The general method of dynamical downscaling uses a coarse-resolution dataset, like global atmospheric reanalysis data, as initial conditions for a numerical atmospheric model. Three ECMWF reanalyses are selected for this study: ERA-20C, ERA-40 and ERA-Interim (Table ). They are all produced by older versions of the Integrated Forecasting System (IFS), the ECMWF's operational forecasting coupled model system. ERA-40 includes conventional observations (e.g., surface stations, buoys, radiosondes), polar satellites and geostationary satellites. ERA-Interim datasets benefit from improvements in assimilation methods and a large expansion of available data, with observation quantity and quality increasing over time. In order to mitigate this inhomogeneity in the 20th century reanalysis, only observations of surface pressure and surface marine winds are assimilated in the ERA-20C dataset. In order to provide the best possible atmospheric conditions for wave and storm surge hindcast, the following ERA datasets are downscaled for each event: ERA-20C for cases before 1957, ERA-40 for the 1957–1978 period, and ERA-Interim for storms occurring in 1979 and thereafter (Table ). The designator “ERA-x” is used in this manuscript to describe a group of cases where more than one ERA reanalysis product is applied.

Hereafter, this study focuses on the advantages of downscaling global atmospheric reanalysis for the development of wave and storm surge hindcasts. Over both the French and Bulgarian domains, numerical weather prediction (NWP) models require high horizontal and temporal resolution, especially for the storm surge model hindcast. For French events, the selected model, ARPEGE (Action de Recherche Petite Echelle Grande Echelle), is the operational global primitive-equation NWP system used at Météo-France and is based on the ARPEGE-IFS software developed in collaboration with ECMWF Table ; . A stretched grid allows for a finer horizontal resolution over France (around 10 km). The version used here has 70 hybrid vertical levels from 17 m to 70 km height. The Bulgarian events are hindcast from ALADIN (Aire Limitée, Adaptation dynamique, Développement InterNational) model, which is a limited-area model based on the ARPEGE system . The model's core characteristics are the same as for ARPEGE.

Two dynamical downscaling methods are examined here, hereafter referred to as D1 and D2, where D2 represents an improved version of D1. For D1, the necessary data from the global fields of ERA-x are interpolated to the plane model domain both on the horizontal and vertical scale for each NWP system, ARPEGE and ALADIN. The upper-air initialization step uses the spectral coefficients of ERA-x data. Then we apply the Schmidt transformation, which is well defined in spectral space to project the fields into the ARPEGE stretched grid. The land-surface initialization is not straightforward, since there are many differences between the ERA reanalyses and the NWP models in terms of the applied land-surface parameterizations and physiographic databases. For instance, the Tiled ECMWF Scheme for Surface Exchanges over Land (TESSEL) scheme of ERA-x uses four soil layers with fixed thicknesses, each layer having its own water content. The land-surface scheme of ARPEGE, however, only uses two layers in our experiments; the top layer has a fixed size of 1 cm, and the second layer overlaps the first one and has a variable depth. Furthermore, for a given grid point, soil types are often very different in the two land-surface schemes. Therefore, using the raw land-surface datasets from ERA-x as initial conditions would be troublesome, since the water saturation fraction depends on the soil type. Thus, we interpolate the surface fields so as to preserve as much as possible the ERA-x surface heat and momentum fluxes . The procedure is based on the conservation of the soil wetness index (a relevant indicator for soil water availability) during the interpolation process, since soil water availability is supposed to regulate the partition of latent and sensible heat fluxes, which, in turn, influence energy and water exchanges between the atmosphere and the land surface. The resulting files are initial conditions (IC-1) for the NWP forecasts (Fig. , top). Then, hourly forecasts are produced twice a day, starting at 00:00 and at 12:00 UTC, and run for 18 h. Only hourly forecasts from +6 h to +18 h are used. The first 6 h are not taken into account to prevent model spin up, and after h+18, the next forecast time is considered (Fig. , top). Forecasts are produced from a week (d-7) before to 2 days (d+2) after the day (d) that the storm impacted the coastline. The D2 method is more complex than D1 (Fig. , bottom). The D2 method also uses hourly forecasts produced twice a day, at 00:00 and at 12:00 UTC, starting from h+06 to h+18, and the forecast starts 9 days (d-9) before and continue until 2 days after (d+2) the day (d) that the storm impacted the coastline. Instead of using independent initial conditions (IC-1) like in D1 for the 00:00 and 12:00 UTC forecasts, the initial conditions for D2 (IC-2) include information from the last 6 h forecast (Fig. , bottom). Consequently, the D2 method allows us to evaluate the importance of taking into account small wavelengths beyond the reanalysis truncation that are not considered in D1. Furthermore, after a short period of time (3 h), non-linearities trigger small-scale processes which are consistent with the large scale. This small-scale information provided by the 6 h forecast is blended with the large-scale information given by the interpolated reanalysis (IC-1; Fig. , bottom). This procedure was cycled 4 times in 2 days before the first 00:00 UTC forecast used as forcing for the wave and storm surge models. Therefore, the determination of one single initial condition (IC-2) uses four reanalyses. The D2 technique is applied to 10 recent French coastal flooding events (Table ). These 10 cases represent a diverse panel of events affecting different coastlines with adequate observational data (satellite altimeters and tide gauges) to evaluate the reconstruction of the wave and storm surge observations and to enable a comparison between D1 and D2.

