The creation and climatology of a large independent rainfall event database for Great Britain

Extreme rainfall studies generally focus on hourly or daily rainfall accumulations. Additionally, studies focus on annual maxima (AM) or ‘peak intensities’. Although this approach is useful, the use of fixed‐duration accumulations simplifies inherently continuous rainfall processes which, at a rain gauge, are experienced as rainstorms of varying duration. A gap also exists in the study of sub‐hourly rainfall extremes which are an important source of flash floods. Here, we present the first large‐scale study of rainstorms in the United Kingdom. We leverage a recently created sub‐hourly resolution rain gauge dataset for Great Britain to identify over 70,000 rainstorms that generated AM rainfall intensities across a range of sub‐hourly to daily durations at 1279 rain gauges up to 2018. Our findings are consistent with previous studies of UK rainfall extremes and their climatology, where strong east–west differences are found in the magnitude of autumn and winter long‐duration (over 12‐h) rainstorms. We observe broad similarities in the behaviour of short (under 4‐h) rainstorms across GB, which are dominated by seasonal variations in convective activity rather than by geographical location. Our study reveals substantial overlaps between AM of different durations, with single rainstorms containing AM across a wide range of durations. We also demonstrate the substantial correlation between rainstorm duration and volume. These results challenge common independence assumptions used in the statistical modelling of rainfall extremes using extreme value theory. Our results represent an opportunity to refine rainfall design methods towards improved, robust representations of rainstorms.

magnitude and extent (Chow et al., 1988Faulkner, 1999Kjeldsen et al., 2005Redfern et al., 2016Cristiano et al., 2017Veldhuis et al., 2018).Extreme rainfall and their characteristics are especially important in urban and fast response catchments due to the rapid onset of runoff in these systems which can lead to dangerous 'flash flood' situations (Westra et al., 2014Archer & Fowler, 2015).
Despite the importance of rainstorm duration, most analysis of rainfall extremes in the United Kingdom and worldwide has been carried out using fixed-duration daily (e.g., Osborn et al., 2000Osborn & Hulme, 2002Fowler & Kilsby, 2003Osborn & Maraun, 2008Jones et al., 2014) or hourly (e.g., Faulkner, 1999Stewart et al., 2013;Blenkinsop et al., 2017Darwish et al., 2018, 2021Kendon et al., 2018) rainfall totals.These studies show that UK winter precipitation has a well-established east-west split, with heavier extremes in the west; while UK summer precipitation shows a north-south pattern, with heavier convective events in the south.Daily extremes are most frequent during the summer for eastern regions, and in the autumn for all other regions.An evident gap in the study of UK sub-hourly rainfall extremes restricts our understanding of events that drive flash flooding.
The fixed-duration approach contrasts with eventsbased modelling of rainfall where independent rainstorms are extracted from timeseries data (Restrepo-Posada & Eagleson, 1982Serinaldi & Grimaldi, 2007De Michele & Ignaccolo, 2013Serinaldi & Kilsby, 2013Jun et al., 2018).Here rainstorm duration is not constrained and is instead determined using statistical or empirical methods.The use of events allows for a determination of the 'true' duration of the rainstorms that result in hourly or daily rainfall extremes (Barbero et al., 2019); it also better reflects the properties of rainfall, as artificial constraints on event duration are avoided.
Event-based studies of UK rainfall have focused on a limited number of extreme events.They show clear differences in the drivers of extreme rainstorms for < or >4-h duration, with convective or frontally forced convection-including mesoscale convective systemspredominantly causing shorter-duration extremes while longer-duration extremes tend to be frontally or orographically driven (Hand et al., 2004Lewis & Gray, 2010Clark & Webb, 2013).
In this paper we make use of a new, quality-controlled sub-hourly rain gauge dataset for GB (Villalobos Herrera et al., 2022) to identify and extract over 70,000 rainstorms associated to fixed-duration annual maximum (AM) rainfall intensities across a range of sub-hourly to daily durations.This represents both the largest study of the characteristics of extreme rainstorms for GB to date, and the first large-scale exploration of rainfall in GB at the sub-hourly scale.
First, in Section 3, we detail the methods used to identify and extract rainstorms that contain AM events.In Section 4. we examine the characteristics and climatology of these rainstorms; we reveal significant overlaps between rainstorms associated with different AM durations and highlight regional similarities among extreme short duration extremes.Finally, in Section 5. we discuss implications of our work for flood risk management and engineering design practice.

