Radar‐based heavy precipitation events in Germany and associated circulation patterns

As projected by multiple climate models, short‐duration heavy precipitation events (SDHPEs) are expected to intensify particularly quickly under the changing climate posing substantial risk to natural and human systems. Yet over the years, SDHPEs have received less scientific attention than long‐duration heavy precipitation events (LDHPEs), mainly due to the limitations of measurement systems. Our aim is to provide insight into spatial and temporal variability of SDHPEs detected by the radar network of the Deutscher Wetterdienst (DWD) in Germany from 2001 to 2020 as well as to explore their links to circulation patterns (CPs). The study is based on the Catalogue of Radar‐based heavy Rainfall Events (CatRaRE) generated using reprocessed gauge‐adjusted data of the DWD radar network as well as a new numerical method for classifying CPs over Central Europe called “Großwetterlagen for Reanalyses” (GWL‐REA). The results have demonstrated that SDHPEs, which are defined based on either locally valid precipitation values with a return period of 5 years (CatRaRE T5) or absolute precipitation values equal to DWD Warning Level 3 (CatRaRE W3), are common phenomena occurring most frequently in the afternoon hours of the summer season. They constitute up to 90% of all heavy precipitation events included in the catalogues covering relatively small areas—the median area of SDHPEs ranges from 22 km2 (CatRaRE T5) to 24 km2 (CatRaRE W3), while the median area of LDHPEs ranges from 175 km2 (CatRaRE W3) to 184 km2 (CatRaRE T5). As compared to LDHPEs, SDHPEs are generated by a wider spectrum of circulation conditions, including not only cyclonic but also anticyclonic CPs. In the warm season, the anticyclonic CPs, often accompanied by air mass advection from the south, can induce high thermal instability leading to the development of relatively small, isolated convective cells, which often cannot be captured by rain gauge stations.

Increasing concentration of water vapour in the Earth's atmosphere being a result of continued global warming has a pronounced impact on precipitation patterns.Numerous studies have reported that particularly affected are heavy precipitation events (HPEs), the frequency and intensity of which have risen over the last few decades in many regions of the world (Li, Xuan, et al., 2018b;Iqbal et al., 2019;Powell & Keim, 2015;Ryan et al., 2021).As projected by multiple climate models, this tendency will continue or even accelerate by the end of the 21st century (Donat et al., 2019;Li, Chen, et al., 2018a;Rajczak & Schär, 2017;Supari et al., 2020).On the global scale, HPEs are expected to intensify at a rate of 6%-7% per each 1 C of air temperature warming following the Clausius-Clapeyron (CC) relationship (IPCC, 2023).However, many regional studies have already shown that the CC rate is more appropriate for long-duration heavy precipitation events (LDHPEs; daily to multidaily events) than for short-duration heavy precipitation events (SDHPEs; hourly to subdaily events), which may increase at twice the rate expected from the CC relationship (Ali et al., 2021;Ali et al., 2022;Ban et al., 2015;Fowler et al., 2021;Lenderink & Meijgaard, 2008;Loriaux et al., 2013).
The observed and projected changes in precipitation patterns pose substantial risk to natural and human systems causing more frequent occurrence of flash floods, landslides and soil erosion as well as leading to economic and life losses (IPCC, 2012).It has been projected that population exposure to HPEs and their secondary effects will continue to increase (Chen & Sun, 2021;Liu et al., 2020).On the local scale, the highest population exposure is expected to occur over urban areas, which are particularly vulnerable to SDHPEs due to the design of drainage infrastructure (Chen et al., 2020).As the urban runoff processes occur rather on the time scales of minutes to hours, the hourly to subdaily precipitation events are far more relevant for drainage infrastructure than the daily to multidaily precipitation events (Arnbjerg-Nielsen et al., 2013;Kang et al., 2016;Kourtis & Tsihrintzis, 2021;Zhou, 2014).Furthermore, knowledge on SDHPEs is highly needed for (1) modelling of flash floods, debris flows and landslides (Luino et al., 2019;Nguyen et al., 2016;Š alek et al., 2006;Yang et al., 2020); (2) nowcasting applications (Panziera et al., 2016;Romang et al., 2011;Spyrou et al., 2020;Zhai et al., 2018) and (3) validation of high-resolution climate simulations (Blenkinsop et al., 2018;Chan et al., 2020;Kendon et al., 2018;Yun et al., 2020).
