An archive of 6-hourly ERA-Interim reanalysis data is used. At the time the current study was performed, data before the year 1989 were not available, so the period considered is 1989 to 2010. ERA-Interim uses the 4D-Var assimilation scheme and the Integrated Forecast System (IFS) release Cy31r2 at a horizontal spectral resolution of TL255. The same system release was operational for the EPS from 12 December 2006 until 5 June 2007, but with horizontal resolution of TL399 (for details refer to ).

This section provides some relevant aspects about the ECMWF EPS. A more detailed description of the EPS can be found in and . The Ensemble Prediction System of the ECMWF became operational in December 1992 (see Table 1 for an overview). Initially, 32 perturbed forecast members (based on the method of singular vectors; in the following abbreviated as “pf”) plus one control forecast (not perturbed against the original analysis, but using the EPS model system instead of its deterministic counterpart; in the following abbreviated as “cf”) were produced. The number of perturbed ensemble members was increased to 50 in December 1996. Since October 1998, some of the EPS runs have been produced including perturbations in the model physics. With increasing computing power, continuous upgrades of the system lead to improvements in the forecast skill (cf. ). The horizontal resolution was increased from T63 as follows: TL159 (December 1996), TL255 (November 2000), and TL399 (February 2006) to eventually (not used in this study) TL639 (January 2010). The resolution of the singular vectors was changed from T21L31 to T42L31 (March 1995), T42L40 (October 1999), and eventually T42L62 (February 2008) . Changes in the data assimilation scheme from 3D-Var to 4D-Var were introduced in November 1997 (cf. ). The EPS integration time is 15 days, but after 10 days of forecast the horizontal resolution is decreased. Since March 2003, the system has been initialized twice a day, at 12:00 and 00:00 UTC. In order to take the major changes into account, the data set was split into periods with constant horizontal resolution (Table ). Data used in this study cover the period until 25 January 2010, thus excluding the latest period with TL639 resolution. Depending on the period, the EPS data are available at 12-, 6-, and 3-hourly temporal resolution. As ERA-Interim is only available at 6-hourly resolution, the EPS data with a 3 h resolution were used in subsets of 6-hourly resolution. For the 12-hourly data, ERA-Interim was also used at this temporal resolution (time steps at 00:00 and 12:00 UTC).

For the identification and characterization of European winter windstorms, an impact-related wind-tracking algorithm is used. It was introduced by and has been further developed since then. An overview of the actual scheme is provided by . It identifies grid points belonging to windstorms by searching for spatial clusters of grid points (extending over an area of at least 1.6 × 105 km2) where the local 98th percentile of wind speed is exceeded. The choice of the 98th percentile is motivated by the relevance of this threshold for storm damages . The identified clusters are connected to a track using a nearest-neighbor criterion. The maximum distance allowed to connect two clusters to a windstorm track is limited by an assumed maximum wind field propagation velocity of 120 km h-1. In the present study a minimum lifetime of 24 h of an identified windstorm must be fulfilled, equivalent to three archived time steps for the 12 h temporal resolution and five time steps for 6 h resolution periods (Table ). By summing the cube of the 98th-percentile exceedances belonging to a track, an objective storm severity measure is determined. This measure, called the storm severity index (SSI), is calculated for each storm over all time steps t and grid points k affected by exceedances of the 98th percentile assigned to a storm. It is meant to characterize the severity of storms, taking intensity, size, and duration of the storms into account, as is shown in Eq. (): SSI=∑tT∑kKmax1,vk,tvperc,k-13⋅Ak. vk,t is the wind velocity in grid cell k at time instance t, vperc,k the 98th percentile in grid cell k, and Ak the area of grid cell k. The SSI values are normalized to a grid cell of unit size. This is done using the grid cell area Ak to reduce the resolution dependence when applying different models and to eliminate a latitude dependence. A resolution dependence can still remain, as models of different resolutions can produce different wind speed distributions. This will be discussed in the following section. The algorithm was originally developed for the application with reanalysis and climate data. The medium-range ensemble EPS consists of single forecasts from which we use the first 10 days. For each day up to twice a day (12:00 and 00:00 UTC initializations) 50 perturbed forecasts and an additional control forecast were produced and archived. The algorithm is applied on each individual forecast. This means that, when combining the members and forecasts with different lead times, a single day is represented by up to (50pf+1cf) × 2 initializations × 10 days = 1020 equivalent days. To avoid boundary effects at the beginning and end of the forecasts, the period had to be reduced to be able to generate representative samples. We restricted our sample to EPS runs initialized at 12:00 UTC with storms starting inside a window of 6 forecast days (to be discussed in Sect. 4.3). This results in an enlargement of the sample deducible from reanalysis by a factor of 300 using perturbed forecasts.

