A climatology of sub-seasonal temporal clustering of extreme precipitation in Switzerland and its impacts

. The successive occurrence of extreme precipitation events on a sub-seasonal time-scale can lead to large precipitation accumulations, a classic trigger of ﬂood events. Here we analyse sub-seasonal clustering in Switzerland, ﬁrst characterizing the tendency of precipitation extremes to cluster in time for each season separately, and second, linking the occurrence of persistent ﬂood events to sub-seasonal clusters of precipitation extremes. We ﬁnd a distinct spatio-temporal pattern in temporal clustering behavior of precipitation extremes, with temporal clustering occurring on the northern side of the Alps in winter, and on their 5 southern side in fall. In winter, the magnitude of precipitation extremes is generally lower, and much of the precipitation falls as snow, therefore temporal clusters contribute little to the occurrence of persistent ﬂood events. In fall, however, temporal clusters associated with large precipitation accumulations over the southern Alps are found to be almost systematically followed by ﬂoods. In addition, discharge magnitudes decrease more slowly after clustered extremes.

We analyse daily discharge observations for 93 small to medium-sized catchments (14-1700 km 2 ) distributed across Switzerland ( Figure 1). These cover a wide variety of catchment characteristics and climates, from glacial and nival runoff regimes at 95 high altitudes to pluvial regimes in the Swiss plateau (see Muelchi et al. (2021) for details on the catchment characteristics).
The data for each catchment range from January 1961 to December 2017; the proportion of catchments with data rises from about 45% in the early 1960s to more than 95% in 1995, at which level it remains until 2015, before rapidly decreasing to 30% by the end of 2017. For each catchment, the analysis is conducted over the period for which discharge data is available. This means that daily discharge percentiles (and precipitation percentiles, when precipitation and discharge are considered together) 100 are calculated over different time periods depending on the catchment.

Sub-seasonal temporal clustering of precipitation
For each dataset, precipitation extremes are defined on a monthly basis as as days that exceed the 99 th all-day percentiles.
Events within each season (winter: DJF; spring: MAM; summer: JJA; and fall: SON) are then analysed together. Trends in 105 extreme daily precipitation percentiles are not taken into account. Taking monthly percentiles, as in Barton et al. (2016), allows to remove the influence of the seasonality in extreme precipitation magnitude. As a result, the rate of occurrence of extreme precipitation events is somewhat constant across the year, which makes it possible to assess the statistical significance of clustering at sub-seasonal timescales. As the individual weather systems associated with extreme precipitation in each season may sometimes last for a few days, the short-term temporal dependence in daily precipitation above extreme quantiles is 110 removed by way of a standard runs declustering procedure (Coles, 2001) with length r = 2 days, well-suited for Switzerland Barton et al. (2016).
The temporal clustering of precipitation extremes is then assessed using Ripley's K function (Ripley, 1981). We give here a quick overview of the methodology and refer the reader to Tuel and Martius (2021) for further details. Applied to a time series, Ripley's K function for a given window size n measures the average number of extreme events in a neighbourhood of n days 115 before and after a random extreme event in the series. This gives information about the tendency toward temporal clustering in the time series. The larger the value of Ripley's K function for a given n, the more clustered the extremes. The significance of temporal clustering is tested by comparing its Ripley's K values to those obtained for a Monte-Carlo sample of 5000 simulated homogeneous Poisson processes with the same average event density as the sample series. In homogeneous Poisson processes, events occur independently from each other and therefore exhibit complete temporal randomness. This procedure yields an 120 empirical p-value for the significance at any n. As we deal with multiple hypothesis tests, we implement a false discovery rate procedure (Wilks, 2016) with a baseline significance level of 5% to identify catchments where clustering is significant. Results are summarized across four timescales: 5-15, 15-25, 25-35 and 35-45 days; clustering is said to be significant for a given time interval if it is significant for at least half of n values in that interval.
Individual extreme precipitation clusters are identified with the automatic algorithm of Kopp et al. (2021). Starting from the declustered binary extreme event series, we calculate the 21-day moving sum of extreme events. The 21-day period with the largest sum is selected if that sum is larger than 2. In the case of multiple periods with the same number of extreme events, the one with the largest precipitation accumulation is selected first. The extreme events included in the selected cluster are then removed from the original series, and the procedure is run again to identify the next cluster. This avoids overlap between 130 selected events. The choice of the 21-day time window is well-suited to quantify clustering at sub-seasonal timescales, and is generally consistent with the length of observed cluster episodes that led to major floods in Switzerland (see introduction).
Results do not differ significantly for slightly shorter or longer (2-4 weeks) windows. troughs. These are connected to potential vorticity (PV) streamers or cut-offs centred west of the Alps, which are most frequent during fall (Martius et al., 2006). In addition to these large-scale considerations, lifting forced by local convective instability during summer also favours heavy precipitation (Stucki et al., 2012). Flood occurrence also strongly varies over time and space (Figure 3). Alpine catchments with high elevations typically reach their most extreme discharge values during summer, mainly due to snow-and glacier melt, but also to heavier precipitation intensities (Figure 2-c). Conversely, over the smaller Jura mountains, floods are most frequent in winter and spring, due to a combination of saturated or frozen soils, relatively large extreme precipitation magnitude (Figure 2-a,b) and a smaller snowto-rain ratio compared to the Alps. In summer and fall, despite slightly heavier precipitation extremes, floods are rare, as 160 evapotranspiration is higher and soils less saturated than in the cold season. In catchments located on the Swiss Plateau, floods are generally equally likely between winter, spring and summer, and rare during the fall season. The Ticino area is the only region where flood occurrence peaks in fall (50-60% of flood events), which is also the season with the heaviest precipitation ( Figure 2-d).