While many papers have already focused on LDHPEs properties, comprehensive studies on SDHPEs are still lacking in the scientific literature.This is mainly due to the limited availability of long-term time series of hourly to subdaily precipitation data.To address this limitation, tremendous efforts have been undertaken in the framework of the European Research Council-funded project "Intelligent use of climate models for adaptation to nonstationary hydrological extremes" (INTENSE), within which subdaily rain gauge precipitation data from across the globe have been collected to form the Global Sub-Daily Rainfall Dataset (GSDR; Blenkinsop et al., 2018;Lewis et al., 2019).However, SDHPEs often cannot be captured by measurements of rain gauge stations, thus requiring an application of spatially contiguous observations of radar networks (Saltikoff et al., 2019;Tapiador et al., 2012).As stated by Lengfeld et al. (2020), only 17.3% of hourly HPEs and 81.8% of daily HPEs detected by the radar network of the Deutscher Wetterdienst (DWD) from 2001 to 2018 were captured by rain gauge stations as well.As a rule, the detectability of precipitation events by rain gauge stations decreases strongly with a decreasing duration (Lengfeld et al., 2019).Unfortunately, application of radar data may be limited as well.In particular, time series of radar observations are an order of magnitude shorter than time series of rain gauge stations, which restricts the research on SDHPEs to relatively short time periods (Barton et al., 2020;Berg et al., 2016;Fairman Jr et al., 2015;Paulat et al., 2008).However, the growing collection of radar data as well as progress in the postprocessing algorithms used for their correction have already enabled the construction of the first radar-based SDHPEs climatologies covering longer, at least 10-years, time periods (Bliž ň ak et al., 2018;Fairman Jr et al., 2017;Kreklow et al., 2020;Panziera et al., 2018).
An important aspect of the research on HPEs is their genesis and links to meso-and macroscale circulation patterns (CPs).Many studies have investigated these links by applying atmospheric circulation indices, such as Arctic Oscillation, El Niño-Southern Oscillation and North Atlantic Oscillation (Dong et al., 2019;Irannezhad et al., 2017;Kenyon & Hegerl, 2010;Merino et al., 2016) or multivariate statistical techniques (Fern andez-Montes et al., 2014;Rimbu et al., 2016;Tan et al., 2019;Ullah et al., 2021).Other widely used tools for assessing CPs constitute circulation type classifications, among which probably the best-known is the manual Großwetterlagen (GWL) classification given by Hess and Brezowsky (1952).The GWL classification and its numerical versions, for example, objective GWL or SynopVis GWL, have been already successfully applied in studies on CPs associated with daily to multidaily HPEs occurring over Central Europe (Brieber & Hoy, 2019;Hoy et al., 2014;Jaagus et al., 2010;Min ařov a et al., 2017a;Min ařov a et al., 2017b;Ustrnul & Czekierda, 2001).To account for mesoscale climate peculiarities, some regional classifications have also been created and implemented in research on LDHPEs (Lupikasza, 2010;Mika et al., 2021;Řehoř et al., 2021;Twardosz & Niedźwiedź, 2001).On the other hand, the genesis of SDHPEs and their links to CPs, although vital, remain largely unstudied.
Therefore, the overarching aim of this study is to gain insight into spatial and temporal variability of SDHPEs detected by the DWD radar network in Germany from 2001 to 2020 as well as to explore their links to CPs expressed in the form of a new GWL-based classification.Our intention is also to present the results in a broader context by comparing properties of SDHPEs and LDHPEs.The paper is structured as follows: section 2 introduces the radar and circulation data as well as outlines the definitions and methods applied; section 3 describes the results obtained; section 4 provides the conclusions and highlights challenges of further research on HPEs.

| Radar data
The study is based on the freely-available Catalogue of Radar-based heavy Rainfall Events (CatRaRE) generated using the reprocessed gauge-adjusted data of the DWD radar network known as RADKLIM (Lengfeld et al., 2021b(Lengfeld et al., , 2021c;;Winterrath et al., 2018).The hourly precipitation fields, available there at the resolution of 1 km × 1 km, have allowed the creation of two versions of the catalogue, both of which contain HPEs of 11 durations (i.e., 1, 2, 3, 4, 6, 9, 12, 18, 24, 48 and 72 h).The two versions differ in terms of the thresholds used to define a heavy precipitation event-CatRaRE T5 applies locally valid, grid-based precipitation values with a return period of 5 years, while CatRaRE W3 applies nationwide absolute values equal to DWD Warning Level 3. Lengfeld et al. (2021a) highlighted that the threshold defined by the return period of 5 years correspond to the minimum requirements for the drainage infrastructure in Germany, while the threshold defined by the DWD Warning Level 3 indicate potentially dangerous precipitation events able to cause both local and widespread regional damages.As shown in Table 1, the threshold applied for detection of the heavy precipitation event in both versions of the catalogue depends on the event duration, while, in CatRaRE T5, it varies also spatially reaching generally higher values in the southern than in the northern Germany.
The identification of HPEs is carried out in two stages.The first stage includes the detection of locally  The last row indicates also the minimum size of the heavy precipitation event depending on the events duration-this value does not differ among CatRaRE versions.
limited contiguous rainfall objects for which the precipitation sums at individual grid cells exceed the threshold defined separately for each time step and event duration.
