How Is Spatial Homogeneity in Precipitation Extremes Changing Globally?

The effect of climate change on precipitation intensity is well documented. However, findings regarding changes in spatial extent of extreme precipitation events are still ambiguous as previous studies focused on particular regions and time domains. This study addresses this ambiguity by investigating the pattern of changes in the spatial extent of short duration extreme precipitation events globally. A grid‐based indicator termed Spatial‐Homogeneity is proposed and used to assess the changes of spatial extent in Global Precipitation Measurement records. This study shows that (a) rising temperature causes significant shrinking of precipitation extent in tropics, but an expansion of precipitation extent in arid regions, (b) storms with higher precipitation intensity show a faster decrease in spatial extent, and (c) larger spatial extent storms are associated with higher total precipitable water. Results imply that in a warming climate, tropics may experience severe floods as storms may become more intense and spatially concentrated.

10.1029/2023GL103233 2 of 9 tropics and even more so over the oceans (Ali et al., 2021). This super C-C scaling is hypothesized to be a result of change in storm dynamics, particularly the morphing of the storm extent and underlying structure (Collins et al., 2013;Lenderink & van Meijgaard, 2008).
Unlike the general acceptance of variation in intensity, the variation in the spatial extent of short duration storms is still debated with two contrasting mechanisms. A storm is affected by both the thermodynamic and dynamic factors, however the behavior of storm's spatial extent with rising temperature can differ depending on weather the dynamic factors control the storm dynamics . The first mechanism suggests a reduction in spatial extent with rising temperature as the dynamic factors dominating the storm dynamics redistribute moisture toward the center (Figure 1a) (Wasko et al., 2016). The second, contrasting mechanism, suggests that when the thermodynamic factors dominate, rise in temperature results in increased spatial extent as stronger cloud dynamics and larger shower clusters bring more moisture from larger areas (Lochbihler et al., 2017). Findings from numerous studies analyzing the effect of temperature on spatial extent support the decreasing spatial extent mechanism (Chang et al., 2016;Guinard et al., 2015;Han et al., 2020;J. Li et al., 2018;Peleg et al., 2018), and several other support the increasing spatial extent mechanism (Bevacqua et al., 2021;Chen et al., 2021;Matte et al., 2022;Prein et al., 2017). However, most past studies have focused on specific regions, or on certain types of storms, or at daily precipitation extremes rather than short duration storms.
To address the ambiguity of whether short duration precipitation extents are expanding or shrinking with rising temperature, this study investigates the global patterns of change in spatial extent. This study proposes a novel metric to quantify grid-homogeneity, termed Spatial-Homogeneity (SH) to compare the changes in spatial extent of extreme storms with different intensity and at different locations. The SH metric can be used for radar as well as satellite measurements and is applicable for both short and long duration precipitation extremes. The study first investigates the global variability in spatial extent of short duration extreme storms in the recent past. Subsequently the relationship between temperature and spatial extent is examined. Finally, the study explores how total precipitable water, warm versus cold years and wet versus dry years impact the spatial extent.
Even though the satellite products are known to underestimate rainfall rates for deep convective systems (Adhikari et al., 2019;Duan et al., 2015;Kucera & Klepp, 2022;R. Li et al., 2021), their high spatio-temporal resolution and global coverage make them useful in assessing change in the spatial extent of precipitation. Therefore, to have an acceptable global resolution, this study adopts satellite data products instead of the sparsely gauged ground observations available to represent variability in spatial extent across the world and to infer changes in this variability with local climatic variables including temperature, precipitation intensity, and total precipitable water.

