Introduction of Lightning into the GSMaP Rainfall Measurements through Optimized Power-Law Model
1. Introduction
Rain is an essential part of Earth’s processes that replenishes freshwater supply on the surface. A huge portion of agriculture worldwide depends on water supplied by naturally occurring rain. The amount of rain received within a period also determines how much volume of water dams will have and how wet or dry the soil will be. The great dependence of humans and animals on rainfall grounds the importance of monitoring and forecasting rainfall globally.
The most basic approach to monitor rainfall amount is by conventional rain gauges. While these rain gauges are usually well maintained by weather bureaus, their measurements can only represent rainfall within its immediate vicinity (Veloria et al. 2021). Moreover, rain gauges are usually absent in remote, mountainous areas due to difficulty in maintenance and data transmission. Considering this, the networks of rain gauges are frequently sparse or lack density in hard-to-reach areas.
Weather radars overcome the limitation of measuring rainfall only within the immediate vicinity by providing measurements within a radial range of up to a few hundred kilometers depending on the band used. Radars send out short pulses of electromagnetic waves and measure the backscattered waves when the pulses hit precipitation particles (Binetti et al. 2022). The radar reflectivity Z is mathematically related to the drop size distribution (DSD), which is the number of drops per unit volume of air as a function of drop diameter. Radar reflectivity may then be used to empirically derive precipitation rates using the Z–R relationship (Yamaji et al. 2020). Due to the spatial coverage and temporal consistency of measurements gained from radars, a radar network can simultaneously provide rainfall measurements on a national scale. However, precipitation observation by ground radars and rain gauges combined only covers about 25% of Earth’s surface, since most regions are covered with water or inland areas that are difficult to access [Earth Observation Research Center (EORC)-JAXA 2024]. Economic constraints in installing and maintaining radars also limit global radar coverage (Solimine et al. 2022).
Satellites measure precipitation through a top-down approach. Observing from space, satellites provide rainfall information at wider spatial coverage than rain gauges and radars. Because it measures precipitation from above, satellites can acquire data even in remote, mountainous areas. Global coverage of precipitation measurements can be obtained through a constellation of satellites. One of the most popular satellite missions for precipitation is the Global Precipitation Measurement (GPM). The GPM Core Observatory satellite was jointly launched by the National Aeronautics and Space Administration (NASA) and Japan Aerospace Exploration Agency (JAXA) (Hou et al. 2014; Liu 2016; Pradhan et al. 2022). The GPM Core Observatory satellite is composed of two instruments, the dual-frequency precipitation radar (DPR) and the GPM Microwave Imager (GMI) (Huffman et al. 2023), which quantify precipitation more accurately and can better detect light and solid precipitation (Hou et al. 2014; Pradhan et al. 2022). Aside from the core observatory satellite, the GPM mission uses measurements from multiple satellites from partner countries that enable global precipitation coverage from 65°N to 65°S (Huffman et al. 2023).
Using the GPM Core Observatory and constellation satellites with additional geostationary satellites, JAXA developed the Global Satellite Mapping of Precipitation (GSMaP) which provides rainfall rates globally (60°N–60°S) for every hour at 0.1° grid resolution (EORC-JAXA 2022; Ushio et al. 2009). The goal of the GSMaP is to derive high-resolution precipitation measurements from satellite data by integrating infrared (IR) and passive microwave (PMW) data (Kachi et al. 2011) into its standard product (GSMaP_MVK). This product (GSMaP_MVK) is generated based on a Kalman filter model that refines the precipitation rate propagated based on the atmospheric moving vector derived from two successive IR images (Ushio et al. 2009; GPM Global Rainfall Map Algorithm Development Team 2014). GSMaP also has other algorithms such as microwave imager algorithm (GSMaP_MWI), microwave sounder algorithm (GSMaP_MWS), microwave imager/sounder algorithm (GSMaP_MWIS), gauge-calibrated rainfall algorithm (GSMaP_Gauge), and near–real time algorithm (GSMaP_NRT) (GPM Global Rainfall Map Algorithm Development Team 2014).
While satellites consistently provide global rainfall data, the accuracy of satellite products is still subject to validation and calibration. Previous research suggests frequent validation and calibration of satellite products to improve accuracy (Dinku et al. 2018). Ground validation based on instrument measurements and then calibrating the satellite product algorithm is usually done to improve the accuracy and performance of satellite-based datasets. Together with the development of the GSMaP_MVK algorithm by Ushio et al. (2009), the initial validation of the satellite-based rainfall in Japan showed that the product tends to underestimate the precipitation, particularly for strong rainfall rates of more than 10 mm h−1 (Ushio et al. 2009). A study in Iran evaluated the GSMaP products against gauge observations at the daily and monthly scales and found that the GSMaP measurements captured well the spatial distribution of precipitation and exhibited good performance during rainy months; however, poor performance was observed during dry months (Darand and Siavashi 2021). In the continental United States, GSMaP also did well in capturing spatial patterns of precipitation but usually underestimates precipitation during winter and overestimates precipitation during summer, especially at rainfall rates of more than 20 mm day−1 (Tian et al. 2010). These highlight that the usability and accuracy of satellite-based precipitation data vary depending on the location and season. Hence, studies have been conducted to assimilate satellite data with ground measurements (Dinku et al. 2018; Massari et al. 2015) to generate more accurate and applicable datasets depending on specific purposes.