The minimum size of the rain object depends, as defined by Lengfeld et al. (2021a), on the event duration-it is equal to 9 km 2 for events lasting no more than 3 h and equal to three times the duration for events lasting more than 3 h, for example, 36 km 2 for an event of 12 h duration (Table 1).Since rainfall can last several hours and exceed the threshold for HPEs for more than one duration (e.g., in the case of 6 h of persistent rain, the threshold for HPEs might not only be exceeded for the 6 h precipitation sum but also for 1, 2, 3 or 4 h precipitation sum), multiple rainfall objects, representing in fact the same event but at different durations, can be detected.Therefore, the second stage aims to ensure the temporal and spatial independence of the rain events.To ensure the temporal independence of two rainfall events that occur in the same area, a minimum time gap between the end of one and the beginning of the next rainfall event is required.This time gap has to be equal or greater than the duration of the shorter event, but not smaller than 4 h.Furthermore, if multiple rain objects are identified in the same time interval, a check for spatial independence is performed-the rain objects that overlap are spatially dependent and described as the same rain event.
If multiple rainfall objects are temporally and spatially dependent, the strongest one, according to Extremity Index defined by Müller and Kaspar (2014), is included in the catalogue.The other rain objects are, in turn, neglected and excluded from further investigation.For more detailed information on the process chain leading to the identification of heavy rainfall events, readers are encouraged to seek out the paper of Lengfeld et al. (2021a).

| Circulation data
As mentioned already, the study applies a new numerical method for classifying CPs over Central Europe called "Großwetterlagen for Reanalyses" (GWL-REA), used here for the first time.This method is based on the wellknown manual GWL classification given by Hess and Brezowsky (1952), in which 29 GWL types have been classified using historical weather charts back to 1881.As part of the tradition, the manual GWL classification is regularly updated at the DWD, although its major disadvantage remains inhomogeneity resulting from the subjective assessments by various meteorologists.To remove this inhomogeneity, a numerical method for classifying GWL was developed by James (2007), successively improved and used in numerous papers (e.g., Drücke et al., 2021;Min ařov a et al., 2017aMin ařov a et al., , 2017b;;Wapler & James, 2015).GWL-REA builds broadly on this previous approach with the aim of further improving its accuracy and efficiency.GWL-REA is produced using pattern correlations between daily and pre-defined, reference climatological patterns constructed for the Europe-North Atlantic domain.The domain covers an area extending from 20 N to 80 N and from 30 W to 60 E on a 2 × 2 latitude-longitude grid.The input data consist of mean sea level pressure, 500 hPa geopotential height, 500-1000 hPa relative geopotential thickness and precipitable water column, gained from the reanalysis dataset ECMWF ERA5, which is currently available from 1959 onwards (Hersbach et al., 2020).Similar to the previous numerical GWL method, reference climatological patterns are required for the pattern correlations.However, while the previous version only used a single pair of seasonally biased reference climatological patterns for each GWL type, the number of the reference climatological patterns distinguished in GWL-REA has been increased to well over 200 in order to account for the within-type variability more effectively, reducing related errors.The resulting large number of correlation coefficients calculated for each daily pattern are then combined onto the 29 GWL types using a manyto-one mapping.
The new method also addresses a specific problem that the daily GWL type obtained from the pattern correlation alone does not always correspond to the specific nomenclature of the given GWL type in terms of the central anticyclonity (cyclonity) or location of the steering high (low).A new postprocessing module calculating parameters derived from the Lamb Weather Types method (LWT; Jenkinson & Collison, 1977) has been implemented to address this issue.The LWT parameters include circularity, cyclonity, flow direction, flow strength and vorticity to flow gradient ratio calculated over seven regions defined in accordance with GWL nomenclature allowing the initial correlation coefficients of a particular GWL type to be reduced systematically in cases where the daily pattern does not correspond to that expected for the given GWL type, according to its nomenclature.
The resulting time-series is also subjected to temporal filtering, which ensures that an event with a particular circulation pattern lasts at least 2 days.This is shorter than the 3-day minimum event duration specified in the manual GWL given by Hess and Brezowsky (1952), but has the advantage of allowing more short-lived events to remain in the time series, which improves correlations with precipitation statistics, for example.
Nonetheless, the 29-type Hess-Brezowsky GWL system has one specific disadvantage with regards to its application in climatological studies that still needs to be addressed, namely that it concentrates on atmospheric circulation alone and largely ignores air mass properties.Some GWL types have consistent air masses over Central Europe, such as the northerly types, Na, Nz and TrM, which are all cold types (Table 2).However, most of the remaining GWL types can have very different air masses at times, with correspondingly different midtropospheric structures over the respective characteristic surface flow patterns.As such, the within-type variability of synoptic structures can be quite high for many of the GWL types, reducing their usefulness for studies that depend on air mass properties, especially for temperature, but also for precipitation; the latter depending on moisture content and air mass boundaries as well as on low-level vorticity.