Data and Methods
The Integrated Multi-satellite Retrievals for Global Precipitation Measurement (IMERG) data set provides continuous records of satellite precipitation observation from 2000-present, as the IMERG algorithm combines Blue indicates lower temperature and red indicates higher temperature. Three-dimensional curves are also presented to emphasize the hypothesis. (b) Representation of the Spatial-Homogeneity methodology. Nine boxes represent the eight neighbors around the highest intensity center. The intensity of gray in each box indicates the intensity of rainfall at that grid. the early precipitation estimates from Tropical Rainfall Monitoring Mission (2000Mission ( -2015 with the more recent precipitation estimates from Global Precipitation Measurement (GPM) (2014-present) (Huffman et al., 2020). However, to maintain the homogeneity of records only GPM IMERG estimates from 2014 to 2021 are used in this study. Due to the focus of this study on spatial extent of instantaneous/extreme precipitation bursts, analysis is performed on IMERG's high spatial and temporal resolution 3IMERGHH (version 6) (Huffman et al., 2020) product available at 0.1° × 0.1° spatial resolution and 30 min time step. Integrated Multi-satellite Retrievals for Global Precipitation Measurement, like any other satellite product has its limitations and uncertainties (Beck et al., 2019;Bulovic et al., 2020;Prakash et al., 2018). However, it performs better than most other satellite and reanalysis products, particularly for hourly and sub-hourly precipitation estimates (Tang et al., 2020). Hourly Integrated Water Vapor or Total Column Water Vapor (TCWV) at 0.25° × 0.25° spatial resolution and hourly 2 m surface air temperature at 0.1° × 0.1° spatial resolution from Earth ReAnalysis (ERA5) are used in this study (Hersbach et al., 2020;Muñoz-Sabater et al., 2021).
To analyze the spatial extent of extreme precipitation events, independent storm fields must be identified. In this study, a storm field is defined by considering a grid cell with extreme precipitation and its eight neighboring cells such that the center pixel corresponds to the center of the storm and receives more precipitation than the neighboring cells. To identify independent storm fields, first the top ten 30-min annual maximum precipitation (AMP) (simply AMP from here on) events at each grid cell of the GPM data set are estimated for each year in the data set. Then starting with AMP, for each grid cell, the precipitation for the eight neighboring cells surrounding the central precipitation event is extracted for the same time of occurrence as the central extreme precipitation event and compared to the center cell. If, for instance, the AMP event at the center cell has the same or lower precipitation than one of its eight neighbors, then the next maximum event (second of the top 10 annual maximum events) is considered and compared with neighboring precipitation at the time of its occurrence. The process is repeated until an event in which the intensity at the center cell is higher than the neighboring cells is found. The validity of independent storm field is enforced by choosing only the maximum event out of the top 10 maximum events which has greater intensity at the center cell than its neighbors.
A new metric, "Spatial Homogeneity" denoted SH, is proposed to investigate and compare the changes in spatial extent of varying intensity extreme storms and at different locations. To understand the homogeneity metric for an extreme storm, precipitation for all the cells in the storm field is sorted in descending order of its intensity and a cumulative normalization is performed. Consider the precipitation in descending order is represented as P 0 , P 1 , P 2 , P 3 , P 4 , P 5 , P 6 , P 7 , P 8 where in P 0 is maximum precipitation and lies at the center of the storm field. The study ascertains the spatially accumulated precipitation average as P 0 /1, (P 0 + P 1 )/2, (P 0 + P 1 + P 2 )/3, … , (P 0 + P 1 + P 2 + P 3 + P 4 + P 5 + P 6 + P 7 + P 8 )/9. Here the last term represents average precipitation for the entire grid for the extreme storm event considered. These values are then plotted against the number of grid points considered in formulating the accumulated spatial average. The above accumulated precipitation distribution can be compared to the case where all neighbors have zero precipitation and only the center point received precipitation. In this scenario, the accumulated rainfall plot would represent P 0 /1, (P 0 )/2, (P 0 )/3 …… (P 0 )/9 against the number of grid points associated. The other comparison represented the case where all grid points receive the same amount of precipitation say P 0 , resulting in a constant value (P 0 ) being depicted against the number of grid cells. An assessment of the spatial distribution of each storm is then formulated by noting how strongly the actual extreme event deviated from the case where precipitation occurs only at the center (marked by "a" in Figure 1b and Equation 1) with reference to the total possible deviation between the case of precipitating only at center versus the case where all grid cells receive the same amount of precipitation (denoted by "a + b" in Figure 1b and Equation 1). Figure 1b provides an overview of the methodology adopted in assessing the spatial structure of the extreme precipitation event surrounding the central grid cell. The SH metric calculated using Equation 1 is used to ascertain the spatial homogeneity/inhomogeneity of the extreme storm field. (1) SH allows a comparison of the extreme storm from a fully uniform case to a case where an isolated extreme falls at the center of the grid. If a warmer future creates more isolated and convective rainfall events, the above metric will collapse to zero. If the opposite were to occur (more uniform extremes) the metric will assume a value of one.