Weather events such as thunderstorms and typhoons are associated with rainfall and lightning, especially during severe cases. Previous studies suggest that rainfall and lightning follow similar trends seasonally and diurnally (Tapia et al. 1998). Depending on the location and the season, the lightning and rainfall relationship can be characterized by a linear (Soula and Chauzy 2001) or a power-law (Xu et al. 2013) relation. Petersen and Rutledge (1998) characterized the relationship between cloud-to-ground (CG) lightning and surface rainfall through rain yield, which is a ratio of the rain flux to the CG lightning flash rate density over areas of the scale 105 km2 and time scale of about 1 month. Their results showed that the rain yield in midlatitude continental United States is about 108 kg per flash and that the rain yield is significantly regime-dependent, with a hundred- to a thousand-fold increase in value from arid continental to tropical oceanic regimes. Rain yields were also able to demonstrate accurate rainfall estimates. Xu et al. (2013) studied the underlying relationship between satellite-based rainfall and lightning measurements and also found the relationship to be regime-dependent and generally follows a power law. They used lightning to identify the convective cores of storms and obtained high positive correlations (r = 0.75–0.85) between the heavy precipitation area and the lightning flash area. Xu et al. (2013) also highlighted the importance of describing the lightning–rainfall relationship at the pixel scale for potential rain estimation because of the direct understanding of how to distribute the convective area and assign rain rates pixel per pixel. In their study, the intense precipitation (high radar reflectivity) regions are generally collocated with the regions of frequent flashes. However, more than 20% of the lightning flashes occur in nonconvective or light rain pixels, possibly caused by the charged ice particles being advected out of the convective core, and charge separation is initiated in the nearby stratiform/anvil region. Additionally, deep reflectivity cores are often tilted in strongly sheared thunderstorms, which resulted in lightning flashes not matching up directly with precipitation at the surface. Soula and Chauzy (2001) also performed quantitative precipitation estimation (QPE) based on the lightning–rainfall model at the pixel scale and showed that at an optimal resolution of 30 km, good spatial correspondence between water height and lightning density can be achieved. To perform QPE on the whole precipitating system, some studies have been done to estimate rainfall separately in the nonlightning and lightning regions through the combined use of infrared brightness temperature data and lightning data (Grecu et al. 2000; Morales and Anagnostou 2003). Lightning and rainfall collocation also varies depending on the weather system. Some studies describe that lightning occurred in the region of highest reflectivity or core of the radar echo (Liu et al. 2013; Peterson and Liu, 2011; Soula and Chauzy 2001), while some report otherwise (Zhou et al. 2002) during mesoscale convective systems (MCSs), squall lines, and storms. These show the importance of understanding the lightning–rainfall relationship based on location, weather systems, and spatiotemporal scales before performing models that estimate either rainfall or lightning based on the other parameters.
Using ground sensors with appropriate frequency bands, radio emissions from lightning can be detected. Lightning location may then be determined using various methods such as the time-of-arrival (TOA) technique (Lewis et al. 1960) and interferometric method (Hayenga and Warwick 1981). However, the detection capability of lightning sensors is limited by their effective coverage, which is determined by their operating frequency. Compared to the ground sensors, satellite-based lightning sensors provide measurements at wider spatial coverage. The Geostationary Lightning Mapper (GLM) is an optical lightning detector onboard the Geostationary Operational Environmental Satellite R Series (GOES-R) (Goodman et al. 2012). GLM is the first satellite-based lightning detector in the geostationary orbit. It was deployed by the National Oceanic and Atmospheric Administration (NOAA) and the NASA in 2016 (Peterson 2019; Rudlosky et al. 2019; Rutledge et al. 2020). The objectives of the GLM mission are to provide early detection, tracking, and monitoring of storm intensification and severe weather; enable increased tornado warning lead time; and provide data continuity for long-term climatology studies (Rudlosky et al. 2019). The GLM provides continuous total lightning measurements over the Americas and adjacent oceans through the detection of both intracloud and cloud-to-ground lightning; however, it cannot natively distinguish between these two lightning types (Rudlosky et al. 2019). The GLM was the first step toward a constellation of satellites aimed to provide continuous lightning data on a global scale. In December 2016, the China Meteorological Administration (CMA) successfully launched the FengYun-4A (FY-4A) satellite, which houses a Lightning Mapping Imager (LMI) that covers lightning measurements in China and surrounding areas (Liu et al. 2020). In December 2022, the European Space Agency together with the European Organisation for the Exploitation of Meteorological Satellites (EUMETSAT) launched the Meteosat Third Generation satellite, which also includes a lightning imager that will provide lightning measurements across Europe and Africa (ESA 2023). The Japan Meteorological Agency (JMA) also envisions a future geostationary satellite with a lightning mapper payload (JMA 2018). These will enable a global scale of lightning information that may complement rainfall missions to provide accurate and timely monitoring of convective systems.
Considering the inherent relationship between lightning and rainfall, we deem that lightning information may be used to further improve the accuracy of satellite-based rainfall data specifically GSMaP. In this study, we explore the viability of assimilating lightning flashes into the GSMaP rainfall to improve its accuracy concerning radar data. We do this by first characterizing the lightning–rainfall relationship considering different case studies at varying grid and time resolutions and then performing parameter optimization that will assimilate lightning data into the rainfall estimates. This endeavor is a significant step toward maximizing the future global coverage of lightning information from satellite-based lightning mappers, specifically aimed toward better rainfall estimates derived from satellites.
2. Data and methods
a. Radar and satellite rainfall data
For the scope of this study, radar rainfall measurements are considered ground truth for rainfall information. Radar rainfall was acquired from the XRAIN Radar Precipitation Data maintained by the Ministry of Land, Infrastructure, Transport and Tourism (MLIT), Japan. XRAIN, composed of 39 X-band radars across Japan, provides rainfall data at 150-m spatial and 1-min temporal resolutions (Harjupa et al. 2018).
The satellite rainfall product is the GSMaP standard product (GSMaP_MVK), version 7. GSMaP_MVK is the combined product from microwave and infrared rainfall measurements (EORC-JAXA 2022). GSMaP_MVK provides hourly rainfall rates (mm h−1) at 0.1° × 0.1° grid box with global coverage spanning from 60°N to 60°S (EORC-JAXA 2022).
For both rainfall sources, only nonzero measurements are considered in the analyses. Moreover, the total rainfall volume over the grid box is analyzed throughout the study by multiplying the rainfall rate by the area of the grid box. The rainfall volumes are expressed in terms of square kilometer millimeters per hour (km2 mm h−1), similar to the previous study by Xu et al. (2013).
b. Lightning data
Lightning flash data were obtained from the Lightning Detection Network (LIDEN) (Ishii et al. 2014) operated by the JMA. It is composed of 30 stations installed across Japan, with an average distance among stations of about 200 km (Ishii et al. 2014). LIDEN records low-frequency pulses of lightning discharges and locates the pulses by the TOA and magnetic direction finding techniques (Wada et al. 2023). LIDEN detects both CG and intracloud (IC) lightning. The lightning location is determined using five or more nearest LF sensors within a 625-km distance (Ishii et al. 2014; Hayashi et al. 2021). The LIDEN system observes CG lightning using time, location, polarity, and estimated electric current, while IC lightning is described using time and location information. A series of CG strokes with a spatial distance of less than 10 km and a time difference within 0.5 s was defined as multiple strokes in a single CG flash, following the JMA (Ishii et al. 2014). The uncertainty in the location of the CG and IC strokes is less than 1 km (Hayashi et al. 2021).
