Deep convective storms in subtropical South America are some of the most intense in the world, and the hydrological cycle plays an important role in both tropical and subtropical South America. Recent studies have suggested that the Tropical Rainfall Measuring Mission (TRMM) precipitation radar algorithm significantly underestimates surface rainfall in deep convection over land. This study investigates the range of the rain bias in storms containing four different types of extreme radar echoes: deep convective cores, deep and wide convective cores, wide convective cores, and broad stratiform regions over South America. Storms with deep convective cores show the greatest underestimation, and the bias is unrelated to their echo top height. The bias in wide convective cores relates to the echo top, indicating that storms with significant mixed phase and ice hydrometeors are similarly affected by assumptions in the TRMM algorithm. The relationship between storm type and rain bias remains similar in both subtropical and tropical regions.
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 The precipitation radar (PR) on the Tropical Rainfall Measuring Mission (TRMM) satellite has revolutionized the study of storms in the tropics and subtropics. Analysis of TRMM PR data, however, has led to the recognition that the TRMM PR algorithm tends to underestimate precipitation in regions of intense deep convection over land [Iguchi et al., 2009]. Understanding the magnitude of the biases for a variety of precipitating cloud systems over different regions is essential for understanding global precipitation and hydrology.
 TRMM observations have led to the realization that intense storms just east of the Andes in southeastern South America, near the western Himalayas, and east of the Rocky Mountains in the U.S. are among the most intense anywhere in the world [Zipser et al., 2006]. The most extreme South American mesoscale convective systems [MCSs, Houze2004] are larger and have more precipitation than in other parts of the world [Velasco and Fritsch, 1987; Durkee et al., 2009]. Houze et al. , Romatschke and Houze , and Romatschke and Houze  have used TRMM PR data to identify the location and frequency of distinct extreme storm types in both South Asia and South America. Rasmussen and Houze  examined the mesoscale organization and structure of MCSs in subtropical South America and showed that they are structurally similar to the leading line/trailing stratiform archetype identified by Houze et al.  for intense rainstorms in Oklahoma. Using AMSR-E data, Cecil and Blankenship  found that northern Argentina and Paraguay have the highest frequency of significant hailstorms over the globe. This combined evidence points to South America being an important natural laboratory for studying intense convective storms and their hydrological impact.
 For a complete perspective of the impact of intense precipitation systems on the hydrologic cycle in South America, it is necessary to assess the contribution from such storms to the climatological rainfall. Indeed, since the convection in South America is robust and strongly defined in its most intense manifestations, the storms of this region constitute an ideal test bed for determining the TRMM PR bias in intense convection in general. The main question addressed in this study relates to the uncertainties in making the precipitation estimate due to known insufficiencies in the rain estimation algorithm for this type of storm over land regions [Iguchi et al., 2009; Nesbitt et al., 2004]. Our study differs from previous work by providing a range of the potential bias in the TRMM PR rain rate estimation, focusing specifically on the most intense convective storms and providing a range of probable errors induced by the algorithm. The results should be extendable to other continental regions that experience intense convection observed by the TRMM satellite, while also highlighting the unique behavior of South American storms.
2 Data and Methodology
 The TRMM PR is advantageous for studying the climatology of storms because it is not obstructed by topography, as are ground-based radars. The TRMM PR has relatively fine three-dimensional spatial resolution (4–5 km horizontal, 250 m vertical resolution at nadir), and its areal coverage is comprehensive between 37.5°N and 37.5°S [Kummerow et al., 1998]. The TRMM PR database has accumulated for over 14 years (1999–2012). In this study, we use TRMM V7 data from the South American sector (37.5°S–15°N, 100°W–30°W) for the austral spring through fall seasons. Following Houze et al. , four types of three-dimensional echo objects have been identified to facilitate a comparison of precipitation produced by various storm types: (1) deep convective cores (contiguous volume of convective echo exceeding 40 dBZ and ≥10 km in height; DCC), indicating severe weather and vigorous convection; (2) wide convective cores (contiguous 40 dBZ echo volume ≥1000 km2 horizontally; WCC), indicating intense convective systems organized on the mesoscale; (3) Deep and wide convective cores (cores that fall into both of previous two categories; DWCC); and (4) broad stratiform regions (contiguous area of stratiform echo ≥50,000 km2; BSR), typically associated with mature MCSs. The first three categories produce hail, lightning, heavy rain, and tornadoes in subtropical South America. The last three echo-type categories are associated with widespread rain and flooding [Rasmussen and Houze, 2011].