| Rainfall data and quality control
Sub-hourly resolution rainfall data was obtained from three rain gauge network operators within GB: the Environment Agency (EA), Natural Resources Wales (NRW), and the Scottish Environment Protection Agency (SEPA), which rely on these networks for water resource and flood risk management, as well as other operational needs.The use of sub-hourly data excludes from consideration most of the UK Met Office (UKMO)'s MIDAS dataset which contains only hourly precipitation.In total, 1279 rain gauges are available for analysis.The quality control and preparation of this sub-hourly rainfall dataset is detailed in (Villalobos Herrera et al., 2022), with QC scripts available at https://github.com/nclwater/intense-qcand https:// github.com/nclwater/SubHourlyQCand the data is available on request from the original providers.
The spatial coverage of the data includes Great Britain and some surrounding islands (Figure 1).Gauge records, after QC, are longest near central England and shortest in the peripheries of Southwest England and the Scottish Highlands.The median record length of the gauges is 17 years and only 42 gauges exceed 30 years (Figure 1a,c), barring any trend analysis.Rain gauges were classified into 5 regions (Figure 1b) defined for hourly extremes (Darwish et al., 2021) to study spatial patterns in the data.Most of the data is held as tip-time records, $38% of gauges have coarser, 15-min accumulation data.

| Annual maximum series and rainstorm definition
Ordinarily samples of extreme rainfall follow either a block-maximum or a peak-over-threshold (POT) approach (Coles, 2001).The block maximum approach is frequently used to study the frequency of extreme rainfall events in the United Kingdom (Faulkner, 1999Fowler & Kilsby, 2003Stewart et al., 2013;Darwish et al., 2018).
Here we use a block length of 1 year to sample, at each rain gauge, the annual maximum series (AMS) of 10 durations that are of interest in engineering applications: 5-, 10-, and 15-min; ½-, 1-, 2-, 3-, 6-, 12-, and 24-h.If a year within a rain gauge's record has more than 15% missing data, then it is excluded from that gauge's AMS.The analysis is focused on sub-hourly to sub-daily AMS as these are the least well understood rainfall extremes in the United Kingdom.Consider rainstorms to be periods of continuous or near-continuous rainfall that are separated by sufficiently long dry spells.This is distinct from rain accumulations of arbitrary durations (e.g., hourly, or daily rainfall totals) as rainstorm durations are not pre-determined.Rainstorms may contain multiple AMs; these are the individual rainfall totals accumulated over an arbitrary duration that make up a rain gauge's AMS.Short-duration AMs embedded within rainstorms are referred to as bursts in some literature (e.g., Ball et al., 2019).The presence of multiple AMs in a rainstorm complicates the extraction and identification of independent rainstorms; an example of this is shown in Figure 2 where five AMs for durations ranging from 2-h to 24-h are part of a larger 39-h rainstorm.
All the AMs in this paper have been calculated using sliding-window accumulations to find the true maximum rainfall at each duration.Tip-time data allows for fullysliding calculations where the start of the accumulation period can be positioned at any point in the timeline; however, 15-min data can only be aggregated using semisliding windows and discretization effects are unavoidable.The use of a combination of sub-hourly data and sliding-window totals implies that the AMs presented here are on average larger than those calculated using hourly data (Stewart et al., 2013;Morbidelli et al., 2017).

| Time between independent rainstorms
The defining characteristic of a rainstorm is the minimum time between independent rainstorms (t b 0 ).This may be defined by using expert knowledge of the climatology of the region under consideration; however, its definition is not straightforward and may contain a degree of subjectivity (Bonta & Rao, 1988Koutsoyiannis & Mamassis, 2001Marra et al., 2020).This subjectivity is associated to the use of discrete events, where there is an inevitable level of arbitrariness in the definition of what constitutes an event.
Work by Restrepo-Posada and Eagleson (1982) established a statistical method to calculate t b 0 based on the consideration that independent rainstorms must follow a Poisson arrival process.We used a modified version of the Restrepo-Posada & Eagleson algorithm (see the Supplementary Information (SI) for more details on the method and algorithm) to calculate t b 0 .In essence the algorithm estimates t b 0 by iteratively testing different dry spell durations until rainstorm arrival times are exponentially distributed and hence, independent.For each gauge we have used the maximum continuous dry day (CDD) index value present in the closest grid of the GHCNDEX (Donat, Alexander, Yang, Durre, Vose, & Caesar, 2013) and HadEX2 (Donat, Alexander, Yang, Durre, Vose, Dunn, et al., 2013) Climdex datasets as an upper bound on the duration of the dry spell between storms.Longer periods without recorded rainfall present in the data are caused by missing data or due to the removal of suspect data during QC, and their presence may lead to bias in t b 0 estimates.CDD represents a reasonable maximum for dry spell duration as it is based on the high-quality daily observations which underpin these indices.Additional details regarding the calculation of t b 0 are identical to those presented in the appendix of Restrepo-Posada and Eagleson (1982) and are included in the SI.The spatial distribution of minimum rainstorm interarrival times in GB shows a clear and remarkably smooth pattern with the minimum t b 0 values in northwest Scotland and elevated western regions of GB such as the Lake District and western Wales, while longer dry spells are required for rainstorm independence in eastern and central England (Figure 3).This matches the spatial distribution of UK annual precipitation and rain days (Hulme & Barrow, 1997Met Office, 2013).It is known that t b 0 varies with climate and tends to be larger in drier climates, allowing for longer dry intervals to exist within independent rainstorms at dry climate locations (Restrepo-Posada & Eagleson, 1982).This is a result of increased rainfall clustering in dry climates: in dry locations with infrequent rainfall, it is likely that consecutive rainstorms are caused by (i.e., dependent on) a single synoptic or mesoscale event.This contrasts with wet regions that have high annual rainfall totals due to more frequent rain that is segregated by shorter dry intervals.The clustering in dry regions leads to larger t b 0 values while wet regions require fewer dry hours (lower t b 0 ) for rainstorms to be statistically independent of each other.Hence the low t b 0 values in the wet, western areas of GB, and the higher t b 0 values in east and central England.

