 2009 and 2011 wet seasons. The majority of annual rainfall occurs during the Kwajalein wet season (Houze et al. 2004); therefore, each precipitation regime meets the rain gauge accumulation (Table 1) requirements set by Rosenfeld et al. (1994) to produce stable Z–R relationships. Data points from all three precipitation regimes are first included in the WPMM derivation and produce a WPMM Z–R relationship qualitatively similar to the annual WPMM results; however, application of the WPMM to the individual precipitation regimes yields three more distinctive Z–R relationships (Fig. 8), where deep isolated and organized regimes are similar in structure but become separated at higher rain rates > 10 mm h−1. The regime-derived Z–Rs qualitatively resemble the data occurring most frequent in radar–rain rate pairs displayed in Fig. 5, and the spread in the regime-based relationships illustrates possible uncertainty within the WPMM retrieval that could be observed in the absence of precipitation regime-based validation.
Rain-rate deviations between the wet-season regime-based WPMM and the annual WPMM relationships illustrate the extent of rain-rate differences for a specified reflectivity in the Z–R relationships (Fig. 9). Similar to the rain gauge results, the annual WPMM relationships overestimate light rain, particularly when identified as stratiform, and underestimate from intense convective rain, and nearly always underestimates rain from shallow convection. The largest differences occur with higher rain rates from organized precipitation regimes where rain-rate retrievals differ up to 10 mm h−1 at Z > 40 dBZ—near the edge of radar–rain rate occurrence in the polarimetrically tuned and convective–stratiform-partitioned estimates (described in the next section). Deep isolated rainfall becomes negatively biased by 2–4 mm h−1 from 35 dBZ < Z < 40 dBZ, where radar–rain rate pairs are more common for the precipitation regime. This pattern of larger rain-rate disparities at higher rain rates, as convective intensity increases, is echoed in the rain gauge biases described in section 3a. Minor differences in the rain-rate deviations exist between the two wet seasons related to the precipitating system characteristics observed annually by the radar and rain gauges. For example, the 2009 annual WPMM improves the representation of light stratiform rainfall compared to the 2011 wet season, as this type of rainfall occurs more frequently near the western Pacific Ocean during El Niño events (Masunaga et al. 2005; Schumacher and Houze 2003; Schumacher et al. 2004). The accuracy of these deviations can be assessed through an independent comparison with the polarimetrically tuned rain-rate estimates and if accurate the bias for all convective states should reduce toward zero.
Rain rates for the 2A53 product and the regime-based WPMM are compared to the polarimetrically tuned rainfall estimates (Table 2). Comparison using the 2009 and 2011 wet-season WPMM Z–R relationships reveals marked improvement with polarimetrically tuned estimates for all cases. The lower biases compared to the 2A53 comparisons instill confidence in the magnitudes of the regime-based deviations; however, the RMSE among the regimes remain nearly identical as the annual WPMM results. The deviations found between the regime-based WPMM and annual WPMM relationships confirm that the Z–R relationship is limited in its ability to represent convective variability. The reduction in bias in both wet seasons found when using the precipitation regimes demonstrates that the errors between the rainfall product are likely consistent over time. It is also important to note that, although not shown, the reduction in error is largely found in convective rainfall while stratiform rainfall remains positively biased by a few percent. While TRMM-GPM GV office produces a convective and stratiform partitioning [based on Steiner et al. (1995)], the operational 2A53 product has no classification or rain-type clustering included. However, the large amount of scatter found in the convective rainfall comparison (Fig. 4) suggests that even climatologically derived convective and stratiform relationships will struggle to fully capture precipitation variability. This enforces the findings of Elsaesser et al. (2010), who found precipitation characteristics to be dissimilar between precipitation regimes for convective cores of equal vertical depth and rain rate. It is reasonable to extend the study of the precipitation regimes to further investigate their impact on radar–rain-rate relationships that improve representation of DSD variability associated with convective and stratiform rain types.
2) Convective and stratiform Z–R relationships
Power-law relations are commonly developed to relate radar reflectivity to rain rate for characteristic modes of DSD variability in convective and stratiform regions—such as implemented in the TRMM-GPM radar retrievals (Iguchi et al. 2000, 2010). For this reason, it can be useful to study satellite biases as a function of their convective and stratiform components (e.g., Liu and Zipser 2014; Seo et al. 2007; Rasmussen et al. 2013); however, we do not understand if these relationships are able to fully capture oceanic precipitation variability associated within defined regimes. To better understand this, convective and stratiform relationships are derived specifically for the 2009 wet season and for the deep isolated and organized regimes and then compared to the polarimetrically tuned estimates. Understanding the sensitivity of the convective and stratiform Z–R relationships provides another measure of the information present in the regimes that can be used in validation to help isolate error estimates.