The increasing convection hypothesis outlined above is depicted in Figure 1a. The SH metric allows assessment of spatial distribution of extreme precipitation events without focusing on the intensity of the event as well as assessment of the spatial distribution of extreme events across the world ( Figure S1 in Supporting Information S1 for examples of SH).
A sensitivity assessment of SH with associated temperature is performed using quantile regression with a focus on the median (50th percentile). The resulting regression coefficient is referred to as "sensitivity" in the remainder of this paper. The quantile regression sensitivity estimator by Wasko and Sharma (2014) has been adopted in this study. As only AMP events are considered, the assessment results presented focus on the 50th percentile (median) instead of rarer percentiles. Details of the sensitivity estimation procedure, its sensitivity to computational needs, and its motivation in the context of identifying trends in a highly variable response, are presented in Wasko and Sharma (2014) and Sharma et al. (2018).
t-test is used to assess the impact of local climate variables on SH and if SH for higher intensity (or high TCWV/ wet year/warm year) storms is statistically different from SH for lower intensity (or low TCWV/dry year/cold year) storms. At any location, among all the annual maxima storms in 2014-2021 period, the annual maxima storm with maximum precipitation intensity is compared to the annual maxima storm with minimum precipitation intensity. This forms a maximum/minimum intensity storm pair at the location. Now, assuming climatic homogeneity in the 4° × 4° (41 × 41 pixels) grid around any location, the sample for t-test at any location comprises of the maximum/minimum intensity storm pairs from all the points in the 4° × 4° grid. The resulting sample with a size of 1,681 is used to calculate t-test and compare the maximum and minimum intensity storm. Similar procedure is applied to the other variables, where the maximum/minimum TCWV are estimated by comparing accumulated TCWV in 24 hr prior to the storm, the wettest/driest years by comparing the total annual precipitation, and warmest/coldest year by comparing the mean annual temperature. Locations with t-statistic close to zero fail the t-test hypothesis for a significance level of 0.05 (5%) ( Figure S5 in Supporting Information S1).

Changes in of Spatial Homogeneity (Spatial Extent) in Recent Past
SH-metric does not give a quantitative estimate of the exact spatial extent of the storm, but it is a quick and resourceful method to track the changes in spatial extent of storm. The SH-metric can also be used to understand the geographic distribution of spatial extent across the globe. The average SH-metric for AMP 30-min storms ( Figure S2 in Supporting Information S1) shows smaller storm extents in tropics and mountainous regions. This is coherent with the findings of Tan et al. (2021), which concluded that extreme storms in tropics are typically smaller than those in northern and southern temperate regions. Figure 2 presents the average change in SH between 2014 and 2021 with reference to the 2014 SH. A running median of 4° × 4° grid has been used to smooth out the variability. The changes in SH from year to year are presented in Figure S3 in Supporting Information S1. The spatial extent of storms in the equatorial regions It is important to acknowledge that these results depict the variability in SH over the specific short period analyzed in this study. This temporal variation of SH can be biased depending on presence of strong climate phenomenon like a strong El-Nino/La Nina event occurring within the time frame. So, to ensure robustness of the conclusions drawn for SH, the subsequent sections investigate the relationship between SH and temperature as well as other climate variables.