 For the purpose of this study, a “core” is defined as the three-dimensional echo object identified by the storm-type algorithm described above, whereas a “storm” is the contiguous echo with reflectivity values greater than zero within which the cores are embedded. We use two different methods to compute rain rates to investigate the performance of the TRMM PR algorithm in estimating precipitation for each echo type. The first method employs the standard TRMM 2A25 V7 near-surface precipitation data [Iguchi et al., 2009]. The second method follows Romatschke and Houze  by using a more traditional Z-R relationship (Z = aRb, where Z is equivalent radar reflectivity factor in units of mm6 m−3 and R is rain rate in mm h−1) to estimate the precipitation from the TRMM PR attenuation-corrected reflectivity data. The lowest nonzero value of Z is used at each data pixel between the surface and 2.5 km above ground level for each precipitation echo, which is similar to the value used in the TRMM PR algorithm. The parameters a and b are constants depending on rain type (convective, stratiform, or other). We use several reasonable estimates of a and b to obtain a range of estimated rain rates based on radar data. The Z-R method used here has uncertainties and possible biases that are related to the choices of a and b. However, these parameters are from the literature and are in no way related to the attenuation-correction method used in the TRMM PR algorithm. The Z-R method is widely used, much simpler, and more transparent than the TRMM PR algorithm. The total volumetric rain rates for each core and storm were calculated using both methods from the footprints of both the core and storm in each relevant overpass. To ensure consistency between the Z-R technique and the TRMM 2A25 output, the volumetric rain rates for all identified storms were calculated using the 2A25 near-surface reflectivity data. The results of this study were not perceptibly changed.
 The underlying premise of this study is that because of the analysis of Iguchi et al. , we expect a priori that the TRMM PR 2A25 algorithm will systematically give lower precipitation rates in the most extreme forms of deep convection over land. The question is how much. In remote regions, rain gauge and ground-based radars are not present in sufficient number to provide a comparison with independent data. Comparison with the rain rates computed from the ensemble of Z-R relations used here is the best available alternative for estimating the possible magnitude of underestimation by TRMM PR in intense convection over land. Table 1 lists multiple physically appropriate values of a and b in the Z-R relationships for the South American region considered here. A combination of Z-R relations from satellite radar algorithms (TRMM PR), operational sources (WSR-88D calibrated values), and those derived from field campaign measurements (MCTEX, TRMM-LBA, and EPIC) was tested for consistency with the Romatschke and Houze  relations. We used the values of a and b in Table 1 to calculate rain rate estimates using the Z-R technique in the tropics and subtropics of South America. By using the above-described method for selecting the most extreme convective entities and applying the Z-R to those cases and comparing the Z-R rates with the 2A25 rain rates, we test the degree to which the 2A25 V7 algorithm systematically produces lower rain rates specifically for the most extreme convective entities over land.
Table 1. List of Z-R Relations Tested in South Americaa
DCC Core Bias (%)
DWC Core Bias (%)
WCC Core Bias (%)
BSR Core Bias (%)
aFor all storm categories, the bias is defined as the average normalized difference in volumetric precipitation amounts (Z-R − TRMM 2A25), expressed as a percentage. The averaged values in each column are from the tropical region (15°N–23.5°S) and subtropical region (23.5°S–37.5°S) cores, respectively.
3 Determination of Bias in TRMM Precipitation Estimates
 Table 1 shows that of the various Z-R relations, Romatschke and Houze's  parameters produce a conservative estimate of underestimation. We therefore use it to further illustrate our results. A compilation of the number of intense storms identified in South America (Figure 1) shows that over the 14 year climatology, the storms containing WCCs are the most common during austral spring through autumn. Figure 2 shows that the TRMM 2A25 volumetric rain rate averaged over 14 years (1999–2012) is systematically lower than the Z-R estimate. For storms with BSRs, it is ~15–20% lower, while storms with DCCs were ~40% lower. Storms with WCCs were 20–30% lower. The relative percentage underestimate is consistent across all months. Table 1 provides average September to April values for the various Z-R relationships tested in the tropical and subtropical regions. DCCs are the most relative rain-underestimated storm type regardless of the particular Z-R relationship used. The relative underestimate is larger for storms with DCCs; however, the areas covered by storms containing WCCs and BSRs tend to be larger in area, so these biases are nonetheless significant for their impact on hydrologic estimates in South America.
 Figure 3 presents comparisons of volumetric rain rates using both precipitation estimation methods. TRMM 2A25 precipitation rates for DCCs and storms containing these echoes consistently exhibit the lowest estimates compared to the Z-R method (Figures 3a and 3b), consistent with the means presented in Figure 2. From Figure 3, it not only appears that problems with the TRMM 2A25 algorithm arise from inconsistencies in estimating precipitation for vertically intense deep convection, but other forms of extreme precipitating systems show a systematic bias as well. Similar to Figure 2, DCCs show the largest relative bias followed in order by DWCCs, WCCs, and BSRs. Figures 3c and 3d demonstrate that subtropical South American storms of all types are more intense and produce larger rain rates compared to the tropics, consistent with previous studies investigating extreme storms in South America [Romatschke and Houze, 2010; Rasmussen and Houze, 2011]. However, although the tropical storms tend to be less intense, the relationship between the relative bias in precipitation and storm type remains the same regardless of different climatological regimes and thus could be important for other regions of the world experiencing various types of extreme storms.
