Historical Shifts in Seasonality and Timing of Extreme Precipitation

Global warming impacts the hydrological cycle, affecting the seasonality and timing of extreme precipitation. Understanding historical changes in extreme precipitation occurrence is crucial for assessing their impacts. This study uses relative entropy to analyze historical changes in seasonality and timing of extreme daily precipitation occurrences on the global domain for 63 years of fifth generation of the European Reanalysis reanalysis data. Our analysis reveals distinct regional patterns of change. During the second half of the 20th century, Africa and Asia experienced high clustering of precipitation extremes. Over the past 60 years, clustering increased in Africa while becoming more spread out in Asia. North America and Australia had initially lower clustering and showed slight increases over time. Extreme events in extra‐tropical land regions mainly occurred in summer, with modest shifts in timing. These findings have implications for risk assessments of natural hazard like flash floods and landslides, emphasizing the necessity for region‐specific adaptation strategies.

• Global assessment of changes  in seasonality and timing of extreme daily precipitation occurrences using relative entropy • Precipitation extremes became more clustered in Africa and less clustered in Asia • Shifts in timing of extreme precipitation by only a few days for most regions

Supporting Information:
Supporting Information may be found in the online version of this article.
occurrence of natural hazards, such as flash floods, landslides (Marc et al., 2018;Steger et al., 2023), and debris flow (Nikolopoulos et al., 2015).Moreover, these changes interact with other climate feedback mechanisms, such as snowmelt runoff, atmospheric rivers, and tropical cyclones, amplifying or mitigating the impacts of climate change on various parts of the hydrological cycle (Gershunov et al., 2017;Miniussi et al., 2020;Tarasova et al., 2023).
In recent decades, relative entropy has emerged as a valuable tool to study the seasonality of precipitation and its extremes.Rooted in statistical physics and information theory (Cover & Thomas, 2005;Greven et al., 2014), this method quantifies the statistical distance between the actual distribution of extreme precipitation occurrences and a uniform distribution (Kullback & Leibler, 1951).Feng et al. (2013) introduced this tool to the field of precipitation research to study the seasonality of monthly rainfall in tropical regions.Since, several studies have used relative entropy to study rainfall seasonality across different time scales and geographical regions (Bal et al., 2019;Limsakul, 2020;Moustakis et al., 2021;Pascale et al., 2015Pascale et al., , 2016;;Sahany et al., 2018).Hitherto, however, a comprehensive global scale assessment of historically observed changes in timing and seasonality of extreme precipitation is missing.
This study aims to bridge this gap by evaluating the seasonality and timing of extreme daily precipitation.Using the relative entropy measure, we assess the degree of seasonality in extreme precipitation and to evaluate historical trends.By defining extreme precipitation above a relative threshold, we investigate the spatial patterns of these changes across different regions.We use the fifth generation of the European Reanalysis (ERA5) reanalysis data set, which provides high-quality and relatively homogeneous precipitation data, allowing for a comprehensive analysis of the observed changes in extreme precipitation seasonality.

Data
Precipitation data were obtained from the ERA5 reanalysis data set (Hersbach et al., 2018(Hersbach et al., , 2020)).This data set was chosen for its continuous coverage and relatively long temporal span at high spatial and temporal resolutions.While reanalysis data sets provide a comprehensive estimate of the global atmosphere-land-ocean system, it has known issues in accurately simulating convective processes, data assimilation inconsistencies, and limited observations over areas like oceans.The performance of ERA5 in capturing precipitation extremes varies depending on the intensity and location (Lei et al., 2022).ERA5 performs well over the extra-tropics, but exhibits larger errors over the tropics (Lavers et al., 2022).Notably, while ERA5 tends to underestimate the heaviest precipitation events, it reliably captures their general patterns, locations, and magnitude of less intense events (Bandhauer et al., 2022;Hénin et al., 2018;Lavers et al., 2022;Shen et al., 2022).
Hourly precipitation data from 01-01-1959 to 31-12-2021 at a resolution of 0.25° latitude × 0.25° longitude (approximately 30 by 30 km at the equator).These data were aggregated into daily estimates covering 63 years.The analysis involved moving 30-year windows through the data set, starting with the first 30 years (01-01-1959 to 31-12-1988) and shifting forward by one calendar year for each new 30-year segment.This resulted in 33 such 30-year windows.

