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  • View in gallery

    A schematic showing the total frequency of precipitation occurrence as a function of rain intensity for the climatology (red) and an individual year (blue). The areas covered below the red and blue curves represent their mean rain amount, and the two colored dashed lines in the vertical represent their mean rain intensities. The black-dashed line in the vertical indicates the minimum detectable rain rate of individual observational instruments. The green-dashed line in the vertical represents a threshold usually used to define extreme rain-producing events.

  • View in gallery

    (a) Summertime and (b) wintertime mean distributions of (top) rain amount (mm day−1), (middle) frequency of occurrence (%), and (bottom) rain intensity (mm h−1) over the U.S. continent based on hourly radar and gauge data between 2002 and 2009.

  • View in gallery

    (top) Fraction of rain occurrence and (bottom) accumulated fraction of rain occurrence as functions of rain intensity for rain events between 2002 and 2009 over the U.S. continent. Values in each rain intensity bin are normalized by the total number of raining samples.

  • View in gallery

    As in Fig. 3, but for rain volume.

  • View in gallery

    (top) Seasonal variations of fraction of rain occurrence and (bottom) fraction of rain volume for rain rates <0.2, 0.3, 0.5, and 1.0 mm h−1, and for rain rate >10 mm h−1.

  • View in gallery

    (a) Horizontal distributions of fraction of rain occurrence during the (left) summer (JJA) and (right) winter (DJF) for rain intensity thresholds (bottom to top) <0.2, 0.5, 1.0, and >10 mm h−1. (b) As in (a), but for fraction of rain volume.

  • View in gallery

    Fractions of (top) rain occurrence (%) and (bottom) rain volume (%) as functions of monthly mean rain rate derived on 1° × 1° grid.

  • View in gallery

    Variations of fractions of (top) rain occurrence and (bottom) rain volume as a function of horizontal resolutions for rain intensity thresholds >10 mm h−1, and <0.2, 0.3, 0.5, and 1.0 mm h−1.

  • View in gallery

    As in Fig. 8, but for as a function of temporal resolutions for rain intensity thresholds >10 mm h−1, between 10 and 1 mm h−1, and <0.2, 0.3, 0.5, and 1.0 mm h−1.

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Estimation of Rain Intensity Spectra over the Continental United States Using Ground Radar–Gauge Measurements

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  • 1 Mesoscale Atmospheric Processes Branch, NASA Goddard Space Flight Center, Greenbelt, Maryland
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Abstract

A high-resolution surface rainfall product is used to estimate rain characteristics over the continental United States as a function of rain intensity. By defining data at 4-km horizontal resolutions and 1-h temporal resolutions as an individual precipitating or nonprecipitating sample, statistics of rain occurrence and rain volume including their geographical and seasonal variations are documented. Quantitative estimations are also conducted to evaluate the impact of missing light rain events due to satellite sensors’ detection capabilities.

It is found that statistics of rain characteristics have large seasonal and geographical variations across the continental United States. Although heavy rain events (>10 mm h−1) only occupy 2.6% of total rain occurrence, they may contribute to 27% of total rain volume. Light rain events (<1.0 mm h−1), occurring much more frequently (65%) than heavy rain events, can also make important contributions (15%) to the total rain volume.

For minimum detectable rain rates setting at 0.5 and 0.2 mm h−1, which are close to sensitivities of the current and future spaceborne precipitation radars, there are about 43% and 11% of total rain occurrence below these thresholds, and they respectively represent 7% and 0.8% of total rain volume. For passive microwave sensors with their rain pixel sizes ranging from 14 to 16 km and the minimum detectable rain rates around 1 mm h−1, the missed light rain events may account for 70% of rain occurrence and 16% of rain volume.

Statistics of rain characteristics are also examined on domains with different temporal and spatial resolutions. Current issues in estimates of rain characteristics from satellite measurements and model outputs are discussed.

Current affiliation: Goddard Earth Sciences Technology and Research, Morgan State University, Baltimore, Maryland.

Corresponding author address: Dr. Xin Lin, Mesoscale Atmospheric Processes Branch, NASA Goddard Space Flight Center, Code 612, Greenbelt, MD 20771. E-mail: xin.lin-1@nasa.gov

Abstract

A high-resolution surface rainfall product is used to estimate rain characteristics over the continental United States as a function of rain intensity. By defining data at 4-km horizontal resolutions and 1-h temporal resolutions as an individual precipitating or nonprecipitating sample, statistics of rain occurrence and rain volume including their geographical and seasonal variations are documented. Quantitative estimations are also conducted to evaluate the impact of missing light rain events due to satellite sensors’ detection capabilities.

It is found that statistics of rain characteristics have large seasonal and geographical variations across the continental United States. Although heavy rain events (>10 mm h−1) only occupy 2.6% of total rain occurrence, they may contribute to 27% of total rain volume. Light rain events (<1.0 mm h−1), occurring much more frequently (65%) than heavy rain events, can also make important contributions (15%) to the total rain volume.

For minimum detectable rain rates setting at 0.5 and 0.2 mm h−1, which are close to sensitivities of the current and future spaceborne precipitation radars, there are about 43% and 11% of total rain occurrence below these thresholds, and they respectively represent 7% and 0.8% of total rain volume. For passive microwave sensors with their rain pixel sizes ranging from 14 to 16 km and the minimum detectable rain rates around 1 mm h−1, the missed light rain events may account for 70% of rain occurrence and 16% of rain volume.

Statistics of rain characteristics are also examined on domains with different temporal and spatial resolutions. Current issues in estimates of rain characteristics from satellite measurements and model outputs are discussed.

Current affiliation: Goddard Earth Sciences Technology and Research, Morgan State University, Baltimore, Maryland.