In the study, the total lightning flashes are considered, accounting for both the IC and CG flashes. A lightning flash is counted on the onset of the first lightning stroke. Subsequent strokes under the same flash are not considered in the calculation of lightning flash rates. The lightning flash rates are expressed as total lightning flash counts over time in minutes (flashes per minute).
c. Lightning and rainfall relationship
The relationship between lightning and radar rainfall at varying spatial and temporal resolutions is analyzed considering the following weather events: 1) isolated thunderstorms, 2) a frontal system, and 3) a typhoon. Radar rainfall and lightning flash rates are used to characterize the lightning–rainfall relation at spatial resolutions from 0.01° up to 3° and temporal resolutions from 1 to 180 min (3 h). The spatial resolutions are analyzed in terms of degrees; however, to simplify the discussions, the spatial resolutions are depicted in terms of kilometers where 1° is approximately equal to 100 km.
The radar and GSMaP rainfall are upscaled to coarser resolutions taking the average rainfall rate within the coarse grid. A similar approach is done with varying temporal resolutions where longer periods are obtained from the average of individual rainfall rates per grid.
Lightning flash rates are then mapped similarly, matching the resolution of the rainfall grids. The lightning flash rate within a specific period in a grid box is the total number of collocated lightning flashes inside the grid divided by the time resolution in minutes. Moreover, a buffer of 0.1° is applied to each lightning flash to account for uncertainty in its location (Kasahara, 2011; Tomioka et al. 2023). With this, a single lightning flash near the edge of grid boxes may be counted in the total lightning flash rates of multiple neighboring grid boxes.
The lightning–rainfall relationship was characterized based on the collocated pixels of the rainfall volumes and lightning flash rates in space and time. The case studies conducted to characterize the lightning–rainfall relationship are summarized in Table 1. The weather events summarized in the table are based on official weather reports from the JMA. For the isolated thunderstorms and frontal system cases, the study region considered is in the Kanto region, while for the typhoon case, the whole country of Japan is covered.
Summary of case studies conducted for lightning–rainfall relationship.
d. Training and validation
To train the model and derive the optimized parameters α, β, and γ, 5 days’ worth of hourly rainfall volume and lightning flash rate data are considered for each case study summarized in Table 2. The optimized parameters α, β, and γ are derived for each weather system considered and for each spatial resolution. The temporal resolution used to derive the optimized parameters is set to 1 h, following the original temporal resolution of GSMaP as well as the good results obtained at this resolution, which will be tackled in the succeeding sections. All the matching lightning flash rate and rainfall volume pixels throughout the study periods across Japan are divided into training and validation datasets. About 75% of the data are used for training the model while the remaining 25% are used to validate the results. Moreover, only flash rates over a 1 flash per minute threshold are considered for training the model due to the high variability of rainfall volumes at low flash rates, which will be discussed in the succeeding sections.
Summary of case studies conducted for parameter optimization training and validation.
3. Results and discussion
The first step toward incorporating lightning into rainfall models is to determine how these two parameters are related. The subsequent sections will focus on the empirical relationship between lightning flash rates and radar rainfall volumes in different case studies.
a. Lightning and rainfall during isolated thunderstorms
The total lightning flash rate and total rainfall volume across the whole study region are first analyzed through the time series shown in Fig. 1. The resolutions depicted in the figure are 1 km and 5 min. The radar rainfall volumes are divided into two, between high and low rainfall rates based on the 10 mm h−1 threshold. Considering the time series, both rainfall volumes follow similar patterns in time with the total lightning flash rate across the study region. High rainfall rates follow the lightning flash rate patterns better than the low rainfall rates. Moreover, multiple lightning and rainfall peaks were observed during the 11-h duration, depicting various isolated thunderstorms that occurred within the study region. Most lightning and rainfall peaks also occurred in the afternoon from 0700 UTC (1600 JST) up to 1200 UTC (2100 JST). These results agree with previous studies suggesting that lightning and rainfall follow similar patterns in time and occur mainly during the afternoon (Tapia et al. 1998; Xu et al. 2013). The subsequent case studies, the frontal system and typhoon, also show similar results with lightning and rainfall following the same patterns in time.
Total radar rainfall volume and total lightning flash rate within the study region across time for (left) rain rates > 10 mm h−1 and (right) rain rates < 10 mm h−1 during thunderstorms on 2 Aug 2019.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
However, a study in the United States by Xu et al. (2013) showed that lightning flash rates and rainfall volumes depicted good agreements only at the convective system scale. At the pixel scale, of which they considered 20 km as the coarsest resolution, only 50% of the lightning flashes collocate with heavy rainfall, while 20% of the lightning flashes occurred in nonconvective or light rain areas. It is important to characterize the lightning–rainfall relationship at the pixel scale because it is easier to derive QPEs at defined spatial grids. Considering this, we explored the collocation of lightning and rainfall at varying spatial and temporal resolutions in the context of Japan.
