The statistical properties of tropic-subtropic precipitation are revealed with 13 years of Tropical Rainfall Measuring Mission (TRMM) precipitation radar (PR) measurements. About 3% of PR observations are raining pixels. The average daily rainfall over 37.5°N–37.5°S is 1.28, 1.18, and 2.46 mm d−1 for convective, stratiform, and total rain, respectively, indicating 51.85% from convective rain and 48.09% from stratiform rain. The related values are 1.300, 1.272, and 2.573 mm d−1 over ocean and 1.22, 0.97, and 2.19 mm d−1 over land, indicating a convective rain fraction of 50.51% over ocean and 55.77% over land. The 92% (93%) and 73% (55%) of rain events over ocean (land) are from stratiform and convective rain <5 mm h−1, respectively, while the associated rainfall contributions in stratiform and convective rain are 62% (68%) and 27% (15%) over ocean (land). Results demonstrate that contributions from large rain intensity events are very importation in total precipitation, especially over land. The rainfall missed by TRMM PR is mostly light rain and does not significantly impact large-scale statistics of convective and stratiform rain amount. Light rain will increase the total precipitation by about 10% and, if considered a separate category, decrease the observed convective and stratiform rain contributions about 10% over the PR domain. These statistical properties of precipitation could be utilized as a baseline in the assessment of precipitation from operational numerical weather prediction and climate models.
Precipitation is one of the most fundamental meteorological variables and a key output of numerical weather prediction (NWP) models. An accurate precipitation observation is important to a NWP data assimilation system in order to generate improved weather forecasts [e.g., Bauer et al., 2011]. It is also crucial in validating NWP performance [e.g., Song and Yu, 2004; Davis et al., 2006]. Due to the limitations of ground-based rain observations, spaceborne sensors are the only viable way to provide valuable precipitation measurements while meeting the temporal and spatial coverage required. Fortunately, the combination of advanced satellite sensors, especially the microwave radiometers and precipitation radar (PR), and associated physical inversion rainfall retrieval algorithms are able to produce accurate global precipitation measurements [Haddad et al., 1997; Kummerow et al., 2001; Iguchi et al., 2000]. The joint NASA-Japan Aerospace Exploration Agency Tropical Rainfall Measuring Mission (TRMM) launched in 1997 has a TRMM microwave imager (TMI) and PR which have led to long-term consistent accurate rainfall measurements [Kummerow et al., 1998; Yang and Smith, 2008; Adler et al., 2009]. The TRMM PR is unique, because it is the first space-aboard PR dedicated to rainfall measurement, and it has a long period of observation from space. Its advantages in measuring precipitation when compared to ground-based radar are obvious because of the global coverage, accurate calibration, downward viewing geometry, and lack of beam blockage. Due to stratiform rain commonly being observed in regions with convective rain in the tropics [Houze, 1997], it is important to have a rain data set that has a superior spatial resolution and separate categories of stratiform and convective rainfall [e.g., Schumacher and Houze, 2003]. TRMM PR has both advantages.
TRMM precipitation data sets are now considered by the Earth science community as the most accurate rain observations from space. These data sets have been widely applied in Earth science applications, such as weather forecast, hydrology, and natural hazard monitoring, and other applications [Nesbitt and Anders, 2009; Arshad et al., 2013; Khan et al., 2012; Liao et al., 2010]. They have even been used to evaluate surface rain gauges and ground radar rain estimates [Anagnostou et al.,2001]. Due to the nature of precipitation in short time-spatial scales, it is very difficult to directly compare instantaneous precipitation between any two different methods. However, the statistical characteristics of precipitation properties are very stable with the long-term accurate TRMM rainfall data sets. These statistical properties of TRMM precipitation can be easily applied for assessing the reliabilities of rain estimates from other techniques.