To address this problem, GWL-REA defines a set of GWL subtypes, which separate the distinct air masses more effectively.Each GWL type is divided into between 1 and 4 subtypes, resulting in 60 subtypes in total.The initial GWL classification then spawns a second, more detailed classification of the GWL subtypes, which could be used directly.However, due to the very large total number of subtypes, a more useful final product can be constructed by concatenating the subtypes into 12 basic circulation-air mass groups, separated into two vorticity classes (anticyclonic-cyclonic), three temperature classes (warm-mixed-cold) and two source region or circulation form classes (e.g., maritime-continental, blocked-zonal).
As a result of this strict grouping of vorticity, temperature and source region classes, this new GWL-derived classification system, referred to as GWL-REA GROUPS and deployed for the first time in this study, is a very effective way of distinguishing between different fundamental synoptic situations, while keeping the total number of CPs relatively small.The definitions and mean frequencies of occurrence of the 29 types and 12 circulation-air mass groups in GWL-REA are listed in Tables 2 and 3, while the reference climatological composites are plotted in Figures 1-3, respectively.

| Remarks on definition of SDHPEs and LDHPEs
A review of scientific literature reveals that the definitions of short-and long-duration precipitation events varies.The subdivision of temporal and spatial scales for atmospheric processes given by Orlanski (1975) assumes that, for example, thunderstorms last up to a few hours covering areas of tens of kilometres, while frontal systems may last more than a day covering areas of hundreds of kilometres.Following this approach, there is also a general consensus that SDHPEs occur on a time scale of several minutes to hours, while LDHPEs occur rather on a time scale of several hours to days.However, the exact distinction between SDHPEs and LDHPEs often remains unclear.For instance, Bliž ň ak et al. ( 2018) defined SDHPEs as events lasting up to 6 h, Lengfeld et al. (2021a) as events lasting up to 9 h, while Oh and Sushama (2020) as events lasting up to 12 h.To maintain the comparability of our research with previous studies conducted on the basis of the DWD radar network data, we have applied the definitions introduced by Lengfeld et al.
(2021a)-SDHPEs are defined as events that last 1-9 h, while LDHPEs are defined as events that last 12-72 h.

| Statistical methods
To gain insight into nature of HPEs, we have computed percentages of the number of HPEs and the area affected by HPEs for each event duration as well as examined the spatial and temporal variability of SDHPEs and LDHPEs.Furthermore, to explore the links between HPEs and CPs, three indices have been defined, namely (1) probability of the occurrence of a particular circulation pattern given the occurrence of a heavy precipitation event, hereafter P(CPjHPE); (2) probability of the occurrence of a particular circulation pattern given the occurrence of a day with heavy precipitation event, hereafter P(CPjDD HPE ) and (3) probability of the occurrence of a day with heavy precipitation event given the occurrence of a particular circulation pattern, hereafter P(DD HPE jCP).These indices may be expressed by following formulas: where P(CP T HPE) is the total number of cases for which a particular circulation pattern occurred simultaneously with HPEs, P(CP T DD HPE ) is the total number of days on which a particular circulation pattern occurred simultaneously with a day with HPEs, P(HPE) is the total number of HPEs included in the given CatRaRE version, P(DD HPE ) is the total number of days with HPEs included in the given CatRaRE version and P(CP) is the total number of days with a particular circulation pattern in the years 2001-2020.
To simplify, P(CPjHPE) shows how often HPEs are accompanied by a particular circulation pattern, P(CPjDD HPE ) shows how often days with HPEs are accompanied by a particular circulation pattern, and P(DD HPE jCP) shows how often a particular circulation pattern leads to a day with HPEs.The P(CPjHPE) values have been calculated separately for SDHPEs and LDHPEs, while P(CPjDD HPE ) and P(DD HPE jCP) values have been calculated for (1) days on which only SDHPEs occurred (DD SDHPEs ); (2) days on which only LDHPEs occurred (DD LDHPEs ) and (3) days on which both HPEs types, that is, SDHPEs and LDHPEs, occurred (DD BothHPEs ).The distinction between P(CPjHPE) and P(CPjDD HPE ) has been introduced to account for the influence of HPEs occurring on the same day.Individual days with a large number of HPEs can skew the results on  For brevity, in the main part of the paper, we present only CPs associated with HPEs included in CatRaRE T5, while the results obtained for HPEs included in CatRaRE W3 are provided in Figures S2 and S3, Supporting Information.