We first examined the lightning and rainfall relationship in isolated thunderstorms. Single-cell thunderstorms, also called ordinary thunderstorms, form when warm, moist air rises and cools, leading to condensation and the development of cumulus clouds, which continue to grow as warm air rises and cools. Within the cloud, the updraft continues, while cool, dry air also flows downward (downdraft). The existence of hydrometeors in different phases and sizes interacting with each other through collisions, freezing, melting, coalescence, and breakup within the thunderstorm builds up electric charges that lead to lightning (Williams et al. 1991). Precipitation starts to fall when the rising air cannot hold them up, and the thunderstorm dissipates when the downdraft is greater than the updraft. Isolated thunderstorms may be in the form of single-cell thunderstorms or multicell thunderstorms, which contain multiple individual cells, with new thunderstorm cells forming on the cold outflow boundary of previous cells (Price, 2013). Isolated thunderstorms typically range in the horizontal scale from approximately 10 km to less than 100 km and last from less than an hour to less than a day (Stull 2017). In thunderstorms, a strong updraft in the mixed-phase region is required to produce lightning (Williams et al. 1991; Deierling et al. 2008; Price 2013). The mixed-phased region in a thunderstorm is between the 0°C isotherm and the ‒40°C isotherm, where supercooled liquid water, ice crystals, snow, hail, and graupel can be found (Price 2013). This mix-phased region is where most of the thunderstorm electrification happens due to the noninductive charging process, which involves rebounding collisions between graupel and ice crystals in the presence of supercooled liquid water (Takahashi 1978; Saunders et al. 1991; Deierling et al. 2008; Price 2013). The presence of a strong updraft is needed to carry the larger hydrometeors up above the freezing level. Additionally, strong updraft enhances collisions between the hydrometeors, which results in increased charge transfer and rapid charge build-up in clouds (Price 2013). Throughout the thunderstorm life cycle, lightning is present during the developing, mature, and decay stages, with IC lightning appearing first, followed by CG lightning, which mainly appears in the mature stage, and both lightning may be present in the decay stage (Price 2013). Some studies suggest that lightning flash cores in thunderstorms occur not exactly but only within the vicinity of the heaviest precipitation (Carte and Kidder 1977) or outside the region of highest reflectivity (Soula and Chauzy 2001). However, some studies also showed that the area of highest lightning activity overlaps with the region of highest precipitation (Liu et al. 2013; Peterson and Liu 2011; Soula et al. 1998). Lightning activity may also precede rainfall by about 10–20 min (Price 2013).
A snapshot of the collocation between lightning flash rates and rainfall volumes at 10 km and 30 min resolution is shown in Fig. 2. In this figure, only nonzero rainfall volumes and lightning flash rates are depicted. It can be observed that within the thunderstorm area, the highest lightning flash rates also overlap with the highest rainfall volumes. However, this is not always the case considering all the matching of rainfall and lightning pixels across space and time throughout the case study. Such results agree with the previous studies where the area of the highest lightning activity may coincide with the area of maximum precipitation; otherwise, it may be located within the vicinity of the peak precipitation region.
Distribution of (left) XRAIN rainfall volume and (right) lightning flash rate at 10-km, 30-min resolution. The sample map obtained from 0700 UTC 2 Aug 2019 to 0729 UTC 2 Aug 2019.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
To determine the level of agreement between lightning flash rates and rainfall volumes at various spatial and temporal scales in thunderstorms, Pearson and Spearman’s rank correlations are calculated as shown in Fig. 3. Sensitivity tests are conducted at varying resolutions by taking the average correlation at specified spatial and temporal resolutions, while the heatmaps present the distribution of correlations across spatiotemporal scales. Both the linear and monotonic correlations tend to increase as the spatial and temporal scales increase. At 300 km, the correlations abruptly decreased due to an insignificant number of sampling points. Monotonic correlations generally tend to be higher, as depicted in both sensitivity tests and heatmaps. Considering a linear relationship, a moderate positive correlation (≥0.5) can be obtained starting at 10-km resolution, and a high positive correlation (≥0.7) starts at 40 km and 30-min resolutions. The linear correlation remains high at coarser grids and longer time periods, with average coefficients ranging from about 0.7 to 0.8. The generally higher monotonic correlation coefficients present suitable monotonic lightning–rainfall relationships at finer resolutions, starting from 15 km and 5 min. From the sensitivity tests, both linear and monotonic correlations present more variability and apparent trends with changes in spatial resolutions than temporal resolutions.
(a),(c) Pearson correlation and (b),(d) Spearman’s rank correlation between lightning and rainfall at varying spatial and temporal resolutions. The shaded region depicts one standard deviation away from the average correlation. (e),(f) Correlation heatmaps with contours.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
As mentioned above, isolated thunderstorms typically range in the horizontal scale from about 10 km to less than 100 km and last within an hour to a day. With this, fine resolutions are usually used to study the development of thunderstorms. The short-lived and small-scale nature of thunderstorms may, in part, be the reason for high positive correlations obtained starting at 40-km and 30-min resolutions for linear relationships and 15-km and 5-min resolutions for monotonic relationships. This is because the mismatch in the location of peak lightning and rainfall activities is averaged out at coarser grids and longer time scales. Additionally, the microphysics and electrification process within this specific thunderstorm may explain these correlations; however, the in-depth analyses of these processes are beyond the scope of the current study.
To better look into the lightning–rainfall relation, the scatterplot of lightning flash rate and rainfall volume for the thunderstorm case study is shown in Fig. 4. Two configurations were shown in the plots, from 40-km and 30-min (left) and 100-km and 60-min (right) resolutions. Additionally, the gray points in the plots represent the individual matching for the lightning flash rate and rainfall volume, while the orange points show the mean rainfall volume calculated at each unique lightning flash rate value. The plots reveal that the rainfall volume is highly variable at very low lightning flash rates, indicating that there are areas with few lightning occurrences even with heavy rainfall. The plots (in logarithmic scale) also show a steeper slope of around 0.7 at the 100-km, 60-min scales. This depicts a more linear relationship between lightning and rainfall at the logarithmic scale, suggesting that at larger spatiotemporal scales, the relationship between the lightning flash rate and rainfall volume can be empirically described by a power law. Based on these results, greater spatial coverage (bigger pixels) can match high rainfall volume measurements with nearby, dense lightning, improving collocation between lightning and rain, which in turn increases their correlation.
Scatterplot of the lightning flash rate and rainfall volume at (left) 40-km, 30-min and (right) 100-km, 60-min resolutions. The axes are depicted in the logarithmic scale. Gray points show the individual measurements, while orange points depict the average rainfall volume at each unique lightning flash rate.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
Considering the high positive correlation obtained from a significant number of data points and the more apparent power-law relationship, the resolutions of 100 km and 60 min (with Spearman’s correlation ρ = 0.86) may be recommended to model the lightning and rainfall in isolated thunderstorms. However, finer resolutions starting from 40 km and 30 min may also be used, considering that these resolutions also exhibited high lightning–rainfall correlations while also capturing the small-scale and short-lived nature of isolated thunderstorms. This recommendation is close to the optimal resolution of 30 km obtained by Soula and Chauzy (2001) in estimating rainfall from lightning density. Depending on the applications, 15-km spatial resolution may also be used but with a longer aggregation time of about 90 min. However, the large variability of rainfall volumes at low lightning flash rates poses a limitation at these fine resolutions.
