NHESSNatural Hazards and Earth System SciencesNHESSNat. Hazards Earth Syst. Sci.1684-9981Copernicus PublicationsGöttingen, Germany10.5194/nhess-16-255-2016An approach to build an event set of European windstorms based on ECMWF EPSOsinskiR.LorenzP.KruschkeT.VoigtM.UlbrichU.ulbrich@met.fu-berlin.dehttps://orcid.org/0000-0001-7558-6622LeckebuschG. C.https://orcid.org/0000-0001-9242-7682FaustE.HofherrT.MajewskiD.Institute of Meteorology, Freie Universität Berlin, Berlin, GermanyCNRM/GAME, Météo-France and CNRS, Toulouse, FranceMeteo Service Weather Research GmbH, Berlin, GermanyGEOMAR Helmholtz Centre for Ocean Research Kiel, Kiel, GermanyGFZ German Research Centre for Geosciences, Potsdam, GermanySchool of Geography, Earth and Environmental Sciences, University of Birmingham, Birmingham, UKMunich Re, Munich, GermanyGerman Weather Service, Offenbach, GermanyU. Ulbrich (ulbrich@met.fu-berlin.de)25January201616125526812January20159February201519November201511December2015This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://nhess.copernicus.org/articles/16/255/2016/nhess-16-255-2016.htmlThe full text article is available as a PDF file from https://nhess.copernicus.org/articles/16/255/2016/nhess-16-255-2016.pdf
The properties of European windstorms under present climate conditions are
estimated on the basis of surface wind forecasts from the European Centre for
Medium-Range Weather Forecast (ECMWF) Ensemble Prediction System (EPS). While
the EPS is designed to provide forecast information of the range of possible
weather developments starting from the observed state of weather, we use its
archive in a climatological context. It provides a large number of
modifications of observed storm events and includes storms that did not
occur in reality. Thus it is possible to create a large sample of storm
events, which entirely originate from a physically consistent model, whose
ensemble spread represents feasible alternative storm realizations of the
covered period. This paper shows that the huge amount of identifiable events
in the EPS is applicable to reduce uncertainties in a wide range of fields of
research focusing on winter storms. Windstorms are identified and tracked in
this study over their lifetime using an algorithm based on the local
exceedance of the 98th percentile of instantaneous 10 m wind speed, which is
associated with a storm severity measure. After removing inhomogeneities in
the data set arising from major modifications of the operational system, the
distributions of storm severity, storm size, and storm duration are computed.
The overall principal properties of the homogenized EPS storm data set are in
good agreement with storms from the ERA-Interim data set, making it suitable
for climatological investigations of these extreme events. A demonstrated
benefit in the climatological context by the EPS is presented. It gives
clear evidence of a linear increase of maximum storm intensity and wind field
size with storm duration. This relation is not recognizable from a sparse
ERA-Interim sample for long-lasting events, as the number of events in the
reanalysis is not sufficient to represent these characteristics.
Introduction
According to the records of insurance and re-insurance companies, windstorms
are the most costly natural hazards in Europe . Fortunately,
the most extreme events occur very rarely, but this makes it difficult to
estimate their recurrence periods and other statistical characteristics,
which can only be estimated with large error bars assigned to them
(cf. ). Studies estimating these parameters make use of
reanalysis and station data (e.g., or
) or climate simulations
(e.g., ). Most recently, a catalogue of damaging European
windstorms was produced by , based on the European Centre for
Medium-Range Weather Forecast (ECMWF) ERA-Interim reanalysis. As one
implication of this study, it can be said that the Ensemble Prediction System (EPS)
provides a reasonable opportunity to enlarge such a catalogue substantially.
So far, statistical models like the random walk or Markov Chain Monte Carlo
models are often used to extend samples for the estimation of the recurrence
of severe storm events or extreme wind speed with return periods of over
1000 years (e.g., ). We use the EPS for the same purpose of
extending the sample size with the distinction that all EPS events are fully
based on a physical model, which has the big advantage of a good consistency
and coverage of the potential storm-related risk. In a statistical sense,
observations represent the realized reality. Ensemble forecasts as part of
the regular weather forecasts demonstrate that individual weather events
could have developed differently, starting from basically the same initial
weather conditions. In this sense, observations do not provide information on
potential alternative developments that could have been reality with a
similar probability.