| HPEs: Spatial and temporal variability
In total, CatRaRE T5 contains 26,881 HPEs and CatRaRE W3 contains 23,020 HPEs.The vast majority of them, up to 90%, constitute SDHPEs.However, the percentage of the total area affected by SDHPEs varies from 35.0% to 41.5%, which implies that SDHPEs, although very frequent, constitute relatively small events occurring on a local rather than regional scale-the median area of SDHPEs equals to 22 km 2 in CatRaRE T5 and 24 km 2 in CatRaRE W3, while the median area of LDHPEs equals to 184 km 2 in CatRaRE T5 and 175 km 2 in CatRaRE W3.As shown in Figure 5, the percentage of the number of HPEs decreases strongly with an increasing duration, while the percentage of the area affected by HPEs increases with an increasing duration.As an example, CatRaRE T5 includes particularly many HPEs with duration of 1 h, which constitute almost 40% of all HPEs, but account for less than 10% of the area affected, while HPEs with duration of 72 h, which constitute less than 1% of all HPEs, account for almost 17% of the area affected.Similar conclusions can be drawn for CatRaRE W3, albeit both the percentage of the number of HPEs and the percentage of the area affected differ slightly among the catalogues.CatRaRE W3 contains, for instance, substantially less HPEs with duration of 1 and 72 h, which account for very similar percentages of area affected by these precipitation types, amounting to about 4%.
As illustrated in Figure 6, the spatial variability of HPEs depends on the catalogue version and definition of HPEs applied therein.CatRaRE T5, which applies locally valid precipitation values with a return period of 5 years, indicates rather homogeneous distribution of both SDHPEs and LDHPEs, while CatRaRE W3, which applies absolute precipitation values equal to DWD Warning Level 3, reflects a general distribution of precipitation over Germany reaching higher values over the high-altitude areas for both SDHPEs and LDHPEs.While LDHPEs included in CatRaRE W3 reach substantially higher number of their occurrence in the mountain areas, for example, in the Alps, Alpine Foothill, Black Forest (located in the western part of the Southwestern Uplands) and Upper Palatine-Bavarian Forest (located in the southern part of the Eastern Uplands), SDHPEs included in CatRaRE W3 are characterized by a slightly higher number of their occurrence only on the border between the Alps and Alpine Foothills.This suggests that orographic enhancement plays far more important role for LDHPEs than SDHPEs.In particular, as stated by Lengfeld et al. (2019), HPEs with duration of 1-4 h occur in Germany in very similar frequency and intensity over flatlands and mountains.Note also that the higher numbers of LDHPEs per single 1 km × 1 km grid point shown in Figure 6 results rather from the size of LDHPEs than their frequency-an individual long-duration precipitation event covers, on average, much more grid points that short-duration precipitation event.In other words, as LDHPEs cover larger areas, the probability that LDHPEs hits a grid point is much higher.Furthermore, as depicted in Figure 7, SDHPEs are subjected to clear annual and diurnal variability.They occur almost exclusively from April to September and tend to begin between 1200 and 1800 UTC, which along with their reduced sizes, suggests that SDHPEs represent small-scale convective cells developing under the conditions of high thermal instability.As a contrast, LDHPEs occur all year round, also reaching a higher frequency from April to September.Relatively often SDHPEs and LDHPEs develop simultaneously, occurring on the same day in more or less distant locations-DD BothHPEs constitute from 22.5% (CatRaRE T5) to 26.3% (CatRaRE W3) of all days included in the given catalogue version.Regardless of the catalogue version, DD SDHPEs are more frequent than DD LDHPEs , consisting of 59.4% (CatRaRE W3) to 66.7% (CatRaRE T5) of all days included in the given catalogue version.

| HPEs: Links to CPs
In CatRaRE T5, SDHPEs are most often accompanied by HNz, BM and HFz, while LDHPEs are most often accompanied by TM, Wz and TrW.The respective CPs together account for about 28% of SDHPEs and about 40% of LDHPEs (Table S1).Overall, in the case of SDHPEs, 13 CPs account for at least 75% of their occurrence, while, in the case of LDHPEs, 9 CPs account for at least 75% of their occurrence.This suggests that SDHPEs are generated by a slightly wider spectrum of circulation conditions, although the results can be partly related to the number of HPEs occurring on the same day, which, as discussed in section 2.4, is usually higher for SDHPEs than LDHPEs.However, the values of P(CPjDD HPE ) presented in Figure 8 (left column) lead to similar conclusions-the three most common CPs account for about 26% of all DD SDHPEs (Wz, BM, TrW) and about 50% of all DD LDHPEs (Wz, NWz, TrM).For LDHPEs, the definition, higher for the more often occurring SDHPEs than for LDHPEs.As an example, for DD SDHPEs , there are five cyclonic and three anticyclonic CPs, for which P(DD HPE jCP) values exceed 20%, while for DD LDHPEs , there are four cyclonic CPs, all with airflow from the western or northern sectors, for which P(DD HPE jCP) values exceed 5%.It is of notable interest that DD BothHPEs is very often associated with TM-a cut-off low pressure system located over Central Europe leads in over 40% of its occurrence to the hydrologically dangerous situation of simultaneous developments of SDHPEs and LDHPEs, appearing on the same day in more or less distant locations.In the summer, such situations are frequently linked to the occurrence of low air pressure dominating the upper troposphere and corresponding depression near the ground, which causes an increasingly unstable stratification of the troposphere intensified by the inflow of warm and humid air masses, usually from the Mediterranean region.An example of such a situation is the lowpressure system "Bernd," which occurred over Central Europe in July 2021 and led to severe precipitation, flooding, serious infrastructure damages and fatalities (Szymczak et al., 2022).Also at that time, southwestern Germany, Belgium, Luxembourg and the Netherlands experienced a combination of persistent and recurrent heavy rainfall related to the slowly moving near-surface depression intensified by the inflow of warm and humid air masses from the then exceptionally warm Baltic Sea.