b. Lightning and rainfall during a frontal system
The spatial distribution of rainfall volume and lightning flash rates on a pixel grid during a frontal system is shown in Fig. 5. In this case, a fine spatial resolution of 10 km and 1 h is used to visualize the lightning and rainfall collocation. Based on the lightning flash rate and radar rainfall volume maps, lightning is not always concentrated on the highest rainfall regions. While the majority are still near the high rainfall region, some lightning flashes are also present in the low rainfall region. The results concur with previous studies, which revealed that lightning is most often located in the strong precipitation area in a squall line (National Research Council 1986), formed along or ahead of a cold front, or just outside the leading edge of the precipitation core (Mazur and Rust 1983). Rutledge et al. (1993) showed that in a MCS, 90% of the total CG lightning is located near or within the convective region, while the remaining 10% (composed of positive CG lightning) occurred in the stratiform precipitation region. For reference, the GSMaP rainfall volume is shown as well in Fig. 5, which reveals that its highest rainfall region also does not collocate well with peak lightning region. The GSMaP rainfall volume measurements are also lower compared to XRAIN, which has more defined and accurate values. Limitations on the lightning-corrected GSMaP (discussed in succeeding sections) may occur considering this scenario. While the concentration of lightning flashes in the top-right portion of the lightning map may still impose an increase in rainfall volume when introduced to GSMaP, the higher flash rates on the bottom-left portion may also intensify GSMaP measurements, which may induce more errors when compared to XRAIN data.
Distribution of (left) XRAIN rainfall volume, (middle) lightning flash rate, and (right) GSMaP rainfall volume at 10-km, 1-h resolution. The sample map obtained from 0700 UTC 20 Aug 2019 to 0759 UTC 20 Aug 2019.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
The Pearson and Spearman rank correlations for the frontal system case study are shown in Fig. 6. Both the linear and monotonic correlations tend to increase with increasing spatial scale. Monotonic correlation also increases with increasing temporal accumulation; however, linear correlation tends to be more constant across varying times. Like thunderstorms, higher correlations were generally obtained using Spearman’s rank correlation, suggesting that the relationship between lightning and rainfall tends to be more monotonic or change together at different rates. Linear correlations are mostly low, with moderate values only obtained at high spatial scales of ≥150 km, as shown in the heatmap. The monotonic relationship between lightning and rainfall is more apparent, as depicted in its correlation heatmap. Moderate Spearman correlations start from 15-km and 5-min resolutions, while high Spearman correlations are limited on scales bigger than 50 km and 45 min. Spatial sensitivity reached the highest average value of about 0.7 from 100 and 250 km. Temporal correlations reach an average value of 0.5 for Spearman’s correlation from the 10-min scale and tend to be constant at 0.6 from the 60-min scale. Frontal systems occupy large areas (from ∼101-to ∼103-km horizontal scale) (Stull 2017). Organized weather systems such as squall lines and MCS may develop along the fronts, which have embedded thunderstorms accompanied by extensive regions of stratiform rain (Rutledge et al. 1993). The relatively better performance at huge spatiotemporal resolutions than fine resolutions can be attributed to the mismatch in the highest concentration of lightning and the maximum precipitation shown in Fig. 5. At larger spatial scales, the contrast between the location of the peak lightning and rainfall measurements is aggregated, providing better matching and consequently higher correlations. However, the embedded thunderstorms are mixed with the stratiform rain at coarse resolutions. This may explain the generally higher correlation coefficients obtained from the isolated thunderstorm case than the frontal system case because the former is mainly composed of convective rain and the collocation with lightning is essentially better. Additionally, the big contrast in linear and monotonic correlations suggests that the lightning–rainfall relationship in frontal systems may be more restricted to nonlinear models.
As in Fig. 3, but for a frontal system case study.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
Like the thunderstorm case, the scatterplot for the frontal system case study also revealed high variability of rainfall volumes at very low lightning flash rates, as shown in Fig. 7. The slope of the scatterplot in the logarithmic scale, even at 100-km scale, is lower than the slope from the thunderstorm case. As frontal systems occupy large areas, coarse resolutions can be best used to empirically describe the lightning and rainfall relationship in this weather system. Spatial resolutions of 50 km or greater may be used paired with longer aggregation times of more than 45 min. From the sensitivity tests, resolutions of ≥100 km and 60 min may be optimal for use.
Scatterplot of the lightning flash rate and rainfall volume at (left) 10- and (right) 100-km resolutions. The axes are in the logarithmic scale. Both plots have a 1-h temporal resolution. Gray points show the individual measurements, while orange points depict the average rainfall volume at each unique lightning flash rate.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
c. Lightning and rainfall during a typhoon
Pixel-to-pixel comparison of the lightning flash rate and rainfall volume during a typhoon at 10-km and 1-h resolutions is depicted in Fig. 8, which focuses on the typhoon’s outer rainbands to visualize collocation. In a typhoon, lightning is primarily located at the eyewall and outer rainbands (Molinari et al. 1999; Zhang et al. 2013; Sakurai et al. 2022). The eyewall region within 100 km of the storm center experiences episodic lightning outbreaks before or during intensification (Molinari et al. 1999) due to an organized microphysical process for electrification involving a high concentration of graupel interacting with small ice particles driving the charge separation (Houze 2010). The inner rainbands within 200 km of the storm center are characterized by minimal lightning and stratiform regions (Zhang et al. 2013). The outer rainbands, >200 km away from the storm center, are indicated by frequent flashes that are produced by processes more associated with environmental airflow and localized convection similar to thunderstorms rather than the electrification mechanism in the eyewall (Houze 2010; Zhang et al. 2013). Considering Fig. 8, the maximum lightning region tends to be located in the maximum rainfall region of the outer rainband, similar to the results for thunderstorms. The maps also depict that the rainfall volumes in the outer rainband tend to remain consistent over huge horizontal areas. Yang et al. (2018) showed that typhoon rain is mainly composed of stratiform rain, occupying about 78% of the total rain in the outer rainband.
