In this study we assess the role of antecedent conditions for floods of different return periods including extreme floods. The floods and associated antecedent conditions are extracted from very long (10 000-year) simulations from a hydro-meteorological modelling chain consisting of a stochastic weather generator optimized for the large-catchment scale, a hydrological model, and a routing system in hourly resolution. We specifically assess

the link between precipitation, antecedent conditions, and return periods for the sub-catchments of the Aare River catchment and

We studied the large-scale Aare River basin, which is one of the largest hydrological catchments in Switzerland, covering 17 700 km2. It includes parts of the Alps, the Swiss Plateau, and the Jura and extends from the confluence with the Rhine at about 310 to 4274 m a.s.l. in the Bernese Alps (average elevation of 1050 m a.s.l.). Land use consists of pasture (36 %), forest (30 %), sub-Alpine grassland (14 %), bare rock (8 %), and glaciers (∼2 %). Streamflow is heavily managed through the regulation of the large pre-Alpine lakes of Biel, Brienz, Lucerne, Murten, Neuchâtel, Thun, and Zurich and through several hydroelectric dams . The basin was divided into 127 sub-catchments, of which we selected 20 (Table , Fig. ) for a more detailed analysis of antecedent conditions, triggering precipitation, and flood return periods. These selected sub-catchments are larger than 200 km2 and vary in elevation range, slope, aspect, and hence hydrological regime (Table , Fig. ).

We used the CS approach paired with a stochastic weather generator producing very long time series (here 10 000 years), which expands the pool of possible flood events and encompasses more extreme events than observations alone. This way, we could analyze many possible but unobserved meteorological conditions causing a wide range of antecedent conditions. This enabled us to study the effect of antecedent conditions on the generation of extreme floods.

To account for many flood-generating configurations relevant in our study catchments, we based our work on simulations at hourly resolution (see average catchment response times (ACRTs) in Table  and ). This also allows for a more comprehensive pool of flood events than using daily data. Moreover, the hourly time step enables a realistic simulation and examination of the interplay of flood peaks coming from different parts of the large river catchment. Note that some runoff generation processes leading to floods that happen at finer temporal resolution are not included and some smaller-scale flood processes are not covered with the structure of the hydrological model. These small-scale processes may occur in parts of most of the catchments, but their relevance diminishes as catchment area increases. For the large Aare basin, the largest events are unlikely to be governed by these processes.

The sub-catchments were selected using an appropriate discretization level regarding the study goals, i.e. to identify large floods for the entire Aare River basin. An even finer discretization might not lead to more insights regarding this goal because regionally confined floods were hardly ever observed to contribute to notable floods in the Aare River basin.

For each of the selected sub-catchments the annual maximum flood (AMF; maximum hourly discharge) and the annual maximum precipitation (AMP) sum over a fixed time window were extracted from the full simulation period of 10 000 years. A fixed window for the precipitation sums is common in meteorological studies for extreme value statistics. However, we adjusted the fixed-window size from the commonly used meteorological windows to a catchment-specific hydrologically more meaningful window, namely the average response time of the catchment. The average catchment response time (ACRT) was estimated by calculating the maximum cross-correlation between precipitation and discharge, making a seasonal distinction, because of possible delays due to snow accumulation and melt in winter and spring see. This means that some catchments may have a fixed window of 12 h to find the AMP, 24 h for others, etc. For our set of sub-catchments, the ACRT varies from 6 to 49 h, with a median of 11 h. The different ACRTs may be explained to some extent by the percentage of karst, river network density, and dominant runoff processes within each catchment. The flood event belonging to the AMF peak is estimated using the recursive Eckhardt filter , defining the start and end of the flood event where baseflow and discharge converge. Therefore, in addition to the flood peak, flood volume was also estimated. The filter works well for most flood events in our catchment selection, but it tends to underestimate the flood volume for double-peak events.