2 Data Sets and Methodology
The accuracy of both TRMM MI and PR rain data sets is comparable on large time-space scales [Yang and Smith, 2008; Yang et al., 2008]. However, we will use the PR data set in this study because TRMM PR has a higher spatial resolution and superior ability to detect precipitation over land, especially colder surfaces than TMI sensor [Stephens and Kummerow, 2007]. In addition, TRMM PR can reliably classify rain into different precipitation types [Awaka et al., 2007]. The coverage of TRMM PR covers all longitudes within the region 37.5°S–37.5°N. Twelve years of TRMM PR level 2 rainfall data sets (2A25 v7) from 1998 to 2010 are used. Since TRMM satellite is in a non-Sun- synchronized orbit, and it can measure the diurnal cycle of precipitation [Nesbitt and Zipser, 2003; Yang and Smith, 2006]. Although the TRMM PR swath is about one third of that of the TMI [Simpson et al., 1988], and there are known issues with the PR retrievals in detecting light rain (below the minimum detectable signal of 18 dBZ [Berg et al., 2010]) and extremely heavy rain (due to attenuation and possible multiple scattering effects) with the PR [Nesbitt and Anders, 2009; Rasmussen et al., 2013], the sampling error of each PR orbit will not be an issue with these long-term data sets. The orbit of the TRMM satellite was boosted from 350 km into 405 km in August 2001 to prolong the TRMM satellite life, leading to the reliable precipitation data sets from December 1997 to present. The impact of this boost on PR-based precipitation is small, as the Japan Aerospace Exploration Agency  demonstrated the consistency and continuity of the v7 PR precipitation before and after the boost. A separate analysis of a subset of 43 months before and after the boost shows that precipitation properties are similar and also consistent with those from the 13 year data sets. Thus, the rainfall properties from the 13 year TRMM PR data set serve the purposes of this study well. While there are other uncertainties in PR rainfall retrieval such as attenuation correction, correct selection of Z-R relationships, and extrapolation of the lowest clutter-free bin to the surface, we put forth the PR climatology as the best available at present. Retrievals from the more sensitive dual-frequency precipitation radar on the Global Precipitation Measurement (GPM) mission will likely be of higher quality [Smith et al., 2007; Hou et al., 2013], but we will await for the data collection to examine its improved retrievals.
Statistical properties are the best parameters to be used for comparison of any meteorological variable obtained from two different sources. The TRMM PR rain rates at pixel scale of each orbit are first grouped at 1°×1° grid resolution, with indices of time and rain types, then analyzed at this spatial grid scale and any other larger grid scales if necessary. The original PR rain types were defined in many categories [Awaka et al., 2007]. For simplicity, especially for evaluating NWP model rain outputs, the rain types are reclassified into three categories (i.e., convective, stratiform, and other) as Yang and Smith  used in their study. Rain rate statistics (including probability density functions (PDFs) and cumulative distribution functions (CDFs)) are examined from pixel and gridded rain data sets.
3 Precipitation Properties
We will focus on key statistical properties of precipitation in this paper. Some basic statistics of PR pixels and rain rates over ocean, land, and overall (combined ocean/land) are summarized in Table 1. The pixel accounts are very large numbers, so that their associated statistics are reliable. More than 96% of PR observations are nonraining pixels, while only about 1.02%, 2.40%, and 3.43% are convective, stratiform, and all rainy pixels over tropical-subtropical oceans, respectively. By the same token, 0.65%, 2.02%, and 2.68% (0.91%, 2.29%, and 3.21%) are the same statistics for land (overall). On average, 50.5% and 49.4% (55.8% and 44.2%) of rainfall are from convective and stratiform rain over tropical-subtropical ocean (land), respectively. It is clear that the contribution of convective rain compared with stratiform rain is higher over land (51.8%) than ocean (48.1%). The rainfall contribution from the other rain category is very small and not significant. These rainfall properties are consistent with the published results [Houze, 1997; Schumacher and Houze, 2003; Nesbitt et al., 2006; Yang and Smith, 2008] but with obvious differences. The quality of TRMM rain products have been steadily improved from its initial version 4 to current version 7. Schumacher and Houze  applied 2 year TRMM PR v5 rain data sets (1998–2000) over tropical region (20°S–20°N), showing 43%, 35%, and 40% stratiform rain contributions over ocean, land, and overall, respectively. The data sets in this study, over the same tropical region, indicate that the stratiform rain contribution is 42.7%, 41.0%, and 42.2% over ocean, land, and overall, respectively. Results from Yang and Smith  based on 7 years of TRMM v6 rain data sets (1998–2005) indicated that the stratiform (convective) rain contribution over the PR coverage is 55.1% (44.8%) and 48.3% (51.5%) over ocean and land, respectively. Therefore, the percentage changes of stratiform/convective rain contributions are significant due to changes from early TRMM algorithms to v7. The TRMM PR v7 rain products likely reveal more accurate values which can be used for the improved evaluations of NWP model precipitation. With a successful launch of the GPM satellite in February 2014 and advances in retrievals, future precipitation data quality will be better than the current TRMM v7 rain data sets.