In order to ensure consistency in our case studies, the selected wave and storm surge models share similar general characteristics, despite being adapted specifically to either the French or Bulgarian coasts.

The effects of the two downscaling techniques on the reconstruction of intense storms are presented for the case of the Lothar storm, an extreme cyclogenesis event (occurring a few hours before the Martin storm described further in Sects.  and ) in December 1999. It is the most severe storm in terms of pressure gradient, surface winds and displacement velocity to hit France within the observational record . This storm did not produce extreme wave and storm surge, and thus it was not selected for hindcasts. Nevertheless, it is interesting to look at the behaviour of both downscaling strategies for this particular case due to its uniquely tight horizontal pressure gradient. For this storm, the D1 method slightly improves the ERA-Interim reanalysis fields, but the D2 downscaling better reproduces the cyclone structure over northern France (Fig. ). Statistical analysis using the mean, the bias, the root mean square error (RMSE) and the standard deviation (SD) error is performed with the 12 meteorological stations available in an area encompassing the low pressure system (48–50∘ N, 2–4∘ E). This analysis confirms that the use of D1 forcing is an improvement compared to using an ERA-Interim reanalysis with respect to surface observations. The use of D2 slightly improves the reconstruction of the observations (Table ).

For the wave reconstruction evaluation, simulated significant wave heights (SWHs) are compared against observations from satellite altimeter data and in situ observations. Several satellites operated over the French and Bulgarian coasts during the storms: TOPEX-Poseidon (1992–2005), ERS2 (1995–2011), ENVISAT (2002–2012) and Jason-1 (2002–2013). In addition, buoys and acoustic Doppler current profiler (ADCP) provide in situ SWH information. The limited scope of each of these observational datasets, together with the coarse resolution of altimeter measurements, preclude a comprehensive validation for all the selected cases. For an initial evaluation of our modelling approach, the results from the wave model driven by ERA-x and D1 data are compared to available altimeter data. The simulated wave heights are collocated with the altimeter tracks within a time window of 3 h. For the 2004, 2007, 2008 and 2010 French Atlantic coast storms and the 2012 Bulgarian storm, data are collected from two satellite altimeters, Jason-1 and ENVISAT. The scatter plots between model and altimeter wave heights indicate that the use of D1 winds provides a better fit to the data (Fig. ). In particular, when compared to the results for the wave model driven by ERA-Interim initial conditions, the use of D1 data reduces the normalized root mean square error (NRMSE) from 17.1 to 13.1 %, largely owing to a significant reduction of bias from -35 to -4 cm (Fig. ). The D1 downscaling also leads to a better fit for high SWHs, providing an important validation for extreme wave events. For the 1998, 1999 and 2000 storms, altimeter wave heights from TOPEX and ERS2 are also used for the evaluation of the modelled SWHs, and the same tendency is found, with an improvement of the reconstruction of SWHs using D1 winds over ERA-Interim winds (not shown).