Flood-triggering precipitation was defined as the precipitation that fell between ACRT before the start of the flood event and the flood peak. Hence, any precipitation that fell before that start point in time (ACRT before the start of the AMF event) was assumed to alter the antecedent conditions but not to directly trigger the flood event. The ACRTs for each catchment are listed in Table . Snow has a dual function as both a temporary storage of precipitation and a delayed precipitation input in the form of snowmelt. Like rain, snow influences the antecedent conditions, and the meltwater can contribute to triggering or intensifying a flood event. We excluded annual maximum precipitation events where precipitation was likely snow and not rain, considering the substantial time gap between snow accumulation and snowmelt. Rain-on-snow events are not covered by this approach and would also not be adequately simulated by the hydrological model used.

Starting from the AMF peak, we extracted a set of characteristics including simulated soil moisture, dynamic catchment storage (consisting of soil water and groundwater storage; see), snowpack at time points before the AMF, and snowmelt contributing to the flood as simulated by the model, as well as the associated triggering precipitation (see Fig. 2). These characteristics collectively describe the conditions during and preceding the flood. The same characteristics were also extracted before the AMP, but here the discharge response to each AMP was extracted. All considered characteristics regarding flood events, antecedent conditions, and triggering precipitation as well as antecedent conditions and reaction to the AMPs are listed in Table .

The soil moisture conditions of the catchment were calculated as relative soil moisture filling. For this the simulated soil moisture [mm] at any time was compared to the absolute maximum soil moisture that was simulated during the full simulation period [mm] in each sub-catchment. Snow conditions in the catchment were included in terms of snowpack before a flood event and in terms of relative snowmelt water contribution to discharge during the flood event. The latter was calculated as the fraction of simulated snowmelt in simulated discharge during the flood event.

Return periods were calculated for all annual maximum flood events and all annual maximum precipitation events. We calculated the empirical return periods of each AMF and AMP based on Weibull plotting positions. The return periods were categorized into return period classes of “10 years” (between 0 and 10 years), “100 years” (between 10 and 100 years), “300 years” (between 100 and 300 years), “500 years” (between 300 and 500 years), “1000 years” (between 500 and 1000 years), and “1000+ years” (more than 1000 years). These classes are based on the different stages of flood safety assessment and formed by definition an unbalanced stratification of the full sample of annual events.

When the AMF was not caused by the AMP, we expect the greatest influence of wet catchment antecedent conditions. In these “non-matching” cases, annual maximum precipitation does not trigger the annual maximum flood, and hence during and before the AMP there might be antecedent conditions that allow for the precipitation to be stored in the catchment and do not lead to an immediate large streamflow response. For the AMFs that were not triggered by the largest precipitation events, there are two possible cases: (1) the catchment was considerably wetter compared to the conditions during the AMP – pointing at the decisive role of antecedent catchment conditions – or (2) the precipitation amount triggering the AMF was very similar to the AMP but did not quite reach the AMP amount. In other words, in these non-matching cases a rainfall event that is slightly or markedly lower than the AMP event leads to much higher runoff production efficiency and thus ultimately to the annual maximum flood.

We considered cases to be “non-matching” when the AMP did not overlap with the window of the flood event plus the preceding ACRT before the flood event. Since we want to focus on hydrologically effective precipitation, we excluded AMPs where the precipitation was presumed to be snow and accumulated.

From a regional-management point of view, the floods that matter are those that occur at the outlet of the river basin or at a point of interest within the basin. Critical conditions at these points are formed by antecedent conditions in specific regions (spatial patterns of wetness for contributing sub-catchments); by the phase, amount, and location of precipitation; and by the combined effect of individual space–time dynamics.

By only examining many catchments individually and how precipitation and antecedent conditions shape the streamflow response at their outlets, the link to the regional importance of floods at the sub-catchment scale would be missing. For instance, if the extreme flood of one catchment always occurs out of sync with the other sub-catchments, then there might not be a great impact expected in the large-catchment context. However, if two or more catchments usually exhibit a strong response to precipitation inputs and their flood peaks combine and reinforce one another, then these cases become critical in the regional-flood-risk context.

In this study, critical floods at the large-catchment scale were defined by the return periods of the floods at the outlet of the Aare River basin. In order to model the return period classes of these critical floods, we set up a classification type random forest. The spatial pattern of the antecedent conditions of the sub-catchments, the triggering precipitation within these sub-catchments, and the conditions at the critical points of the routing were used as features for this random forest.