Studies on the EPS are mainly focused on the quality of the prediction. An
example of such a study related to European winter storms can be found in
, where the focus lies on the predictability of the heavily
impacting winter storms of the year 1999. has
analyzed the predictability of storm tracks and extratropical cyclones using
a cyclone-tracking algorithm by .
focused on the application of the EPS for the oil and gas industry. The output
of the ECMWF EPS in an impact-based study was used for estimating the range
of potential storm surge events at the German bight . The small
area investigated in this study is, however, not representative of winter
storms in Europe. The current study aims at assessing climatological
properties of European winter storms, produced by the operational ECMWF
Ensemble Prediction System. Such an approach requires minimizing the effects
from inhomogeneities in the EPS introduced by the regular updates of this
operational system. They could potentially produce systematic deviations from
observed storms, the latter being represented by the ERA-Interim reanalysis
in our study. Beyond these changes, there could be systematic
forecast-lead-time-dependent trends in the EPS data set, affecting storm characteristics
like severity, duration, or the affected areas. Possible breaks (e.g., between
different model cycles), trends (e.g., a model drift), and biases
(e.g., different wind speed distributions according to different model resolutions)
caused by the EPS inhomogeneities in the detected storm properties must be
initially addressed in order to carry out climatological investigations.
The paper aims at demonstrating that it is possible to produce statistics of
storms under observed climate conditions based on EPS forecasts, leading to
more reliable results than traditional approaches based on reanalysis data.
Our aim is a representation of the recent climate, which distinguishes our
approach from others based for example on climate projections. To summarize,
our study intends to describe a possibility of producing more reliable storm
statistics which are still very close to the observed climate. The final
event set is comparable to those which are stochastically generated based on
a fixed historical sample, with the distinction that the stochastics is
replaced by the application of a physical model in our case.
Data
Instantaneous 10 m wind speed data at different archiving time steps as
mentioned farther below are considered. The area of investigation covers the
Atlantic–European region spanning from 40∘ W to 40∘ E and 25 to 80∘ N. For
part of the studies in this paper (explicitly mentioned in the respective
sections), the entire Northern Hemisphere was used in order to avoid boundary
effects. An extended winter season is used from September to May.
ERA-Interim
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 ).
ECMWF Ensemble Prediction System
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).
Overview of general characteristics of the EPS
(used temporal resolution) pf: perturbed forecast; cf: control forecast.
Time frameSpatial resolutionTemporalNumberInitialisations atresolution(h)of member21 Nov 1992–9 Dec 1996*T631232pf+1cf12:00 UTC10 Dec 1996–12 Jan 2000TL1591250pf+1cf12:00 UTC13 Jan 2000–20 Nov 2000TL1596 (12)50pf+1cf12:00 UTC21 Nov 2000–24 Mar 2003TL255650pf+1cf12:00 UTC25 Mar 2003–27 Jun 2005TL255650pf+1cf00:00 and 12:00 UTC28 Jun 2005–31 Jan 2006TL2553 until 126/144 h and 6 (6)50pf+1cf00:00 and 12:00 UTC1 Feb 2006–25 Jan 2010TL3993 until 144 h (6)50pf+1cf00:00 and 12:00 UTC
* Before January 1994 only three forecasts per week available,
major change on the system with introduction of the IFS in March 1994 and the
introduction of IFS cycle 12r1, which led to a significant reduction in the
model bias of 10m wind speed (http://www.ecmwf.int/en/forecasts/documentation-and-support/evolution-ifs/cycle-archived/1994-summary-changes).
MethodsIdentification and characterization of storms at midlatitudes – wind tracking
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.
Homogenization of the EPS
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).