Convective and stratiform Z–R relationships are derived using matched pairs of radar and rain gauge data averaged over 3-min intervals centered on the radar scan time. Data from the 2009 wet season are used to derive the relationships for deep convective and organized precipitation regimes and the TRMM GV 2A54 convective and stratiform classification product partitions rain rates. Because of possible spatiotemporal differences that occur between gauge and radar comparisons, rain-rate and reflectivity information are only utilized if the nearest neighboring pixels share the same precipitation type. This helps to minimize “leakage” that may occur in defining rain rates from one precipitation type to another when calculating the Z–R relationships. To start, we use orthogonal linear regression to derive the power-law relationships to help minimize errors in the R and Z directions perpendicular to the best-fit line (Campos and Zawadzki 2000). The relationships are applied to the KPOL reflectivities and compared to the matched polarimetrically tuned estimates, providing an independent comparison of the rain rates.
Overall, convective and stratiform relationships for all raining systems agree well with estimates from the DYNAMO field experiment (Thompson et al. 2015), which is not surprising as the two studies are climatologically similar. Clear separation exists between the convective and stratiform relationships (Fig. 10). These relationships can vary when gauges are integrated over different time scales (Steiner et al. 2004); however, the overall result for each case remains similar. Error statistics comparing polarimetrically tuned rain rates and the derived convective and stratiform Z–R relationships are shown in Tables 3 and 4. The derived relationships perform well over all precipitating systems, with the biases between the gauges and radar-derived convective and stratiform power-law relationships of a few percent. The derived Z–R relationships seem to capture the majority of rain rate-reflectivity pairs partitioned by the TRMM GV 2A54 product providing proper separation of DSD variability that the operational WPMM could not. The RMSE still remains similar to the WPMM methods pointing to variability in rainfall still unaccounted for. This becomes more evident when the Z–R relationships are further defined by each precipitation regime.
Using the methodology above, convective and stratiform relationships are partitioned by the regimes (Fig. 11). Differences are most notable with convective cases where data points from the deep isolated convection more or less straddle the convective power law; however, while there is overlap, the largest frequency bins in organized convective rainfall are found to be somewhat separated. Compared to the polarimetrically tuned estimates, the single convective Z–R relationship is biased high for deep convective systems and biased low for organized convection for 2009 by +4.2% and −8.7%, respectively. The most frequently occurring points captured by the gauges in organized convection lie to the right (below) the Z–R relation derived for all convective cases and deep isolated convective points lay on or slightly to the left (above) the Z–R relation. The differences in the stratiform cases are not as high in magnitude, with organized systems negatively biased and the deep convective systems positively biased. The segregated cases indicate that regime-specific information may help to better represent the offset data points from the single convective and stratiform Z–R relationships. To test this, the convective and stratiform relationships are rederived specifically for the deep isolated convective and organized regimes. The regime-based convective and stratiform Z–R relationships are shown with dashed lines in Fig. 11. The regime relationships provide better fits for both precipitation regimes as demonstrated by the reduced bias in Table 3. The new relationships reduce the bias for all cases, with the relationship specific to organized convection reducing the strong negative bias to 1.6%.
The resulting reduction in error is significant as it demonstrates that uncertainty in the WPMM methodology cannot be removed by the introduction of convective and stratiform relationships; even with convective and stratiform partitioning, the precipitation regime dependence remains an important element to consider. Using convective and stratiform relationships for GV may be an overall improvement compared to operational application of TRMM-GV WPMM; however, season-to-season GV evaluations may not be robust, as precipitation regime occurrence will vary spatially over time. When evaluating satellite and GV products, the physically relatable precipitation regimes provide improved information content on rain estimation sensitivity that would go unnoticed if precipitating systems were not segregated. The differences found between the regimes are not simply from random storm-to-storm variability, but instead are from direct differences in the precipitation microphysics between the two regimes (as described in section 3b). Changes in precipitation microphysics have been theoretically shown to alter Z–R relationships (Steiner and Smith 2004) and have been found in individual case studies previously at the Kwajalein Atoll (Bringi et al. 2012).
4. Conclusions and discussion
Ground validation is an essential component of the TRMM-GPM missions to aid in the evaluation of rain-rate retrievals derived from spaceborne satellite observations. This study presents a novel approach to evaluate oceanic radar–rain rate estimates through the introduction of self-similar precipitation regimes. The regimes, identified using a clustering analysis first described by Elsaesser et al. (2010) and Elsaesser and Kummerow (2013), segregate the rain-rate comparisons to evaluate the regime-based variability in rainfall estimates derived from WPMM, and polarimetrically tuned rainfall, and convective- and stratiform-partitioned Z–R. This methodology is advantageous as it can quantitatively distinguish the contribution of error in GV and satellite-based rain-rate retrievals related to the defined precipitation regimes, which are consistent over the tropical oceans.