The precipitation conditions and antecedent conditions for each sub-catchment were extracted for the individual sub-catchments, trying to capture the seasonality of streamflow to travel from the outlet of each sub-catchment to the basin outlet. The conditions of the routing system that were considered features in the random forest were the discharge values at critical locations preceding the floods at the outlet of the Aare River basin. Again, we accounted for travel times from the outlet to each potentially relevant routing system location. The distributions of the features for the precipitation, antecedent soil moisture conditions, and conditions at potentially relevant routing system locations can be found in the Supplement.

The random forest was grown using a stratified sampling to improve the detection of the rarer return period classes given the very biased distribution of the number of flood events per return period class. The stratified sampling was set to 26, the size of flood events of the rarest class (500+). For the random forest, 5000 trees were grown and we applied 26 variables at each split, which is more than the default square root of the number of features but what is recommended in as being better for high-dimensional classification type data sets. The optimal number of trees was determined by incrementally testing different numbers of trees and evaluating the overall out-of-bag estimate of the error rate for misclassifying the return period class of flood events. We examined the variable importance of the different predictors for each flood return period class using the mean decrease in the Gini index (MDI), which measures node impurity, i.e. how well the random forest trees split the data.

We found that only about 18 % to 44 % (depending on the sub-catchment) of the annual maximum precipitation (AMP) events and annual maximum flood (AMF) events occurred simultaneously in the simulations, highlighting the importance of antecedent conditions for the generation of large floods. When looking more closely into the non-matching events, we found that numerous AMPs occurred after the AMF of that year. This means that these AMPs neither directly triggered the flood event nor contributed to wetting up the catchment prior to the flood event (Fig. ). For the rain- and snow-dominated catchments, 60 % or more of the events of the AMP occurred after the AMF, while for the glacier-influenced catchments about 40 % of the AMPs occurred after the AMF. While this could be an artifact of forcing a link between AMP and AMF using blocks of years, we found that the cases with a suspicious time difference in this regard were less than 2 %.

In addition to the general decrease in the number of events for increasing return periods, the matching and non-matching AMPs and AMFs are not evenly distributed per return period class (Fig. ). With higher return periods there were more matching events. This indicates that increasingly extreme flood events are primarily explained by large amounts of precipitation and less by existing antecedent conditions. Nevertheless, even for very large return periods, the antecedent conditions still seemed non-negligible and for single sub-catchments, with even large fractions of AMF not being explained by AMP (>25 % up to 75 % for the class of 1000+ years). The points indicating a high percentage of non-matching events in the large return periods come from the Wigger River catchment (Fig. ).

Figure  shows the distribution of soil moisture conditions for matching and non-matching events separately and grouped for the different return period classes. Applying this separation reveals that the soils are wetter during the non-matching events than in the matching events (Fig. ). This implies that even smaller precipitation events can lead to large floods if the antecedent conditions are wetter. When comparing different return period classes, it appears that soil moisture filling increases for the more extreme events (higher return periods) in the non-matching event years. In some catchments, only matching events were found in the higher-return-period classes, meaning that the highest precipitation amount triggered the largest flood. In most of the catchments studied, for a return period class of 500 years or more, only matching events were noted. This indicates the diminishing influence of antecedent soil moisture conditions on the occurrence of rarer flood events. The Wigger River catchment stands out among the selected catchments due to the presence of non-matching events across all return period classes. In addition, only one matching event occurred for each return period class of 500 years or more. This catchment has a specific seasonality with numerous floods driven by snowmelt that result in AMF, rather than summer rainfall events.