Corresponding author address: Dr. Xin Lin, Mesoscale Atmospheric Processes Branch, NASA Goddard Space Flight Center, Code 612, Greenbelt, MD 20771. E-mail: xin.lin-1@nasa.gov

1. Introduction

Statistics of rain intensity and frequency of occurrence have received more and more attention in recent years since the important climate trend affecting the hydrologic cycle and energy budget could be more clearly detected in the characteristics of rain events relative to the temporally and spatially averaged total rain accumulation (e.g., Englehart and Douglas 1985; Chen et al. 1996; Karl and Knight 1998; Meehl et al. 2000; Dai 2001; Trenberth et al. 2003; Groisman et al. 2005; Sun et al. 2006; Lau and Wu 2006; Dai et al. 2007). Figure 1 is a schematic showing the frequency distribution of rain events as a function of rain intensity between the climatology and an individual year. The areas covered below two colored curves represent the mean rain amount for the climatology and the individual year, respectively. Averaged over the globe or large domains, while the changes in the mean rain amount could be small and/or difficult to distinguish, the changes in the frequency distribution can be identified easily. Therefore, although the public attentions have been focusing mostly on changes in mean rain amount and limited numbers of devastating rain-producing weather events and severe droughts, it is ultimately the change–shift within the entire intensity spectrum of global or regional rain events that contribute to the short- and long-term climate variations in the hydrologic cycle.

Fig. 1.
Fig. 1.

A schematic showing the total frequency of precipitation occurrence as a function of rain intensity for the climatology (red) and an individual year (blue). The areas covered below the red and blue curves represent their mean rain amount, and the two colored dashed lines in the vertical represent their mean rain intensities. The black-dashed line in the vertical indicates the minimum detectable rain rate of individual observational instruments. The green-dashed line in the vertical represents a threshold usually used to define extreme rain-producing events.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00151.1

Many observational studies have examined the characteristics of rain events in terms of rain intensity and frequency of occurrence (e.g., Englehart and Douglas 1985; Petty 1995, 1997; Karl and Knight 1998; Dai 2001; Trenberth et al. 2003; Short 2003; Groisman et al. 2005; Lau and Wu 2006; Dai et al. 2007; Ebert et al. 2007; Berg et al. 2010). For example, Petty (1995) investigated frequencies and characteristics of global oceanic precipitation from shipboard weather reports and noted large seasonal and geographic variations for different rain groups including thunderstorms and drizzle. Similarly, Dai (2001), using 3-hourly global weather reports, estimated the seasonal and interannual climatology of rain frequency over both land and ocean for various types of precipitation including drizzle and nondrizzle precipitation, showery and nonshowery precipitation, thunderstorms, and snow. With quantitative information on precipitation rates, various thresholds of rain intensity or frequency of rain occurrence have been developed to categorize long-term observational rain data records and explore the climate trend affecting different rain event ensembles (e.g., Karl and Knight 1998; Groisman et al. 2005; Lau and Wu 2006). For example, Karl and Knight (1998), using long-term daily rain gauge data over the contiguous United States, found almost a 10% increase in the heavy and extreme daily precipitation events over the past century. Lau and Wu (2006) examined the probability distribution function of pentad tropical rainfall and noticed that two commonly used satellite–ground-blended rain products all indicated a positive trend in the occurrence of heavy and light rain events during 1979–2003 and a negative trend in moderate rain events. More recently, Berg et al. (2010) collocated instantaneous satellite rainfall retrievals from a precipitation radar (PR) and a cloud-profiling radar (CPR) and examined the entire rainfall intensity spectra over tropical and subtropical oceans. In addition to the advance in observational studies on rain characteristics, evaluations of model results against observations using statistics of rain intensity and frequency of rain occurrence have also provided key metrics for testing the influence of model physical parameterizations on the hydrological cycle (e.g., Chen et al. 1996; Meehl et al. 2000; Trenberth et al. 2003; Sun et al. 2006; Dai 2006; Ebert et al. 2007, etc.).

Rain intensity and frequency of occurrence are strong functions of the temporal and spatial scales. Because of the limited availability and quality of long-term station data records, many earlier observational studies on characteristics of rain events were based on rain rates averaged over a day or even longer, thus essentially they provided estimations biased toward statistics of large rain systems with heavy and intermediate rainfall. Although light rain events are well known to occur much more frequently than heavy and intermediate rain events, there are large uncertainties in estimating contributions of light precipitation to rain incidence and rain volume (e.g., Petty 1995). For example, there could be two different types of “light rain” at daily time scale. It is possible that a region characterized by persistent, light precipitation throughout the day has the same daily mean rain rate as a region with intermittent but heavy convective precipitation. Their impact on the vertical heating and moistening profiles as well as the surface water runoff and soil moisture can be drastically different. Using pointed station data to estimate averages over larger domains may induce large representativeness errors since precipitation is highly variable in the horizontal. Furthermore, applying the same rain intensity or rain frequency thresholds (say, 10 mm day−1 to distinguish heavy rain events) on domains of different horizontal resolutions (e.g., a 1° × 1° grid, versus a 2.5° × 2.5° grid) could include many different rain event ensembles, thus potentially leading to contradicting statistics of rain characteristics. Given these concerns and uncertainties, it is important and necessary to quantitatively examine the characteristics of entire rain event spectra at fine temporal and spatial scales.

Satellite observations are widely utilized to extract instantaneous estimates of rainfall information on the global scale, providing a promising way to examine characteristics of rain spectrum at fine temporal and spatial resolutions. Among various remote sensing instruments, microwave sensors that directly respond to the absorption and scattering of cloud hydrometer particles provide the backbone of space-based precipitation measurements. However, the quality of rain retrievals varies with the sensitivity of satellite instruments and retrieval algorithms as well as sensor spatial resolutions. Each satellite rainfall retrievals has its own minimum detectable rain rate, in which below the threshold, its detection capability is quickly degraded (e.g., Petty 1995, 1997; Lin and Hou 2008; Berg et al. 2010). For example, the rain retrieval from the PR (Meneghini and Kozu 1990; Kummerow et al. 1998, 2001; Iguchi et al. 2000) on board the Tropical Rainfall Measuring Mission (TRMM; Simpson et al. 1988, 1996) satellite has the minimum detectable rain rate ranging between 0.5 and 0.7 mm h−1 at the footprint resolution of 5 km. Rain retrievals from passive microwave (PMW) sounders such as the Advanced Microwave Sounding Unit-B (AMSU-B) instruments on National Oceanic and Atmospheric Administration (NOAA)-15, -16, and -17 satellites have the minimum detectable rain rate of 1.1 mm h−1 over land at the footprint resolution of 16 km (Dr. R. Ferraro 2006, personal communication). Rain retrievals from PMW imagers are more accurate than those from PMW sounder data over the ocean, but they tend to have similar uncertainties and similar minimum detectable rain rates over land as those from the sounder data. It is not clear how the varying detection capability could affect the contribution of different rain intensity categories to the total rain incidence and rain volume, and how the statistics of rain characteristics would change with rain samples averaged over different horizontal resolutions.

