Improving Geostationary Satellite Rainfall Estimates Using Lightning Observations: Underlying Lightning–Rainfall–Cloud Relationships

Weixin Xu Earth System Science Interdisciplinary Center, University of Maryland, College Park, College Park, Maryland

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Robert F. Adler Earth System Science Interdisciplinary Center, University of Maryland, College Park, College Park, Maryland

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Nai-Yu Wang Earth System Science Interdisciplinary Center, University of Maryland, College Park, College Park, Maryland

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Abstract

This study quantifies the relationships among lightning activity, convective rainfall, and associated cloud properties on both convective-system scale (or storm scale) and satellite-pixel scale (~5 km) on the basis of 13 yr of Tropical Rainfall Measuring Mission measurements of rainfall, lightning, and clouds. Results show that lightning frequency is a good proxy to separate storms of different intensity, identify convective cores, and screen out false convective-core signatures in areas of thick anvil debris. Significant correlations are found between storm-scale lightning parameters and convective rainfall for systems over the southern United States, the focus area of the study. Storm-scale convective rainfall or heavy-precipitation area has the best correlation (coefficient r = 0.75–0.85) with lightning-flash area. It also increases linearly with increasing lightning-flash rate, although correlations between convective/heavy rainfall and lightning-flash rate are somewhat weaker (r = 0.55–0.75). Statistics further show that active lightning and intense precipitation are not well collocated on the pixel scale (5 km); for example, only 50% of the lightning flashes are coincident with heavy-rain cores, and more than 20% are distributed in light-rain areas. Simple positive correlations between lightning-flash rate and precipitation intensity are weak on the pixel scale. Lightning frequency and rain intensity have positive probabilistic relationships, however: the probability of heavy precipitation, especially on a coarser pixel scale (~20 km), increases with increasing lightning-flash density. Therefore, discrete thresholds of lightning density could be applied in a rainfall estimation scheme to assign precipitation in specific rate categories.

Corresponding author address: Dr. Weixin Xu, Earth System Science Interdisciplinary Center, University of Maryland, College Park, 5825 University Research Court, College Park, MD 20740-3823. E-mail: wxinxu@umd.edu

Abstract

This study quantifies the relationships among lightning activity, convective rainfall, and associated cloud properties on both convective-system scale (or storm scale) and satellite-pixel scale (~5 km) on the basis of 13 yr of Tropical Rainfall Measuring Mission measurements of rainfall, lightning, and clouds. Results show that lightning frequency is a good proxy to separate storms of different intensity, identify convective cores, and screen out false convective-core signatures in areas of thick anvil debris. Significant correlations are found between storm-scale lightning parameters and convective rainfall for systems over the southern United States, the focus area of the study. Storm-scale convective rainfall or heavy-precipitation area has the best correlation (coefficient r = 0.75–0.85) with lightning-flash area. It also increases linearly with increasing lightning-flash rate, although correlations between convective/heavy rainfall and lightning-flash rate are somewhat weaker (r = 0.55–0.75). Statistics further show that active lightning and intense precipitation are not well collocated on the pixel scale (5 km); for example, only 50% of the lightning flashes are coincident with heavy-rain cores, and more than 20% are distributed in light-rain areas. Simple positive correlations between lightning-flash rate and precipitation intensity are weak on the pixel scale. Lightning frequency and rain intensity have positive probabilistic relationships, however: the probability of heavy precipitation, especially on a coarser pixel scale (~20 km), increases with increasing lightning-flash density. Therefore, discrete thresholds of lightning density could be applied in a rainfall estimation scheme to assign precipitation in specific rate categories.

Corresponding author address: Dr. Weixin Xu, Earth System Science Interdisciplinary Center, University of Maryland, College Park, 5825 University Research Court, College Park, MD 20740-3823. E-mail: wxinxu@umd.edu

1. Introduction

Precipitation plays a key role in the earth’s climate system, particularly in the aspect of its water and energy balance. Accurate rainfall estimation is of fundamental importance to climate research, flood watches and warnings, short-term precipitation forecasting, water resources, model evaluation, and so on (Hong et al. 2007; Ebert et al. 2007). Conventional rain gauge measurements are precise but are limited by their sparse distribution and unavailability in remote areas such as mountains, oceans, and tropical rain forests. Meteorological radars have greater spatial resolution and cover larger areas than gauges, but they have their own limitations: ground clutter (e.g., urban, mountains, and forests), attenuation problems, nonuniform beam fillings, and precipitation-regime-dependent reflectivity–rainfall (ZR) relationships (Joss and Waldvogel 1990; Yuter 2002). Although some polar-orbiting satellites carrying passive and even active microwave sensors offer fine-spatial-resolution rainfall estimates with significant accuracy, they overpass the same location only 2 times per day (Kidd et al. 2003; Joyce et al. 2004). In contrast, geosynchronous satellites with infrared (IR) instruments provide cloud, surface, and moisture information at high temporal resolution (~30 min) for a variety of applications (e.g., estimating rainfall), although IR-based algorithms are limited by “seeing” only the cloud tops because of the limitations of IR frequencies (Arkin 1979; Negri and Adler 1981; Vicente et al. 1998; Kuligowski 2002). These geostationary satellite-based rainfall estimates, although retrieved indirectly from the cloud tops, are uniquely complementary to estimates from gauge, radar, and polar-orbiting satellite measurements because of their high temporal resolution, which is important for diagnosing the highly variable evolution of rain systems (Vicente et al. 1998; Kuligowski 2002).