| Rainstorm timeseries extraction
The second sampling step is to extract the time series data for the independent rainstorm associated with each AM.To obtain complete rainstorms we have implemented an extraction algorithm similar to that used in the development of the Australian Rainfall and Runoff design guidance (WMAwater, 2015Ball et al., 2019) where search windows are iteratively used to identify rainfall which may be apportioned to a rainstorm.
The extraction algorithm has three main phases, in the initial phase (Figure 4a) the time series data belonging to a single AM of any duration is identified and treated as the core of the rainstorm.The AM timeseries is examined and all dry intervals t d,i are compared against t b0 , if any t d,i ≥t b0 then the timeseries is split and the AM is classified as a compound annual maximum (CAM) as it contains two or more independent rainstorms.These events can also be viewed as rainstorm clusters.CAM rainstorms are extracted as two or more rainstorms but are otherwise treated similarly to AM rainstorms.
Once the rainstorm core(s) is identified, the main phase begins (Figure 4b).Here a series of w search windows are used to expand the rainstorm timeseries forward and rearward.The behaviour of each search window is controlled by the window duration, T w [h], and a threshold depth, D w [mm].The functioning of each search window is explained below, followed by a description of the durations and thresholds used.
The forward search is executed first.Any non-zero observations within T w time of the rainstorm's first observation, F, are identified and their total depth R w [mm], is calculated.If R w ≥D w then the candidate observations are added to the rainstorm time series and the first of these candidates is used as F and the search is repeated.If R w <D w (or if there are no candidates) then the candidates are discarded, and the rearwards search is started.An analogous search at the rear of the rainstorm timeseries is carried out after the forward search; once this is complete the algorithm proceeds to the next search window, until all windows have been exhausted.
Various combinations of w, T w , and D w were tested before settling on using 3 windows.The first window w =1 ð Þ is designed to add any observations that are 'adjacent' to the AM core by setting D 1 under the minimum resolution (0.2 mm) for tipping-bucket rain gauges and T 1 as 15-min to match the temporal resolution of the sub-hourly gauges that do not have tip-time data.Window 2 requires at least two non-zero observations within an hour (D 2 =0:4 mm, T 2 =1 h) and is used as an intermediate window between immediately adjacent rainfall, extracted by window 1, and more distant rainfall extracted by window 3. The final window ensures independence between a rainstorm and any adjacent rain by using t b 0 as T 3 .An initial value of 0.2 mm was used as D 3 , however this led to some very long rainstorms that included isolated single tips before or after the main burst.To avoid this, window 3 avoids the use of a fixed rainfall threshold and instead requires that a minimum rainfall intensity of 1 mm h −1 be present for data to be added to the rainstorm, therefore D 3 (in mm) is set as equal to T 3 (h).This reduces the possibility of long dry spells being present between a rainstorm and isolated single tips as more substantial rainfall is required to include it in the rainstorm.Tests with T 3 =2 h and D 3 =1 mm prior to the use of t b 0 (not shown) are largely consistent with our results.
In the final phase, a regular time series is generated from the sub-hourly data after identifying all the observations that make up a rainstorm.A 5-min accumulation period is used for tip-time data and a 15-min accumulation period is used for gauges with this temporal resolution.A set of summary statistics, described in Section 3.3 are calculated at this point before the algorithm is repeated on another AM value (Figure 4c).
An example of the functioning of the extraction algorithm is presented in Figure 2 for a very large rainstorm registered in the Lake District during the floods of November 2009.In this instance the 31 mm/2-h AM registered in the 120-min period ending at 23:50:25 on 18 November 2009 was used as the rainstorm core (segment C in Figure 2).Window 1 added 329.8 mm of rain over a period of 31.4-h to the rainstorm, before window 2 appended a 1.5-h period to the end of the rainstorm with 6.8 mm of rainfall that is separated from the main body of the rainstorm by a 45-min gap.Finally, window 3 identified a 3-h period with 17.6 mm which closes the rainstorm.This additional data is separated by 2:10 h from the rest of the rainstorm, well under the 5-h t b 0 for this rain gauge.There is 0.4 mm of rainfall within the 5-h window 3 that precedes the rainstorm, which is too little rainfall to be added to the event.Finally, the next rainfall registered at this gauge occurred 24-h after the rainstorm's end and so constitutes a separate rainstorm.