In this study, we use a high-resolution rainfall product derived from 8-yr surface radar and gauge data to explore rain intensity spectra over the U.S. continent. Statistics of rain occurrence and rain volume including their geographical and seasonal variations are documented between 2002 and 2009. In particular, we intend to estimate the fraction of light rain occurrence and volume and try to assess the impact of a number of satellite sensors’ detection capabilities because of missing light rain events. The precipitation product is at 4-km horizontal resolutions and at 1-h intervals covering the entire U.S. continent, providing an excellent opportunity to estimate the complete rain intensity spectra over land at fine temporal and spatial resolutions and mimic what different satellite rain observations would detect.

The Global Precipitation Measurement (GPM) mission (Hou et al. 2011, manuscript submitted to Bull. Amer. Meteor. Soc.), being developed as an international science partnership, is planning to advance observations of precipitation to both the tropics and higher latitudes with enhanced sampling frequencies and improved measuring capabilities. Specifically, GPM will have a CORE satellite carrying a Dual-Frequency Precipitation Radar (DPR) and a high-resolution, multichannel PMW rain radiometer known as the GPM Microwave Imager (GMI), which has innovative capabilities to measure light rain and falling snow. Along with CORE are a number of constellation satellites (with variable life cycles and different sensor characteristics) in sun-synchronous and nonsun-synchronous orbits, with each member having its unique scientific or operational objectives but contributing data to GPM to produce uniformly calibrated global precipitation products. The work reported in this paper involving rain detection capabilities of the current and future sensors will potentially provide important guidance to the GPM mission.

The purpose of the study is to 1) document the climatology of rain intensity spectrum distribution over the U.S. continent using surface radar and gauge data, including their seasonal and regional variations; 2) examine the fraction of light rain occurrence and volume relative to the total rain occurrence and volume, thus providing preliminary estimates of rain events missed by satellite sensors because of their detection capabilities; and 3) discuss and clarify some current issues in estimates of rain frequency and rain intensity from satellite measurements and model outputs. Section 2 introduces the dataset and analysis methodologies and discusses sensitivity tests conducted to evaluate the contribution of heavy and light rain events. Section 3 presents the seasonal and regional climatology of rain characteristics over the U.S. continent. Section 4 examines statistics of rain occurrence and rain volume and investigates the impact of satellite sensors’ detection capability on precipitation statistics. Sections 5 and 6 estimate sensitivities of rain characteristics on rainfall averaged on different temporal and spatial resolutions. Section 7 presents the final conclusions of the study.

2. Data and analysis methods

The surface rainfall data used in this study are the merged surface radar and rain gauge product from the National Centers for Environmental Prediction (NCEP) National Hourly Multisensor Precipitation Analysis Stage IV (Lin and Mitchell 2005). The ground radar bias correction technique and the radar–gauge merging methodology are developed by Smith and Krajewski (1991) and Seo (1998), respectively. This dataset collects hourly radar rainfall estimates from about 140 Weather Surveillance Radar-1988 Doppler (WSR-88D) operational radars over the U.S. continent, merging with about 3000 hourly gauge reports. The Stage IV data are preliminarily quality controlled and calibrated. The precipitation product is on a 1121 × 881 polar stereographic grid and is at the 4-km resolutions. It covers the entire U.S. continent at 1-h intervals from 2002 to the present. Although it is understandable that there might still be some uncertainties on issues such as data quality and calibration, this merged surface rainfall dataset offers excellent “truth” information at fine temporal and spatial resolutions, with continuous sampling of various rain events over the continental United States.

In the following sections (unless specifically mentioned), statistics of rain volume and rain occurrence are calculated as functions of rain intensity using the rain data at the 4-km resolutions and 1-h intervals as individual precipitating or nonprecipitating samples. Horizontal distributions of mean rain amount and frequency of occurrence are also calculated in a similar way but are tabulated onto a 1° × 1° grid.

One of the major objectives in this study is to estimate rain intensity spectra over land and evaluate the impact of missing light rain events due to satellite sensor detection capability. Among the current and near-future active microwave sensors that provide rainfall measurements, the footprint resolution of the current TRMM PR rain pixel is about 5 km at nadir, and its minimum detectable rain rate is about 0.5 mm h−1. The DPR onboard the on-planning GPM mission CORE satellite will also have a footprint resolution of 5 km (for Ku band), and the expected accuracy is 0.2 mm h−1 sensitivities. It should be noted that these minimum detectable rain rates from PR and DPR are reasonable approximations, and they could vary a little depending on the drop size distribution and the horizontal variability within the field of view (FOV). Nevertheless, the horizontal resolution of the merged surface rainfall product is close to the rain pixel resolutions of both PR and DPR. As for temporal resolutions, the satellite rainfall retrievals from PR and DPR are snapshots for a period of less than a second while the surface radar and gauge merged rain product is an hourly dataset. Although the rain statistics from instantaneous measurements may be slightly different from the statistics from hourly averages, we assume that the characteristics of rain events do not change much within one hour, so that the hourly surface rainfall product is adequate to infer statistics of instantaneous satellite rainfall estimates. It should be pointed out that this steady-state assumption likely performs poorly in regions and seasons where transient showers dominate. This issue will be further discussed in sensitivity tests carried out in later sections. To compensate for some of the uncertainties arising from the difference in temporal and spatial resolutions between rain retrievals from spaceborne radars and the surface rain product, four rain intensity thresholds—0.2, 0.3, 0.5, 1.0 mm h−1—are used to estimate the impact of missing light rain events, with thresholds 0.2 and 0.5 mm h−1 more closely representing GPM DPR and TRMM PR’s detection capability. Another rain intensity threshold, 10 mm h−1, is used to distinguish heavy rain events.