Precipitation Extremes
We defined precipitation extremes as the highest 3 events per year on average, corresponding to the highest 90 events per 30-year window (or the 99.18th percentile of all day precipitation, or a return period of 0.335 years).Different thresholds were explored to quantify rainfall extremes across various regions, with little impact on the observed trends.Inclusion of more events reduced seasonality (see Figure S1 in Supporting Information S1), likely because that incorporates precipitation from various precipitation-generating mechanisms which may be characterized by different magnitudes and seasonal occurrence.This results in more evenly distributed occurrences throughout the year.

Relative Entropy as a Measure for Seasonality
To assess the seasonality of extreme precipitation occurrences, we use Relative Entropy, also known as Kullback-Leiber distance (D KL ; Kullback & Leibler, 1951).Relative entropy is a measure of the statistical distance between two probability distributions: (a) the actual monthly distribution of extreme precipitation occurrences and (b) the uniform distribution (Cover & Thomas, 2005).The calculation of relative entropy (D KL ) is represented by the following equation: In this equation, p m represents the actual probability distribution of monthly extreme precipitation occurrences, while q m denotes the uniform distribution of monthly occurrences.p m is calculated by dividing the number of monthly extreme precipitation occurrences (n m ) by the total number of occurrences (N = 90).Therefore, p m = n m /N.The uniform distribution (q m ) is approximately 0.083 for each month, taking into account the actual number of days in each month.The resulting value of D KL is measured in bits, as the base of the logarithm is 2 (Cover & Thomas, 2005), with a range between 0.005 and 3.7.Higher values indicate a clustering of extreme precipitation occurrences, while lower values suggest a more evenly spread distribution throughout the year.Figure 1 serves as a reference to aid in the interpretation of D KL .A single D KL value is calculated for each 30-year window, resulting in 33 values per grid cell.We note that if two areas have a similar D KL value, that does not mean that the rainfall events in both areas have similar magnitude, precipitation-generating mechanism, or timing.

Timing
To evaluate the timing and duration of precipitation extremes, the centroid (C) and the spread (Z) of the seasonal distribution were computed as the first and second moments of n m , respectively.The formulas for calculating C and Z are as follows: C represents the timing, while Z indicates clustering of the extremes around the centroid.Even though C can be estimated for each grid cell, it is not useful for locations with low D KL values, as there is no clear clustering of extremes.These metrics were only estimated for gridcells where the mean D KL > 0.27, indicating clustering of extremes in less than 10 months.To address potential errors related to events around November to February, a 6-month shift was applied and C and Z were recalculated and then shifted 6 months back, yielding C shift and Z shift .The choice between the original and shifted values depended on which produced a lower mean spread for each grid cell.The mean of the original C and C shift as well as Z and Z shift are included in Figure S2 in Supporting Information S1.Another approach to do this is using the circular mean as in Dey et al. (2021), but it yields similar results.

Regional Analysis
The regional analysis was conducted for IPCC WGI reference regions (WGI-v4; Iturbide et al., 2020), focusing on land regions.We pooled all events within a region, weighed them by cell size, and calculated the regional D KL , C and Z (Equations 1-3).To ensure a focus on regions with significant precipitation patterns, areas with very low rainfall, such as the Sahara, were excluded from this study.These dry areas were identified as cells where the mean value of the 90th highest rainfall event in the 30-year windows was below 5 mm day −1 (gray cells in Figure 2a).In the regional analysis, we only included regions containing at least 50% of the cells meeting this criterion, excluding the Sahara, Arabian Peninsula, and Eastern Antarctica.  1) when all extreme rainfall occurrences are evenly distributed over 1-12 months.

