Historical Winter Storm Atlas for Germany (Gewisa)

atmosphere

Article Historical Winter Storm Atlas for Germany (GeWiSA)

Christopher Jung * and Dirk Schindler Environmental Meteorology, Albert-Ludwigs-University of Freiburg, Werthmannstrasse 10, D-79085 Freiburg, Germany * Correspondence: [email protected]; Tel.: +49-761-203-6822

Received: 31 May 2019; Accepted: 8 July 2019; Published: 11 July 2019

Abstract: Long-term gust speed (GS) measurements were used to develop a winter storm atlas of the 98 most severe winter storms in Germany in the period 1981–2018 (GeWiSa). The 25 m 25 m × storm-related GS fields were reconstructed in a two-step procedure: Firstly, the median gust speed (GSf) of all winter storms was modeled by a least-squares boosting (LSBoost) approach. Orographic features and surface roughness were used as predictor variables. Secondly, the quotient of GS related to each winter storm to GSf, which was defined as storm field factor (STF), was calculated and mapped by a thin plate spline interpolation (TPS). It was found that the mean study area-wide GS associated with the 2007 storm Kyrill is highest (29.7 m/s). In Southern Germany, the 1999 storm Lothar, with STF being up to 2.2, was the most extreme winter storm in terms of STF and GS. The results demonstrate that the variability of STF has a considerable impact on the simulated GS fields. Event-related model validation yielded a coefficient of determination (R2) of 0.786 for the test dataset. The developed GS fields can be used as input to storm damage models representing storm hazard. With the knowledge of the storm hazard, factors describing the vulnerability of storm exposed objects and structures can be better estimated, resulting in improved risk management.

Keywords: gust speed; roughness length; European Settlement Map; storm damage; digital elevation model

1. Introduction Strong storms chronically lead to enormous socio-economic damage [1]. In the period 1981–2018, storm events around the world caused total losses of about US$ 2115bn and led to approximately 446,000 fatalities [1]. The spatiotemporal extent of storm events greatly varies depending on the geographical location and the time during the year [2]. In Central Europe, storm events can roughly be classified into two categories: small-scale thunderstorms, which mainly occur from May to September [3–6], and large-scale winter storms mainly occurring from October to March, which are related to intense low-pressure systems [2,7–10]. As a part of Central Europe, Germany was often hit by severe winter storms, causing total losses of about US$ 37bn and 300 fatalities since 1981 [1]. The most destructive feature of winter storms are high-impact gusts, which are short-time fluctuations of the horizontal wind vector [11,12]. High gust speed (GS) seriously affects numerous sectors including forestry [13–15], insurance [16], local authorities [17], wind energy [2], waterways transport [18] and air traffic [19]. In these sectors, there is great interest in spatially explicit modeled GS fields for improving the identification of storm damage risk factors [15]. Among the approaches used to model storm characteristics including GS, mechanistic models [7,8] can be differentiated from statistical (empirical) models [20–23]. Mechanistic models are useful tools for characterizing and investigating physical processes that determine storm formation, storm life cycle and storm-related GS dynamics. However, one of the major challenges in the application of mechanistic models is the knowledge of and the control over the large number of input parameters and the rather extensive initialization as well as parameterization for particular datasets.

Atmosphere 2019, 10, 387; doi:10.3390/atmos10070387 www.mdpi.com/journal/atmosphere Atmosphere 2019, 10, 387 2 of 17

The second, widely used approach is statistical (empirical) modeling, which is based on measured GS values. Although statistical approaches provide only general insights into the physical mechanisms of GS dynamics, they can be applied to assess GS field dynamics associated with winter storms. However, due to measurement errors, missing data and low temporal resolution, the quality of many GS time series is poor [24]. Comprehensive preparation is usually a basic prerequisite for the scientific analysis and interpretation of GS data. This mostly includes breakpoint analysis, measurement height correction and gap filling [25]. Moreover, long-term GS measurements are rare [26]. The small number of high-quality GS time series is a serious issue, since GS is one of the fastest varying atmospheric variables [27]. Complex land cover pattern and orographic obstacles at and around GS measuring sites further reduce the spatial representativeness of the few available long-term GS measurements [28,29]. To improve the spatial representativeness, statistical approaches making use of relationships between surface properties and GS were applied to model GS on high spatial resolution grids. For instance, the 98th percentiles of daily maximum GS time series were modeled for Switzerland on a 50 m 50 m × resolution grid [20]. Return periods of extreme GS were mapped in Germany on a 1000 m 1000 m × resolution grid [21]. In another study, 69 GS time series were used to model GS distributions on a 50 m 50 m resolution grid in Southwestern Germany [22]. Using terrain and roughness-related × information as predictor variables (PV), storm event-related GS was modeled on a 50 m 50 m grid in × Southwest Germany [23]. The above-mentioned studies investigated either the statistical properties of GS distributions or individual storm events. Since all storms have a unique track, the results of these studies are either not related to a particular storm event or individual showcases. To combine both approaches, it is necessary to consider the tracks of many storms in the statistical modeling of GS. This allows improved statements to be made about the spatiotemporal GS variability and the associated storm damage. The combined analysis of many storm events allows not only statements about central tendencies of GS during storms, but also about the deviation of individual storm events from the central tendencies. Considering these aspects, the goals of this study are (1) reconstructing the storm fields associated with the most destructive winter storms in Germany in the period 1981–2018 and (2) high-spatial resolution modeling of GS associated with these storms. The mapping of the GS fields yields the winter storm atlas for Germany (GeWiSA).