For many current PMW radiometers and sounders such as the TRMM Microwave Imager (TMI), the Special Sensor Microwave Imager (SSMI) on the Defense Meteorological Satellite Program (DMSP) F-13, -14, and -15 satellites, and the Advanced Microwave Scanning Radiometer for the Earth Observing System (AMSR-E) on the Aqua satellite, as well as the AMSU-B on NOAA-15, -16, and -17 satellites, their rain pixel sizes are typically larger than 5 km and may vary with the frequency channels being used. Their minimum detectable rain rates also vary with the algorithms being used as well as the land surface background. Their sensitivities on horizontal resolutions will be discussed and examined in section 5.

3. Seasonal mean distributions

Many studies have examined the climatology of rain characteristics over the continental United States based on gauge data and weather reports (e.g., Englehart and Douglas 1985; Chen et al. 1996; Dai 2001; Sun et al. 2006; Dai 2006). Using the merged radar and gauge data at fine spatial and temporal resolutions, we reexamine the seasonal mean distributions of rain amount, frequency of rain occurrence, and rain intensity in Fig. 2. For each 1° × 1° grid box over the continental United States, each surface rainfall data at its original resolution (4-km horizontal resolution, and 1-h intervals) is considered as an individual sampling pixel. Mean rain amount here, following the same way as used in earlier studies, is defined as the ratio of the total accumulation of precipitation to the total number of sampling pixels within a 1° × 1° grid box for any given seasons. Similarly, mean frequency of rain occurrence is calculated as the ratio of the number of raining pixels to the total number of sampling pixels, which is essentially the fraction of raining area relative to the total area. Mean rain intensity is calculated as the ratio of the total amount of precipitation to the total number of raining pixels.

Fig. 2.
Fig. 2.

(a) Summertime and (b) wintertime mean distributions of (top) rain amount (mm day−1), (middle) frequency of occurrence (%), and (bottom) rain intensity (mm h−1) over the U.S. continent based on hourly radar and gauge data between 2002 and 2009.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00151.1

Similar to what is found in earlier studies, there are large regional and seasonal variations in the climatology of rain characteristics over the United States. During the summer season [June–August (JJA), Fig. 2a], the North American monsoon combined with moisture from the Gulf of Mexico bring frequent thunderstorms to the southern and central parts of the United States. Tropical cyclones from the Atlantic Ocean also bring a significant amount of precipitation to the southern and eastern parts of the United States. As a result, large precipitation amounts can usually be noticed over the southeast part of the United States during summer, especially along the coastal areas with the amounts gradually decreasing inland. A maximum in frequency of rain occurrence (6%–10%) can be observed extending from the southern states northeastward all the way to Maine. The central part of United States also has frequent rain events, with a maximum of 5%–6% over Nebraska–Oklahoma–Kansas located parallel to the orientation of the Rocky Mountains. This area, as noted by Wallace (1975), tends to feature frequent nocturnal thunderstorms. The average rain intensity is about 3–4 mm h−1 in the Gulf Coast area and decreases to 2–3 mm h−1 in higher latitudes. Comparing to the central and eastern parts of United States, the mean rain amount over the western United States is generally very light. While the Rocky Mountain area indicates some topography-related rain events (with likely some underestimations of small and shallow systems that ground radars cannot detect because of the topography blocking), the West Coast region is very quiet with few rain activities during summer.

During the winter season [December–February (DJF), Fig. 2b], precipitation amount over the southeastern part of the United States is significantly reduced. The largest mean rain amount is less than 5 mm day−1 and is located between Louisiana, Mississippi, and Tennessee. Frequent rain occurrence (10%–20%), however, can still be observed over the central and eastern United States. These precipitating events are likely to be associated with wintertime frontal systems featuring more persistent, lighter precipitation arising from large-scale ascending. Mean rain intensity also gradually decreases from the Gulf Coast region to higher latitudes, suggesting a consistent transition of precipitating events from a more convective environment to an environment characterized by large-scale ascending–descending. On the other hand, being associated with a major wintertime storm track, frequency of rain occurrence over the western United States significantly increases in the winter with the maximum ranging between 20% and 40%. Although the mean rain intensity is light (<2 mm h−1), the mean rain amount over the northwest United States is quite large. These broad features generally agree with what is found in earlier studies based on gauge data and weather reports (e.g., Chen et al. 1996; Dai 2001; Sun et al. 2006).

4. Rain intensity spectra

a. Fractions of rain occurrence and volume

For rainfall estimations, some interesting yet still intriguing questions to ask are as follows. What are the contributions of rain events within different rain intensity ranges to the total rain incidence and total rain volume? For a given minimum detectable rain rate, what percentage of rain occurrence and rain volume might be missed by certain satellite instruments? This kind of exploration can provide very useful information on the impact of satellite sensor detection capabilities, which could eventually lead to a better understanding of the short-term and long-term climate variability of light rain. Figure 3 depicts the fraction of rain occurrence as a function of rain intensity using all the merged high-resolution surface rainfall data over the U.S. continent between 2002 and 2009. Values in each rain intensity bin are normalized by the total number of raining samples. Although no information is provided for the minimum detectable rain rate for the surface rainfall product, the number of raining samples drops rapidly and becomes negligibly small for rain intensity at and below 0.1 mm h−1, probably suggesting that the minimum detectable rain rate for the merged radar and gauge rainfall product is about 0.1 mm h−1.

Fig. 3.
Fig. 3.