Statistical Significance
Spearman rank correlation was performed to assess positive and negative monotonic relationships between D KL and C over time in grid cells and regions.The correlation coefficient (ρ) ranges from −1 to 1, indicating the strength of the relationship.Significance was determined for p < 0.05.We also have repeated this analysis testing for field significance, following the false discovery rate approach described in Wilks (2016, Equation 3), with minimal impact detected (see Figure S3 in Supporting Information S1).When comparing the relative entropy of extreme precipitation occurrences in ERA5 (Figure 2a) to that of extreme precipitation of gauge data and a regional climate model in the US (Moustakis et al., 2021, their Figures 7a and  7b), the results look largely similar.The main difference is that our threshold of extreme events exhibits a stronger seasonality along the entire west coast and lower seasonality in Arizona and Utah than Moustakis et al. (2021, their Figures 7a and 7b).Furthermore, a comparison of our results to that of monthly precipitation in GPCC (Pascale et al., 2015;Pascale et al., 2016, their Figure 1c), CMAP (Pascale et al., 2015, their Figure 1d), and CMIP5 historical simulations (Pascale et al., 2016, their Figure 1d), similar patterns emerge again.However, the relative entropy of extreme occurrences is higher, indicating a greater clustering of extreme events compared to monthly precipitation.Regions such as northern North America, northern Europe, and various parts of Asia show a particularly pronounced clustering of extremes.Additionally, the geographical features of mountain ranges and coastlines are more prominent in the relative entropy of extreme occurrences compared to monthly precipitation.

Results
Figures 2c and 2d demonstrate the changes in relative entropy between the first and last window for each grid cell and for WGI-v4 reference regions, respectively.The observed changes display a mixed pattern of increases and decreases in precipitation seasonality.Notably, Sub-Saharan Africa, Australia, and North America exhibit increasing trends, suggesting a greater clustering of extreme events.Western Africa and North-Eastern Africa shows the highest increase in D KL , indicating a further intensification of extreme event clustering.Conversely, Asia, the Caribbean and North-East South America display decreasing trends, implying a transition toward a more even distribution of extreme events.
Figures 2e and 2f present the Spearman rank correlation coefficient of D KL over time.The correlation patterns align closely with those seen in Δ D KL , albeit with stronger signals.The correlation coefficient is statistically significant (p < 0.05) in 73.0% of all cells and 73.4% of land cells (see Table 1).Out of the significant cells, approximately half of the land cells have become more and less clustered.When correcting for field significance, the results obtained in Figure 2e do not change appreciably (see Figure S3a in Supporting Information S1).
Figures 3a and 3e showcase the zonal means of D KL for each latitude on respectively the global domain and over land only.Lower D KL values are evident in the southern hemisphere, with greater variability observed over land.The subtropics and most northern latitudes exhibit high D KL values.Drier areas display the highest inter-annual spread, encompassing the southernmost and northernmost latitudes, as well as the range between approximately −15 and −5° latitude.
The multidecadal variability in D KL for each WGI-v4 land region are depicted in Figures 3b-3d and 3f-3h.Regions such as the Caribbean, South American Monsoon and Northern Australia display substantial variability, whereas regions such as Western Africa or eastern South Africa show long-term increasing trends.Conversely, regions such as East North America, Southern South America, the Mediterranean, and New Zealand exhibit consistent relative entropy patterns over the years analyzed.Moreover, the highest values of D KL , so the highest The mean seasonal centroid C, which represents the timing of extreme precipitation occurrences, is presented in Figure 4. Panel a displays the mean of all 30-year windows for each grid cell, while panel b shows C per WGI-v4 reference region over land.The centroid of extreme precipitation occurrences over extra-tropical land regions predominantly falls in the summer months, with December-February in the Southern Hemisphere and June-August in the Northern hemisphere.The exception is the Mediterranean and west central Asia, where C occurs in winter (January -February).These patterns are comparable to those observed in the GPCC data set over land (Pascale et al., 2015;Pascale et al., 2016, respectively their Figures 15a and 1g), and CMIP5 historical simulations (Pascale et al., 2016, their Figure 1h), indicating a similarity between the centroid of extreme precipitation occurrences and all precipitation.Furthermore, our results closely align to those of Dey et al. (2021, their Figures 2a and 2d), who estimated the timing of extreme precipitation over Australia, defined as the maximum consecutive 5-day precipitation, using the circular mean instead of C. 4d present the difference in the number of days between the centroids of the first and last window.In most WGI-V4 regions, there is a difference of only a few days between the first and last window, shown on the map in that panel.The x-axis presents the middle of a 30-year window.Dry areas, defined as cells with a mean value of the 90th highest rainfall event below 5 mm day −1 in all 30-year windows, are removed from this analysis.