Sensitivity of Spatial Homogeneity (Spatial Extent) to Temperature
To comprehensively understand the effect of local climate and atmosphere on the spatial extent of extreme storms, analysis of spatial extent with temperature, intensity of precipitation and TCWV is performed. Sensitivity of spatial extent with instantaneous temperature is presented in Figure 3. Sensitivity of SH with temperature is calculated only for cells presenting statistically significant trend in SH, when SH are ordered as per rising temperature. Statistical significance of trend is asserted using Mann-Kendall Test at 5% significance. A 4° × 4° moving median is then applied on the sensitivity to smooth out the variability. ERA5-land provides hourly temperature data, but GPM provides 30-min precipitation so the instantaneous temperature here refers to the temperature at the time of the storm or in the hour before the storm. It is evident from the study that the tropical regions dominated by convective precipitation have strong negative relation between spatial extent and instantaneous temperature. Parts of the Amazon and Indonesian Tropical Regions observe 4%-5%/°C reduction in spatial extent. On the other hand, the arid regions particularly Eastern Sahara (SA), the Thar desert in India, Southern Arabian Peninsula (AP), Taklamakan and Gobi Desert (TGD), and Western Coast of United States (WUS) show positive sensitivity and will observe spatially larger storms with the warming climate. The northern and southern temperate regions generally present slight positive sensitivity of spatial extent with temperature with slightly negative sensitivity seen in central and northern Europe (EU) (0.1%-1%/°C), southern New Zealand (NZ), and Southern Argentina (PD) (0.1%-1.5%/°C).
This study uses instantaneous temperature rather than widely used mean daily temperature (Lenderink & van Meijgaard, 2008) because in case of convective storms, particularly in tropics, temperature tends to drop at the advent of the storm and using daily temperature for sensitivity will result in inaccurate conclusions (Ali & Mishra, 2017;Ali et al., 2018). On comparing Figure S4 in Supporting Information S1 and Figure 3, it is evident that the impact of using daily versus instantaneous temperature is concentrated around equator. Moreover, the This study finds that both the findings are accurate and the behavior of spatial extent with temperature is indeed dependent on the geographic location and the local climate.

Effect of Local Climate on Spatial Homogeneity (Spatial Extent)
The impact of local climate on SH is assessed by mapping the variation of the t-test statistic in SH when comparing maximum and minimum intensity storm (Figure 4a), maximum TCWV and minimum TCWV (Figure 4b), wettest and driest year storm (Figure 4c), and warmest and coldest year storm (Figure 4d). A higher magnitude t-statistic indicates large differences between SH for maximum versus minimum intensity (or TCWV/wettest vs. driest/warmest vs. coldest year) storms, while sign of t-statistic implies the impact of higher versus lower intensity (or other variables) on SH of a storm. A positive t-statistic implies increase in SH for higher intensity (or high TCWV/wettest/warmest year) storms while negative t-statistic implies decrease in SH.
The overall trend indicates that globally a rise in intensity of storms leads to a lower spatial extent (Figure 4a). A larger spatial extent for more intense storms is observed in Sahara, Arabian Peninsula, Central Russia, and southern Argentina. The overall global trend suggests that the moisture is being redistributed from storm boundaries to the storm center. The findings from Figures 3 and 4a support the hypothesis presented in Figure 1a implying that a rise in temperature results in more intense and spatially concentrated extreme storm bursts. On the other hand, TCWV has an overall reinforcing relation with the SH. A rise in TCWV results in greater SH implying that at most locations, with exceptions of Eastern US and central Russia, spatially larger storms are associated with higher TCWV (Figure 4b). Considering the behavior of SH with temperature, storm peak intensity and TCWV, it can be argued that for convective storms in tropics, an increase in temperature leads to intensified storm peak. Moreover, under the moisture limited conditions at higher temperatures, moisture tends to concentrate towards the center of the storm, resulting in reduced spatial extent of the storm.