2. Material and Methods

2.1. Overview The development of GeWiSA comprises the following main steps (Figure1): (1) obtaining a GS time series of 307 measurement stations operated by the German Meteorological Service (DWD) in the period 1981–2018, (2) breakpoint analysis and correction of GS time series, (3) extraction of GS associated with the 98 most destructive winter storms, (4) calculation of median GS (GSf), (5) calculation of the storm ﬁeld factor (STF), (6) estimation of roughness length (z0), (7) assessment of relative elevation (η) and orographic sheltering (σ), (8) modeling of GS based on a LSBoost approach and PV, (9) thin plate spline interpolation (TPS) of STF, (10) multiplication of GSf by STF yielding GS. Atmosphere 20192019,, 10,, 387x FOR PEER REVIEW 3 of 1716

86 FigureFigure 1. Overview 1. Overview of the of methodology the methodology applied applied to develop to develop Germany’s Germany’s winter winter storm storm atlas (GeWiSA),atlas 87 with(GeWiSA) STF being, with the STF storm being field the factor,storm GSfieldis factor, the gust 퐺푆 speed is the and gustGSf speedis the and median 퐺푆̃ is of theGS .median of 퐺푆. 2.2. Study Area and Evaluated Winter Storms 88 2.2. Study Area and Evaluated Winter Storms Germany has a size of about 357,000 km2. The German landscape consists of four large natural 89 Germany has a size of about 357,000 km². The German landscape consists of four large natural areas: the North German Plain, the Central German Plain, the Alpine Foothills and the Alps in Southern 90 areas: the North German Plain, the Central German Plain, the Alpine Foothills and the Alps in Germany [30]. Germany’s surface is covered by agricultural areas (59%), forests (30%) and artificial 91 Southern Germany [30]. Germany’s surface is covered by agricultural areas (59%), forests (30%) and surfaces such as urban areas, airports and road and rail networks (8%) [30,31]. 92 artificial surfaces such as urban areas, airports and road and rail networks (8%) [30,31]. In total, 98 severe winter storms were included in GeWiSA (Table1). The storms were selected 93 In total, 98 severe winter storms were included in GeWiSA (Table 1). The storms were selected based on the overall losses (inflation-adjusted 2018 $) from Munich Re’s NatCatSERVICE [1]. The first 94 based on the overall losses (inflation-adjusted 2018 $) from Munich Re’s NatCatSERVICE [1]. The winter storm contained in Munich Re’s NatCatSERVICE occurred in 1981. A maximum number of five 95 first winter storm contained in Munich Re’s NatCatSERVICE occurred in 1981. A maximum number severe winter storms per year was selected with overall losses being at least US$ 3.0m. According to 96 of five severe winter storms per year was selected with overall losses being at least US$ 3.0m. the overall losses, the most severe storms were Kyrill (US$ 5100 m), Lothar (US$ 2200m) and Friederike 97 According to the overall losses, the most severe storms were Kyrill (US$ 5,100m), Lothar (US$ 2,200m) (US$ 1900 m) [1]. A year with several severe winter storms was 1990. In this year, storms Daria, Vivian 98 and Friederike (US$ 1,900m) [1]. A year with several severe winter storms was 1990. In this year, and Wiebke occurred, causing US$ 1800 m each. 99 storms Daria, Vivian and Wiebke occurred, causing US$ 1,800m each.

