Storm surges were simulated with the DFLOW FM model using a flexible mesh setup (forced with 6-hourly wind and atmospheric pressure fields) (17, 20, 21, 29). Waves were simulated with the model Wavewatch III (17, 20, 22) (forced with a 6-hourly wind field). Astronomical tides were simulated every 6 hours using the FES2012 model (29, 31), which makes use of satellite altimetry data. The resulting sea level data are available every ~25 km along the coastline. Comprehensive validation and detailed information of the models can be found in (17, 2022, 29). Our analysis was based on quantile values; therefore, we did not bias correct simulated data. Sea level and precipitation data were based on ERA-Interim and six selected models from the CMIP5 multimodel ensemble (i.e., ACCESS1-0, ACCESS1-3, GFDL-ESM2M, GFDL-ESM2G, CSIRO-Mk3-6-0, and EC-EARTH). CMIP5 models were selected on the basis of the skill in representing the synoptic climatologies and interannual variations across the northeast Atlantic region (17, 2022). The GFDL-ESM2G model was not considered along the Black Sea coast because of instabilities of the surge model. Choosing well-performing CMIP5 models reduces the risk of artifacts caused by the delta change approach (27) (see below).

Precipitation was taken from the grid point nearest to each coastal location and, on each day, we considered accumulated precipitation within a time range of ±1 days. This choice allows for indirectly accounting for a range of large-scale weather systems that may produce CF. Grid point precipitation represents a rather large area of typically well beyond 100 km by 100 km. In a moving cyclone, precipitation at the daily scale is strongly correlated in space, and in particular, 3-day aggregated precipitation represents a large area quite far upwind. In addition, we accounted for very heavy precipitation falling in convective cells embedded in a large-scale weather system; these events would show up as heavy even in a 3-day aggregation and may cause CF in rather small catchments.

The effect of SLR on the astronomical tide was quantified through dynamic tidal ocean simulations (using the DFLOW FM model) (fig. S8). The simulations considered SLR scenarios resulting from the combination of steric changes with three land-ice scenarios of water contributions from ice sheets and glaciers (18). The analysis is described in detail in (17) with the only difference that we considered changes in the complete time series, rather than in the daily maxima only. Since the sensitivity of the final tide amplitude to the land-ice scenarios is very small (17), we considered the median of the three scenarios only. The actual observed time lag between the surge and astronomical tide sequences is random. The estimated CF return periods are thus just one random realization of all possible time lags between surges and astronomical tides. To get an estimate of a more likely CF return period, we computed the median of all possible estimates. We observe that this procedure does not allow one to take into account the variability of the return periods caused by the natural variability of the meteorological conditions. For the ERA-Interim–driven data, we obtained this estimate by calculating 240 individual estimates based on the superposition of (i) the simulated surge time series (including waves) and (ii) the randomly shifted tide time series. The part of the tide series beyond the length of the surge series was moved to the start date. From this ensemble, we computed the median of the CF return periods (Fig. 2). It turned out that the difference between the standard estimate and the bootstrap-based estimate was small. As this procedure is computationally expensive, we therefore refrained from applying it to the CMIP5-based data.

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