98th percentile as average over all land boxes (according to
land-sea masks of the data set) in the domain from 40∘ W to 40∘ E and 25 to
80∘ N for different EPS subperiods with corresponding 98th ERA-Interim land
box percentile: climatological ERA-Interim percentile based on ERA-Interim
for period 1989–2010 (ERA-Interim clim), ERA-Interim percentiles for the
periods of the corresponding EPS periods (ERA-Interim
subEPS), percentiles of raw EPS data (EPS), and climatologically
adjusted EPS percentiles (EPS climERA-Interim).
Climatological scaling
Subdividing the EPS data set into periods which are homogeneous in terms of
the horizontal resolution of the model system (see Table )
reflects the finding that different resolutions of the EPS system produce
different wind speed biases and, as a consequence, biases in SSIs, storm
duration, and size. A model with a coarse resolution represents an average of
a larger grid cell area than a model with a fine resolution. The finer the
model resolution, the better the orographic effects that can be captured. This
influences the wind speed distributions, but differences in wind speed
characteristics for the periods considered can also originate from
climate variability. The latter becomes evident when the ERA-Interim data are
used for estimating this threshold for the whole period and for the same
subperiods: Fig. shows 98th ERA-Interim percentiles using all
land grid points in the Atlantic–European area chosen. Land grid points are
shown, as the major interest is related to storm damages over land, but the
method is applied on all individual cells of the entire grid. The estimates
for the four subperiods vary from the percentile computed for the
complete period 1989 to 2010. The percentiles of the EPS versions with
coarser horizontal resolution are found to be lower than those with higher
resolution. The effect from TL159 to TL255 is
much stronger than from TL255 to TL399. Note
that for this intercomparison an interpolation towards the ERA-Interim grid
had to be performed. The correction factor for the 98 % quantile of each grid
cell is computed taking the factor due to climate variation (as estimated
from ERA-Interim) into account.
Visualization of tail differences in the wind speed distribution of
the four subperiods (see Table ) of the EPS. Shown: relative
exceedance of 98th EPS percentile as land average. Internal climate
variability of the disjunct periods is excluded by utilization of the
climatological scaling (for details see text).
Average of 98th percentile (m s-1) for different forecast lead
times (right axis, h after initialization): for T63 12-hourly (a, e),
TL159 12-hourly (b, f), TL255 6-hourly (c, g), and
TL399 6-hourly (d, h). (a)–(d) for land
grid boxes, (e)–(h) for sea grid boxes.
Scaling of exceedance
After climatological scaling of the identification threshold, the wind speeds
exceeding this 98th percentile still differ between the subperiods, as shown
in Fig. . The presented differences in the tail seem to be very
small, but as the cubic of these values is used and summed over a larger
quantity of grid cells for the SSI calculation, cf. Eq. (), they
are impacting the results. For this reason, a quantile–quantile mapping is
used. It is a standard method used for a bias correction; see, e.g., .
The method chosen estimates empirically percentiles in
equidistant steps (0.1 %) for both EPS and ERA-Interim. A wind value in the
EPS, which corresponds to the ith percentile of the EPS wind speed
distribution, is corrected in the way that it has afterwards the value of the
ith percentile of the ERA-Interim wind distribution. After both
climatological scaling and quantile–quantile mapping, the ERA-Interim 98th
percentile and the exceeding wind speeds mapped on the ERA-Interim
distribution can be used for the SSI calculation in every subperiod. A
quantile–quantile mapping for the different periods without previous
climatological scaling is not suitable, as it would completely remove the
(real) climate variations.
EPS storm validationSpin-up effects, threshold, and diurnal cycle
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.
SSIs for representations of the storm Emma (28 February 2008, 18:00 UTC, detected in
ERA-Interim) in 50 EPS members: (a) 6 h lead time, initialized
28 February 2008 at 12:00 UTC and (b) 90 h lead time, initialized 25 February 2008 at 00:00 UTC.
Representation of the storm Emma
(28 February 2008, 18:00 UTC, detected in ERA-Interim) in 50 EPS members initialized
28 February 2008 at 12:00 UTC. (a) Average cluster size (km2), (b) duration (h).
Modifications of observed storms in the EPS: storm “Emma”
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.