For the glaciated catchments, the ranges of antecedent soil moisture conditions were very similar between matching and non-matching events, indicating generally more persistent wet soil moisture conditions in these catchments. This can be also be seen in the reference daily soil moisture distribution of all years. The difference in soil moisture conditions between matching and non-matching events decreases as we move from rain-dominated to snow-influenced and glaciated catchments. In rain-dominated catchments, antecedent soil moisture conditions vary widely for both matching and non-matching events. However, there is a tendency towards wetter soil moisture conditions for the non-matching events. The ranges of soil moisture conditions tend to be narrower in the snow-influenced catchments compared to the rain-dominated catchments. Here, the difference between matching and non-matching events in terms of soil moisture conditions diminishes and all events occur under wetter conditions compared to the rain-dominated regime type catchments. The glaciated catchments show the narrowest range and are characterized by consistently wetter antecedent soil moisture conditions for both matching and non-matching events, as they do also for the daily reference throughout the year. Generally and for all regime types, we see a more pronounced difference between the matching and non-matching events as we move towards higher return periods. It is important to keep in mind that as the return period increases, the depicted density functions are constructed from a decreasing number of events. For the more frequent events, a larger pool of events is available, with a wider spread for both matching and non-matching events. Conversely, for the rarer flood events, there are only few to very few events to compare.

We analyzed the contribution of snowmelt to both matching and non-matching annual maxima of precipitation and discharge by calculating the volume of simulated snowmelt relative to the flood volume (Fig. ). As for the antecedent soil moisture conditions, there was more snowmelt contribution in non-matching events than in matching events. In the rain-dominated catchments we found a rather large difference for the snowmelt contribution to the streamflow when comparing matching and non-matching events. For the snowmelt-dominated catchments this difference is smaller, reflecting that these catchments frequently experience snowmelt-influenced floods. Also the Wigger catchment, which has a rain-dominated regime, aligns with the description provided in the part about antecedent soil moisture conditions above. It shows important snowmelt contributions in the AMF up to the highest-return-period class. The catchments with glacier-melt-influenced regimes display similar distributions of snowmelt contributions to floods for both matching and non-matching events.

The confusion matrix of the random forest (Table ) displays how accurately the random forest attributed the floods of a specific return period class to that same class based on the provided features. For instance, in the confusion matrix (Table ), the return period class of 10 years was matched 6278 times. However, it was misclassified in the return period class of 100 years 1325 times and in the return period class of 300 years 50 times. The random forest model appeared to have difficulty classifying the 300-year return period class, with a classification error of 52 % (see Table ), compared to the other return period classes.

The maps in Fig.  illustrate the variable importance of the antecedent conditions regarding snow and soil moisture, triggering precipitation and routing node conditions split up for the different return period classes. The higher the mean decrease in the Gini impurity (MDI), the higher the variable importance. From these maps, it appears that for lower return periods (100 years), soil moisture is the most important feature for all analyzed sub-catchments. Snowpack conditions are assigned little importance in general but slightly more for the glacier- and snow-influenced Alpine catchments. However, triggering precipitation is only important for some sub-catchments and not important for all the glacier-influenced catchments from the sub-catchment selection. The triggering precipitation of the Simme, Emme, and Suhre sub-catchments gets slightly more importance than the other considered sub-catchments. The MDI indicates some but little importance for the discharge conditions at all locations of the routing system.

Moving to higher return periods the pattern of the attribution of the individual sub-catchments changes and precipitation generally becomes more important in explaining the attribution to the very high-return-period class and here also for the catchments with a glacier-influenced regime. The attribution level assigned by the MDI to the triggering precipitation for the 300-year return period class is very homogeneous. While the pattern of the variable importance of antecedent soil moisture conditions remains about the same as in the lower-return-period class, the importance of triggering precipitation increases compared to the soil moisture conditions when looking at the 300-year return period. Snowpack instead loses importance in classifying the return period class. For the 300-year return period class the locations in the routing system cascading downstream of the Sarine sub-catchment gain variable importance, while there was barely any assigned to these routing system locations for the return period class of 100 years.

In the return period class of 500+ years, the variable importance is mainly attributed to the triggering precipitation of all sub-catchments and particularly to the Reuss and Muota. Also in the Broye sub-catchment, triggering precipitation becomes more prominent in assigned variable importance for these events, while it was negligible for the lower-return-period classes. Soil moisture does not help much in determining this return period class, with some importance being assigned to the Kander sub-catchment and some but even less assigned to the Sense, Wigger, Suhre, and Dünnern sub-catchments. The Muota sub-catchment did have very little variable importance in the lower-return-period classes but becomes more important in the classification of events for the return period class of 1000+ years.