(top) Fraction of rain occurrence and (bottom) accumulated fraction of rain occurrence as functions of rain intensity for rain events between 2002 and 2009 over the U.S. continent. Values in each rain intensity bin are normalized by the total number of raining samples.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00151.1

As expected, light precipitation generally dominates the rain intensity spectra in terms of the fraction of rain occurrence over the continental United States, with 62.5% of raining samples having rain rate less than 1 mm h−1 (Fig. 3). These are consistent with earlier findings over both land and ocean (Petty 1995, 1997; Dai 2006; Haynes et al. 2009; Berg et al. 2010) that light rain events tend to occur more frequently than heavy and intermediate rain events. The fraction of intermediate rain events (1.0 mm h−1 < R < 10 mm h−1) is 34.9%, about half of the fraction of light rain events. On the other hand, heavy rain events, defined as raining samples with rain rates >10 mm h−1, occur much less frequently than light and intermediate rain events (with only about 2.6% of total rain incidence). For rain intensities setting at 0.2, 0.3, and 0.5 mm h−1, there are 11.3%, 24.5%, and 43.1% of total raining cells below these thresholds respectively. If we assume that 0.2 and 0.5 mm h−1 are close to the thresholds that GPM DPR and TRMM PR are able to detect, the light rain occurrence that GPM DPR can detect but TRMM PR cannot accounts for more than 30% of total rain occurrence.

The fraction of rain volume (Fig. 4) indicates that heavy and intermediate rain events dominate the total rain volume falling over the continental United States. Although heavy rain events occur much less frequently than light and intermediate rain events, they contribute about 27%, more than a quarter of the total rain volume. Combining both heavy and intermediate rain events, they contribute 84.6% of total rain volume over the U.S. continent. On the other hand, the contribution of light rain events (below 1 mm h−1) is also very important and can reach 15.4% of total rain volume. For rain intensity thresholds setting at 0.2, 0.3, and 0.5 mm h−1, their contributions to the total rain volume over the U.S. continent are about 0.8%, 2.6%, and 7.0%, respectively. If we assume that DPR and PR’s minimum detectable rain rates are 0.2 and 0.5 mm h−1, DPR may only miss about less than 1% of total rain volume on its scan over land, while TRMM PR could miss more than 6% of total rain volume.

Fig. 4.
Fig. 4.

As in Fig. 3, but for rain volume.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00151.1

Berg et al. (2010) assessed the distribution of rain volume as a function of rain rate by employing collocated CloudSat CPR estimates below 1 mm h−1, and TRMM PR estimates above 2 mm h−1 at 5-km resolution. They estimated that the rain volume contribution of oceanic rain rates below 0.2, 0.3, and 0.5 mm h−1 are 2.5%, 4.7%, and 8.3%, respectively, very close to what is obtained from surface radar and gauge product over land.

b. Seasonal and geographical variations

As noted in Fig. 2, both rain occurrence and rain volume have large seasonal and geographical variations across the continental United States. Therefore the contributions of light and heavy rain events may also vary accordingly. Figure 5 shows seasonal variations of monthly fractions of rain occurrence and rain volume for rain rates less than 0.2, 0.3, 0.5, and 1.0 mm h−1, and for a rain rate larger than 10 mm h−1.

Fig. 5.
Fig. 5.

(top) Seasonal variations of fraction of rain occurrence and (bottom) fraction of rain volume for rain rates <0.2, 0.3, 0.5, and 1.0 mm h−1, and for rain rate >10 mm h−1.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00151.1

Fraction of heavy rain occurrence is generally small throughout the year over the U.S. continent. It follows the seasonal solar cycle with a maximum (5%) during the summer and a minimum (1.3%) during the winter. For rain events with intensity below 1.0 and 0.5 mm h−1, their rain occurrence shows moderate seasonal variations with maxima during winter and minima during summer. The average fractions of rain occurrence range from 70% and 45% during the winter to about 55% and 40% during the summer. These seasonal variations, as shown in Fig. 2, indicate seasonal transitions from persistent, light, and large-scale precipitation during the cold season to vigorous, intermittent, and convective precipitation during the warm season. For lighter rain events, the seasonal variations are considerably small, and the fractions of rain occurrence are about 10% and 25% for rain intensities below 0.2 and 0.3 mm h−1.

Although heavy rain events occur much less frequently than intermediate and light rain events, they make important contributions to the total rain volume throughout the year. Heavy rain events have a strong seasonal variation in fraction of rain volume, with a minimum of 13% in February and a maximum of 36% in July. This is consistent with the seasonal transition over the U.S. continent from a large-scale, more baroclinic environment during the cold season to a more barotropic environment during the warm season featuring frequent, vigorous convection. The fraction of rain volume does not change much with seasons for rain events with rain intensity below 0.3 mm h−1. The average fractions of rain volume are about 1% and 4% for rain rates below 0.2 and 0.3 mm h−1. For larger rain thresholds, their seasonal variations become larger, with the light rain contribution ranging from 10% during the winter to 6% during summer for rain events below 0.5 mm h−1 and from 23% during the winter to 10% during summer for rain events below 1.0 mm h−1. Therefore TRMM PR, with a detectable rain rate of 0.5 mm h−1, could miss about 6%–10% of total rain volume, while GPM DPR, with a detectable rain rate of 0.2 mm h−1, can capture about 99% of total rain volume throughout the year. Considering that the contribution of rain events with rain intensity below 0.1 mm h−1 (the possible threshold for the surface rainfall product) is likely much more smaller, these results suggest that without considering the orbital sampling issue, the contribution of light rain events that may be missed in GPM DPR scans will be negligibly small over the continental United States in terms of total rain volume. Again it needs to be pointed out that the minimum detectable rain rates for PR and DPR are not fixed, and they could vary significantly depending on the drop size distribution and the horizontal inhomogeneity within the FOV.