Distribution of (left) XRAIN rainfall volume and (right) lightning flash rate at 10 km, 1 h resolution. Sample maps were obtained (top) from 0600 UTC 4 Sep 2020 to 0659 UTC 4 Sep 2020 and (bottom) from 0800 UTC 4 Sep 2020 to 0859 UTC 4 Sep 2020.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
Like the previous case studies, the monotonic correlation tends to be higher in average values as shown in Fig. 9, suggesting a more nonlinear relationship between lightning and rainfall in a typhoon. Linear correlation tends to decrease with increasing spatial scale, while the average monotonic correlation is the highest at 50–100-km resolution and decreases from there. Considering that lightning flashes in typhoons are concentrated in the eyewall (<100 km from the storm center) and outer rainbands (>200 km from the center), aggregating the lightning and rainfall at spatial scales greater than 100 km mixes the highly concentrated lightning flashes in these regions with the infrequent lightning flashes in the inner rainbands. Additionally, the inner rainbands are composed mostly of stratiform clouds that are also aggregated with higher rain rates from the convective cores in the eyewall and outer rainbands. Correlation at increasing temporal accumulation also tends to remain constant for a linear relationship while it increases considering a moderate monotonic relationship. In this regard, the rate of change in the lightning flash rates may not necessarily correspond to a linear increase or decrease in rainfall because typhoon rain tends to be more uniform across large spatiotemporal scales. In general, both Pearson’s and Spearman’s correlations are the lowest from the typhoon case followed by the frontal system case, and the highest correlations are obtained from the thunderstorm case. The heatmaps also reveal that linear correlations are predominated by very low values, while moderate coefficients can only be obtained for monotonic correlations from 30- to 150-km spatial resolutions and temporal resolutions beyond 30 min.
As in Fig. 3, but for the typhoon case study.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
Based on Fig. 10, the scatterplots of the lightning flash rate and rainfall volume for the typhoon case study show consistent average rainfall volumes at varying lightning flash rates. This agrees with the maps depicted in Fig. 8 where typhoon rain tends to be uniform while lightning varies. This also supports the low correlation obtained especially from the Pearson correlation. The complexity of the typhoon system, with different electrification mechanisms between its regions of high flash density, may partly be the reason for the poor matching of the lightning flash rate and rainfall volumes across varying space and time resolutions. The innate lag between the peak lightning occurrences and peak surface rain rate and the varying frequencies in CG lightning before and after the landfall (Zhang et al. 2013) may also contribute to the complexity of the lightning–rainfall relationship in typhoons. As the current study is more focused on the space and time collocation of lightning and rainfall at the pixel scale, the complex behavior of lightning and rain within the typhoon system will not be tackled in detail.
Scatterplot of the lightning flash rate and rainfall volume at (left) 10-km, 60-min, and (right) 100-km, 180-min resolutions. Gray points show the individual measurements, while orange points depict the average rainfall volume at each unique lightning flash rate.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
In the typhoon case study, obtaining the lightning–rainfall relationship may not be very effective at the pixel scale. However, the spatial resolutions of 30–150 km and temporal resolutions of 30 min and beyond may be used, but the abovementioned limitations should be carefully considered.
d. Assimilating lightning with GSMaP rainfall
Using the case study that best exhibits the power-law relation between the lightning flash rate and rainfall volume, parameter optimization to introduce lightning into GSMaP rainfall measurements was done for isolated thunderstorm cases with 5 days’ worth of data. Initially, lightning was assimilated with GSMaP rainfall at the resolution of 100 km and 60 min. This is considering the high positive correlations obtained at these scales, without changing the base temporal resolution of GSMaP.
Because of the high variability of rainfall volume at very low lightning flash rates, a threshold of 1 flash per minute is used to train the model to derive optimized parameters that will minimize the squared errors between the lightning-corrected GSMaP rainfall volume and radar rainfall volume. Figure 11 shows the results of the model training as well as the validation of the corrected GSMaP rainfall volume derived from the optimized parameters for isolated thunderstorm cases. At 100-km and 60-min resolution, rainfall volumes during thunderstorms may be corrected with parameters α = 100.0, β = 0.53, and γ = 0.12. Based on the validation results, the lightning-corrected GSMaP tends to lie closer to the 1:1 line with the radar rainfall volume than the original GSMaP. Moreover, an increase in the Pearson correlation was observed from 0.6 to 0.7 with a decrease in RMSE of about 59%.
Results of parameter optimization (left) using training data and (right) applying the optimized parameters to validation data at 100-km, 60-min resolution. The blue points represent the original GSMaP data, while the orange points show the lightning-corrected GSMaP.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
Sample maps of lightning flash rates and rainfall volumes during thunderstorms are shown in Fig. 12 from 0700 UTC 1 August 2019 to 0759 UTC 1 August 2019. Based on the maps, the lightning-corrected GSMaP rainfall volumes become closer in value to the XRAIN radar rainfall volume. This suggests that at this scale, lightning information is successful in reducing errors in GSMaP rainfall data concerning radar measurements.
Sample maps of (a) lightning flash rate, (b) XRAIN rainfall volume, (c) original GSMaP rainfall volume, and (d) lightning-corrected GSMaP rainfall volume at 100-km and 60-min resolution.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
The method is further tested considering all case studies at varying spatial resolutions, from 10 km, which is the base GSMaP spatial resolution up to 300 km. The radar and GSMaP rainfall are upscaled to coarser resolutions taking the average rainfall rate within the coarse grid. The temporal resolution remains at 60 min considering the moderate positive correlations of more than 0.5 at this scale for all cases. Five days’ worth of data are also considered for the frontal system and typhoon case studies. Furthermore, to assess the performance of the optimized power-law parameters in improving the GSMaP, rainfall volumes are also calculated using the lightning–rainfall relationship derived by Xu et al. (2013) in the United States. For the rest of the discussion, the rainfall volumes calculated using the lightning–rainfall relationship derived by Xu et al. (2013) will be called “LRR_US.” The RMSE in the succeeding validation results is made more intuitive by normalizing the units in rainfall volumes back to rainfall rates. This was done by dividing the RMSE by the total area of the grid cell.