While the contribution of snowmelt to the flood at the small sub-catchment scale showed a distinct difference between the matching and the non-matching events, underscoring their importance for some events of this return period class, it barely contributed to the flood return period classification at the river basin outlet, particularly for the rarer flood events. This can be explained by the different seasonality of floods occurring at the sub-catchment scale compared to the floods at the outlet, which are mainly summer floods. For both snow and the flow conditions at locations in the routing system there were no noteworthy instances of assigned variable importance. Interestingly, when looking only at the change in variable importance for the conditions at the routing system locations, some changes in attribution can be seen for the different return period classes. The attribution of variable importance for the lower-return-period class (100 years) is at the locations closest to the Aare River basin outlet, for the higher-return-period class (300 years) it moves to the locations in the cascade downstream of the Sarine catchment, and for the highest-return-period class it moves to the outlet of Lake Thun.

With our study design we could not analyze if the precipitation event was patchy or not (spatial analysis of the rain event), as for instance did within the hydrological catchments. However, we could analyze the spatial interplay of the sub-catchments of the Aare River basin with regard to large floods at its outlet. We used a lumped hydrological model for each sub-catchment with mean areal input. This means that we could not find patterns within the sub-catchments that are particularly critical for the large system. These patterns might have been informative for some flood events in specific sub-catchments, since the relationship between performance of the streamflow simulation and spatial resolution of precipitation is both scale and catchment dependent as shown for instance by for France. However, from the regional perspective, we could analyze how the interplay of antecedent sub-catchment conditions and precipitation input as well as buffering and timing upstream of the outlet of the Aare River basin influenced the floods at the outlet.

The robustness of the results depends, in part, on the type of precipitation events that is used to force the hydrological model. This assigns a crucial role to the weather generator at the beginning of the modelling chain. However, for this study the main goal was to find conditions that lead to extreme flood events and determine the role of antecedent conditions therein. The way in which the weather generator was set up and optimized might not represent the full range of possible events at each sub-catchment in the region. Nevertheless, we do not expect major changes in the antecedent conditions prior to a large precipitation event, as these generally build up over a longer period of time. Note that the variability of extreme floods is inherently a multivariate variability, which as such is never well captured by multi-decadal observations. Moreover, decadal climate variability as discussed e.g. by cannot be accurately represented by stochastic weather generators such as the one used in this study.

As outlined in the Introduction, the approach of using a weather generator in a regional (large-catchment) context, in combination with a hydrological model and routing, has several advantages. It implicitly “reshuffles” the initial conditions and combines them with plausible weather events for that region. This approach results in a larger and more diverse pool of flood events compared to using only observations or making assumptions about the antecedent conditions. The approach could also be applied to different large catchments within a comparable climate, dominated by similar regime types. However, one important prerequisite for generating long weather time series using a weather generator is the availability of a sufficient number of weather stations with sufficiently long records for robust estimation of plausible weather.

As in other studies comparing flood and precipitation events, such as GRADEX e.g., or future and past frequency distributions of the two variables, there are some thresholds or tipping points that emerge. These thresholds are associated with the influence of the antecedent conditions and appear to remain important even for remarkably high flood return periods in our study. This underlines their importance and emphasizes that they should not be neglected. Comparative studies applying different flood estimation methods, both event-based using statistical approaches based on streamflow data alone and continuous simulation, concluded that at sub-daily time resolution such a threshold does not occur in the event-based approaches and that these tend to underestimate floods and particularly their volume and duration for small catchments . , in their comparative study – which also included historical and paleo-data, various event-based statistical approaches, and continuous simulation – additionally emphasize that event-based approaches often lack robustness, in particular when the available database spans only a few decades. developed a framework to compare different statistical and hydrological modelling methods for estimating design floods with up to 1000-year return periods and also concluded that large differences in flood estimates can arise depending on the method chosen. However, due to the large uncertainties inherent in each method, they recommend that these methods should be used in a complementary manner in practice. Consequently, the transfer from precipitation frequency distributions to flood frequency distributions should be checked for appropriateness in each specific case.