Considering GWL-REA GROUPS , HPEs included in CatRaRE 5 are more often accompanied by cyclonic than anticyclonic vorticity classes.The cumulative value of P(CPjDD HPE ) depends, however, strongly on the DD HPE type, ranging for the cyclonic vorticity classes from 61.0% for DD SDHPEs to 89.4% for DD LDHPEs .As illustrated in Figure 9 (left column), the vast majority of DD LDHPEs is accompanied by the three cyclonic situations with maritime circulation forms (ZWm, ZKm and ZGm).These systems dividing distinct air masses across Central Europe and situations with returning, warmed polarmaritime air masses, in which the air mass is typically too warm to be included in the cold cyclonic maritime group.This latter group (ZKm) is most often characterized by low-level air flow from the northwest or north underneath an upper trough.While the moisture source here is often from the North Sea or nearby North Atlantic, in some cases very moist Mediterranean air can eventually become entrained into the trough from the east, having spread northwards during the preceding days and leading to prolonged downpours and severe flooding.For DD LDHPEs , the circulation-air mass groups ZWm, ZKm and ZGm reach also the highest values of P(DD HPE jCP) shown in Figure 9 (right column), ranging from 4.6% for ZGm to 7.3% for ZWm.On the other hand, DD SDHPEs are characterized by slightly more equally distributed values of P(CPjDD HPE ) and P(DD HPE jCP), implying that a wider spectrum of air masses might contribute to SDHPEs development.Moreover, the circulation-air mass group which most often accompanies DD SDHPEs and most often leads to DD SDHPEs consists of anticyclonic situations with warm continental air masses (AWc)-the AWc group not only accompanies every fifth DD SDHPEs , but also every third case of AWc occurrence leads to DD SDHPEs .Relatively high values of P(CPjDD HPE ) and P(DD HPE jCP) are also achieved by the quite diverse cyclonic situations with a surface frontal trough or with warm advection into a cold air mass (ZGr) and cyclonic situations with warm air masses from the Mediterranean (ZWc).For DD BothHPEs , in turn, P(CPjDD HPE ) and P(DD HPE jCP) reach the highest values for the circulationair mass group ZGr.This group includes the cut-off low pressure system located over Central Europe, that is, TM in the GWL-REA classification, which has already been identified as the CP most often leading to the simultaneous development of SDHPEs and LDHPEs.

| CONCLUSIONS
In this paper, we have provided insight into the spatial and temporal variability of SDHPEs detected by the DWD radar network in Germany from 2001 to 2020 as well as their links to CPs expressed in form of the new numerical method for classifying CPs over Central Europe abbreviated here as GWL-REA.It has been confirmed that SDHPEs, which are defined based on either locally valid precipitation values with a return period of 5 years (CatRaRE T5) or absolute precipitation values equal to DWD Warning Level 3 (CatRaRE W3), constitute common phenomena occurring most frequently in the afternoon hours of the warm season, implying an essential role of thermal instability for their development.Regardless of the CatRaRE version, the number of SDHPEs is an order of magnitude higher than the number of LDHPEs.Yet over the years, SDHPEs have received substantially less scientific attention than LDHPEs, principally due to the limitations of the measurement systems.These limitations are to a large extent related to the relatively small area of SDHPEs.The median area of SDHPEs ranges from 22 km 2 (CatRaRE T5) to 24 km 2 (CatRaRE W3), while the median area of LDHPEs ranges from 175 km 2 (CatRaRE W3) to 184 km 2 (CatRaRE T5), as a result of which SDHPEs often cannot be captured by rain gauge stations.This has, in turn, important implications not only for monitoring and understanding of SDHPEs but also for the quality of numerical weather predictions and climate model simulations.For instance, the comprehensive validation of convection-permitting models remains challenging, since the availability of highresolution radar products is distinctly limited in time and space (Kendon et al., 2021;Prein et al., 2015).Regardless of the catalogue version, SDHPEs are also far less related to topography compared to LDHPEs, which corresponds to the findings of other studies (e.g., Formetta et al., 2022;Marra et al., 2022;Panziera et al., 2016) stating that the spatial variability of HPEs depends on the event duration.For the north-eastern Italian Alps, as an example, Formetta et al. (2022) have identified two modes of orographic relationship: (1) a reverse orographic effect for precipitation with subhourly and hourly durations as well as (2) an orographic enhancement for precipitation with durations of more than 8 h.Whether this relationship also applies to other mountain ranges remains an open issue.Another still open issue is whether local factors, such as urban heat islands or enhanced surface roughness, may induce or modify SDHPEs (Marelle et al., 2020;Xiao et al., 2021).