As satellite altimeters provide data along a track, these observations can be useful for mapping the spatial distribution of the SWH. For further examination, we present the 2012 Bulgarian storm as an example of a more detailed evaluation of the reconstruction against observations. The wave model outputs using ERA-Interim or D1 initial conditions are first compared to the 214 along-track data points measured by the Jason-1 and ENVISAT satellite altimeters on 7 and 8 February 2012. The wave reconstruction given by D1 forcing more closely matches the satellite observations, especially in terms of wave intensity over the southern part of the satellite track (Fig. ). However, the maximum observed SWH value is not reached by the model for both the ERA-Interim winds and the D1 winds. Regarding the temporal evolution of the 2012 Bulgarian storm, we use in situ ADCP to check if the peak SWH occur at the same time in the observations and the reconstruction. In Fig. , we compare the SWH data from the ADCP located at Pasha Dere beach at 20 m depth provided by the Bulgarian Institute of Oceanology to our wave model outputs. The use of D1 generally overestimates the measured SWHs, while the use of ERA-Interim underestimates the wave heights. However, the use of D1 winds leads to better matching of the temporal structure of the wave. The overall improvement of the SWH reconstruction by using D1 is confirmed by the statistical analysis in Table . The temporal evolution of a storm can also be evaluated with in situ buoys. For example, for the 2010 Mediterranean storm, we compare the time series of SWHs from model and buoy data (43.4∘ N and 7.8∘ E) off the coast of Nice, France, at the peak of the storm (Fig. ). The results show that the SWH induced by using D1 data more closely matches the buoy observations when compared to the ERA-Interim data forcing. Given our validation of the D2 approach discussed in Sect. , the D2-driven SWH hindcasts of the 2004, 2007, 2008 and 2010 French Atlantic storms are also compared to satellite altimeter data. The statistical analysis (bias and NRMSE) reveals that the use of D2 winds leads to better results than the use of D1 winds (Fig. ). Biases of SWHs are slightly improved using D2 winds over D1 winds; however, D2 winds slightly increase the NRMSE of SWHs for the 2004, 2007 and 2008 storms. The D2 method only slightly improves the NRMSE of SWH for Cyclone Xynthia (February 2010). While the application of the D2 method winds does not lead to an improved result over D1 in all cases, D2 appears to show better skill for events with higher wind speeds, such as the ones observed during the Lothar storm.

Storm surge hindcasts can be evaluated by tide gauge measurements. A network of 25 tide gauges along the French coasts is maintained to validate the surge model implemented at Météo-France. Furthermore, an additional 12 hydro-meteorological stations are located along the Bulgarian coasts for validation purposes. Depending on the storm extent and instrument condition, the number of available data points is different for each storm (Table ). For a global hindcast evaluation of tide gauges, all available measurements with a peak in storm surge are selected. Weighted normalized observation error (WNOE) is calculated to highlight the overestimation and underestimation of the simulated maximum storm surges with respect to available measurements, and it is defined in Eq. (). WNOE=100⋅α(tsim)⋅Xsim-XmeaXmea

In this simple calculation, tsim(mea) is the time related to the simulation outputs (measurements, in hours), Xsim(mea) is the simulated (measured) value of maximum storm surge (in centimetres) and α is the weighting coefficient. The value of α is equal to 0.9 if the simulated maximum of storm surge falls within a time window of ±3 h with respect to the observed peak time; if it is sooner or later, the weighting coefficient is set equal to 1.1 to reflect greater bias. For some cases, when no time information is available, no weighting is applied, and thus α=1. When ‖WNOE‖<20 %, we consider errors to be low or moderate. Moreover, the values are evaluated regarding the number of samples (Table ). First, we evaluate the impact of using wind and mean sea-level pressure data from D1 instead of from ERA-x. The storm surge outputs using ERA-x forcing have a tendency to underestimate maximum storm surge compared to D1 forcing (Figs. , and ). Cases with low or moderate errors represent a larger proportion of storm surge events when D1 data are used. In particular, 63 % of storm surge events were associated with low and moderate error in the ATL basin, 54 % for BUL and 100 % for the MED domain. This represents a general improvement over the ERA-x data, which had low/moderate errors for 21 % of storm surge events for ATL, 0 % for BUL and 100 % for the MED domain (Table ).