Figure 6 shows the horizontal distributions of fractions of rain occurrence and rain volume averaged over 8 summers (JJA) and 8 winters (DJF) for rain intensity thresholds above 10 mm h−1 and below 0.2, 0.5, 1.0 mm h−1. Similar to what is shown in Fig. 2 for mean rain amount and mean frequency of rain occurrence, there are large seasonal and geographical variations for heavy and light rain events in terms of rain occurrence and volume. In general, although heavy rain events occupy a small fraction of total rain incidence, they tend to make important contributions to the total rain volume. Light rain events usually account for a large fraction of total rain incidence, but they only contribute to a small fraction of total rain volume. During summer, the fraction of heavy rain occurrence shows maxima over the southern, southeastern, and central parts of the United States, with 5%–10% of rain events with rain intensity above 10 mm h−1. The corresponding fraction of rain volume also indicates a similar pattern with the contribution of heavy rain events to the total rain volume ranging between 30% and 50%. The western part of United States, except for a narrow region along the California coast, indicates few heavy rain events. During winter, occurrence of heavy rain events is significantly reduced and is only limited near the coastal regions of the southern United States. Except for some spotty areas, the volume fraction of heavy rain is generally smaller over the continental United States. For rain events with rain intensity below 1.0 mm h−1, the area-averaged fractions of rain occurrence during summertime are about 60%–90% over the western United States, 50%–60% over the central and northern United States, and 40%–50% over the southern and southeastern United States. The corresponding rain volume contribution ranges between 20% and 50% over the western United States, 10% and 20% over the central and northern United States, and below 10% over the southern and southeastern United States. During wintertime, except for the area near the southern part of the United States, which shows 40%–60% of rain incidence for rain intensity below 1.0 mm h−1, most parts of the United States are dominated with rain events with rain intensity below 1.0 mm h−1, indicating the significant contribution from persistent, light precipitation arising from large-scale ascending. The volume fraction increases with latitudes varying from 10%–20% over the southern and southeastern United States to 60%–90% over the northern United States.

Fig. 6.
Fig. 6.

(a) Horizontal distributions of fraction of rain occurrence during the (left) summer (JJA) and (right) winter (DJF) for rain intensity thresholds (bottom to top) <0.2, 0.5, 1.0, and >10 mm h−1. (b) As in (a), but for fraction of rain volume.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00151.1

For rain events with rain intensity below 0.5 mm h−1, these are the rain event ensembles that may not be detected by TRMM PR. We can infer that light rain events missed by TRMM PR may account for 60%–80% of rain incidence over the western United States and 30%–40% over the central and eastern United States during summer. However, they only account for about less than 30% of total rain volume over the western United States and less than 10% of total rain volume over the central and eastern United States. During winter, the fraction of occurrence and volume increase over the northern United States. The light rain volume missed by PR may account for about 40%–60% of total volume near the wintertime storm track.

For rain events with the rain intensity threshold setting at 0.2 mm h−1, these are the rain event ensembles that may not be detected by GPM DPR. Except for the arid area over Idaho, Nevada, Utah, and Arizona showing 30%–50% of rain incidence and 5%–10% of total rain volume, most parts of the United States indicate smaller contributions of rain incidence (below 10%) and rain volume (below 2%). Therefore, despite the fact that the minimum detectable rain rate for PR and DPR are not fixed and could vary significantly depending on the drop size distribution and the horizontal inhomogeneity within the FOV, GPM DPR has the capability to detect most rain events that contribute meaningfully to the total rain volume over the continental United States, particularly for the frequent light precipitation resulted from both warm season convection and cold season large-scale ascending.

To further examine the geographical variation of the light rain contribution, we collocate the monthly mean fractions of light rain occurrence and light rain volume with monthly mean rain amount on each 1° × 1° grid box. Therefore, for any given monthly mean rain amounts that can be easily calculated from data, the contribution of monthly-averaged light rain occurrence and light rain volume can be quantitatively estimated over the continental United States.

Figure 7 shows the probability distribution function of the fraction of rain occurrence and fraction of rain volume as functions of monthly mean rain amount on a 1° × 1° grid box. Regions with larger monthly mean rain rates typically feature smaller fractions of light rain occurrence and light rain volume. For regions with monthly mean rain amount at 10 mm day−1, the ensemble mean fraction of light rain occurrence is about 5%, 15%, 25%, and 45% for rain events with rain intensities below 0.2, 0.3, 0.5, and 1.0 mm h−1. The corresponding fractions of light rain volume are 0.3%, 1.1%, 4.1%, and 9.2%. For regions with monthly mean rain amount at 1.0 mm day−1, the ensemble mean fraction of light rain occurrence is about 15%, 30%, 50%, and 73% for rain events with rain intensities below 0.2, 0.3, 0.5, and 1.0 mm h−1. The corresponding fractions of light rain volume are about 3.1%, 7.2%, 19.2%, and 36.4%. Therefore, if TRMM PR, which has a minimum detectable rain rate at 0.5 mm h−1, is used to sample a region with the monthly mean rain rate at 1.0 mm day−1, it is possible that about 50% of raining samples and 20% of total rain volume may be missed by PR. If GPM DPR, which has a minimum detectable rain rate at 0.2 mm h−1, is used to sample a region with the monthly mean rain rate at 1.0 mm day−1, there are only about 15% of raining samples and 4% of total rain volume missing. Certainly for regions characterized by very low monthly rain amounts, although the relative contribution of light rain (either missed or detected) is likely very high, its absolute contribution remains pretty small and therefore may not affect much on the local hydrological applications.

Fig. 7.
Fig. 7.

Fractions of (top) rain occurrence (%) and (bottom) rain volume (%) as functions of monthly mean rain rate derived on 1° × 1° grid.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00151.1

5. Variations at different horizontal resolutions

Results shown in previous sections are for rain intensity spectra at 4-km horizontal resolutions, which are close to rain pixel sizes of TRMM PR and GPM DPR. For many current rainfall retrievals derived from PMW radiometers and sounders, their rain pixel sizes typically range from 14 to 16 km or even larger, and each sensor may have different minimum detectable rain rates over land and ocean. Since statistics of rain characteristics are strong functions of horizontal resolutions, the larger the averaging grid box, the more likely the rain intensity spectra tend to shift to lower rain rates until reaching the domain mean rain intensity.