| Rainstorm filtering
In cases such as the rainstorm in Figure 2, where there are multiple AM embedded within a single event, the algorithm above will output a rainstorm time series for each individual AM.While this could be prevented by selecting only 1 AM per rainstorm, the extent of each rainstorm cannot be known a priori; therefore, repeated rainstorms within each rain gauge were filtered after they were all identified.Events were filtered by checking for matching rainstorm start and end times to avoid duplication.

| Summary statistics
Once the time series for an extreme rainstorm has been extracted using the algorithm above, a series of summary statistics are calculated.These rainstorm properties are combined with rain gauge metadata such as latitude, longitude, and elevation, as well as the timing of the rainstorm, to generate a comprehensive summary of each rainstorm.
Given that a rainstorm with total duration T [h] is composed of N discrete intervals, i, each with t i [h] duration and r i [mm] rainfall, then total rainstorm rainfall is: The maximum rainfall intensity within each rainstorm is calculated as: Note that I max was calculated using either 5-min or 15-min data (with t i = 1 12 h and 1 4 h respectively) depending on the data resolution.Gauges with tip-time data can report higher I max values as they can capture rapid changes in rainfall intensity.
We also define P dry as the proportion of rainstorm duration which has no rainfall: This allows us to estimate the average intensity of the wet periods within a rainstorm, the effective rainstorm intensity I e , defined as: Finally, the rainstorm's centre of mass, C m is calculated as: This is analogous to the first moment of area or first moment of the rainstorm, it identifies the centroid of the rainstorm and serves as an indicator of the location of the heaviest rainfall within the storm (Marshall & Bayliss, 1994).A C m value close to 0.5 would indicate rainfall that tends to be symmetrically distributed in the rainstorm (either centrally peaked or uniformly distributed), values under (over) 0.5 show rainfall is front (back) loaded within a rainstorm.P dry and C m are dimensionless values to enable comparisons between different rainstorms.

| Seasonality and circular statistics
Frequency plots, radial plots and circular statistics have been used to explore the seasonality of extreme rainstorms.Circular statistics were used to calculate the mean day of the year θ, and the concentration of seasonal distribution, r, for the rainstorm families that generate each different AMS duration.r 0, 1 ½ and values close to 1 show rainstorms are concentrated at the same time of year (Blenkinsop et al., 2017Villalobos, 2017).
The radial coordinate of a date θ is: Where m is the number of days in a year.θ and r are calculated with the aid of two auxiliary variables: Where n is the number of events.Finally, θ and r are: 2.5 | Empirical quantiles of extreme rainstorms Univariate methods for regional frequency analysis are well established-for example, Hosking and Wallis (1997); however, the bivariate character of rainstorm analysis prevents their use here.While methods have been recently developed to cluster bivariate river gauge flood data (Pappadà et al., 2018), these have not been extended to bivariate analyses of rain gauge data.Therefore, a simple empirical approach to describe rainstorm extremes is used by pooling data across regions previously defined for hourly rainfall extremes in the United Kingdom (Figure 1b, Darwish et al., 2021) and calculating the rainfall volumes associated with empirical exceedance probabilities (EP) for events in different rainstorm duration bins.This provides an indication of the magnitude expected from the most extreme rainstorm events in each region without resorting to a statistical model and without ascribing to rainstorms a return period or annual exceedance probability.The duration bins used for the quantile calculations are bounded by 0.25-, 0.5-, 1-, 2-, 4-, 8-, 16-, 32-, and 64-h.Within each duration bin the following empirical quantiles of rainstorm volume are calculated: 0.9, 0.95, 0.98, 0.99; these represent the lower bound for the top 10%, 5%, 2% and 1% rainstorms in each duration bin.

| Rainstorm samples
The $ 2 × 10 6 peak intensities belonging to the various AMS series identified through conventional methods, are embedded in $ 7:0 × 10 5 independent rainstorms.Each AM-generating rainstorm contains an average of 3.29 AMs.This confirms that overlaps between different duration AMs, like those seen in Figure 2, are the norm.
A clear correlation exists between rainstorm duration and volume (Figure 5, main panel-Kendall's rank correlation coefficient for this data is 0.67).The marginal distribution of rainstorm volume (Figure 5, right panel) is unimodal and approximately log-normal (Figure S1), while the distribution of rainstorm duration (Figure 5, top panel) is multimodal with peaks at the discrete durations used to sample the AMS series.This can be mitigated by only using short duration AMS series as cores for rainstorms, leading to much smoother rainstorm duration distributions (Figure S2); however, this excludes some long-duration rainstorms that are important from both an engineering and climatological perspective.
An upper bound on rainstorm duration can be observed in both samples, with few rainstorms exceeding 48 h (Figures 5 and S2), this coincides with the time low pressure systems take to traverse GB (Chandler & Gregory, 1976).The volume of the largest rainstorms in the sample can exceed 400 mm: these are exceedingly rare (with 2 instances from $70,000 rainstorms) and are linked to well-known flood events in Cumbria during 2009 and 2015.
Nearly 10% of 24-h AMs are caused by compound or clustered rainstorms.CAM events result from the combination of two or more rainstorms with a wide variety of durations and volumes.However, approximately a quarter of all CAM events are the result of contrasting combinations where one of the rainstorms involved contains the majority (>90%) of the original AM volume.The small-volume components of CAM events are absent in Figure S2, as CAM events are not present when using short duration AMS as rainstorm cores.