Figures 4c and
indicating minimal changes in the timing of extreme precipitation occurrences.In some specific regions, such as Australia, western South America, northeastern Europe, the Mediterranean and South Asia, the centroid falls a few days earlier in the year.Conversely in Western North America, South Central America, the Caribbean, eastern South America, and most regions in Sub-Sahran Africa, the centroid occurs a few days later in the year in the last window compared to the first.The pattern for West Africa is in agreement with findings by Van de Giesen et al. (2010), who noted that the onset of the rainy season has shifted to 10 days later in the year.
Figures 4e and 4f present the Spearman rank correlation coefficient of C over time.Like with Figures 2e and 2f, the correlation patterns are similar with those seen in ΔC. Figure S3b in Supporting Information S1 shows Figure 4e correcting for field significance, displaying very similar patterns.The regional Spearman rank correlation coefficient is significant in 30 of the 38 included regions, half of them have a positive and negative correlation coefficient.
When comparing the significant trends of the relative entropy (D KL , Figure 2f) and seasonal centroid (C, Figure 4f) interesting global patterns emerge.In Australia, the Mediterranean and northwest North America, the value of D KL increases while C decreases.This means a higher degree of clustering combined with extremes that occur earlier.In southern Asia, northwest South America and southeastern Africa, the value of D KL decreases while C decreases too, so more evenly spread out extremes and earlier in the year.In western Africa, central Africa, eastern Southern Africa and Madagascar, both D KL and C are increasing.The same is observed over western North America and Greenland.

Conclusions
In this study, we examined the seasonality of extreme daily precipitation occurrences using a metric based on relative entropy (D KL ) as an indicator of intra-annual clustering.By analyzing more than 60 years of precipitation data from ERA5 (1959-2021), our findings highlight significant historical shifts in the seasonality of extreme precipitation occurrences across different regions.In Africa, characterized by large seasonality at the beginning of the analyzed time period, we observed a further increase in the concentration of extreme precipitation events during specific times of the year.In Asia, although initial D KL values were also high, a decrease in clustering was observed over time.Australia and North America, characterized by initially low D KL values, experienced an increase in the clustering of extreme precipitation events.In parts of South America D KL has decreased, whereas in Europe D KL has remained relatively constant.Future work may seek to extend this analysis and that of Pascale et al. (2015Pascale et al. ( , 2016) ) by evaluating whether historical climate model simulations capture the trends in extreme rainfall seasonality we observed in ERA5 reanalysis.Such an approach could then be used for improved projections of future changes in extreme precipitation seasonality.
Examining the timing of extreme precipitation occurrences, we found that the peak of extreme events over extra-tropical land regions typically falls within summer.The observed patterns align with those of monthly precipitation, suggesting a similarity in the seasonality between extreme event occurrence and total precipitation amounts.The observed shift in timing of the centroid usually just spans a few days, suggesting a modest change in the timing of the extreme precipitation events.Changes in the timing of precipitation extremes have implications for flood risk (Blöschl et al., 2017;Wasko et al., 2020aWasko et al., , 2020b)), for instance when earlier extreme precipitation occurrences are combined with earlier snowmelt due to increasing global temperatures (Tarasova et al., 2023).Conversely, when extreme events occur outside of the main rainy season, the probabilities of soil erosion and landslides are higher (Steger et al., 2023).As such our work highlights the importance of taking changes in timing of extremes into account in climate adaptation scenarios.
Figures were made with cartopy version 0.20 (Met Office, 2010-2015;Elson et al., 2022) and Matplotlib version 3.4.3(Hunter, 2007).The python scripts and NetCDF data for repeating our analyses and recreating the figures and table in this manuscript are stored on the 4TU Repository (Gründemann et al., 2023b).Dutch National Supercomputer Snellius.The results contain modified Copernicus Climate Change Service information 2020.Neither the European Commission nor ECMWF is responsible for any use that may be made of the Copernicus information or data it contains.Nick van de Giesen acknowledges support of the European Horizon Europe Programme (2021-2027) under grant agreement number 101086209 (TEMBO Africa).

Figure 1 .
Figure 1.The value of the relative entropy D KL (Equation1) when all extreme rainfall occurrences are evenly distributed over 1-12 months.