Clouds with cold tops in the IR imagery are generally associated with deeper clouds and greater precipitation depth and thus more rainfall than those with warmer tops (Arkin 1979; Negri and Adler 1981; Arkin and Meisner 1987). Therefore, techniques that are based on IR cloud-top temperature are used to retrieve surface rainfall (Griffith et al. 1978; Scofield 1987; Adler and Negri 1988; Goodman et al. 1994; Kuligowski 2002). In practice, additional factors such as environmental moisture, cloud growth, and cloud-top structure (e.g., temperature gradients) may be considered to separate convective rain from stratiform precipitation or nonraining cirrus clouds (Negri and Adler 1981; Adler and Negri 1988; Vicente et al. 1998). In addition, The International Satellite Cloud Climatology Project uses both IR and visible measurements to differentiate convective clouds from cirrus (Rossow and Schiffer 1991). Infrared retrievals still can be confused by the presence of thin cirrus clouds and nonprecipitating cold cloud anvils of mesoscale convective systems (MCS), however, resulting in erroneous surface rainfall estimates (Anagnostou et al. 1999) or even mislocated convective-rain regions. The IR-based techniques may misrepresent linear convective features, may falsely treat extremely cold cirrus clouds as active convection, and may miss convective cores under large cold cloud shields (Adler and Negri 1988; Vicente et al. 1998). These techniques may completely miss or underestimate rainfall produced by warm-rain systems in which cloud tops are relatively warm but rainfall is heavy. To address these issues, additional storm information, especially precipitation structure and microphysics-related information, should be considered. Calibration of IR-based techniques by microwave observations may improve the retrievals (Sorooshian et al. 2000; Todd et al. 2001; Kuligowski 2002; Kidd et al. 2003) but is limited by large gaps between overpasses and missing features in either the IR or microwave data. Lightning information, especially if available at a similar time resolution, should be a complementary additional (to the IR) factor in estimating convective-system rainfall because of its direct association with convection intensity and cloud microphysics (Zipser 1994; Toracinta et al. 2002; Petersen et al. 2005; Williams and Stanfill 2002; Williams et al. 2002; Altaratz et al. 2010; Yuan et al. 2011).

The next-generation series of the Geostationary Operational Environmental Satellite (GOES-R; launches in 2015) will carry an Advanced Baseline Imager (ABI, including IR channels; Schmit et al. 2005) and the first-ever Geostationary Lightning Mapper (GLM; Christian 2008). GLM will monitor the total lightning (both in cloud and cloud to ground) activity with a near-uniform spatial resolution of approximately 8 km continuously day and night over the Americas and adjacent ocean regions (Christian 2008). In addition to helping to improve severe-thunderstorm forecasts and warnings, GLM will provide additional microphysics-related storm information (lightning activity) for potential use in improving geostationary satellite–based rainfall estimates in combination with ABI (on the same platform) data.

Numerous studies have documented close relationships between lightning activity and convective precipitation (or convective properties). In short, the initiation of charge separation in thunderstorms requires the development of a robust ice-phase region in either noninductive (Takahashi 1978; Saunders 1993, 2008; MacGorman and Rust 1998) or inductive (Brooks and Saunders 1994; Saunders 2008) charging mechanisms. Abundant precipitation-sized ice particles, small ice crystals, and supercooled liquid water are observed in lightning-active clouds (Stolzenburg et al. 1998; Lang and Rutledge 2002; Atlas and Williams 2003; MacGorman et al. 2005). As a result, lightning frequency is roughly proportional to the ice flux or content (precipitation size and ice crystals) in the charging zone (Baker et al. 1999; Blyth et al. 2001; Deierling et al. 2005; Petersen et al. 2005; Gauthier et al. 2006; Sherwood et al. 2006) or cold cloud depth (Ushio et al. 2001; Price and Federmesser 2006; Xu et al. 2010; Liu et al. 2012). Since the melting of a large amount of precipitation-size ice particles will produce heavy rain at the ground, a strong positive correlation between lightning frequency and convective precipitation is expected, especially in warm-season continental regimes whose rainfall is mostly contributed by ice-based precipitation processes (Rosenfeld and Lensky 1998; Petersen and Rutledge 2001; Williams and Stanfill 2002; Phillips et al. 2007). In fact, observational studies have shown well-defined, although regime-dependent, correlations (Zipser 1994; Petersen and Rutledge 1998) between convective rainfall and lightning, both for individual or ensemble storms (Soula and Chauzy 2001; Seity et al. 2001) and for long temporal periods and large spatial domains (e.g., Sheridan et al. 1997; Petersen and Rutledge 1998; Soriano et al. 2001).

Lightning–rainfall relationships have further been employed for estimation of convective rainfall (Tapia et al. 1998; Grecu et al. 2000; Morales and Anagnostou 2003; Chronis et al. 2004). For example, Tapia et al. (1998) designed a simple model using the lightning–rainfall ratio (or rain yield) to derive rain rate at every 10-km-diameter circle using cloud-to-ground lightning-flash information in Florida. Grecu et al. (2000) combined surface-based lightning and GOES IR information to identify convective cores through defining lightning clusters and assigned rain-rate values. This first, relatively simple, lightning-enhanced scheme reduced bias by 15% on rain volume estimates relative to an IR-only scheme. Morales and Anagnostou (2003) developed a more comprehensive rainfall retrieval algorithm and reduce the overall bias of IR-only rainfall estimates by 31% in selected samples. Chronis et al. (2004) similarly developed a technique using surface-based lightning and satellite IR measurements over Europe to estimate rain volume and rain rate for cloud features (255-K isotherm) resulting in 25%–40% improvements over IR-only retrievals. These earlier studies confirm that IR-based rainfall retrievals could be significantly improved by including lightning information.

These previous lightning-enhanced IR schemes provide a foundation for this work but are based on cloud-to-ground lightning, which is a small fraction of total lightning, and that fraction can vary greatly with storm type and evolution. Our long-term goal is to develop an IR–lightning rainfall estimation scheme applicable for use with GOES-R sensors, including the GLM optical sensor, which measures all types of lightning. A new scheme is needed that is based on sufficient statistics, well-defined lightning–rainfall relationships (at least over specific regions), and lightning and IR measurements on the same platform. Since the Tropical Rainfall Measuring Mission (TRMM) satellite contains similar IR channels and a lightning sensor similar to the GOES-R GLM, TRMM measurements are ideal for aiding in the development of a prelaunch GOES-R lightning-enhanced IR rainfall algorithm.