| AMS overlaps
Rainstorms associated with all AM durations show overlaps with each other.Table 1 shows the percentage of overlap between the rainstorms associated with different AM durations.Adjacent AM durations show the most overlap-77.1% of all rainstorms with 2-h AMs also have a 3-h AM-while distant durations show the least overlap-only 11.6% of rainstorms with a 5-min AM also contain a 24-h AM.Rainstorms with very short duration AMs (≤15 min) have little overlap (<25%) with those that contain AMs over 3-h.Rainstorms associated with AMs over 12-h overlap most often with each other and with 6-h AM rainstorms, but not with rainstorms with shorter AM durations.These overlaps between AMS are significant because rainfall of different durations are often treated as independent during the construction of intensity-frequency-duration (IDF) or depth-duration-frequency (DDF) curves, including in United Kingdom rainfall frequency analyses such as those in Faulkner (1999) and Stewart et al. (2013).

| Rainstorm properties
The duration of rainstorms associated with each AM have very different distribution shapes, ranging from unimodal distributions for 5-min and 24-h AM to multimodal for intermediate 6-or 12-h AM.Peaks in rainstorm duration coincide with the durations sampled by each AMS (Figure 6a).All AMS are generated by rainstorms with a wide range of durations; however, sub-hourly AMs tend to be generated by rainstorms shorter than 6-h.
The distributions of rainstorm volume for different AM durations are approximately log-normal in shape, especially for short AMs (Figure 6b).The variance of rainstorm volume distributions increases with AM duration.Quantile plots for each AMS show that rainstorm samples for AMs over 30-mins have heavier tails than expected from a log-normal distribution, and they become more heavy-tailed as the AM duration increases (Figure S3).The unimodal, well-defined shape of rainstorm volume distributions contrast with rainstorm duration distributions (Figure 6a).This is a result of the sampling methodology, since AM durations have been fixed while volume has been allowed to vary.
The distribution of P dry (Figure 6c) shows that significant portions of rainstorms consist of dry interludes.The rainstorms associated with longer-duration AMs tend to have the highest values; approximately half of 24-h AM-generating rainstorms have P dry >50%.Rainstorms associated with sub-hourly AMs are those most likely to contain zero P dry ; however, large intermittency values are also present here as short duration AMs can be embedded in longer duration rainstorms (Figure 6a).Near-zero P dry values at very short durations are expected as these rainstorms' duration is close to the measurement resolution, for example, for a 15-min AM event with 0 P dry it is likely that the actual rainstorm duration was under 15-min.
AMs of durations <24-h tend to form a small fraction of the total volume contained in their associated rainstorms (Figure 6d).This is most notable for rainstorms associated with short AMs which tend to be embedded in longer, more voluminous rainstorms, while longer duration AMs tend to become a larger fraction of rainstorm volume.All instances where the AM volume is larger than their associated rainstorm volume are due to CAM events, where the sum of two or more clustered rainstorms matches the AM value.These CAMs have been excluded from Figure 6.The relative position of rainstorms' C m varies as AM duration increases, from a forward position for rainstorms associated with sub-hourly AMs, towards a more central position for 24-h AMs (Figure 6e).This indicates that the shorter-duration rainstorms that generate subhourly AMS bursts tend to concentrate most of their rainfall towards the first half of the event.Further analysis into the temporal distribution of rainfall within rainstorms will be discussed in future work.
Finally, I max decreases as AM duration increases (Figure 6f).Rainstorms with AMs over 6-h have very similar distributions of peak intensities, rarely exceeding 25 mmÁh −1 , while rainstorms with sub-hourly AMs can easily exceed this value and have much broader distributions with much higher peak intensities.Rainstorms with