Emma
(28 February 2008) as an example in more detail. At a lead time of 6 h, all of
the 50 EPS runs produce a storm fulfilling our criteria that can be assigned to
the observed one (Fig. a). The majority of the simulated events
are weaker than the intensity computed from ERA-Interim, but for 12 members
the simulated storm is stronger than observed. At a lead time of 90 h,
taken as a second example (Fig. b), in several runs no storm is
found. One member, however, produces a storm of about double the
observational SSI. The variations in SSI originate from variations in the
intensity at individual grid points, in area and in storm lifetime, as
depicted in Fig. for the 6 h lead time. The track of
Emma in ERA-Interim and in the individual EPS members (Fig. )
is found by identifying a storm core from the weighted local
SSI contributions of all storm grid points at a time step, and connecting the
centers from different time steps . While in many
other cases the observed storm is found close to the center of the EPS
ensemble member storms, all EPS tracks of Emma at this lead time are
located northward of the ERA-Interim storm (Fig. a). For the
90 h lead time (Fig. b), the spread between the modified
Emma tracks is larger. A notable feature of Emma is the fact that the
observed Emma tends to be at the border of the EPS ensemble also for
the long lead time. This example demonstrates that extreme EPS events can be
feasible representations, but the northward shift is not systematic in the
EPS. SSI values for all events detected in ERA-Interim and the EPS (starting
inside a 6-day window; see Sect. 4.3) over the period 2001 to 2010
are shown in Fig. . Over the entire period, the range of SSI in the
EPS is much larger than in ERA-Interim. A larger range of SSI values was
expected, as the EPS can include forecasts with slightly higher wind
velocities. The definition of the SSI, using cubic exceedances, enlarges the
range of values. As the motivation for the SSI definition is damage
potential, the additional events help to better estimate potential storm
risks for Europe, in particular with respect to the occurrence of the most
extreme storms.
Tracks for representations of the storm Emma (28 February 2008, 18:00 UTC, detected
in ERA-Interim) in 50 EPS members initialized on (a) 28 February 2008 at 12:00 UTC and
50 members initialized on (b) 25 February 2008 at 00:00 UTC.
SSIs for all storms in the period 13 January 2000 (10 m wind available at
6-hourly resolution for the EPS) to 25 January 2010 for ERA-Interim and for the EPS with
initializations at 12:00 UTC. The months June, July, and August are excluded.
Comparison of storm properties in the EPS and ERA-Interim
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.
* Based on data from 1 January 1995 to 9 December 1996.
No. of storm events per year subdivided according to the severity,
for the four individual subperiods with constant horizontal resolution:
(a) T63, (b) TL159, (c) TL255, and
(d) TL399 of the EPS (T63 and TL159 at 12-hourly
resolution for EPS and ERA-Interim). First bar is for ERA-Interim, the other
for the EPS (bars from left to right): second – EPS raw data; third – processed by
climatological scaling; fourth – processed by scaling of exceedance; and fifth – applying
both scaling techniques on the data.
Fit of normal distributions to logarithm of SSI for (a) EPS in
TL255 and (b) EPS in TL399 without scaling
techniques, with climatological scaling, with exceedance scaling, and with both scaling
techniques together. Raw EPS data and climatologically scaled data are similar and
differ more greatly from the observation than using the exceedance scaling or
both together.