To understand how precipitation regimes can impact GV efforts, the regimes are first implemented to test if GV products can capture convective variability during the wet-season months of September–November for 2009 and 2011. The TRMM 2A53 product and polarimetrically tuned estimates are compared with spatiotemporally matched quality-controlled gauge rain rates located on Kwajalein Atoll segregated by each regime. The 2A53 rain rates relative to the ground gauges underestimate all wet-season precipitating systems by 9.3% in 2009 and 13.1% in 2011; these underestimates are largely related to the organized convective systems where biases at higher rain rates reach 35%. The annual WPMM relationships used in the 2A53 product typically overestimate stratiform rainfall and underestimate shallow convective rainfall. The polarimetrically tuned rainfall estimates revealed improved biases compared to the 2A53 product as well as increased correlations with gauges and a reduction in scatter as evidenced in reduced RMSE values. Further, polarimetrically tuned radar–rain rate pairs demonstrate a multitude of solutions that cannot be captured by the 2A53 WPMM estimates that are seemingly consistent between the two wet seasons. In particular, deep isolated convection is commonly underestimated for Z > 30–40 dBZ and similar for organized convection with underestimations extending toward more extreme rain rates where Z > 40 dBZ.
The regimes are then used to identify how predominant regimes may influence WPMM and convective–stratiform rain-rate relationships. WPMM Z–R relationships are first derived specifically for each individual regime. WPMM Z–R relationships derived for rainfall occurring in shallow precipitation regimes highly resemble that of a convective Z–R power-law relationship, while deep isolated convection and organized convection relationships shift from a stratiform-like relationship at lighter rain rates then toward a convective relationship as the rain rate increases. Differences between the regime-based relationships and the 2A53 Z–R relationships differ by a few mm h−1 (approaching 10% difference); however, the deviations show a near-monotonic increase as rain intensity increases. The improved information content found from regime-oriented validation is also demonstrated by implementing comparisons with convective and stratiform Z–R relationships. Individual convective and stratiform relationships do not eliminate regime-based biases from deep isolated convective (+4%) and organized precipitation regimes (−9%). These regime-based biases are greatly reduced when convective and stratiform Z–R relationships are derived specifically for the deep isolated convective and organized precipitation regimes where biases are reduced to less than 3%.
While the qualitative and quantitative assessment of the rain retrievals is necessary to improve our validation capabilities, it is beneficial to identify how the errors affect the retrievals on the observed seasonal time scale. To visualize this, comparisons of rainfall accumulation between radar-derived estimates and gauges for all raining systems during the 2011 wet season are shown in Fig. 12. The 2A53 product consistently underestimates rainfall as the negative bias associated with convective rainfall continually drives the radar accumulations farther from the gauges. The regime-based WPMM and derived convective–stratiform Z–R accumulations compare quite well to the gauge accumulation, which is consistent with the low biases described in Tables 2 and 3. It should be noted, however, that the convective–stratiform Z–R relationships used to derive the accumulation in Fig. 12b exhibited increases in bias when split into deep and organized precipitation regimes. For this reason, we test if accumulation is affected if rain is only accumulated for an individual precipitation regime. The convective- and stratiform-based accumulations seem to be balanced by deep convective systems (organized systems), which are found to overestimate (underestimate) over the 2011 wet season, consistent with the bias patterns found in Table 3; therefore, the accumulations could be temporally dependent as changes in the occurrence of the precipitation regimes could skew the overall accumulation. The negative biases in the polarimetrically tuned estimates are caused by individual heavy rainfall events throughout the wet season. The rain accumulations match very well with the gauges except for a few organized convective events. Overall, the polarimetric retrieval performs well for each regime; however, errors may exist in more extreme rainfall.
The divergence in rainfall accumulations in the 2A53 estimates encourages discussion pertaining to previous validation studies at the Kwajalein site. For example, Wolff and Fisher (2008) stated that both TRMM PR and TRMM TMI underestimate rainfall relative to the 2A53 by 13.7% and 7.9%, respectively. The underestimation was consistent for multiple years related to issues with the retrievals at higher rain rates. The results of this study suggest these bias estimates may be underestimated more than originally described depending on the precipitation regimes observed over that period. Future studies evaluating TRMM rain rates would benefit from the use of dual-polarimetric estimates, as they are able to capture the DSD variability; however, this capability is not always available. In this case, specific convective and stratiform relationships provide improved estimates if proper partitioning is possible (Bringi et al. 2003, 2009; Thompson et al. 2015) or specific regime-based estimates if enough data are available. Moreover, the results of this study encourage further use of precipitation regimes in future TRMM-GPM GV endeavors—particularly to further differentiate satellite bias estimates with GV-radar estimates. Because of the self-similar nature within the precipitation regimes, it is likely that similar error patterns could be recorded at other GV sites.
This research was supported by NASA Precipitation Measurement Missions Grants NNX16AE23G and NNX13AG30G. The authors thank two anonymous reviewers and Dr. Gregory Elsaesser (NASA GISS) for their comments on this paper, which have greatly improved its discussion and flow. We also acknowledge Dr. Elizabeth Thompson (CSU) and Jianxin Wang (NASA) for their helpful comments and suggestions in deriving rain relationships and assisting with interpreting GV datasets.