| Regional and seasonal variation in rainstorm characteristics
Rainstorm volume is heavily influenced by location.Rain gauges with the highest median AMS-generating rainstorm volume (>50 mm) are concentrated along the higher elevations of western GB.The Channel coast to the south, and moderate elevations such as the Pennine range and southern Scotland, have the next largest median rainstorms ($50-30 mm); while rain gauges in central and eastern England have smaller values (Figure 7a).This geographic pattern is particularly strong in autumn and winter and is weakest during summer.Seasonal patterns in rainstorm volume are also evident, with winter concentrating the heaviest rainstorms, followed by autumn and spring, while summer tends to have the lowest median rainstorm volumes.
Seasonal changes dominate variations in rainstorms, with summer rainstorms generally shorter than those in spring or autumn, and winter clearly showing the longest rainstorm durations (Figure 7b).Spatial variations are visible within each season and annually, with a similar pattern to that of median rainstorm volume (Figure 7a).Variation in mean I e is also dominated by seasonal effects (Figure 7c), and predictably has the inverse pattern to rainstorm duration, with highest intensities during the summer as events become shorter and more convective.Two clusters of rain gauges have relatively higher mean intensities during all seasons, one is in the Lake District and another along the south coast, east of the Isle of Wight and on the southern edge of the South Downs National Park.Both locations are adjacent to the coast and at high and moderate elevations respectively.Central England has high annual I e as this region is furthest from the coast and tends to receive short duration events (Figure 7b-Annual).
Seasonal changes in the relative frequency of different duration events (Figure 8) are clearly related to the variation in median T and mean I e (Figure 7b,c).Short duration events (T<4-h) of all magnitudes are very concentrated in the summer months (r =0:58), with a few exceptions for coastal gauges along the English Channel and western coasts.This coincides with the peak frequency of rainstorms that contain AM durations under 3-h shown in Figure S4a.This summer peak shows little regional variation, although the SW shows a higher frequency of short-duration rainstorms in May compared with other regions and a lower peak frequency in summer.For extreme short-duration rainstorms (Figure 9), the top 10% of events has a relatively uniform spatial distribution; however, the top 2% rainstorms become sparser in Scotland relative to the rest of GB.
Long-duration rainstorms (T≥12-h) show a much more heterogeneous pattern.They are most frequent in winter over the Scottish Highlands, the high ground of the west coast and along the Channel coast (Figure 8), these same locations concentrate the largest (top 2%) long-duration rainstorms (Figure 9).In contrast, these rainstorms are most frequent in summer and early autumn in low-lying areas along the eastern coast and central England (Figure 8), whilst top 10% extremes are also observed during summer months in these areas (Figure 9).These regional differences are evident in the monthly frequency of rainstorms that contain 12-h and 24-h AM (Figure S4b); these peak during summer in the SE and ME regions, during autumn in the NW and SW regions, while the NE region has a relatively flat distribution from June to January and with a decrease during spring.
Note that some events among the top 2% of longduration rainstorms lie outside the high ground along the western coast of GB.These correlate to well-known flooding events and are almost always observed in more than one rain gauge: for example, a cluster of five gauges near Gloucester correlates to flooding in the region during July 2007 (Figure 9).
Intermediate-duration rainstorms show a mix of these patterns, with a high frequency of events between July and October, with higher-elevation and western gauges favouring autumn and central and eastern regions favouring summer (Figure 8).The top 2% events are most frequent during July and August, while the top 10% rainstorms are slightly more evenly distributed in time, with relatively high frequencies during October; winter events have a similar spatial distribution to the most extreme long-duration events, while summer events have a much broader spatial distribution (Figure 9).The NE and SW stand out at a regional level, the first by showing a very pronounced peak in frequency during the summer, while the latter has a peak in October, mirroring the peak frequency of long duration rainstorms.All other regions show peak frequency in August (Figure S4a) An interesting characteristic only observed in extreme intermediate duration rainstorms is the presence of events along the southern coast during May (Figure 9).Finally, it is evident that very few rainstorm extremes occur during March and April at any duration (Figures 8, 9 and S4).

| Frequency and intensity of extreme AMS-generating rainstorms
Not all AM events generate flooding (Ledingham et al., 2019), therefore it is useful to study the frequency characteristics of large-more extreme-rainstorms in more detail.There are large regional differences in the empirical return level estimates of long-duration rainstorms; the NW region of GB shows much larger expected rainstorms than the SE, with the remaining three regions showing very similar intermediate behaviour, while differences in the quantiles of short-duration rainstorms are small (Figure 10).Quantiles of rainstorms with durations under $3-h follow nearly linear trends in Figure 10, suggesting a power relationship describes the scaling of short rainstorm volume relative to duration.Above 3-4 h, the growth of rainstorm magnitude relative to duration exceeds a power relationship for most regions, with the SE being the only exception.This pattern is observed for all EPs.