The results have demonstrated that SDHPEs can be generated by a wide spectrum of circulation conditions, which can be classified into two major groups.The first group constitute cyclonic CPs commonly known as those linked to the development of precipitation and its extremes-good examples are here TrM, TrW, NWz, SWz and Wz, which are associated both with SDHPEs and LDHPEs.Also, TM shows dependencies with both types of HPEs, leading often to hydrologically dangerous situations of the simultaneous occurrence of LDHPEs and SDHPEs, appearing on the same day in more or less distant locations.The second group constitute, in turn, diverse anticyclonic CPs, such as BM, HFa, HNa, HNFa, Sa and SWa.These CPs are associated with the development of SDHPEs, while being at the same time largely irrelevant for LDHPEs.As compared to previous studies, CPs included in the first group have already been described as those related to the development of HPEs over the various regions of Central Europe (Min ařov a et al., 2017a(Min ařov a et al., , 2017b)), while CPs included in the second group have usually been considered far less important for the development of precipitation and its extremes.Based on the manual GWL series, Gerstengarbe and Werner (2005) stated, for instance, that BM, HFa, HNFa, Sa and SWa are characterized in the summer by positive deviations of air temperatures and by negative deviations of precipitation sums.Considering that their study was based on precipitation data gained from rain gauge stations, we can assume that the relatively small-scale convective cells developing under the conditions of high thermal instability were poorly resolved by station-based data, which ultimately led to underestimation of the role of anticyclonic CPs for SDHPEs development.
Furthermore, the application of GWL-REA GROUPS has allowed for an effective and refined identification of circulation-air mass groups associated with the occurrence of various HPEs types.While the vast majority of LDHPEs is related to cyclonic situations with the advection of maritime air masses, SDHPEs may develop under the influence of more diverse circulation-air mass groups, including not only cyclonic but also anticyclonic vorticity classes.The circulation-air mass groups related to SDHPEs development are (1) blocked anticyclonic situations with warm air masses; (2) cyclonic air mass boundary situations with a surface frontal trough or with warm advection into a colder air mass; (3) cyclonic situations under an upper trough and (4) cyclonic situations with warm air masses from the Mediterranean or the Atlantic.Interestingly, these conclusions are very similar for both CatRaRE version (results obtained for CatRaRE W3 are provided in Figures S2 and S3), despite different definitions of HPEs used therein, resulting in diverse spatial distribution of HPEs.From the methodological point of view, GWL-REA GROUPS constitutes a promising tool for assessing meso-and macroscale CPs associated with various meteorological phenomena and can be widely used in follow-up research.
The findings presented in this paper may serve as a baseline for further in-depth studies on the behaviour of SDHPEs under various atmospheric circulation patterns and changing climate, including, for example, studies on projected future intensification of SDHPEs.Such studies are of particular importance for weather forecasting and early warnings, thus serving also as a guidance for investigating (flash)-flood hazards.

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Reference climatological patterns of types 1-15 included in the GWL-REA classification, showing annual means of daily precipitation (blue filled contours at 2, 4, 6, 10 and 16 mmÁday −1 ), 2 m temperature anomaly (boxes, C), total cloud coverage (grey background shading, shown here qualitatively) and mean sea level pressure contours (light blue tinge for lower values, yellow-orange tinge for higher values, with high (H) and low (L) centre labels, shown qualitatively).The maps have been generated based on data gained from the reanalysis dataset ECMWF ERA5 [Colour figure can be viewed at wileyonlinelibrary.com]F I G U R E 2 As Figure 1, but for types 16-29 included in the GWL-REA classification [Colour figure can be viewed at wileyonlinelibrary.com]P(CPjHPE) by overestimating the role of the circulation pattern occurring on such days.As shown in Figure 4, this can be particularly true for SDHPEs-the number of SDHPEs occurring on the same day (either on DD SDHPEs or DD BothHPEs ) relatively often exceeds 100, while the number of LDHPEs occurring on the same day (either on DD LDHPEs or DD BothHPEs ) barely reaches 25.It should be also noted that all indices have been computed for a circulation pattern occurring at the beginning of a respective heavy precipitation event, although CPs may change in the course of the event.Obviously, this is much less common for SDHPEs than for LDHPEs.As an example, CPs change in around 9% of HPEs with duration of 6 h and in around 70%-90% of HPEs with duration of 72 h.