Flood events
Surface conditions, like soil saturation, presence of snow/ice, vegetation cover, or evaporative demand, vary substantially from 165 one season to the next. Hence the discharge response to a same heavy precipitation magnitude may differ depending on the season. Combined with the seasonality in extreme precipitation, it supports our defining extreme precipitation on a monthly instead of an annual basis.

Seasonal cycle of clustering significance
We now turn to the analysis of Ripley's K values and their implications in terms of sub-seasonal temporal clustering. Several 170 coherent areas exhibit K values that are significantly larger than those expected for homogeneous Poisson processes with no temporal dependence (Figures 4 and 5). In winter, significant temporal clustering of precipitation extremes is generally found along the Alpine ridge, concentrated at the 15-25 and 25-35 day timescales (5-a and b). In spring, two catchments in Northern Switzerland as well as a few catchments in Southeastern Switzerland also exhibit significant clustering (5-c and d). By contrast, results for the summer season show a complete absence of temporal clustering significance (5-e and f). Finally, in fall, 175 significance is found at all timescales over both the western tip of Switzerland and the southern side of the Alps (5-g and h). Similar patterns are found by comparing to the coarser-resolution precipitation datasets (ERA5, TRMM, EOBS, CPC and CMORPH, with some notable exceptions. Clustering significance over the Alps in winter is also present in the coarserresolution data (Figure 6-a). In spring, however, there are no signs of significant temporal clustering anywhere in Switzerland, including along the northern and southern borders where significance was found in RhiresD (Figure 6-b). All the datasets 180 agree nevertheless on the absence of clustering in summer (Figure 6-c), and on significant clustering in southern and southeastern Switzerland during the fall season (Figure 6-d). Temporal clustering does not appear particularly significant, however, in western Switzerland during fall. This regional approach allows to highlight the strong spatial coherence in the clustering significance patterns. In winter, clustering significance extends over a large region stretching from the Mont Blanc massif in France to eastern Switzerland along the Alpine ridge, in good agreement with RhiresD ( Figures 5-a and 6-a). Similarly, 185 southern Switzerland is part of a larger region exhibiting significant clustering, encompassing northern Lombardy and possibly extending southwards to the Mediterranean shore (Figure 6-d).

Cluster event characteristics
The previous statistical analysis identifies regions with a tendency to temporal clustering of precipitation extremes. By taking an event-based approach and identifying individual cluster events over 21-day periods, we can estimate average metrics for 190 these events, like the number of extremes or total event precipitation. From the perspective of surface impacts, two potentially relevant metrics are the average contribution of clusters to seasonal precipitation and their contribution to extreme precipitation accumulations. Results for these two metrics are broadly consistent with the statistical analysis of section 3.1. In winter, extreme precipitation clusters contribute an average of ≈10% to total winter precipitation along the Alpine ridge where clustering is statistically significant (Figure 7-a). Additionally, about 60-70% of extreme 21-day precipitation accumulations (larger than 195 the corresponding 99 th percentile) occur at the same time as clusters of extreme precipitation (Figure 8-a). Elsewhere, clusters contribute little both to seasonal and extreme precipitation accumulations. Cluster contribution to spring precipitation is generally weak, even for the catchments exhibiting clustering significance in RhiresD (Figure 7-b). Yet, clusters seem strongly linked to extreme 21-day accumulations over Western Switzerland (Figure 8-b). Consistent with the absence of clustering at that time of the year, clusters are not contributing much to summer precipitation. Finally, in fall, cluster contribution to seasonal 200 precipitation reaches maxima of 12-16% in Southeastern Switzerland, and remains high (≥10%) in Western Switzerland as well (Figure 7-d). In Southeastern Switzerland in particular, clusters occur almost always in conjunction with extreme precipitation accumulations (Figure 8-d). Since floods in this area are most common during fall, this suggests a possibly important role of extreme precipitation clusters in high-impact weather events in this region and at that time of the year.