Table 1. Some Statistics of TRMM PR Pixel Distributions During 1998–2010a
aC, S, R, and T are for convective, stratiform, raining, and total pixels, respectively. RR is for the daily rain rate in unit of mm d−1.
2.35 × 108
5.56 × 108
7.94 × 108
2.31 × 1010
5.99 × 107
1.87 × 108
2.48 × 108
9.27 × 109
2.95 × 108
7.43 × 108
1.04 × 109
3.24 × 1010
Pixel contribution (%)
Mean RR (mm d−1)
RR contribution (%)
The global tropical distributions of mean daily rainfall, convective, and stratiform rain contributions on a 1° grid are presented in Figure S1 in the supporting information. The well-known precipitation regimes such as intertropical convergence zone (ITCZ), the South Pacific convergence zone, monsoon regions, the African and South American tropical rain maxima, and the subtropical storm tracks are clearly depicted in this rainfall map. A secondary ITCZ rainfall pattern around 5°S over central eastern Pacific is also present. Convective rainfall is dominant over the tropics especially over land and coastal regions, while stratiform rainfall is prominent over the subtropics. Over light-rainfall regions, such as the subsidence regions over southeastern Pacific and Atlantic Oceans, more than 70% of precipitation is from convective rain, while more than 50% of precipitation is from stratiform rain over the northeastern Pacific and Atlantic Oceans. Over the Inter-American Seas-western North Atlantic Ocean region, convective rain is about 40–100% more than stratiform rain. The ratio of convective and stratiform rainfall shows a detailed pattern in their relative contributions to total precipitation.
Figure 1 presents PDFs of TRMM PR raining pixels (rain rate >0 mm h−1) over ocean, land, and overall, respectively. In order to show the rain probability at large rain rates, an uneven rain rate bin is applied (the rain rate bin size is increased at rain intensity of 3 and 10 mm h−1). It is obvious that these PDF patterns are similar. There is a high probability of raining pixels with rain rates <2 mm h−1. The vast majority of rainy pixels are with rain intensities <5 mm h−1. However, there exists a very small frequency of rain rate greater than 50 mm h−1. The small increases of PDF at rain rate bins of 3–3.5 and 10–11 mm h—1 are due to the increase of the rain rate bin from 0.2 to 0.5 mm h−1 at 3 mm h−1 and from 0.5 to 1 mm h−1 at 10 mm h−1. The results shown here have small sampling errors due to large sample sizes.
The CDFs of convective, stratiform, and total rainfall over land and ocean are displayed in Figure 2. For oceanic precipitation, about 46%, 68%, and 62% of convective, stratiform, and total raining pixels are from rain intensity <2 mm h−1, respectively (Figure 2a). These numbers are about 73%, 92%, and 85% for rain intensity <5 mm h−1. However, about 10%, 30%, and 19% of convective, stratiform, and total rainfall are from rain intensity <2 mm h−1, respectively (Figure 2c), while these rain contributions become 27%, 62%, and 43% from rain rates <5 mm h−1. For continental precipitation, by the same token, these values are 30%, 70%, and 60% (55%, 93%, and 84%) for convective, stratiform, and all raining pixels for rain intensity <2 (5) mm h−1 (Figure 2b). Their rainfall contributions are only about 5%, 33%, and 17% (15%, 68%, and 38%) for rain <2 (5) mm h−1 (Figure 2d).
These results demonstrate that a vast majority (84–85%) of rainy pixels are light rain with intensity <5 mm h−1 while 60–62% for rain intensity <2 mm h−1. It is quite different from what is shown in the limited 1 min accumulation interval rain gauge data over Miami, Florida, which indicated that about 69% (40%) of all precipitation events are from rain rates <5 (2) mm h−1 [Jones and Sims, 1978]. Data from rain gauges are a point measurement, while TRMM PR is a 5 × 5 km averaged rain rate, and TRMM PR retrievals observe a variety of precipitation systems. Results based on TRMM PR measurements are more useful in the applications of the observed precipitation to evaluate NWP and climate model outputs. Obvious differences exist between convective and stratiform rain over ocean and land, especially for convective rain. There are significantly less convective raining situations with rain intensity <5 mm h−1 over land than ocean, indicating that more convective rain over land falls at ≥5 mm h−1. Actually, more than 85% of the convective rainfall over land is from rain intensity ≥5 mm h−1 while only about 73% over ocean. The related values are about 32% and 38% for stratiform rain <5 mm h−1.