Figure 2 .
Figure 2. Relative entropy of extreme daily precipitation occurrences (D KL , Equation 1).Presented as (a) the mean of all 30-year windows analyzed per grid cell, where a low value signifies an even distribution of extreme rainfall throughout the year, and a high value suggest clustering in a specific period.Panel (b) shows D KL calculated per WGI-v4 reference region over land.Panel (c) shows the difference in D KL between the first land last windows for each grid cell (Δ D = D 1992−2021 − D 1959−1988 ), with a negative Δ D indicating a more even distribution of rainfall extremes and a positive Δ D indicating more clustering.Panel (d) shows the same difference calculated per WGI-v4 reference region over land.Panel (e) shows the Spearman rank correlation coefficient of D KL over time, the non-white values indicate statistical significance (p < 0.05).Panel (f) shows the correlation coefficients calculated per WGI-v4 reference region over land.Dry areas, defined as cells with a mean value of the 90th highest rainfall event in all 30-year windows below 5 mm day −1 , are masked in gray.Regions in panels (b), (d) and (f) only include those containing at least 50% of the cells.

Figure
Figure 2a displays the relative entropy (D KL ) of daily extreme precipitation occurrences as the mean value over all 30-year windows per grid cell.D KL follows geographical features like mountain ranges and coastlines.Notably, mountain peaks exhibit low D KL values, while slopes have higher values.Examples are found in the Andes, Patagonia, Scandinavia, Ural Mountains, and Himalayas.Coastlines also display distinctive D KL patterns, with land areas often exhibiting higher values compared to adjacent oceans, seen around western Europe and Morocco, the Red Sea, the coast of eastern Africa, eastern Madagascar, western India, Myanmar, eastern Malaysia, and western Australia.In ERA5, D KL is generally higher on land than over oceans, with the exceptions of the South Pacific ocean, subtropical Atlantic and Arabian Sea.Panel b shows the D KL for each WGI-v4 reference region over land, with regions like Madagascar, Western Africa, and parts of Asia displaying the highest regional D KL values.Conversely, Eastern and Western United States, Southern South America, Southeast Asia and Southern Australia and New Zealand exhibit the lowest D KL values on land.

Figure 3 .
Figure 3.The relative entropy D KL indicating seasonality of extreme daily precipitation occurrences (Equation1) presented as: (a) mean value for each latitude across grid cells and (e) across land cells.The colorbar in the legend of these panels indicate the middle of a 30-year window.The mean value across all 30-year windows is presented by the dashed black line.Panels (b-d and f-h) show D KL calculated for each WGI-V4 land region.Each line corresponds to a region with the same color as shown on the map in that panel.The x-axis presents the middle of a 30-year window.Dry areas, defined as cells with a mean value of the 90th highest rainfall event below 5 mm day −1 in all 30-year windows, are removed from this analysis.

Figure 4 .
Figure 4. Mean seasonal centroid of the seasonality of extreme daily precipitation occurrences (C, Equation 2).Presented as (a) the mean of all 30-year windows analyzed per grid cell, and (b) calculated per WGI-v4 reference region over land.Panel (c) shows the difference in C between the first and last window for each grid cell in number of days (Δ C = C 1992−2021 − C 1959−1988 ), with a negative Δ C indicating that the central date of extreme rainfall occurrences are taking place earlier in the year and a positive Δ C indicating later in the year.Panel (d) shows the same difference calculated per WGI-v4 reference region over land.Panel (e) shows the Spearman rank correlation coefficient of C for each grid cell, the non-white values indicate statistical significance (p < 0.05).Panel (f) shoes the correlation coefficients calculated per WGI-v4 reference region over land.Cells with D KL < 0.27 (rainfall occurrences occurring in more than 10 months) are excluded.Also dry areas, defined as cells with a mean value of the 90th highest rainfall event in all 30-year windows below 5 mm day −1 , are masked in gray.Regions in panels (b), (d), and (f) only include those containing at least 50% of the cells based on the two criteria above.
Dry areas, namely the cells in which the mean value of the 90th highest rainfall event in the 30-year windows is below 5 mm day −1 , are not included.Statistical Significance (p < 0.05) of D KL Trends With Time, Using the Spearman Rank Correlation Coefficient clustering of precipitation extremes, are observed in geographically diverse regions, specifically Western Africa, Madagascar, Tibetan Plateau, Eastern Siberia, Russian Arctic, and Northern Australia.