Extreme precipitation clusters and persistent floods 205
To assess the link between clusters of precipitation extremes and persistent floods, we begin by considering precipitation data during persistent flood events and in the 10 days before. Unsurprisingly, persistent floods, regardless of L and N values, are systematically associated with extreme precipitation accumulations for catchments with mean elevations up to about 1500m (Figures 9-a,b and 10-a), a clear sign of the glacial/nival runoff regime dominance above that altitude. By contrast, extreme precipitation clusters precede persistent flood events chiefly in the Ticino area of southern Switzerland and locally over the 210 eastern parts of the Swiss Plateau and the Jura (Figure 9-c,d). The dependence to catchment elevation is similar, with a much weaker intersection of cluster events and floods at high elevations, but less robust with a larger spread of values at low elevations ( Figure 10-b).
An interesting question is whether the discharge response at the catchment scale after an extreme precipitation event differs between single extreme events and events that are part of clusters. Figure 11 shows that it is indeed the case for most catchments, 215 particularly those below 1500m elevation. In the five days following an extreme precipitation event, the fraction of days exceeding either the 95 th or the 99 th percentiles of daily discharge is larger when that event belongs to a cluster. The difference is particularly large over northern Switzerland and in the Ticino area where, for instance, the 99 th percentile of daily discharge values is exceeded on average 20-30% of the time in the days following an extreme precipitation event during a cluster, but only 10-15% if the extreme occurred outside of a cluster. The occurrence of a cluster of precipitation extremes greatly increases 220 7 https://doi.org/10.5194/nhess-2021-93 Preprint. Discussion started: 6 April 2021 c Author(s) 2021. CC BY 4.0 License. the likelihood of high-discharge events, particularly at low elevations ( Figure 12). A "reference" flood day probability can be estimated for each catchment by first identifying cluster events and then calculating the flood probability for the days of the year during which clusters were observed, using data from all available years. Doing so, we find that daily discharge is more than 7 (respectively 10) times more likely to exceed its 95 th (respectively 99 th ) percentile during and after a cluster in Northeastern Switzerland, for instance. The analysis of the distribution of daily discharge percentiles around the time of occurrence of 225 extreme precipitation events confirms these results: while the probability of observing a flood on the day following an extreme event is not very different between clustered and non-clustered extremes, that probability decreases much faster in the days following non-clustered extremes ( Figure 13).

230
Section 3.1 showed that clustering significance was found mainly over the Alpine ridge during winter and in southern and southeastern Switzerland during fall. The robustness of the results over these two regions across timescales and datasets suggests that specific physical processes are responsible for the clustering. Our definition of extreme precipitation events based on the exceedance of monthly percentiles of daily precipitation removes the influence of seasonality in extreme precipitation magnitude ( Figure 2). By applying Ripley's K function to the resulting time series, we can thus focus on short-term tempo-235 ral dependence in extreme precipitation occurrence driven by sub-seasonal dynamics or intra-annual variability (e.g., climate modes). It is therefore interesting to speculate about what the physical drivers of clustering may be.
Whether in winter or in fall, clustering significance is chiefly concentrated at timescales below 30 days, which seems to preclude any dominant role of seasonal SST anomalies. During winter, extreme precipitation events in northern Switzerland usually occur in connection with high IVT structures, like atmospheric rivers, and the associated extreme water vapour transport 240 converging onto the orography (Froidevaux and Martius, 2016;Giannakaki and Martius, 2016). The concentration of clustering significance over the Alps possibly results from a spatial anchoring of precipitation at high elevations, through orographic lifting and convergence, during an atmospheric river event, while precipitation in the lower-lying area is spatially more dependent on the presence of cold-air pools upstream of the mountains. Over the Euro-Atlantic sector, cyclonic weather regimes and their strong westerlies favour the occurrence of atmospheric rivers in Western Europe (Pasquier et al., 2019). The North 245 Atlantic Oscillation (NAO) also modulates the frequency of atmospheric rivers (Zavadoff and Kirtman, 2020), but its relevance for Switzerland remains unclear (Yang and Villarini, 2019).
During fall, several major clusters of precipitation extremes were related to recurrent Rossby wave breaking over western and southwestern Europe (Barton et al., 2016), the resulting PV anomalies leading to enhanced low-level moisture transport from the Mediterranean towards the Alps (Martius et al., 2006). Why wave breaking would be recurrent in this region and at that 250 time of the year remains unclear. Recurrent cyclogenesis and extratropical transition of tropical cyclones upstream over the western Atlantic seem to play a role, but not necessarily a systematic one. Persistence in blocking conditions in the northwestern Atlantic also contributed to upper-level wave amplification and the subsequent occurrence of precipitation extreme clusters