The objective of the current study is to better understand and quantify relationships between lightning and convective rainfall in the context of a potential IR–lightning coupled rainfall algorithm for GOES-R. Lightning–rainfall relationships are carefully examined on both the convective-system scale (100–1000 km) and on the satellite-pixel scale (5–20 km) using 13 yr of TRMM measurements. This paper first investigates how lightning information can be used to help to discriminate storms, identify systems with convective cores, and remove false IR-defined intense convective features or heavy precipitation. The analysis focuses on the continental United States (CONUS) but also examines South America, tropical oceans, and tropical continents. Lightning-flash rates and lightning-flash areas of precipitation systems are directly related to convective volume rainfall, convective area, and convective rain-rate for lightning-producing precipitation systems over the CONUS. Relationships between lightning-flash rate and precipitation intensity are further studied for different spatial resolutions. How these lightning–rainfall relationships could be applied in an IR–lightning coupled rainfall algorithm is discussed.

2. Data and method

a. TRMM satellite measurements

This study examines 13 yr (1998–2010) of TRMM measurements. The TRMM satellite houses four functioning instruments (Kummerow et al. 1998), including the precipitation radar (PR), TRMM Microwave Imager (TMI), Lightning Image Sensor (LIS), and Visible and IR Scanner (VIRS). The PR provides three-dimensional storm information (radar returns) at approximately 5-km horizontal and 250-m vertical resolution. Since radar reflectivity is directly associated with hydrometeor size, it provides an excellent proxy for convective strength, precipitation intensity, and rain type. The LIS monitors lightning activity in a 600 km × 600 km area during a period of 40–90 s with a footprint of ~5 km and a temporal resolution of 2 m s−1 (Christian 1999). LIS is an optical sensor that measures radiance from the earth and the clouds below the satellite. The LIS algorithm separates lightning events (5 km; 2 m s−1) with strong irradiance from the background and defines lightning flashes as clusters of adjacent events that occur within 330 m s−1. LIS detects ~90% of all lightning flashes within its field of view (FOV) during nighttime, but the detection efficiency decreases to ~70% near local noon (Boccippio et al. 2000). The GOES-R GLM will operate very similarly to LIS, except that the GLM is a staring sensor with a broader FOV (13 000 km × 13 000 km) and coarser resolution (8 km). Since the TRMM IR radiometer and GOES-R ABI detect clouds using common channels (10.5–12.6 μm), a TRMM lightning–IR combined rainfall algorithm should be a good approximation of future GOES-R capabilities.

b. Analysis on the convective system scale

Lightning–rainfall relationships are first examined on the convective-system scale or storm scale, using the TRMM precipitation-feature (PF) database (Liu et al. 2008). PFs are identified as contiguous raining areas near the surface and are derived from the PR. For each PF, measurements from different instruments (with different footprints) are collocated and grouped into its PR pixels through the adjacent-pixel method and parallax correction (Liu et al. 2008). In other words, a PF includes not only three-dimensional radar reflectivity measurements but also the TMI microwave ice scattering signatures, LIS lightning observations, and VIRS IR cloud-top temperatures. PFs can be individual convective cores but are usually raining areas with multiple convective cores and associated stratiform regions.

This study selects a suite of PF parameters to serve as proxies for various storm properties. These PF parameters include area (or volume) of convective rain, maximum radar reflectivity at certain altitudes, and the maximum height (or echo top) of 20-, 30-, and 40-dBZ radar reflectivity values. The 20-dBZ echo top indicates the highest level to which the updraft is lofting precipitation-size ice particles. The higher the echo top is, the deeper is the convection (Liu and Zipser 2005). Along the same line, the 30- and 40-dBZ echo tops are indicative of convective intensity (Liu et al. 2008, 2012). Convective systems with 40-dBZ radar echoes reaching the mixed-phase altitude (from −10° to −25°C) are very likely to produce lightning (Dye et al. 1989; Williams et al. 1992; Xu et al. 2010; Liu et al. 2012). The PF information also includes the minimum polarized corrected temperature (PCT) at 85 GHz, which is defined as PCT85 = 1.82T85v − 0.82T85h, where v indicates vertically polarized and h is horizontally polarized. The 85-GHz PCT depends on the scattering of upwelling radiation by the lofted column of ice, which is often expressed as ice water content integrated over a depth, or ice water path (Vivekanandan et al. 1991).

The PFs also contain LIS information such as lightning-flash rate and illuminating area. Lightning flashes that occur within an individual PF during the LIS viewing time are attributed to that feature. The LIS instrument views each ground location with a different view time (up to 90 s). A feature’s flash rate is defined as the total flash count divided by the viewing time. The lightning-flash (or illuminating) area is defined as the total area of pixels with at least 1 flash and is calculated for different pixel resolutions, that is, 5, 10, 15, and 20 km. In reality, an individual lightning flash extends across about 10–15 km.

This study only examines PFs that are larger than 200 km2. Lightning features are PFs with at least 1 flash per minute (abbreviated hereinafter as fl min−1), and no-lightning features have no lightning flashes during the LIS observation. Table 1 lists PF sample sizes for different regions of interest. These regions include the United States (30°–35°N; 80°–120°W), South America (SAM; 30°S–0°; 40°–80°W), land only (covering the whole globe from 30°S to 30°N) and ocean only (covering the whole globe from 30°S to 30°N). The land dataset used in this study is limited to the warm season (April–October), and the oceanic dataset is limited to Northern Hemisphere summer (June–August).

Table 1.

Samples of PFs above certain criteria in different studied regions during specific periods.

Table 1.

c. Analysis on the satellite-pixel scale

Quantifying storm-scale relationships between lightning and convective rainfall (using the PF database) helps to identity convective cores and define convective rain area. Allocating convective core area to specific pixels and determining pixel precipitation rate require the examination of lightning–rainfall relationships on the satellite-pixel scale (~5 km). The TRMM PR and LIS data both have ~5-km horizontal resolution, and their common FOV pixels are collocated in this study. A total of ~2 million raining pixels from about 5000 lightning PFs at full (~5 km) resolution are selected over the CONUS during the warm season. Since the location of active lightning and heavy precipitation may not exactly match at such a small scale, the radar and lightning data are also degraded to 10-, 15-, and 20-km scales for additional analyses.