The effect of total annual precipitation is regionally distinct as Sahara, Arabian Peninsula, India, Central Asia, and Europe have larger spatial extent storms in wetter years. On the other hand, drier years observe larger spatial extent storms in tropical regions in Southern America, Africa, South East Asia, and Northern and Western Australia (Figure 4c). Mean annual temperature does not have a overall strong impact on SH globally (Figure 4d). The study here presents a preliminary analysis of the impact of these local climate variables on change in spatial extent and a more extensive analysis may result in significant regional trends.

Discussion
While the data length used in the study is shorter than that used for point-based studies of spatial extent done in the past, it is interesting to note the conclusions drawn from short time period are also valid for longer time period (Figures S6 and S9 in Supporting Information S1).
The study uses 9 cells (3 × 3 grid) to define the storm field and estimate SH. This 9-cell grid structure implies that the storm field extends over 30 × 30 km which will be smaller than that observed for daily storms, but it is sufficient for short duration (30 min) precipitation extremes. It is noteworthy that using a larger size storm field (25 neighboring cells or more) quantitatively changes the overall SH for short duration storms ( Figure S7b in Supporting Information S1) however, using a larger storm field does not alter the patterns for change in SH. The overall conclusions regarding sensitivity of spatial extent (SH) with temperature and other parameters remain the same whether using 9-cell storm field or 25-cell storm field ( Figure S8 in Supporting Information S1). It must also be noted that smaller spatial scale convective storms with size smaller than 100 km 2 may not be sampled using the GPM (0.1° resolution) data set, however the SH methodology can be used to capture these using finer resolution data.
These short duration storm systems are susceptible to presence of zero precipitation cells in the storm field thus presenting larger inhomogeneity and less linearity in spatially accumulated average precipitation. Although, the formulation of SH metric uses linear proportionality to estimate the SH, a sensitivity analysis using non-linear proportionality to calculate SH did not significantly alter SH estimates. This establishes that linear proportionality can capture the SH even for short duration storms. It is also noteworthy that the zero-precipitation cells primarily affect SH for precipitation sparse arid regions ( Figure S7a in Supporting Information S1) which are hotspots for increasing spatial extent with temperature.

Conclusions
The results of this study show that the geographic location and the local climate play a crucial role in how moisture is being distributed around a storm, particularly for short duration extreme storms. The following conclusions are drawn from this study: 1. Spatial extent of short duration precipitation extremes has increased around the equator and decreased in the northern and southern temperate in the recent past. However, sensitivity of spatial extent with temperature has contrasting results. 2. An overall global trend of moisture accumulation toward the storm center as spatial extent decreases with a rise in temperatures. 3. Spatial extent of storms in arid regions (excluding Australia) and parts of central Europe tends to increase with increasing temperature.
Some other conclusions from the preliminary analysis with other local climate variables can also be made. Higher intensity storms typically result in lower spatial extent storms. Furthermore, the study finds that spatially larger storms are globally associated with higher total precipitable water. Wet years in Sahara, Arabian Peninsula, India, Central Asia, and Europe have larger spatial extent storms whereas dry years observe larger spatial extent storms in tropical regions in Southern America, Africa, Southeast Asia, Northern and Western Australia. Warm versus Cold year do not have a consistent impact on spatial extent, although a more regressive analysis may result in concrete conclusions.
These results along with previous understanding that intensity of extreme storms increase in warmer climate, have significant implications as short duration extreme storms in warmer climate will be more intense and concentrated. If these trends of spatial extent continue as the global temperature rise, the tropics may experience intense and concentrated storms which may lead to severe floods.
Future studies may focus on analyzing the climate drivers responsible for the year-to-year spatial extent variation, and whether similar patterns are present for longer duration storms. This study concludes that short (sub-hourly) extreme storms show significant change alteration in spatial extent, however the change in spatial extent may not be equally conspicuous for longer duration storms. This is routed in the fact that super CC scaling is observed for shorter duration storms and becomes less prominent as the duration of storm increases.