Validation results at varying spatial resolutions for isolated thunderstorm cases are shown in Fig. 13. At resolutions of 20 km and below, the RMSE of LRR_US is higher than the RMSE from the original GSMaP. Starting from the 30-km resolution, the RMSE of LRR_US becomes lower than the RMSE of the original GSMaP, suggesting closer rainfall rate estimates with the radar. However, in general, the RMSEs obtained from the optimized parameters are lower than those of the original GSMaP and LRR_US. Pearson correlations with respect to the radar data are the highest using the optimized power-law parameters, while the lowest are obtained using LRR_US. Correlations are low when using LRR_US because the derived rainfall volumes from this approach tend to be clustered in the range from about 5 × 103 to 5 × 104 km2 mm h−1 after doing a manual check. This behavior is not observed when using the optimized power-law parameters, which show variable rainfall volumes depicted in Fig. 11. These results show that using the optimized power-law parameters to correct and introduce lightning into the GSMaP gives more accurate rainfall volume estimates than LRR_US. These also support the assumption that the lightning–rainfall relationship varies significantly with location; hence, there is a need to derive location-specific parameters to estimate rainfall volumes from lightning flash rates.
Validation results at varying spatial resolutions of lightning-corrected GSMaP using optimized parameters and lightning-estimated rainfall using LRR_US in thunderstorms.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
Focusing on the results of introducing lightning into the GSMaP using optimized power-law parameters, at resolutions below 40 km, we can see that GSMaP correction from finer resolutions shows improvements in the RMSE with low positive correlations. The RMSE at these resolutions ranges from about 16.9 mm h−1 down to 7.8 mm h−1, which are still relatively high. Starting from 40 km, the RMSE started going down to about 5.4 mm h−1 and lower, with moderate positive correlations. The highest correlation coefficient after GSMaP correction and the biggest improvement in RMSE (about 59% reduction) was obtained at 100 km, which was the initially tested resolution shown in Fig. 11. Interestingly, a huge improvement in the correlation from around 0 to 0.7 is obtained at 250-km resolution. However, the corrected correlation dropped again at 300-km resolution. This behavior may be due to the few data points analyzed at these scales.
The technique to correct GSMaP with lightning is also tested considering the frontal system and typhoon cases as shown in Figs. 14 and 15. For consistent comparison, the rainfall volumes were also derived using the LRR_US for these cases. Similarly, the normalized RMSEs in rainfall rate units are presented. The behavior of the validation results is different from the isolated thunderstorm case, especially for the correlation between radar rainfall volume and GSMaP rainfall volume before and after correction. Improvements in correlation coefficients were not mostly observed for these case studies even at huge spatial scales. For frontal systems, low positive correlations were obtained from 80- to 150-km resolutions, with a moderate positive correlation of 0.66 at 120-km resolution. For typhoons, it can be observed that the original correlation between radar and GSMaP has been moderately positive from 60 to 180 km. This may be due to the consistent rainfall volume at huge horizontal scales during typhoons, making both radar and GSMaP have closer values. Because of this, there is not much improvement in correlations after lightning correction to GSMaP. The correlations obtained using LRR_US remain lower than the original GSMaP and lightning-corrected GSMaP, suggesting that the equation derived by Xu et al. (2013) to relate rainfall and lightning in the United States is not applicable in Japan for all the cases considered. The RMSEs obtained from the lightning-corrected GSMaP are consistently lower than the original GSMaP for both cases. For the typhoon case, the RMSEs after lightning correction are below 5 mm h−1 starting from 40-km resolution. For the frontal system case, the RMSE is lower than 5 mm h−1 starting from 50-km resolution, increased to about 9.7 mm h−1 at 70-km resolution, and becomes consistently lower than 3.5 mm h−1 from 80-km resolution.
Validation results at varying spatial resolutions of lightning-corrected GSMaP using optimized parameters in frontal system cases.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
Validation results at varying spatial resolutions of lightning-corrected GSMaP using optimized parameters in typhoon cases.
Citation: Journal of Atmospheric and Oceanic Technology 42, 6; 10.1175/JTECH-D-24-0040.1
The validation results show that the optimized parameters to incorporate lightning into the GSMaP rainfall measurements are most effective in isolated thunderstorm cases. While there are improvements in RMSE, correlations may remain the same when this technique is applied to frontal systems and typhoons. Moreover, the technique works best at 100-km resolution for isolated thunderstorms, but moderate positive correlations and RMSEs lower than 5 mm h−1 can be obtained starting at the 40-km mark.
The optimized power-law parameters derived for each case study and for the spatial resolutions from 10 to 300 km are shown in Table 3. Note that the temporal resolution for these parameters is held constant at 60 min for the same reason mentioned above and to retain the original GSMaP temporal resolution. The α parameter tends to be close to 100, the β parameter appears to be increasing together with increasing spatial resolution and ranges from about 0.3 to 0.6, and the γ parameter varies across the cases and spatial scales but ranges from about 0.1 to 0.4. While the parameters appear to be limited to a certain range, the parameters vary across the case studies per spatial resolution. In this regard, using a generalized set of parameters for all cases and all spatial resolutions may not result in consistent improvements in the rainfall volume estimates. Moreover, the results of the varying lightning–rainfall relationship for different weather systems at different spatial and temporal resolutions discussed in sections 3a–c suggest different considerations for these cases.
Summary of optimized power-law parameters for the isolated thunderstorms, frontal systems, and typhoons case studies.
4. Summary and conclusions
Lightning and precipitation are typically associated with each other, especially during severe weather events. Their occurrence and inherent relation have been subjects of various studies, paving the way for a better understanding of these two parameters together. In this study, we focused on characterizing the relationship between lightning and rainfall at varying pixel and time resolutions. This approach was done to determine the optimal resolutions that maximize the correlation between lightning and rainfall from which a lightning-corrected satellite-based rainfall product can be derived.
In this study, we performed analyses on the lightning–rainfall relationship considering three cases: isolated thunderstorms, frontal systems, and typhoons. For all the case studies, the total lightning flash rate and total rainfall volume follow similar patterns in time at the system scale. However, peak lightning flash rates are not always collocated with the highest rainfall volumes considering a pixel-to-pixel comparison. The behavior of lightning and rainfall collocation also varies depending on the weather system.
In isolated thunderstorms, high flash rates may be located within the extent of the weather system coinciding with high rainfall volumes. This happens more frequently compared to the other two cases, especially when the rainfall pixels are aggregated at large spatial and longer temporal resolutions. Good matching can be obtained even from resolutions of 40 km and 30 min, which are relatively better than the other cases. Correlations between the lightning flash rate and rainfall volume are the highest in this case study. Empirically, the power-law relationship between lightning and rainfall is also most apparent considering isolated thunderstorms. With a Spearman rank correlation of 0.86, the resolutions of 100 km and 60 min may be recommended to model the lightning–rainfall relation in thunderstorms. However, finer resolutions starting from 40 km and 30 min are still recommended, but limitations on the huge variability of rainfall volumes at very low flash rates must be considered. Depending on the applications, 15-km spatial resolution may also be considered together with a longer aggregation time of more than 90 min.