3. Storm discrimination by lightning information

Vigorous updrafts (or intense convection) are essential to set up the favorable environment for charge separation, that is, abundant hail/graupel, small ice particles, and supercooled liquid droplets. Therefore, active lightning is a good indicator of intense convection (Zipser 1994; Zipser et al. 2006), and the updraft–lightning relationships in specific regimes have further been quantitatively examined (Lang and Rutledge 2002; Tessendorf et al. 2005; Deierling and Petersen 2008). This section investigates how lightning information could serve to separate convectively intense storms from their weaker counterparts and eventually help to identify clouds with strong convection.

a. Storm properties of lightning and no-lightning systems

Figure 1 illustrates the occurrence of lightning and no-lightning storms as functions of various storm properties. In general, storms with lightning are clearly separated from those without any lightning in terms of precipitation tops (maximum 20-dBZ height; Fig. 1a), intense echo tops (maximum 30-dBZ height; Fig. 1b), ice scattering signature (minimum PCT of 85 GHz; Fig. 1c), and cloud-top temperature [minimum IR brightness temperature (Bt); Fig. 1d]. Most lightning features have precipitation-size hydrometeors (20 dBZ) above 10 km, but this condition occurs in less than 5% of no-lightning storms (Fig. 1a). The presence of large precipitation particles (30 dBZ; Fig. 1b) at or above the deep mixed-phase (e.g., 8 km) level and the total column ice content (minimum 85 PCT; Fig. 1c) also reveal a clear separation between the lightning and no-lightning storms. The lightning and no-lightning storm groups have somewhat larger overlaps (about 30%) in terms of cloud-top temperature (minimum IR; Fig. 1d), however. For example, more than 10% of no-lightning storms have cloud tops above the −60°C (213 K) altitude. This set of storms likely includes decayed MCSs that have anvil debris at high altitudes but no strong updrafts to lift hail or graupel for charge separation. It is very likely that the fact that these decaying MCSs have extremely cold Bt but have no strong convection could potentially confuse an IR-based rain algorithm. Section 3b will demonstrate how this set of storms can be discriminated from regions of heavy precipitation or intense convection.

Fig. 1.
Fig. 1.

Occurrence frequency of precipitation features categorized by (a) maximum height of 20-dBZ radar echo, (b) maximum height of 30-dBZ radar echo, (c) minimum PCT at 85 GHz frequency, and (d) minimum IR Bt. Red lines represent lightning-producing storms, and blue lines represent storms without any lightning flashes.

Citation: Journal of Applied Meteorology and Climatology 52, 1; 10.1175/JAMC-D-12-040.1

b. Occurrence of heavy precipitation under cold cloud shields

A key objective of this study is to understand whether and how lightning information can be used, in combination with IR data, to identify deep convective elements concealed by thick cirrus anvils (mainly associated with mature convective complexes). To address this question, features with very cold cloud tops (colder than −60°C) are selected for study. Figure 2 shows the frequency of features as functions of precipitation intensity (Fig. 2a) and intense echo tops (Fig. 2b) under these cold precipitating clouds. Note that heavy precipitation [by reflectivity decibels (dBZ)] indicates at least four radar pixels reaching that reflectivity threshold value. Under no-lightning cold cloud shields, moderate-precipitation cores (e.g., 25–30 dBZ) occur frequently but heavy-precipitation cores (>45 dBZ) are rare (Fig. 2a). Conversely, lightning-producing cold cloud shields may often conceal heavy surface precipitation (45–50 dBZ). Evident contrast is also found on the occurrence of intense convection (e.g., 40 dBZ above 6 km) between cold clouds with and without lightning. For example, the cumulative occurrence frequency of 40 dBZ above 6 km for the lightning cold clouds is greater than 50%, whereas it is only a few percent for no-lightning cold clouds. All these results are consistent with the general lack of lightning in weaker convection (Zipser 1994; Zipser et al. 2006). These results also suggest that lightning information is potentially very useful in identifying convective cores or screening out false IR signatures in the presence of thick anvil cloud. It is unlikely that extremely cold cloud shields without lightning would conceal extreme precipitation, especially during the warm season over the continents where ice-based precipitation processes dominate.

Fig. 2.
Fig. 2.

Occurrence frequency of heavy precipitation or intense convection in very cold precipitation features (minimum IR Bt < −60°C or 213 K): (a) near-surface radar reflectivity (area > 100 km2) and (b) maximum height of 40-dBZ radar echo. Red lines represent lightning-producing storms, and blue lines represent storms without any lightning flashes.

Citation: Journal of Applied Meteorology and Climatology 52, 1; 10.1175/JAMC-D-12-040.1

c. Identification of convective cores by lightning information

As has been mentioned, IR-based rain estimation techniques may treat very cold cirrus clouds as having heavy and convective rainfall and may have difficulty in defining convective cores under large cold cloud shields. To address this issue, we directly define convective cores (or precipitation cores) inside precipitation systems (PFs) using TRMM PR measurements. Four types of precipitation cores (near-surface radar reflectivity areas larger than 100 km2) are defined: 1) cores of convective rainfall as determined by the TRMM PR rain-type algorithm (2A23; Awaka et al. 1997), 2) cores of echoes > 35 dBZ, 3) cores of echoes > 40 dBZ, and 4) cores of echoes > 45 dBZ. All PFs are then stratified by precipitation core type and lightning frequency (flash rate) to determine occurrence frequency.