To comprehensively examine the sensitivity of rain characteristics on horizontal resolutions, the merged surface radar and gauge data at the original 4-km horizontal resolution are averaged onto domains ranging from 4 km to 96 km at 4-km intervals. Figure 8 shows the variations of fractions of rain occurrence and rain volume at different horizontal resolutions for rain intensity thresholds larger than 10 mm h−1 and smaller than 0.2, 0.3., 0.5, and 1.0 mm h−1. It provides an estimation of detection capability for all the satellite rainfall retrievals over land. Generally speaking, as the horizontal averaging domain increases, fractions of light rain occurrence and volume tend to increase for a given rain intensity threshold. This is not surprising since more zero-rain pixels are likely included and may effectively reduce the domain-averaged rain rate. For TRMM PR and GPM DPR (minimum detectable rain rates at 0.5 and 0.2 mm h−1 and both rain pixels at 5-km horizontal resolutions), missed light rain events account for about 45% and 11% of total rain occurrence, and 7% and 1% of total rain volume. Results on the 14–16-km horizontal resolution can be used to infer the rainfall characteristics for PMW radiometers and sounders. For example, rainfall retrievals derived from AMSU-B sounders on board the NOAA-15, -16, and -17 satellites have minimum detectable rain rates at 1.1 mm h−1 at rain pixel resolution of 16 km (R. Ferraro 2006, personal communication). The missed light rain events by AMSU-B therefore may account for about 70% of total rain occurrence and 16% of total rain volume over land. Rain retrievals from PMW radiometer data (TRMM TMI, DMSP/SSMI, and Aqua AMSR-E) have similar minimum detectable rain rates and rain pixel resolutions over land (14–15 km); therefore, they tend to have similar statistics on light rain occurrence and volume. On the other hand, it should also be kept in mind that current PMW retrievals over land are mainly empirically derived from scattering-based algorithms. They are less capable of detecting precipitation from warm-topped clouds (Petty 1999; Joyce et al. 2004; Huffman et al. 2007).

Fig. 8.
Fig. 8.

Variations of fractions of (top) rain occurrence and (bottom) rain volume as a function of horizontal resolutions for rain intensity thresholds >10 mm h−1, and <0.2, 0.3, 0.5, and 1.0 mm h−1.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00151.1

Many studies have used satellite rainfall data to evaluate model output in terms of rain occurrence and rain intensity and to examine their variations associated with climate change. By doing so, satellite data are usually averaged onto model gridbox sizes and fixed rain intensities (1 or 10 mm h−1) are used as thresholds to distinguish light and heavy rain events, respectively. However, the included rain event ensembles may be different for the same rain intensity threshold at different horizontal resolutions. Figure 8 further illustrates that fraction of heavy rain occurrence accounts for about 0.2%, 0.06%, and 0.01% of total rain incidence at 25-, 50-, and 100-km resolutions for rain intensity larger than 10 mm h−1, and they may contribute to about 17%, 11%, and 6%, respectively, of the total rain volume. On the other hand, if 1.0 mm h−1 is used as a cutoff rain rate to define light rain events, they can account for 76%, 83%, and 90% of total rain occurrence and contribute to about 18%, 24%, and 32% of total rain volume. Therefore caution should be taken when interpreting results of rain occurrence and rain volume averaged on different horizontal resolutions.

6. Sensitivities on temporal resolutions

Under the assumption that the characteristics of rain events do not change much within an hour, instantaneous satellite rainfall estimations are simulated using hourly surface radar and gauge data to examine the impacts of satellite sensors’ detection capability on rain volume and rain occurrence as shown in the above sections. Precipitation, however, can be highly variable and is well known to be a strong function of temporal resolutions, particularly for those transient light rain events that could develop and dissipate within a very short time. To evaluate the steady-state assumption, a sensitivity test is conducted in this section using the ongoing next generation quantitative precipitation estimates (Q2) product (Vasiloff et al. 2007). This experimental Q2 rainfall product, being jointly developed by NOAA and university research communities, is on 1-km resolutions and provides rainfall estimations over the entire U.S. continent at 5-min intervals. The primary sensor used in Q2 is the WSR-88D operational radar, with updated rain-reflectivity algorithms. A minimum detectable rain rate of 0.25 mm h−1, corresponding to the lowest rain amount (0.01 inch) that a rain gauge could observe–record, is used in the original data to reduce contaminations of radar errors associated with ground clutter and nonprecipitating targets (Dr. P.-E. Kirstetter 2011, personal communication).

One month of original Q2 rainfall data (May 2010) are first horizontally averaged onto 4-km resolutions, and then temporally averaged to durations of 10, 20, 30, 40, and 60 min. Shown in Fig. 9 are fractions of rain occurrence and rain volume as a function of temporal resolutions. Fractions of rain incidence for heavy rain (R > 10 mm h−1) and intermediate rain (1 mm h−1 < R < 10 mm h−1) events decrease slightly with longer averaging time intervals. The heavy and intermediate rain events are usually associated with large, more organized rain systems with life time typically longer than a few hours, and they are expected to have similar fractions of rain occurrence. For light rain events, fractions of rain occurrence tend to increase slightly as the averaging duration becomes longer since many zero-rain samples could effectively reduce the averaged rain rate. The lighter the rain events, the larger the fraction difference between data averaged over 5 min and data averaged over 60 min, indicating that the steady-state assumption indeed becomes weaker for highly transient cases such as fast-evolving convection and/or a short-lived shower. These mesoscale and small-scale features could sometimes bring large biases to the regional and seasonal rain statistics, particularly during spring and summer when transient convection dominates. During the cold season when widespread and persistent precipitation arising from large-scale ascending dominates, the sensitivity of rain incidence on temporal resolution is likely to be small. On the other hand, fractions of rain volume for light rain events indicate that their values do not change much with varying temporal resolutions. The heavy and intermediate rain events do indicate some sensitivity on temporal resolutions, and these variations are probably associated with temporal and horizontal inhomogeneity so that some rain events fall to the intermediate rain category from the heavy rain category after averaging. Overall, although there are biases associated with transient precipitation events, it is generally a valid assumption to use hourly surface rainfall data to simulate instantaneous satellite rainfall estimations and examine the impacts of satellite sensors’ detection capability on rain volume and rain occurrence.