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I G U R E 3 As Figure 1, but for circulation-air mass groups 1-12 included in the GWL-REA GROUPS classification [Colour figure can be viewed at wileyonlinelibrary.com]

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I G U R E 4 Variability in the number of SDHPEs and LDHPEs occurring simultaneously on DD SDHPEs , DD LDHPEs and DD BothHPEs for CatRaRE T5 (left) and CaRaRE W3 (right) in the years 2001-2020.The boxplots visualize the following summary statistics: the box hinges correspond to the first and third quartiles (Q 25th , Q 75th ) showing also the interquartile range (IQR = Q 75th − Q 25th ), the central solid line through the boxes indicates the median (Q 50th ), the upper whisker extends from the Q 75th to the largest value no further than 1.5 × IQR from the hinge, and the lower whisker extends from the hinge to the smallest value at most 1.5 × IQR.Data beyond the end of the whiskers are plotted individually (blue or red dots) [Colour figure can be viewed at wileyonlinelibrary.com]

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I G U R E 5 Percentage of the number of HPEs (upper row) and percentage of the area affected by HPEs (lower row) depending on the event duration for CatRaRE T5 (left column) and CatRaRE W3 (right column) in the years 2001-2020.The percentage of the number of HPEs of a particular duration has been calculated as a ratio between the total number of HPEs of a particular duration and the total number of all HPEs included in the given version of CatRaRE, while the percentage of the area affected by HPEs of a particular duration has been calculated as a ratio between the total area covered by HPEs of a particular duration and the total area covered by all HPEs included in the given version of CatRaRE [Colour figure can be viewed at wileyonlinelibrary.com]

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I G U R E 6 Spatial variability of the number of SDHPEs (upper row) and LDHPEs (lower row) per 1 km × 1 km grid point for CatRaRE T5 (left) and CatRaRE W3 (right) in the years 2001-2020.The black borders and numbers represent natural regions in Germany, based on the classification of Meynen and Schmithausen (1959): (1) Northwestern Lowlands, (2) Northeastern Lowlands, (3) Western Lowlands, (4) Uplands east of the Rhine, (5) Central Uplands and Harz, (6) Eastern Valleys and Hills, (7) Uplands west of the Rhine, (8) Upper Rhine Lowlands, (9) Southwestern Uplands, (10) Eastern Uplands, (11) Alpine Foothills, (12) Alps [Colour figure can be viewed at wileyonlinelibrary.com] pivotal role is played by Wz, which alone accompanies almost one third of DD LDHPEs .Moreover, 75% of all DD LDHPEs are accompanied by 8 CPs, while 75% of all DD SDHPEs are accompanied by 15 CPs, half of which constitute anticyclonic CPs, such as BM, Sa, SWa, NEa, HFa, HNFa and HNa.In turn, the cyclonic CPs which often accompany DD SDHPEs , DD LDHPEs and DD BothHPEs are consistent among each other; in particular, there are Wz, NWz, SWz, TrM and TrW.On the other hand, the values of P(DD HPE jCP) presented in Figure 8 (right column) indicate that CPs which most often lead to the occurrence of DD SDHPEs are HNz, HNFa and TrW, while CPs which most often lead to the occurrence of DD LDHPEs are Wz, Ww and TM.The values of P(DD HPE jCP) are, by F I G U R E 7 Annual and diurnal variability of the median number of SDHPEs (upper row) and LDHPEs (lower row) for CatRaRE T5 (left column) and CatRaRE W3 (right column) in the years 2001-2020.The colors indicate time of the beginning of HPEs [Colour figure can be viewed at wileyonlinelibrary.com]F I G U R E 8 The values of P(CPjDD HPE ) (left column) and P(DD HPE jCP) (right column) for DD HPEs included in CatRaRE T5 for the GWL-REA classification in the years 2001-2020.The colors indicate various types of DD HPEs , while the numbers in each bar represent the values of P(CPjDD HPE ) (left column) and P(DD HPE jCP) (right column) of the respective circulation pattern marked on the y-axis.Results obtained for DD HPEs included CatRaRE W3 are provided in Figure S2 [Colour figure can be viewed at wileyonlinelibrary.com] three groups are distinguished according to air mass temperature.Both ZWm and ZGm have a midlatitude Atlantic source of moisture-the warm group (ZWm) is dominated by moist-warm air masses, while the boundary group (ZGm) features quasi-stationary frontal F I G U R E 9 The values of P(CPjDD HPE ) (left column) and P(DD HPE jCP) (right column) for DD HPEs included in CatRaRE T5 for the GWL-REA GROUPS classification in the years 2001-2020.The colors indicate various types of DD HPEs , while the numbers in each bar represent the values of P(CPjDD HPE ) (left column) and P(DD HPE jCP) (right column) of the respective circulation pattern marked on the y-axis.Results obtained for DD HPEs included CatRaRE W3 are provided in Figure S3 [Colour figure can be viewed at wileyonlinelibrary.com] Abbreviations, definitions and frequencies of the 29 types included in the GWL-REA classification T A B L E 2 T A B L E 3 Abbreviations, definitions and frequencies of the 12 circulation-air mass groups included in the GWL-REA GROUPS classification