In general, lightning activity is a good indicator of storms with convective cores (Fig. 3). Furthermore, higher lightning-frequency thresholds help to isolate more intense convective cores. If one focuses on the United States (Fig. 3a), it is seen that less than 40% (5%) of no-lightning storms contain convective precipitation cores (heavy-precipitation cores: 40- or 45-dBZ cores). Thus, storms with significant areas of heavy precipitation are unlikely in the absence of lightning. Conversely, more than 90% of lightning-producing storms (at least 1 fl min−1) contain convective rain or 35-dBZ precipitation cores. Of all precipitation systems with lightning-flash rate greater than 5 fl min−1, approximately 90% contain heavy-precipitation areas (>40 dBZ). Since these lightning–convective core relationships are very similar for the other geographical regions (Figs. 3b–d), lightning frequency seems to be of great value for identifying storms with convective cores. There are some cases in which convective cores or areas of heavy precipitation could be missed by using lightning alone, however. Storms having strong convection and precipitation intensity occur without producing lightning, especially in the oceanic or monsoon regimes (Williams and Stanfill 2002; Williams et al. 2002; Xu and Zipser 2012). Alternatively, 10% of total lightning occurs in the stratiform-precipitation or cloud-anvil region (Peterson and Liu 2011). Thus, even though identification of heavy-rain areas associated with convection by lightning-only methods does have limitations and exceptions, the statistics indicate a very strong connection.

Fig. 3.
Fig. 3.

Occurrence frequency of precipitation features with different precipitation cores (near-surface radar reflectivity areas > 100 km2). Gray, blue, and red histograms represent precipitation features without any lightning, storms that have at least 1 fl min−1, and storms that produce at least 5 fl min−1, respectively.

Citation: Journal of Applied Meteorology and Climatology 52, 1; 10.1175/JAMC-D-12-040.1

4. Correlations between lightning and rainfall on the convective system scale

a. Overview

Many studies have reported close relations between lightning frequency and convective rainfall, in terms of rain yield per flash or correlations (Sheridan et al. 1997; Petersen and Rutledge 1998; Soula and Chauzy 2001; Seity et al. 2001). Correlation coefficients r between total rainfall and lightning frequency over a region (or in storms) typically range from 0.4 to 0.7, depending on the rainfall regime. The best and least-variant lightning–rainfall correlations are found over continental regions during the warm season. If one considers only large precipitation systems, the correlation between lightning frequency and rainfall volume could reach 0.8 over a specific region (Grecu et al. 2000). Most of the aforementioned studies are based on limited samples, however, especially those on the storm scale. The current study examines a large number of precipitation systems to better quantify lightning–rainfall relationships.

Relations between lightning frequency and convective volume rainfall for the PFs are nonlinear, exhibiting a power-law relation (exponents of 0.41–0.77; Fig. 4). To be specific, convective volume rainfall increases with increasing lightning-flash rate following a power-law function that is very similar for continental systems at different locations (Figs. 4a–c). The power-law exponent is smaller for oceanic systems, however (Fig. 4d). Note that high-flash-rate ocean events typically occur very near land (Zipser et al. 2006). Convective volume rainfall in oceanic systems also has a somewhat weaker correlation with lightning. Weaker lightning–rainfall relationships within maritime precipitation systems have been reported by many others (Zipser 1994; Toracinta et al. 2002; Williams and Stanfill 2002; Xu et al. 2010). The power-law model shows a good fit between the mean convective volume rainfall and lightning frequency over land, exhibiting smaller deviations from mean values than over ocean. This land–ocean difference seems reasonable since ice-based precipitation processes dominate over land while warm-rain processes have more contribution over ocean. Different microphysical processes within different climate regimes may influence the lightning–rainfall relationships. For example, the Amazonian forest and oceanic convection may produce very heavy rainfall but little lightning because of dominant warm-rain microphysical process (raindrop size increases below the freezing level). Clean conditions (fewer cloud condensation nuclei) and less CAPE (and thus weaker updrafts) are thought to contribute to these particular microphysical processes (Williams and Stanfill 2002; Williams et al. 2002). The increase of aerosol under these conditions may invigorate the intensity of convection (updrafts) and enhance the lightning activity (Altaratz et al. 2010; Yuan et al. 2011).

Fig. 4.
Fig. 4.

Convective volumetric rainfall as a function of lightning-flash rate for precipitation systems over different regions. Filled diamonds are mean values, and the error bars are ±1 std dev.

Citation: Journal of Applied Meteorology and Climatology 52, 1; 10.1175/JAMC-D-12-040.1

The previous section shows a strong correlation between lightning and convection intensity; we note, however, that convective strength (indicated by convective proxies) is not always equivalent to precipitation intensity at the surface. Relationships between rainfall intensity and convective proxies may vary by rainfall regimes and storm microphysics. For example, maritime clouds can produce intense precipitation events with warm-rain processes while the convective strength remains very weak. Stratiform-rain intensity can also be very high, despite the lack of strong convection or ice-based processes. The following section analyzes lightning and rainfall relationships in the warm season when most rainfall is contributed by ice-based processes; thus, better relationships between convective strength and precipitation intensity exist. Again, lightning information may not have a perfect or near-perfect relation to rainfall, but it can complement and improve cloud information used in rainfall estimation from geostationary satellites, especially in the definition of intense convection/heavy rain.

b. Lightning information in determining convective area

Overall relationships between lightning frequency and volume rainfall alone are not sufficient for use in IR–lightning algorithm development. Quantified relationships between lightning activity and convective area (or heavy-precipitation area) on the storm scale are also required (Grecu et al. 2000; Morales and Anagnostou 2003; Chronis et al. 2004). As stated previously, large cold IR clouds typically associated with MCSs (see example in Fig. 5a) make it difficult to identify convective cores using IR information alone. A typical MCS often contains convective or heavy-precipitation cores that are concealed by the cold cloud shield (Figs. 5b,c). Ice-based microphysical processes within convective cores very often are active enough to produce lightning flashes (Fig. 5d). Lightning occurs in both convective and stratiform precipitation areas, but the greatest lightning frequencies correspond most strongly to heavy precipitation. Therefore, lightning information (i.e., flash rate, flash density, and flash area) may help IR-based techniques better delineate convective and stratiform regions.