Fig. 9.
Fig. 9.

As in Fig. 8, but for as a function of temporal resolutions for rain intensity thresholds >10 mm h−1, between 10 and 1 mm h−1, and <0.2, 0.3, 0.5, and 1.0 mm h−1.

Citation: Journal of Climate 25, 6; 10.1175/JCLI-D-11-00151.1

7. Summary and discussion

Accurate estimations of rain intensity spectra provide an essential approach to evaluate the impact of climate trends on the hydrological cycle and energy budget. In this study, a high-resolution rainfall product merging surface radar and gauge data, the NCEP National Hourly Multisensor Precipitation Analysis Stage IV (Lin and Mitchell 2005), is used to estimate rain characteristics over the continental United States as a function of rain intensity. By defining data at 4-km horizontal resolutions and 1-h temporal resolutions as an individual precipitating–nonprecipitating sample, the climatology of rain incidence and rain volume statistics including their geographical and seasonal variations is documented over an 8-yr period between 2002 and 2009.

Consistent with many earlier studies on the climatology of rain characteristics (e.g., Chen et al. 1996; Dai 2001; Trenberth et al. 2003; Sun et al. 2006; Dai et al. 2007), mean rain amount, mean rain frequency, and mean rain intensity have large seasonal and geographical variations across the continental United States. During the warm season, the central, southern, and eastern parts of the United States, being influenced by the North America monsoon and Atlantic hurricanes, receive large precipitation amount with frequent convective rain events. The West Coast region, mainly under the control of a strong subtropical high off the California coast, is generally very quiet with few rain activities. During the cold season, the central and eastern United States still feature frequent rain occurrence but mean rain amount and rain intensity reduce significantly, reflecting a seasonal transition of rain events frequented by persistent, light precipitation arising from large-scale ascending.

Averaged over the continental United States, the high-resolution surface rainfall product indicates that heavy rain events (>10 mm h−1), although occupying only 2.6% of total rain occurrence, may contribute to 27% of total rain volume. Light rain events (<1.0 mm h−1), occurring much more frequently (65%) than heavy rain events, can also make important contributions (15%) to the total rain volume.

Quantitative estimations are also conducted to evaluate the impact of missing light rain events due to satellite sensors’ detection capabilities. Results indicate that for minimum detectable rain rates setting at 0.5 and 0.2 mm h−1, which are close to sensitivities of the current and near-future spaceborne precipitation radars TRMM PR and GPM DPR, there are about 43.1% and 11.3% of total rain occurrence below these thresholds, and they respectively represent 7% and 0.8% of total rain volume. These statistics obtained from rainfall observations over land are close to those estimated over the tropical and subtropical oceans (e.g., Berg et al. 2010). Further examination of fractions of rain occurrence and rain volume over different seasons and different geographical locations confirms that, although the volume contribution of light rain events missed by the current TRMM PR could be still large, it will be negligibly small when the future GPM DPR is operational.

PMW radiometers and sounders are the backbone of space-based precipitation measurements. Their rain pixel sizes are considerably larger than 4-km resolutions, and their minimum detectable rain rates may vary significantly, particularly over land. Statistics of rain occurrence and rain volume are further examined on different spatial domains for given rain intensity thresholds, providing a useful guide for many other satellite sensors’ rain detection capabilities. For passive microwave sensors with their rain pixel sizes ranging from 14 to 16 km and the minimum detectable rain rate at 1 mm h−1, the missed light rain events may account for about 70% of total rain occurrence and 16% of total rain volume over land.

The estimation of precipitation characteristics is very sensitive not only to the temporal and spatial scales but also to the observational data quality and applicability. In this study, a number of potential biases in the data and analysis methodologies are noted and they could bring some uncertainties to the estimation of regional rain characteristics and evaluation of satellite sensors’ detection capabilities. For example, 1) the merged surface rainfall product is likely to have significant biases in regions of snowfall because of the current surface radar’s incapability to accurately retrieve wintertime solid precipitation; 2) instantaneous satellite observations are simulated using hourly surface data and such a steady-state assumption may be less valid when and where transient and/or short-lived rain systems dominate; and 3) the minimum detectable rain rate may vary with different hydrometeor profiles and the inhomogeneity within the FOV, as well as land surface backgrounds particularly for PMW radiometers and sounders. It also needs to be pointed out that, in addition to minimum detectable rain rates typically used in satellite observations, the fraction of precipitation could be missed owing to the maximum detectable rain rates resulted from the sensor signal saturation. No matter how perfect the retrieval algorithm is within the range that the sensor can measure, the truncation rain thresholds at the high and low ends can lead to significant biases in statistics of precipitation volumes and frequency of occurrence, and these biases may be also strong functions of the location and season as well as the time–space averaging. Therefore careful considerations must be taken when evaluating and interpreting satellite-observed and simulated climate trends in terms of frequencies of rain occurrence and rain volume.

Further studies are underway to explore rain characteristics changes that are associated with short-term climate variations. The seasonal mean diurnal variation of rain intensity spectra will also be examined using the high-resolution surface rainfall data. These analyses could provide more objective information on the impact of satellite sampling and retrieval errors as well as the applicability of satellite–model comparisons in terms of the rain intensity spectra.

Acknowledgments

The NCEP surface radar and gauge Stage IV data are obtained from National Center for Atmospheric Research Earth Observing Laboratory. Thanks to Professor Hong Yang at University of Oklahoma for providing one-month Q2 rainfall data used for the sensitivity test. Special thanks to three anonymous reviewers for very constructive comments that greatly improved the paper. This research is supported by the GPM Project at the NASA Goddard Space Flight Center in Greenbelt, Maryland.

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