 Figure 4a illustrates that the precipitation bias in DCCs (40 dBZ echo top height ≥10 km) is independent of the maximum height of the 40 dBZ echo and is in fact a systematic bias for this type of convective storm. A similar analysis for the WCCs (Figure 4b) shows that the altitude reached by horizontally extensive 40 dBZ cores is proportional to the underestimate of precipitation. The fact that the height of the DCCs is unrelated to the rain bias indicates that the effect of mixed phase and ice hydrometeors complicates the precipitation retrieval and tends to bias the rain estimates for these types of storms. When the echo height of the horizontally contiguous 40 dBZ WCCs are above the 0°C level (~4–5 km), the bias in precipitation becomes apparent, again probably in relation to mixed phase hydrometeor effects.
 Well-documented problems with near-surface precipitation estimates in deep convective storms over land from the 2A25 algorithm have been partially attributed to errors in the drop size distribution (DSD) parameter (ε), which tends to negatively bias the Z-R calculations of rain rate [Iguchi et al., 2009, equation 6]. The nondimensional DSD parameter (ε), which is a by-product of the attenuation correction method, adjusts the vertical profile model (ζ) to estimate the effect of DSD variations [Kozu et al., 2009]. The values of a and b used to estimate R are related to the values of ε and ζ. For high echo tops, the vertical profile model in the algorithm tends to be overestimated because of assumptions used in mixed phase and ice regions [Iguchi et al., 2009], thus leading to an artificially smaller a parameter in the Z-R relation and an underestimation of the rainfall rate. The TRMM PR precipitation algorithm currently assumes a particle model that is based on the size and density of a snow particle [Iguchi et al., 2009], which is inappropriate for deep convection over land with significant precipitation ice in the form of graupel and/or hail. This assumption may have a large effect on the near-surface rain rate estimates. The future Global Precipitation Mission (GPM) satellite will have a dual-wavelength precipitation radar, which will entail new algorithm design for better ice particle representation, allowing this bias to be mitigated. However, nearly continuous rain estimation from TRMM through to GPM will require an understanding of the assumptions in the current algorithms for a smooth transition into the GPM era.
 Previous studies suggested that the TRMM PR algorithm tends to underestimate precipitation rates of deep convection over land [Iguchi et al., 2009; Kozu et al., 2009] and subtropical South America has some of the deepest convective storms in the world [Zipser et al., 2006]. The TRMM PR algorithm exhibits bias in all four extreme echo types considered here when the algorithm rates are compared to a range of conventional Z-R relations. The bias appears in the monthly-averaged rainfall as a negative difference between the TRMM 2A25 algorithm and the Z-R method for every echo type. The difference is greatest for storms containing DCCs (up to ~40% underestimate). WCCs and BSRs also have significantly lower estimates (~25% and ~15%, respectively). By calculating the precipitation bias using seven different Z-R relationships, we find the relation between the storm type and relative precipitation underestimate to be robust in both tropical and subtropical regions. Although the bias for storms containing WCCs and BSRs is less than for DCCs, they are nevertheless likely to produce major hydrologic impacts because of the large areas they cover. The subtropical region tends to have more intense precipitating systems than the tropics, but the relationship between the TRMM PR rain bias and storm type is the same regardless of the climatological regime. Differing from previous studies that only identified deep convection over land as being problematic in TRMM PR precipitation estimates, the current investigation has shown that lower estimates by the algorithm are particularly biased for extreme precipitating systems that contain significant mixed phase and/or frozen hydrometeors.
 The regions of South America that experience the most frequent extremely deep convective storms are in the subtropics and not regions that regularly receive large amounts of climatological rainfall [Zipser et al., 2006]. Therefore, a significant percentage underestimation of the convective precipitation in storms containing DCCs and/or WCCs can greatly affect our perception of the climatology and hydrology of these relatively arid regions. In contrast, but equally important, horizontally intense storms (i.e., those containing WCCs and/or BSRs) frequently occur over the wet Amazon Basin [Romatschke and Houze, 2010]. These storms are less impacted by the TRMM precipitation bias; however, because they account for so much rain in the largest rainforest in the world, their bias is also of great hydrologic significance. These lessons for South America imply further that for understanding the global distribution of precipitation, it is necessary to examine the biases in precipitation estimates from not only deep convective storms but all systems that extend above the 0°C level that have significant precipitation ice. The results presented here can therefore likely be extended to similar regions around the low-latitude world observed by the TRMM satellite while we await the more advanced radar and algorithms of GPM.
 The authors thank Edward Zipser, Daniel Cecil, and Stephen Nesbitt for reviews that improved the manuscript. This research was sponsored by NASA grants NNX13AG71G and NNX10AH70G and a NASA ESS Graduate Fellowship (NNX11AL65H).
 The Editor thanks Stephen Nesbitt, Edward Zipser and Dan Cecil for their assistance in evaluating this paper.