Fig. 5.
Fig. 5.

A convective precipitation system observed by TRMM over the Great Plains (34.6°N, 91.2°W) at 0128 UTC 12 Jun 2003: (a) cloud cover defined by IR Bt, (b) radar reflectivity near the surface, (c) rain types defined by radar algorithm (2A23), and (d) lightning-flash density (spots in 10-km resolution).

Citation: Journal of Applied Meteorology and Climatology 52, 1; 10.1175/JAMC-D-12-040.1

Figure 6 shows correlations between lightning-flash rate and convective area for different precipitation intensity levels over CONUS. Since lightning-flash rate within a precipitation system is associated with both convective area and intensity, it demonstrates a significant positive correlation with convective area (Xu et al. 2010; Liu et al. 2011). Lightning-flash rate is best correlated with areas of extremely heavy precipitation (>45 dBZ). This result is consistent with previous studies: lightning frequency is best correlated with areas of active ice processes (Deierling et al. 2005; Xu et al. 2010; Liu et al. 2011), and large amounts of large ice particles at the mixed-phase levels caused by active ice processes will eventually fall and turn into heavy rain at the ground. The correlation coefficient between lightning frequency and convective area is less well defined (r = 0.4–0.7), however. Two factors may contribute to this: 1) storm complexes with large convective regions may only contain some smaller, stronger cells that have the ability to produce lightning and 2) some small convective cells may still have strong updrafts and thus high lightning frequency. Therefore, although correlations are stronger for higher reflectivity (and rain rate), there are limitations in using lightning-flash-rate information alone to estimate convective area.

Fig. 6.
Fig. 6.

Scatter diagrams of lightning-flash rate vs area of precipitation cores: (a) radar-defined convective rain (2A23), (b) radar echoes > 35 dBZ, (c) radar echoes > 40 dBZ, and (d) radar echoes > 45 dBZ. Blue digits (R values) are the correlation coefficients.

Citation: Journal of Applied Meteorology and Climatology 52, 1; 10.1175/JAMC-D-12-040.1

This section further examines the relation between lightning-flash area and convective-rain area (Fig. 7). Lightning-flash area is defined as the area of pixels (10 km) with at least one flash within precipitation features. Lightning-flash area is also calculated for different pixel resolutions, that is, 5, 15, and 20 km. In general, lightning-flash area (Fig. 7) is much better correlated with the core area of convective/heavy rainfall than is lightning-flash rate (Fig. 6). Results show that convective area best relates to lightning-flash area for 10–15-km resolution (10-km results are shown in Fig. 7). In general, lightning-flash area shows a significant linear correlation with convective core size (r = 0.75–0.85). For example, the area of convective rainfall Y could be quantitatively derived by flash area X with a function of Y = 310 + 1.48X. In specific terms, the defined lightning area underestimates the area of convective rainfall or moderate precipitation (Figs. 7a,b) but overestimates the size of regions with very heavy precipitation (Figs. 7c,d). These results suggest that lightning-flash area could be used to estimate the area of convective cores through statistically defined functions (e.g., linear).

Fig. 7.
Fig. 7.

As in Fig. 6, but for lightning-flash area (10-km resolution) vs area of precipitation cores.

Citation: Journal of Applied Meteorology and Climatology 52, 1; 10.1175/JAMC-D-12-040.1

5. Pixel-by-pixel lightning–rainfall relationships

This last section moves away from the convective-system or storm scale using the PF database and examines lightning–rainfall relationships on the pixel scale. These finer-scale analyses are important for potential rain-estimation applications because they improve our understanding of how to distribute convective area and assign rain rate pixel by pixel (Grecu et al. 2000; Morales and Anagnostou 2003). Therefore, this section focuses on relationships between precipitation intensity and lightning activity on the pixel scale.

a. Collocations of lightning and precipitation

As shown previously in this paper, lightning activity and convective rainfall are closely collocated and show a clear positive correlation on the convective-system scale (Figs. 57). Recall that lightning frequency is roughly proportional to the ice flux in the mixed-phase region of a storm (Baker et al. 1999; Blyth et al. 2001; Petersen et al. 2005; Deierling et al. 2005) and that intense convection can support strong ice flux, lightning activity, and heavy precipitation in a given storm. The remaining question is whether similar lightning–rainfall relationships can be found on the pixel scale.

Figure 8 provides examples and statistics of the collocation of lightning and precipitation on the pixel scale. In general, intense-precipitation regions (indicated by high radar reflectivity) are generally collocated with the regions of frequent lightning flashes (Fig. 8). Some strong radar echoes only correspond to occasional lightning, and others have no lightning flashes (white circles in Figs. 8a,b). In contrast, some relatively weak precipitating or nonraining regions are collocated with substantial numbers of lightning flashes (black circles in Figs. 8a,b). Figure 8c presents statistics that are based on ~2 million raining pixels at 5-km resolution and shows that 85% of lightning flashes are located in regions of convective rain. Only 50% of lightning flashes are collocated with heavy rainfall (>40 dBZ), and more than 20% of lightning flashes occur in nonconvective or light-rain areas (i.e., <25 dBZ). Most nonconvective flashes occur as charged ice particles are advected out of the convective core and charge separation is initiated in the nearby stratiform/anvil region (Dye et al. 2007; Peterson and Liu 2011). Additional situations may also contribute to the lightning–rainfall displacement. For example, deep reflectivity cores are often tilted in strongly sheared thunderstorms. As a result, lightning flashes might not match up directly with precipitation at the surface. In addition, strong updrafts that loft large precipitation particles to midtroposphere can prevent those particles from falling directly beneath the lightning centroid. In the “lightning holes” situation, the updraft can be too strong to allow precipitation-particle generation, significant charge separation, or precipitation fallout. Therefore, it is difficult to define a clear positive function between lightning-flash rate and rain intensity on the PR pixel scale (5 km). We suggest that pixel-scale relationships between lightning-flash rate and rain intensity should improve at coarser resolution (e.g., 10, 15, or 20 km), and this possibility is explored below.