Storm properties in the EPS compared to ERA-Interim
The average number, size, and duration of storm events per year found in the
four different time periods characterized by the specific EPS resolutions are
given in Table , both for the EPS and ERA-Interim. The number of
events in the EPS is the ensemble average over all available ensemble
members, initializations per day, and over the forecast length limited to
storms lying inside the described 6-day window (cf. Sect. 4.3). This
number can thus be directly compared to the ERA-Interim values given in the
same table. The respective values are similar between the two data sets,
meaning that the storm properties in the EPS ensemble average are in good
agreement with ERA-Interim. In order to compare the severity distributions of
the EPS and ERA-Interim events, seven severity classes were formed making
sure that there is a reasonable number of events in each of the classes to
permit statistical tests. Subperiods with constant horizontal resolution of
the EPS are again distinguished. Note that the SSI values calculated from
data with 12-hourly resolutions (T63 and TL159) are
expected to be lower than those from 6-hourly resolutions
(TL255 and TL399) (Fig. ) due to
the additional time steps included for the latter. It can be seen how the
results of the wind tracking differ for the EPS without using any scaling
technique, using only the climatological scaling, the scaling of exceedance,
or both together. When both scaling techniques are used together, the severity distributions
of the EPS and ERA-Interim are comparable for all subperiods except for EPS
T63. For the latter, the scaling corrects for an overestimation of severity,
resulting in a good agreement in the highest four severity classes. The
larger number of weak events has its origin in model biases of 10 m wind
speed
during the early years (1992 to 1994) of the data period of the T63 EPS. As
it is difficult to evaluate the benefit of the scaling techniques visually,
a normal distribution was fitted to the logarithm of the SSI. The
Anderson–Darling test indicates that the logarithm
of the SSI is normally distributed. The benefit from the scaling techniques is
illustrated in Fig. . Looking for the raw EPS data at
TL399 resolution, one sees that they concur better with ERA-Interim than
the data in TL255. The effect of the climatological scaling
is relatively small. Using both scaling techniques together, the
distributions between the EPS and ERA-Interim look very similar. The fit
parameters are shown in Table . Fit parameters were estimated
using maximum likelihood. The exact standard errors of the parameters are
very small in the EPS case due to its very large sample. The mean and
standard deviation lies in between the error resulting from ERA-Interim. This
means that the EPS ensemble mean represents well the storm climate which can
be found in ERA-Interim. Storm representations in the EPS and ERA-Interim
with comparable SSI values show, on average, comparable storm duration as
well as the storm size (not shown).
Parameters and their errors of fitted normal distribution to
logarithm of SSI for the EPS using both scaling techniques together and
ERA-Interim.
ModelMeanSDError meanError SDERA-Interim (period of EPS TL255)0.731.300.0770.055EPS TL2550.771.320.0030.002ERA-Interim (period of EPS TL399)0.721.350.0860.061EPS TL3990.761.330.0050.004Spatiotemporal EPS storm propertiesPure and modified EPS storms
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.
Sketch of definition for pure and modified EPS storms.
EPS storms during the forecast time
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.
Temporal evolution of the number of first storm detections during
the integration time (h) after initialization (a) TL255 –
12:00 UTC; (b) TL399 – 00:00 UTC; and (c) TL399 – 12:00 UTC.
Values for ERA-Interim at 00:00, 06:00, 12:00, and 18:00 UTC are repeated.
Spatial distribution of storms
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.
Accumulated yearly number of detected storms (sum of footprints per
year) for time frame of the EPS resolution TL255 (a, c)
and TL399 (b, d), ERA-Interim (a, b), and EPS (c, d)
normalized by ensemble size by dividing by 50 members and 6 forecast
days.
Modified vs. pure EPS storms
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 .
Percentage of number of EPS storms affecting the grid cell and being
pure in the EPS with TL255 initialized at 12:00 UTC.
Storm intensity vs. duration
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.
Wind field size during storm duration for storm duration between
30 and 84 h; (a) for ERA-Interim and (b) for the EPS.
Storm severity during storm duration for storm duration between 30 and
84 h; (a) for ERA-Interim and (b) for the EPS.
Conclusions
Atlantic–European windstorms were identified in the archived data set of the
ECMWF Ensemble Prediction System forecasts in the period December 1992
to January 2010. The identification of potentially damaging windstorms was
based on the excess over the local 98th percentile of wind speeds
, only taking into account events which
have a minimum area at a single archived time step and a minimum duration of
24 h (with fulfillment of the minimum area criterion in each of them).
The fact that the operational EPS changed its characteristics during the data
period led to changes in the value of the 98th percentile of wind speed. Hence
a homogenization procedure was applied to four subperiods characterized by
different spatial resolutions of the system. Temporal variation of the
percentile due to climatic variations and variations with respect to the
cubic excess over the percentile (assumed to be model version specific) were
taken into account. A diurnal cycle in the 98th percentile of the 10 m
wind speed was observed in the EPS, which is also present in ERA-Interim.