Second, the D2 method is applied to two examples of storm surge reconstruction (the Atlantic 2004 and 2007 storms in France) with corresponding statistical analysis. For the December 2004 storm, a deep low of 980 hPa crossed the northern French coasts from west to east, generating high waves and surge along the British Channel and the North Sea coasts due to strong northwesterly winds wrapping behind the system. The maximum observed surge exceeded 1 m at St Malo and Dunkirk during a period of below-average tide (Fig. ). Over the course of this event, the application of ERA-Interim winds result in an underestimation of the surge by roughly 60 cm at St Malo and 20 cm at Dunkirk (Fig. ). However, the use of D1 forcing successfully captures the peak of the surge in St Malo and Dunkirk. The use of D2 winds induces an overestimation of the surge of 20 cm at St Malo and roughly the same surge as D1 at Dunkirk. The second example of storm surge hindcast is provided by the November 2007 storm. This event affected the whole North Sea (including Dunkirk and Calais on the French coast) and parts of the eastern British channel. It was associated with a strong northwesterly wind on the North Sea and lasted nearly 24 h. At the peak of the storm event, a surge of 2.30 m was recorded at Dunkirk (Fig. ). While the ERA-Interim forcing significantly underestimates the surge by 80 cm (Fig. ), a good fit is obtained by the model with both the D1 and D2 data forcing. For this particular storm, the D2 winds give slightly better surge results on 11 November 2007 at 00:00 UTC. These two storms are examples of the various responses of the storm surge hindcast with both types of downscaling: no significant trend could be highlighted. Overall, the dispersion of WNOE values for the D2 results is larger than for D1 (Fig. ), and Atlantic cases are better hindcasted with D2 forcing data (Table ). The ability of D2 to simulate very deep cyclones could explain this point, since the mesoscale processes involved in strong winds are better described with the D2 approach.

The 20th century extreme events that occurred before 1957 can be hindcast by using ERA-20C, the 20th century reanalysis ECMWF project . For these cases, even if there were no available wave observations, a storm surge evaluation is possible due to the availability of reliable sea-level observations.

To validate the concept of downscaling using ERA-20C reanalyses, we concentrated on the major storm that occurred in the North Sea in February 1953 (Fig. ). It caused severe damage along the Dutch, Belgian and English coasts. Wind intensity around force 10 on the Beaufort scale (around 90 km h-1) were measured in Scotland and northern England. The winds and the low atmospheric pressure combined with exceptional equinox tides were responsible for the surge, which was additionally exacerbated by the funnel shape and shallowness of the North Sea. The Netherlands were the worst affected, resulting in 1836 deaths and widespread property damage . Most of the casualties occurred in the southern province of Zeeland; an additional 307 people were reported killed in England, 19 in Scotland and 28 in Belgium as a result of the storm. The most striking feature along the Dutch coast was a long swell with a peak period of 20 s, which induced wave flooding. In our reconstruction of the event, the MFWAM results using the D1 winds indicate SWH exceeding 16 m in the western part of the North Sea at 00:00 UTC on 1 February 1953 (Fig. ). The storm surge hindcast produces a high surge which is unusual for this area; in particular, along the Dutch and Belgian coastlines storm surges exceeded 3 m either with ERA-20C or D1 data forcing (Fig. ). The improvement of storm surge reconstruction induced by D1 forcing was particularly marked at IJmuiden, Ostend, Brouwershaven and Dieppe, where the recorded peaks of storm surge are better represented than for ERA-20C (Fig. ).