Maps of the spatial distribution of CDF characteristics are presented in Figure 3, showing the contributions to counts and accumulation from rain rate <5 mm h−1, overlapped with mean daily rainfall contours of 3.5 and 1 mm. It can be seen that the CDF distribution patterns are very consistent with the daily rainfall spatial distribution. In general, PR pixels with rain rate <5 mm h−1 contribute more than 90% (less than 84%) of the total raining pixels over areas of mean daily rainfall <1 mm (>3.5 mm) (Figure 3, bottom). Over land and the heavy-rainfall regions, pixels with rain intensity <5 mm h−1 contribute less to the total raining pixels than over other areas. For rainfall contributions from these pixels (Figure 3, top), the percentage rate is less than 40% (greater than 60%) over areas of daily rainfall greater than 3.5 mm (less than 1 mm). Results reveal that the light rain dominates rain probability, while its contribution to total precipitation is only important in light-rainfall regions. Over more rainfall regions, higher-intensity rain dominates its contributions to total precipitation.
These overall statistics for convective, stratiform, and total rainfall over ocean and land are important parameters that can be easily used to evaluate the relative accuracy and reliability of other satellite rainfall retrieval algorithms as well as NWP and climate model-predicted precipitation. Especially for climate model simulations, there are no actual measurements of precipitation to evaluate the model precipitation outputs for future time periods. However, the accurate statistical properties of precipitation can be applied to assess the model rain properties in terms of rain distribution patterns, mean rain intensity, convective, and stratiform rain contributions [e.g., Kidd et al., 2013] in the present climate. In addition, the long-term TRMM PR rain data sets are able to create the reliable rain statistical properties at high spatial-temporal resolutions or the desired climate model grid time-space scales so that the NWP model precipitation could be evaluated at different temporal-spatial resolutions [Nesbitt and Anders, 2009; Biasutti et al., 2012]. Thus, the NWP model precipitation can be regarded as reliable if its statistical properties match well with that from the long-term TRMM PR rain data sets or future GPM precipitation products at various spatiotemporal scales.
The limitation of the TRMM PR rain minimum detection at 18 dBZ indicates that PR will miss light rainfall. It is difficult to quantify the amount of rainfall missing from the PR rain products and its time-spatial distributions from currently available precipitation data sets until future more capable satellite sensors are available (e.g., GPM). However, missed light rainfall apart from topography can be estimated from the matched CloudSat cloud profiling radar (CPR) and TRMM PR because of the CPR's capability of detecting light rain. Based on a detailed analysis of the comparison between CPR and PR over ocean [Berg et al., 2010], the missed light rain is about 10% of the total precipitation over the PR coverage, while only about 1% in moist regions of the deep tropics to nearly 20% over the drier extratropical regions. The overall light rain contribution over land should be <10% because of lesser rainfall contributions from light rain over land than over ocean [Nesbitt et al., 2006]. A quantitative assessment of the impact by the missed light rain on statistical properties of convective and stratiforn rain cannot be analyzed with the precipitation data set in this study, while the impact is expected to be small over all but dry regions or regions that experience frequent drizzle (e.g., stratocumulus regions and orography). The convective and stratiform rain contributions to total precipitation as well as the total rainfall are impacted by the PR-missed light rain (see the supporting information).
4 Discussion and Conclusions
Based on 13 years of TRMM PR data, only about 3% of the observations are raining pixels. The overall averaged daily rainfall is 2.46 mm d−1, while 1.28 and 1.18 mm d−1 are for convective and stratiform rain, respectively, indicating 51.85% from convective rain and 48.09% from stratiform rain. Their respective values are 2.57, 1.30, and 1.27 over ocean and 2.19, 1.22, and 0.97 mm d−1 over land, respectively, indicating convective rain of 50.51% over ocean and 55.77% over land. The boost of TRMM satellite does not impact the overall quality of the PR rain products and its long-term rain continuity. In general, there is more convective rainfall in tropical regions especially over land, coastal areas, and light-precipitation regions, while the stratiform rain is dominant in subtropical areas. The stratiform rain contribution is equally important as convective rain over the ITCZ.