These diurnal variations comprise a systematically higher value of the
threshold percentile for 12:00 UTC only, which is about 1 m s-1 larger than
the respective values at the other 6 hourly time steps. This effect also
leads to a diurnal variation in the number of storm initiations and ends, as
detected by the here-applied storm identification scheme. Averaged over a
large number of storms, this diurnal variation can be seen in the severity at
different times of day. This behavior is, however, partly hidden in the EPS
with TL255 resolution, as these forecasts additionally
exhibit an 18 h periodicity in the threshold for individual time steps
presumably assigned to the specific stochastical perturbations imposed in the
ensemble-generating process during the respective period. None of these
effects had an apparent strong impact on the subsequent evaluations of the
EPS as all forecast time steps inside a 6-day window were taken into
account. The overall EPS storm properties were found to be similar to
ERA-Interim storm properties. On average the EPS produces the same number of
storm days as ERA-Interim. There is no systematic tendency over lead time in
the total number of storms. The EPS produces developments of storms which
have no observational counterpart. While the principal statistical properties
are the same as for modifications of modified representatives of real
storms, their share in the total number increases with increasing lead time.
They have a spatial distribution of occurrence that is different from the
observed and modified storms, with a focus on the Mediterranean and eastern Europe.
As the spatial distribution and the number, the size, and duration of
events of same severity are in good agreement with “real” storm events,
the EPS can be used to increase the sample size for European winter storm
studies by a factor up to the number of ensemble members, initializations per
day, and forecast time. As we used 50 perturbed members and storms starting inside
a 6-day window, we get a sample size increase of 300 times. The statistics
of the storms indicate a clear increase of maximum intensity and extension of
Atlantic–European storms with their duration. This result from the EPS cannot
be obtained easily from reanalysis as the number of very strong events is too
low to provide stable statistics. Another example of analyses possible by
using the huge sample of storm events deducted from the EPS is the estimation
of return periods of specific storms and intensities. Such return periods
will naturally be associated with smaller uncertainties than those in other
studies (e.g., ). However, for such a study, it has to be
taken into account that storm representations are not statistically
independent; see . They are also limited to climate
conditions (e.g., SSTs) during the 10 year period considered. Still, the
consideration of EPS storms enables us to estimate the potential for an
occurrence of storms more extreme than observed based on a physical modeling approach.
The range of severity in the EPS is much larger than in ERA-Interim. Model
biases resulting from different model versions and/or resolutions were
eliminated using the quantile–quantile mapping approach. Spatiotemporal
properties of the storms are realistic compared to ERA-Interim, and also the
range of wind velocity is realistic. For this reason, also the SSI values are
realistic. The range of SSI values is larger, because the EPS contains a wide
range of storm modifications, including those with higher wind speeds.
Modifications to stronger winds are additionally amplified when calculating
the SSI by utilizing the cubic threshold exceedance.
The climatology based on the EPS is intended to be close to the observed
development of climate conditions, and it must be distinguished from alternative
approaches such as climate simulations for present-day greenhouse gas and solar forcing,
for example, which allow the models to produce windstorms largely independent
from the observed development of weather and climate in the time period
considered. If independence from observations is a requirement, coupled general circulation model (CGCM) runs may
be the better choice. In the sense of an event set, we do not expect complete
independency but just variations of storms, as is done, e.g., for stochastic
event sets out of a fixed historical sample. Finally, the way that events are
selected for construction of an event set will be dependent on the specific
purpose of that event set, and so approaches are not discussed further in this paper.
To sum up, the EPS shows realistic storm properties with a wide range of
modifications in the storm properties, where storms can be found with a
higher possible impact than appeared as in reality; thus the ability to use
this data set for statistical studies is given.
Acknowledgements
For the possibility to carry out this study we would like to thank the
Munich Re for their financial support and the open-access publication fund
of the Freie Universität Berlin for financing this publication. We are also
grateful to the German Weather Servive (DWD) and the ECMWF for providing
access to the EPS data and ERA-Interim reanalysis. The authors thank the two
anonymous referees for their constructive comments.
Edited by: M.-C. Llasat
Reviewed by: two anonymous referees
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