Frontal systems, with greater horizontal scale and lifespan than thunderstorms, showed that the region of the highest lightning flash rates may be located near the precipitation core or the highest rainfall volume area. Some densely concentrated lightning may also be in low rainfall volume zones, which are natural for frontal systems with embedded thunderstorms surrounded by stratiform regions. This made the linear and monotonic correlations lower than that of the thunderstorms. Still, the matching of lightning flash rates and rainfall volume at the logarithmic scale revealed a power-law relationship. The huge variability of rainfall volumes at low flash rates persists in this case study. Moderate Spearman’s rank correlations were consistently obtained from 50-km and 45-min resolutions and beyond. Sensitivity tests show consistent moderate correlations at resolutions ≥ 100 km and 60 min. Hence, the lightning–rainfall relationship in frontal systems may be best depicted empirically in these resolutions.
Typhoons have the greatest horizontal scale and longest lifespan among the case studies. In this weather system, lightning mainly occurs in the eyewall and outer rainbands. The outer rainbands are predominantly composed of stratiform rain, which makes the rainfall volumes consistent at huge spatial scales. Because of this, the changes in lightning flash rates do not correspond well with rainfall volumes that remain constant. This is apparent in both lightning–rainfall collocation maps as well as scatterplots at the logarithmic scale. Moderate positive correlations may still be obtained from 30- to 150-km spatial resolutions and ≥30-min temporal resolution considering a monotonic relationship. These results suggest that correcting rainfall measurements with lightning information in typhoons may be less effective considering a pixelwise approach.
Optimization was done to derive parameters that will assimilate lightning with the GSMaP rainfall volume with the objective of reducing RMSE concerning radar rainfall volume data. Five days’ worth of data with isolated thunderstorm occurrences were used, with 75% of the total dataset utilized for training, while the remaining was allocated for validation. Initially, the technique was employed at the best-case resolutions of 100 km and 60 min. Using the optimized parameters, a decrease of about 59% in RMSE (from 4.9 to 2.0 mm h−1) and an improvement in Pearson correlation from 0.6 to 0.7 were obtained after comparing the lightning-corrected GSMaP rainfall volume with the XRAIN radar rainfall volume. The approach was then performed at other spatial resolutions and the results revealed that while the performance fluctuates, moderate positive correlations with RMSE of about 5 mm h−1 and less are achieved from resolutions of 40 to 250 km. From these results, lightning can be introduced into the GSMaP rainfall to increase its accuracy starting from 40-km resolution, with peak performance at 100-km, 1-h resolution for isolated thunderstorm cases.
Parameter optimization to introduce lightning into the GSMaP rainfall volume measurements was also done for the frontal system and typhoon cases. Improvements in the correlations after lightning correction were not observed, with values usually close to the original correlation. The correlations from typhoons were also higher in values, from moderate to high positive correlation, suggesting that the original GSMaP corresponds well with the XRAIN rainfall measurements considering that this weather system has consistent rainfall at huge spatial scales. In general, a decrease in RMSE is observed in these cases (<5 mm h−1) but fluctuates depending on the resolution.
Rainfall volumes using the lightning–rainfall relationship derived by Xu et al. (2013) in the United States (LRR_US) were also obtained to describe the relative performance of the lightning-corrected GSMaP. Rainfall volumes derived from LRR_US showed even lower correlations than the original GSMaP when compared to XRAIN radar data. The RMSE was also higher considering resolutions below 30 km. In general, the lightning-corrected GSMaP performed better than the LRR_US, highlighting the location-dependence of the lightning–rainfall relationship and consequently the need for deriving correction parameters through regional case studies.
Overall, the lightning–rainfall relationship is most apparent in isolated thunderstorm cases. Empirically, a power-law model can be used to describe the lightning–rainfall relation and this model is more effective at huge spatial and temporal scales. Finer resolutions may still be considered; however, the high variability of rainfall volumes at low lightning flash rates poses a limitation. Moreover, this study showed that lightning is a viable parameter to induce corrections to a satellite-based precipitation product, specifically GSMaP, with significant improvements in correlations and RMSE, especially in isolated thunderstorms. Furthermore, the empirical power-law relationship demonstrated in this study can be a significant addition to the nonlinear indices used to provide feedback information to the Kalman filter employed in the GSMaP_MVK algorithm in estimating rainfall rates.
This study highlights that there is still a lot of work to do to incorporate lightning information into rainfall estimates. The results of this study will feed into the future global coverage of satellite-based lightning mappers that will enable better short-term weather monitoring and forecasting capabilities. It is recommended that further investigation on the rainfall correction using lightning be done, such as separate analyses for convective and stratiform regions and lightning and nonlightning regions. A long-term analysis may also be pursued to establish a more generalized relationship between lightning and rain considering various rainfall types and weather events. Machine learning models may also be explored to derive lightning-corrected GSMaP, considering the nonlinear behavior of the rainfall-lightning relationship. Downscaling techniques may be explored to turn back the lightning-corrected GSMaP to a fine spatial resolution, considering the abovementioned limitations. Last, the integration of lightning before the actual GSMaP rainfall rate estimation may be done through simultaneous analyses with brightness temperature measurements, improving the Kalman filter in the GSMaP algorithm.
Acknowledgments.
The authors would like to acknowledge the support of JAXA, JMA, and MLIT for providing the necessary data analyzed in the study. This work was supported by the 4th Research Announcement on the Earth Observations of JAXA (ER4GPF008). Moreover, Mr. Veloria also received scholarship support from the Japan Ministry of Education, Culture, Sports, Science and Technology (MEXT).
Data availability statement.
The XRAIN radar rainfall data maintained by MLIT were obtained from the Data Integration and Analysis System (DIAS) (https://apps.diasjp.net/xband/). The GSMaP MVK, version 7, product was obtained from the JAXA G-Portal (https://www.gportal.jaxa.jp/). The LIDEN lightning data from JMA are available upon request.
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