| DISCUSSION
The rainstorm extraction method used here has allowed an unprecedented examination of rainfall in GB.However, it has been limited here to the use of conventional AM durations as a starting point for rainstorm extraction.This is desirable as AM values are of interest to engineers and scientists that analyse rainfall extremes using these durations, but it results in a biased sampling of rainstorm durations (Figure 5).Different sampling approaches, for example, extracting every rainstorm as defined by minimum time between independent rainstorms (t b 0 ), may be more adequate if unbiased sampling is desired.
There is confidence in the validity of the results due to the extensive QC process that the data has been subject to and because the patterns observed in the results agree with existing knowledge regarding the seasonal and regional drivers of precipitation in GB (Hulme & Barrow, 1997Met Office, 2013).Seasonal variation in extreme rainfall duration and volume is explained by the presence of convective rainfall during the summer months and dominance of cyclonic or frontal systems during the autumn and winter months.
The short (<4-h), high intensity (>10 mmÁh −1 ) rainstorms that generate most hourly and sub-hourly AMs are most frequent in the summer, when convection is active over GB.As temperature decreases with the annual cycle, so does the frequency of extreme rainstorms of short F I G U R E 1 0 Regional rainstorm volume estimates associated with different empirical exceedance probabilities (EPs) for rainstorms of different durations.Edges for rainstorm duration bins were set to 0.25-, 0.5-, 1-, 2-, 4-, 8-, 16-, 32-, and 64-h.[Colour figure can be viewed at wileyonlinelibrary.com] duration (Figure S4).The most extreme short duration rainstorms behave similarly across GB.This is seen in the small differences in their empirical frequency across different regions (Figure 10), coupled with their widespread distribution south of Scotland (Figure 9).The lower frequency of this type of event in Scotland is likely due to lower rain gauge density, shorter records, and the relative coolness of Scottish summers due to its high latitude.This may make Scotland more susceptible to impacts of climate change related to storm intensification than the rest of GB, as events that occur most often in southern GB today may increase their future frequency in northern GB (Chan et al., 2018).Today's short duration extremes in southern GB may therefore serve as useful analogues for the events in future northern GB.
Long (>12-h) and medium (4-h ≤ T < 12-h) duration rainstorms increase in frequency between October and January when low-pressure systems and winter storms are most frequent (Figure 8).Orographic effects exert important controls over the volume of these rainstormsthe heaviest of these rainstorms are concentrated over high ground along the western coast of GB (Figure 9).These same areas of GB (with high-volume winter and autumn rainstorms) have long median rainstorm durations which, coupled with relatively low intensities, suggests that these high volumes are due to more wet hours.Therefore, the effect of orographic enhancement is primarily to increases in rainfall occurrence, extending the duration of rainstorms.
In contrast, long-and medium-duration rainstorms in eastern regions, where orographic enhancement is absent, have their peak frequencies during summer and early autumn (Figures 8,9 and S4).Mechanisms for these events are frontal, with or without convective components, as their duration excludes purely convective forcings (Hand et al., 2004).
The largest rainstorms (and AM values) on record are the result of sustained high hourly intensities over more than 24-h; for example, the event in Figure 2 has an average intensity of $9.9 mmÁh −1 , which is a high value more typical of summer I e (Figure 7).Atmospheric rivers have been linked to events with sustained high-intensity rainfall as they can provide an extended supply of warm, moist air which triggers heavy precipitation when advected over high terrain (Lavers et al., 2011Gimeno et al., 2014Griffith et al., 2020).The effect of heavy, long-duration rainstorms is likely to be more wide-spread than shortduration extremes as the mechanisms that cause large events can affect a wider geographical area than the convective systems associated with shorter duration rainstorms.In addition, long-duration rainstorms are more likely to generate flooding downstream than short-duration rainstorms, and the impacts of the events seen in Figure 9 can be perceived at large distances from the rain gauges where they were recorded.For example, heavy rains in western Wales may cause flooding in Herefordshire or the Severn catchment days after they have occurred.
Rainstorm duration and volume are correlated and (Figure 5) and they vary continuously because of the different conditions and processes that generate rainstorms in GB.The significant overlaps between different AM values we observe in Table 1 are unsurprising and result from the use of discrete durations to study rainfall-itself a historical necessity driven by the relatively coarse (hourly or daily) resolution and discretised nature of rainfall measurements.These overlaps and correlations pose a challenge to independence assumptions used in the conventional derivation of IDF and DDF curves (e.g., Faulkner, 1999;Stewart et al., 2013).
The AMs used for drainage and water management infrastructure design occur in rainstorms with a wide range of volumes, durations, and peak intensities (Figure 6) which can generate very different hydrological responses in a catchment.Consider for example a catchment that has a 1-h time of concentration and 20 mm of rain as the 30-year return period (i.e., a 20 mm/1-h design event).The 13 instances where this occurs in the database contains such vastly different examples as a brief 20.5 mm/65-min shower and a much larger 109 mm/12.4-hstorm.It is unlikely that a single storm design that considers the first event will respond equally well to the second (although this is also dependent on catchment properties) and it is naïve to believe that catchments only respond to rain with duration equal to their time of concentration.A more robust alternative to using a single storm is the use of ensembles of events for design, as it should allow for a better characterization of the extremes a catchment is likely to face.The large amount of data present in the database could be used to inform stochastic models where rainstorm characteristics, such as their peak intensity, and C m are modelled based on their empirical distributions.
The limited duration of the records prevented the analysis of trends in frequency or magnitude present in the data; however, plausible future changes to the rainstorm characteristics observed here may be justified using physical mechanisms and climate model output.Extreme precipitation has increased in frequency and intensity since the 1950s, and further increases are very likely in most regions with additional global warming (IPCC, 2021).The intensity of heavy daily or multiday precipitation events, including the ones explored here, show increases at a rate close to the Clausius-Clapeyron (CC) relationship of 6%-7% K −1 , with regional modulations due to large-scale circulation changes (Fowler et al., 2021).Analysis of hourly UK data shows higher than CC scaling with respect to dew point temperature (Ali et al., 2021) and other studies project changes to storm velocity (Kahraman et al., 2021), the spatial extent of wintertime precipitation extremes (Bevacqua et al., 2021), and storm intensity (Wasko, Nathan, et al., 2021).These projected changes pose an additional challenge to rainfall design methods and how best to incorporate robust knowledge regarding current and future rainstorm properties in flood estimation guidance (Wasko, Westra, et al., 2021).