The PDF and CDF of precipitation from the PR reveal that light rain is the most frequent phenomenon, with 62% and 85% over ocean, and 60% and 84% over land of all rain activities are from rain intensity <2 and 5 mm h−1, respectively. Ninety-two percent (93%) and 73% (55%) of rain events over ocean (land) are from stratiform and convective rain <5 mm h−1, respectively. About 40% of the precipitation is from rain intensity <5 mm h−1. Only 15% and 27% of convective rainfall over land and ocean are from rain <5 mm h−1, respectively, while stratiform rainfall contributes 68% over land and 62% over ocean. These results demonstrate that contributions from large rain intensity events such as convective systems are very important in total precipitation, especially over land.
The horizontal patterns of CDFs for rain activities and total precipitation from rain rate <5 mm h−1 are so consistent with the total precipitation map that these characteristics of precipitation could be used as an accurate evaluation tool for NWP precipitation forecasts and climate model output. Up to 84% of rain events over regions of rainfall more than 3.5 mm d−1 are from rain <5 mm h−1, while they contribute less than <45% and 35% of precipitation over ocean and land, respectively.
The relatively long term data set provides the confidence that statistical properties of precipitation from the PR are both accurate and reliable, and the error structure of the retrievals is most consistent compared with microwave only or products that combine different inputs over land and ocean (e.g., rain gauge bias corrections). However, the minimum rain detection and clutter regions of the TRMM PR indicate that light rain is missed in the PR precipitation data sets. We are currently unable to accurately describe the amount of light rainfall missed by PR, its rain types, and spatial distributions, until a more capable precipitation radar is available in the future. The PR-missed light rain will not impact the convective and stratiform rain properties discussed in this study in a significant manner; however, it will increase the mean total precipitation into 2.86, 2.43, and 2.73 mm d−1 over ocean, land, and overall, respectively. Its impact on the spatial distributions of rain properties over most of the ITCZ is likely not significant, while it could be more important over climatologically dry regions or mountainous areas [e.g., Comstock et al., 2005; Nesbitt et al., 2008; Wilson and Barros, 2014].
Rainfall statistical properties are important parameters to evaluate other algorithms and NWP and climate models as well as impact studies where precipitation products are involved. A recent intercomparison study of precipitation forecasts from five operational global NWP models against rain gauges indicates that differences in skill between the models are consistent and small compared to seasonal and geophysical variations [Haiden et al., 2012]. They also suggest that about one half of the current forecast error at day 1 in the extratropics can be attributed to the fact that gridbox values are verified against point observations. The limitations of using ground rain gauges for precipitation validation are its uneven geophysical distribution and the land-only coverage. The advanced and long-term rain data sets from TRMM could overcome the above issues because of its global tropic-subtropic coverage. These rain properties are extremely important in the assessment of the climate model simulations, because no direct observations of precipitation are available for future time periods. The reliable rain properties from the long-term TRMM PR rain data sets can been obtained at various spatial resolutions or the desired model grid scales at different time scales such as daily, monthly, seasonally, and annually to evaluate the NWP and climate model simulations. Other blended precipitation products from the combined microwave-radar-IR-rain gauge approach such as TRMM multisatellite precipitation analysis and Climate Prediction Center morphing method could provide more detailed spatiotemporal information for direct rain intercomparisons over global 60°N–60°S [Huffman et al., 2007; Joyce and Xie, 2011; Kidd et al., 2013]. Therefore, these statistical properties of precipitation are also useful for the verification of precipitation in climate models. If the statistical properties of precipitation from NWP or climate models and other algorithms are consistent with what is shown in this study or future analysis, the confidence is high on their performance in terms of precipitation.
The authors appreciate the TRMM PR level 2 rain data sets provided by the joint NASA-JAXA TRMM project through the TRMM Science Data and Information System. The first author is funded by a Navy BE 6.2 base program for cloud property study. The second author is supported by the NASA Precipitation Measurement Missions grant NNX13AF86G under Ramesh Kakar.
The Editor thanks Ralph Ferraro and an anonymous reviewer for their assistance in evaluating this paper.