Fig. 8.
Fig. 8.

(a),(b) Two convective systems in terms of radar pixels (shaded) and lightning spots (black dots); white circles indicates regions with high reflectivity but no lightning, and black ellipses mark regions with low reflectivity but frequent lightning. (c) Statistics of lightning flashes’ location related to radar reflectivity on the basis of samples of 220 939 lightning flashes and 2 038 774 radar raining pixels.

Citation: Journal of Applied Meteorology and Climatology 52, 1; 10.1175/JAMC-D-12-040.1

b. Correlations between lightning frequency and rain intensity

Figure 9 presents the lightning-flash rate as a function of mean near-surface radar reflectivity at 5-, 10-, 15-, and 20-km resolutions. The correlation coefficients between lightning frequency and radar reflectivity are poor (r = 0.2–0.3), and the finer the pixel resolution is, the poorer the correlation is. Unlike at the convective-system scale in the previous sections, a continuous positive function, either linear or power law, cannot be defined for lightning frequency and precipitation intensity on the pixel scale. Probably because of this fact, Morales and Anagnostou (2003) apply probabilistic relationships rather than a continuous function to assign pixel rainfall rates from lightning information. Robust lightning activity (i.e., high flash rates) occurs mainly in the heavy-precipitation region (high reflectivities), however, especially on the 15–20-km scales. The lightning-frequency peak for intense echoes (40–50 dBZ) is weak on the original PR/LIS scale (5 km). At a coarser scale (15–20 km), however, regions with lightning flashes have a greater probability of heavy rainfall. This situation suggests that lightning often occurs in the vicinity of convective cores but is not always exactly collocated with the strongest reflectivity. Therefore, when lightning occurs within both the heavy-rain and light–moderate-rain regions, the larger pixel (e.g., 15 vs 5 km) could smooth edges between convective cores and a surrounding stratiform region.

Fig. 9.
Fig. 9.

Scatter diagrams of lightning-flash rate vs mean radar reflectivity in grids with different horizontal resolution: (a) 5, (b) 10, (c) 15, and (d) 20 km. The correlation coefficients are given by the R values. The contours indicate number of density.

Citation: Journal of Applied Meteorology and Climatology 52, 1; 10.1175/JAMC-D-12-040.1

c. Probability of precipitation in specific intensities

Since continuous functions could not be derived to estimate rain rate from lightning frequency on the pixel scale, we next examine a probabilistic approach (Calheiros and Zawadzki 1987; Morales and Anagnostou 2003). Figure 10 shows the occurrence probability of precipitation intensity (i.e., radar reflectivity) as a function of lightning-flash density at different spatial resolutions. In general, the occurrence probability of heavy precipitation increases with increasing lightning-flash density. For a common lightning-flash density, coarser-scale pixels have a greater probability of heavy precipitation. Discrete functions could be defined between lightning density and precipitation intensity on the basis of probabilistic relationships. For example, pixels (15- or 20-km scale) with 2, 4, 10, or 20 fl min−1 (100 km2)−1 would have a 95% probability of having rain intensity equal to 30, 35, 40, or 45 dBZ, respectively. Note that occurrence probability on finer-scale pixels (5 or 10 km) does not converge to a significant level (95%). These results suggest the use of probabilistic methods at coarser resolutions (e.g., 15 or 20 km) for developing the lightning-enhanced rainfall algorithm.

Fig. 10.
Fig. 10.

Probability of occurrence of mean radar reflectivity in grids with different resolution that reaches specific values: (a) 30, (b) 35, (c) 40, and (d) 45 dBZ. Probability is shown as a function of lightning-flash density.

Citation: Journal of Applied Meteorology and Climatology 52, 1; 10.1175/JAMC-D-12-040.1

6. Summary, conclusions, and discussion

This study aims to better quantify relationships between lightning activity and convective rainfall (or heavy rainfall) on both convective-system (storm) scale and satellite-pixel scale for use in a blended IR–lightning rain-estimation technique. Lightning activity is linked to various aspects of convective rainfall, including storm properties, occurrence of convective cores, convective volume rainfall, area of connective rainfall, and rain intensity. The documented relationships between lightning activity and convective precipitation provide background for future development of lightning-enhanced IR rainfall estimates. This study examines 13 yr of radar, lightning, IR, and microwave measurements from the TRMM satellite, with the emphasis on the continental United States. More than 80 000 precipitation features over CONUS are thoroughly examined on various aspects of lightning–rainfall relationships. Over 1 million raining pixels are further analyzed to determine relationships between lightning frequency/density and precipitation intensity on different spatial scales.

a. Conclusions

Lightning storms are statistically different from no-lightning storms using convective proxies such as echo-top heights, radar echo intensity, and microwave ice-scattering signature. That same separation is weaker with regard to IR cloud-top temperature, however. Lightning also serves as a good proxy to discriminate between convective cores and anvil debris associated with mature and decaying mesoscale convective systems. Lightning frequency (or flash rate) also helps to identify clouds with convective cores. For example, storms with a frequency of 1 (5) fl min−1 have a 95% probability of being associated with convective rainfall (heavy precipitation > 40 dBZ).

Significant correlations are found between storm-scale quantities of lightning and convective rainfall for systems over CONUS. Both convective volume rain and convective area increase near linearly with increasing lightning-flash rate. Storm-scale lightning-flash area also has a well-defined linear relation with convective area (or heavy-rain area), and this correlation (r = 0.85) is much better than that between lightning-flash rate and convective area.