The improvements introduced into the operational EPS system mentioned above will affect the results of the tracking procedure in different ways, but a main impact is due to the changes in spatial and temporal resolution. Hence, we subdivide the data into subperiods of the same spatiotemporal resolution and apply a two-step procedure to homogenize windstorm identification and SSI calculation across these subperiods: first, the 98 % quantiles of each subperiod are scaled towards a common basis, using the ERA-Interim data set as a reference. We call this the “climatological scaling” of the threshold used for windstorm identification (see Sect. 3.2.1). Second, a quantile–quantile mapping approach (cf. ) is used for exceedances of the 98th percentile to provide matching shapes of the upper tail of the wind speed distribution, which is a requirement of SSI calculations, homogenous across all subperiods. This second step is called “scaling of exceedance” in the context of this study (see Sect. 3.2.2).

Even though spin-up effects in numerical simulations are well known, their magnitudes in the ECMWF EPS have not been a major issue in the scientific literature. An exception is the report by focusing on humidity in the upper troposphere. Results of an analysis on systematic variations of 98 % quantiles of wind speed are given in Fig.  for the T63, TL159, TL255, and TL399 resolutions. Average values over all land and all sea boxes in the area considered have been computed for archiving steps of the forecasts. For both land and sea grid points a small initialization effect in the first 6 to 12 h of the forecasts becomes visible. The percentile value in the TL159 resolution over land, for example, is about 0.5 m s-1 higher during the first one to two archiving time steps than subsequently. Over sea, there seems to be an effect with opposite signature (lower initial values) in the first 12 to 18 forecast hours. The data for TL399 over sea show the same initialization effect. The dominant feature in Fig.  is, however, a diurnal cycle with an amplitude of about 1 m s-1 over land. Maxima occur at the forecast time steps valid at noon (12:00 UTC). Note that a corresponding cycle is also found in the ERA-Interim data, with about the same amplitude (not shown). Conventional observations confirm that the daily cycle in the 10 m wind speed over land is a realistic feature . The EPS with TL255 is characterized by an interfering daily periodicity and an 18 h periodicity. As the daily cycle is small over sea, the 18 h periodicity is clearly visible in Fig. g. The irregular behavior of the EPS with TL255 resolution is apparently related to the stochastic perturbations of the model physics used during the respective period (A. Beljaars, personal communication, November 2012) as the unperturbed control forecast produces a regular daily cycle (figure not shown). A more thorough investigation of the 18 h cycle is beyond the scope of the present paper. We have not attempted to remove it from the investigation, but in comparing the windstorm statistics for this EPS resolution with the other periods we found no evidence for a systematic effect.

Different EPS members started at different lead times will produce modifications of observed storm events in terms of their genesis time, track, and intensity. Before considering the respective statistics for the whole time series, we consider the storm event named

Names are given by the Institute of Meteorology of the Freie Universität Berlin.

In order to compare the entire ensemble of storms in the EPS with those detected in the ERA-Interim data set, events not entirely captured in a forecast must be excluded. They would erroneously be taken as short(er)-lived storm events. This situation may be present if a storm is detected at the initialization time. In this case, it may have existed before but could not be completely tracked on the basis of the driving data. Removing all storms existing at the start of the forecast, however, allows the full range of storm durations to enter the statistics without a bias. A similar kind of problem would occur with storms existing at the end of the 10-day forecast time. Here, the same solution cannot be applied as it would prefer short-duration storms for genesis occurring rather late in the forecast period. We decided to restrict the evaluated storms to those generated a maximum of 6 days after forecast initialization, leaving 4 days as a maximum duration. There is still a problem with storms lasting 4 days or longer. According to ERA-Interim, only 0.8 % of storms are this long-lasting, and only some of them (namely, those generated at one of the time steps just before the 6-day limit) are affected. We expect the impact on the results to be small. Also, the choice of 6 days is motivated in the fact that it leads to an equal frequency of evaluated time steps at 0, 6, 12, and 18 h forecast time, thus ameliorating the effects of the 18 h periodicity in intensities mentioned earlier.

Initializations at 00:00 UTC are only available after March 2003, as is shown in Table . We wanted to be sure to avoid an overrepresentation of the period 2003 to 2010 in the statistics and thus use only the 12:00 UTC initializations. Nevertheless we looked into the forecasts initialized at 00:00 UTC and found no systematic difference compared with the runs starting at 12:00 UTC. Using the 6-day window, one initialization per day, and 50 perturbed forecasts for the period 2000 to 2010 yields a storm sample 300 times larger than available from reanalysis data for the same period.