| CONCLUSIONS
The results confirm well-established patterns in temporal and spatial distributions of rainfall, previously studied using fixed-duration totals (see Section 5, while providing new insight into the characteristics of the rainstorms that cause AM rainfall totals. First, AM values with durations under 3-h most frequently originate from short-duration summer rainstorms with convective components that occur widely across GB.AM values with duration over 3-h are caused by multiple rainstorm types, in western GB they are caused by long-duration rainstorms (over 12-h long) associated with low-pressure systems (i.e., frontal systems or winter storms) during autumn and winter.In eastern GB (SE, ME and NE regions) AM values with duration over 3-h tend to be caused by shorter rainstorms (relative to western GB) in the summer or early autumn and are likely to contain both frontal and convective components.
Second, AM values of different duration are frequently caused by a single rainstorm, resulting in overlapping AMs that contradict assumptions used when constructing IDF and DDF curves.Unlike the design storms used in engineering applications, real-life AM values occur as part of rainstorms with properties, such as total duration and volume, that vary widely and are correlated with each other.
These results pose challenges to conventional univariate analyses of rainfall extremes which reduce rainstorm variability to a variation in volume at fixed durations.The presence of dependencies between rainstorm characteristics and between AM values of different durations, and the large variability of AM-generating rainstorms' characteristics suggest that rainstorms may be represented much more robustly using multivariate tools such as copulas.These have been demonstrated to work well for frequency estimation and other multivariate hydrological applications (e.g., De Michele & Salvadori, 2003;Salvadori & De Michele, 2004;Grimaldi & Serinaldi, 2006;Serinaldi & Kilsby, 2013).The large sample size of our database could facilitate the use of empirical copulas, avoiding the use of parametric model copulas to describe the dependency between rainstorm properties.These empirical copula models may then be used to generate ensembles of rainstorms that exhibit the same properties as observed AM-generating rainstorms for use in engineering design, and flood estimation methods.This should lead to infrastructure that will be better prepared to face the observed variability of extreme rainstorms.
Map of rain gauge locations and record duration after QC (a), histogram of record duration after QC (b), and regions of extreme 1-h rainfall (Darwish et al., 2021) with number of gauges, N, per region (c).[Colour figure can be viewed at wileyonlinelibrary.com]F I G U R E 2 Rainstorm of 18 to 20 November 2009 at the Honister_Tel EA gauge.Five embedded AM values of different durations are indicated using coloured rectangles below the 5-min resolution time series data.The dashed vertical lines indicate how each labelled segment was identified and added to the rainstorm by the event extraction algorithm, described in Section 2.2.3.[Colour figure can be viewed at wileyonlinelibrary.com]

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I G U R E 3 Minimum storm interarrival time, t b0 (hours), for rain gauges in Great Britain.[Colour figure can be viewed at wileyonlinelibrary.com] U R E 4 Rainstorm extraction algorithm, initial phase (a), main phase (b) and final phase (c).

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I G U R E 5 Heatmap of AM-generating rainstorm density (centre) with marginal distributions of rainstorm duration (top) and volume (right), sampled using all AM durations.[Colour figure can be viewed at wileyonlinelibrary.com]

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Percentage of overlap between rainstorms containing different duration AMs.I G U R E 6 Density distributions for rainstorm duration T (a), volume R (b), percentage dry time P dry (c), ratio of AM volume to rainstorm volume (d), rainstorm centre of mass C m (e), and peak instantaneous intensity I max (f) associated with different duration AM.Note that although CAM events have been excluded, a single rainstorm containing multiple AM values will be present in multiple distributions.[Colour figure can be viewed at wileyonlinelibrary.com] U R E Seasonal median rainstorm volume R (a) and duration T (b) for all rain gauges with at least 10 years of record.Seasonal mean effective rainstorm intensity I e (c) is calculated as V/D eff , where V is rainstorm volume and the effective rainstorm duration D eff is the wet portion of the total event duration D. [Colour figure can be viewed at wileyonlinelibrary.com] intermediate AM durations are transitional between the distributions of rainstorms as they contain short and long AM bursts.

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I G U R E 8 Month of θ per gauge (a) and temporal distribution (b) of rainstorms, both classified by their duration, T [h], r is shown in b).Colours represent the month where rainstorms occur on average according to radial statistics.[Colour figure can be viewed at wileyonlinelibrary.com]

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I G U R E 9 Geographical (a) and temporal (b) distribution of extreme percentiles of rainstorm volume [mm] for three duration bins, colours represent the month of each rainstorm.Sample size is indicated in the panel headers.The rainstorm with largest volume was plotted if a rain gauge was represented more than once in each duration and volume category.[Colour figure can be viewed at wileyonlinelibrary.com]