Statistics at the finer pixel scale (5 km) reveal that ~85% of lightning flashes are collocated with regions of convective rain, whereas only 50% of the lightning flashes collocate with heavy rainfall (>45 dBZ), and more than 20% of lightning flashes occur in nonconvective or light-rain areas. Also, a simple functional relation (e.g., linear or power law) could not be defined between lightning-flash rate and precipitation intensity on the pixel scale. Probabilistic relationships are found on the pixel scale, however, with the probability of heavy precipitation increasing with increasing lightning-flash density, especially for pixels averaged to a coarser resolution (~15 km). This analysis supports a conclusion that probabilistic distribution of the aforementioned lightning–rainfall relationships can be applied to estimate precipitation intensity.

b. Discussion and future work

Most previous studies have examined lightning–rainfall relationships in terms of regional total lightning (or cloud to ground) versus total rainfall (Sheridan et al. 1997; Petersen and Rutledge 1998; Soula and Chauzy 2001; Seity et al. 2001; Soriano et al. 2001) or of storm-scale lightning frequency versus rainfall volume (or intensity) on the basis of a limited number of cases (Grecu et al. 2000; Morales and Anagnostou 2003; Chronis et al. 2004). This study documents statistical relationships between lightning activity and convective rainfall on both the convective system and pixel scales to provide a basis for GOES-R lightning-enhanced IR rainfall estimation. Despite these differences, our results are generally consistent with those in the literature.

This study shows clear lightning–rainfall relationships and suggests that knowledge of these relationships could be applied to improve IR-based rainfall estimates. For example, certain lightning-frequency thresholds could be used to identify clouds with convective cores while helping to screen out thick cirrus cloud or cold-cloud debris that are not associated with intense convection or heavy precipitation. These techniques could be applied to GOES-R IR-defined cloud features (e.g., <235 K) to decrease the probability of defining false convective clouds (especially intense convection) in precipitation systems.

Lightning information can be used to define the area (or volume) of convective rainfall cloud by cloud (e.g., Grecu et al. 2000; Morales and Anagnostou 2003; Chronis et al. 2004). This study derives clear power-law functions between storm-scale area (or volume) of convective rainfall and lightning-flash area (or frequency) for systems over CONUS. Morales and Anagnostou (2003) found similar lightning–rainfall correlations on the basis of approximately 300 cloud features. The study presented here also quantifies relationships between lightning activity and large rain rates. These empirical relationships (or functions) will help IR-based techniques to better locate convective (or heavy rain) regions, especially for systems concealed by cold cloud shields without any overshooting features. Our results support previous findings that coupling lightning and IR information should lead to better rainfall estimates than using IR or lightning information alone (Grecu et al. 2000).

Following the identification of convective regions, the next step is to assign rain rate to individual pixels, which motivates our analysis of lightning–rainfall relationships on the pixel scale (5–20 km). Because lightning activity and convective rainfall (or heavy rain) are not well collocated on the pixel scale (5–20 km), however, well-defined correlations (or continuous functions) cannot be found between lightning frequency (or density) and precipitation intensity, although there is a strong correlation between precipitation-size ice mass in the mixed-phase region and lightning activity (Deierling et al. 2005; Gauthier et al. 2006; Xu et al. 2010). This lack of rainfall–lightning correlation on the finescale is related to advection of large-ice particles (associated with lightning) away from the main updraft into the stratiform anvil and/or a strongly tilted deep convective core (Zipser 1977; Houze 1989). In general, at the ~5-km scale, locations of the mixed-phased region rich in large-ice particles (also lightning locations) do not necessarily match the region of heavy surface rainfall at this scale. Therefore, although positive continuous functions (e.g., linear or power law) cannot be defined between lightning-flash rate and rain rate, useful probabilistic relationships are found, especially at coarser spatial resolutions (15–20 km). We suggest a probabilistic approach may be efficient enough to discretely define pixel rain rate at this resolution. For examples, lightning-density thresholds of 2, 4, 10, and 20 fl min−1 (100 km2)−1 correspond to mean pixel precipitation intensity (in radar reflectivity) of 30, 35, 40, and 45 dBZ, respectively, with a probability of greater than 95%.

Despite our thorough analysis of lightning–rainfall (convective) relationships for precipitating clouds over the southern CONUS, additional aspects will be considered in future studies. For example, clouds observed by both the TRMM and GOES satellites will be further analyzed to expand our current findings and to determine their applicability for a future GOES-R rainfall algorithm. Also, additional rainfall regimes will be examined (e.g., oceanic regimes, monsoon regimes, and South America) to explore regime-dependent variability of lightning–rainfall relationships. Last but not least, we may also consider the storm life history such as time lag between peaks of lightning and rainfall. Some studies show that there is lightning–precipitation lag ranging from −5 to 15 min on the storm scale (Tapia et al. 1998; Soula and Chauzy 2001; Gungle and Krider 2006). In the usual case, the stronger the convection intensity is (or the larger is the storm size), the larger is the time lag between the lightning peak and rainfall peak (Gungle and Krider 2006). This might be due to the fact that strong updrafts can prevent immediate fallout of precipitation-size ice particles or supercooled liquid drops from the mixed-phase region where lightning charges are generated. As compared with the life cycle of thunderstorms (e.g., MCSs; 60–120 min), the lag time (e.g., 10 min) is relatively short. In addition, most geostationary satellite rainfall estimates have a temporal resolution of ~15 min. Therefore, the lighting–rainfall time lag effect may be less important for the GOES-R rainfall estimates on storms with a relatively longer life cycle (e.g., MCSs). Storm evolution is certainly a factor to be considered in the future, however, especially when GLM observations are available.

In the near future, the information that we have gained from this study and previous studies in the literature will be applied to the initial development of an IR–lightning rain-estimation scheme using the VIRS and LIS data on TRMM and/or current geostationary IR data combined with ground-based lightning information. This approach is part of our overall effort to develop and test an approach applicable to the ABI and GLM data from the GOES-R satellite in a few years.

Acknowledgments

This research was supported by the NOAA GOES-R Risk Reduction (GOES-R3) program. Special thanks go to Professor Edward Zipser and Dr. Chuntao Liu at the University of Utah for providing the TRMM precipitation-feature dataset. We thank Dr. Daniel Cecil as well as two anonymous reviewers for their constructive reviews. The authors also thank Dr. Scott Rudlosky for providing helpful suggestions on the manuscript.

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