Most considerations in this paper are based on the assumption that the EPS produces modifications of storms in the real world (subsequently called “modified EPS storms”), or, for some ensemble members, low wind speeds and thus no storm at all. However, the EPS can produce storm events that have no real-world counterpart. As for statistical investigations independent and identically distributed (iid) random variables are necessary; such pure events are particularly interesting, because they can increase the sample of independent events. Figure  shows a sketch of the definition of pure and modified storms in this study. To identify pure EPS storm events, events are sought for which no simultaneous counterpart can be found in ERA-Interim. We also regard events as pure if there is a spatial distance of more than 1500 km between contemporaneous events, as this is a typical synoptic scale of the investigated phenomena.

Using the aforementioned method to separate pure and modified storms, it can be assumed that close to the initialization time almost only modified storms can be found in the EPS (Fig. ). All ensemble members are likely to produce the storm that actually occurred, even if properties like size and duration as well as severity vary between the different realizations. For long lead times, however, there is an increased number of pure EPS storms (grey lines in Fig. ). The example of the storm Emma illustrates that for longer lead times a number of ensemble members do not show the storm at all, and a larger variability can be found in the intensities. Note that the average number of all storms in the EPS is nearly constant over the forecast time in spite of the small variation in the percentile values (Fig. ) over forecast time. This number is similar to its ERA-Interim counterpart, supporting our approach to use the individual period's own percentile for storm identification. A diurnal variation in the number of storms related to the diurnal variation in the 98th percentiles (Fig. ) is reflected in Fig. . As the percentile values used for the wind tracking are based on all data, their values lie between the minimum and maximum value of the 6-hourly or 12-hourly resolution. As at 12:00 UTC the 98th-percentile value is above the 98th percentile of the entire data set, the probability of an exceedance at this time of the day is larger than for the other times. For this reason the number of both first and final storm track detections is larger at 12:00 UTC than for the other times.

In order to investigate whether there is a difference in the spatial distribution of European winter storms between ERA-Interim and the EPS, the effect of each grid cell by all detected storms per EPS subperiod is computed. The footprint (region of grid cells which is affected by a storm) of each detected storm is analyzed, and for each grid cell the number of footprints affecting this particular grid cell is counted. Figure  shows the results, and for comparability the area effects for ERA-Interim are calculated for the same time frames as the EPS subperiods. The results with the ERA-Interim and EPS TL255 resolutions have identical grid points and are thus comparable without interpolation. For the comparison for the EPS with TL399 resolution, the result for ERA-Interim was interpolated to this resolution. For this specific analysis, the entire Northern Hemisphere was used for the tracking to avoid boundary effects caused by a limitation of the area. The basic distribution of the effects is similar in ERA-Interim and the EPS. The lower number (300 times; EPS with 50 members lasting over 6 days) of events available in the observational data causes a much noisier distribution than what is obtained from the EPS. There are local maxima in ERA-Interim for example over north Africa and the Mediterranean which the forecast model is not able to reproduce.

The interest in pure EPS storms originates from the wish to find events that are independent of modifications of ERA-Interim storms. Using the same procedure as in the section before to determine the spatial effects, but only for footprints of pure EPS storms, defined after the method explained in Fig. , the results are shown in Fig.  for the EPS with TL255. Over the Atlantic the number for the pure EPS storms is lower than over north Africa and eastern Europe. The major pathway of the storm systems is not so strongly affected by pure EPS storms as the regions where storms appear less frequently. The absolute number of pure events can be seen by combining Fig.  with Fig. . Then we have about 1 pure event over the Atlantic and about 1.5 to 2 over central Europe. This has the consequence that the use of pure EPS storms as a supplemental amount of events for increasing an independent sample of modified storms leads to a bias in the spatial distribution of storms. Using the presented method, the dependency between events to create an iid sample is defined by a comparison to ERA-Interim. Another feasible approach is to use a matching criterion in between all of the EPS events or a bootstrap-like sampling of alternative realizations of the past. Such approaches using the ECMWF EPS were successfully applied for estimations of return periods of European winter storms by .

A benefit of storm statistics based on the EPS instead of reanalysis is the larger number of storms available for statistical studies of typical midlatitude storms. Figure  shows a clear correlation between the storm duration and the maximum wind field size, which is the maximum of the area of exceedance of the 98th percentile that is assigned to the storm at each particular time step. For storms with durations of up to 54 h, ERA-Interim shows a comparable picture to the EPS. This can be explained by the fact that the number of observed storms of this timescale is large enough to provide reliable statistics. The EPS indicates that the average growth rate of storms is independent of their duration, while the duration determines the maximum size of the wind field. For long-lasting events there seems to be an asymmetry between the growth and the decline, where the growth seems to be faster than the decline. With respect to storm severity, a similar interdependence is found (Fig. ). Again, the intensification rate of storms on average is nearly independent of storm duration.