Table 1. Winter storms included in GeWiSA [1]. 100 Table 1. Winter storms included in GeWiSA [1]. Winter Losses Winter Losses ID Duration LossesID Winter Duration Losses ID WinterStorm Storm Duration (US$m) StormID Duration (US$m) (US$m) Storm (US$m) 1 - 3 January 81 51 50 Winnie 24–25 October 98 130 1 2 -- 3 February3 Jan 81 81 2551 51 Lothar50 Winnie 26 December24–25 99 Oct 98 2200130 2 3 -- 15–16 December3 Feb 8281 2625 52 Anatol51 Lothar 3–4 December26 Dec 99 99 4102,200 3 4 -- 9 October15–16 82 Dec 82 1326 5352 Lara Anatol4–6 February3–4 Dec 99 99 140410 5 - 10 December 82 8 54 Ginger 28 May 00 310 4 6 -- 18 January9 Oct 83 82 13013 55 Kerstin53 Lara 29–30 January4–6 Feb 00 99 120140 5 7 -- 26–28 November10 Dec 8382 1308 56 Oratia54 Ginger 29–30 October28 May 00 00 93310 6 8 -- 1 February18 Jan 83 83 110130 5755 - Kerstin 10–11 December29–30 Jan 00 00 15120 9 - 22–24 November 84 220 58 - 9 November 01 31 7 - 26–28 Nov 83 130 56 Oratia 29–30 Oct 00 93 10 - 3 January 84 58 59 Jeanett 26–28 October 02 1700 8 11 -- 20 October1 Feb 84 83 29110 6057 Anna - 26–27 February10–11 Dec 02 00 73015 9 12 -- 7–8 February22–24 Nov 84 84 3220 61 Jennifer58 - 28–29 January9 Nov 02 01 41031 10 13 -- 6 December3 Jan 85 84 4458 62 Calvann59 Jeanett 2–3 January26–28 03 Oct 02 3601,700 14 - 6 November 85 29 63 January 21 December 03 120 11 15 -- 19–20 December20 Oct 8684 43029 64 Hanne60 Anna 12–14 January26–27 04Feb 02 330730 12 16 -- 20–23 October867–8 Feb 84 4303 6561 - Jennifer 17 December28–29 04 Jan 02 320410 13 17 -- 19–20 January866 Dec 85 43044 66 Oralie62 Calvann 20–21 March2–3 04Jan 03 270360 14 - 6 Nov 85 29 63 Jan 21 Dec 03 120 15 - 19–20 Dec 86 430 64 Hanne 12–14 Jan 04 330

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Table 1. Cont.

Winter Losses Winter Losses ID Duration ID Duration Storm (US$m) Storm (US$m) 18 - 12 November 87 9 67 Queenie 31 January–1 February 04 170 19 - 29 February–1 March 88 86 68 Gerda 12–13 January 04 140 20 - 7–8 October 88 26 69 Cyrus 15–16 December 05 530 21 - 8–9 October88 17 70 Thorsten 25–27 November 05 320 22 - 6 December 88 9 71 Erwin 8–9 January 05 160 23 - 19 December 88 5 72 Ulf 12–13 February 05 140 24 - 4–6 April 89 18 73 Ingo 21 January 05 74 25 Daria 25–26 January 90 1800 74 Britta 31 October–2 November 06 520 26 Vivian 25–27 February 90 1800 75 - 30 December 06–1 January 07 130 27 Wiebke 28 February–1 March 90 1800 76 Vera 8 December 06 67 28 Herta 3–4 February 90 900 77 Kyrill 18–19 January 07 5100 29 Ottilie/Polly 13–15 February 90 270 78 Franz 11–12 January 07 93 30 Nora 17–18 October 91 30 79 Fridtijof 2–3 December 07 51 31 Undine 6–9 January 91 7 80 Emma 1–2 March 08 840 32 Ismene 26 November 92 730 81 Kristen 12 March 08 250 33 Coranna 11–12 November 92 280 82 Resi 31 January–1 February 08 4 34 - 13 March 92 7 83 Annette 23–24 February 08 3 35 Wilma 26 October 92 4 84 Quinten 9–10 February 09 53 36 - 2–3 December 92 3 85 Xynthia 28 February 10 920 37 Verena 13–14 January 93 500 86 Joachim 16–17 December 11 200 38 Barbara 23–24 January 93 240 87 Andrea 5–6 January 12 240 39 Quena 8–9 December 93 200 88 Ulli/Emil 3 January 12 82 40 Victoria 19–21 December 93 160 89 Christian 27–29 October 13 830 41 Agnes 22–23 January 93 150 90 Xaver 5–7 December 13 260 42 Lore 27 January 94 520 91 Niklas 30 March–1 April 15 1200 43 Grace 4–5 November 95 7 92 Elon/Felix 8–11 January 15 260 44 Sonja 27–29 March 97 260 93 Xavier 5 October 17 500 45 Daniela 19–20 February 97 210 94 Herwart 29 October 17 290 46 Gisela/Heidi 25 February 97 100 95 Sebastian 13–14 September 17 160 47 - 13–14 February 97 78 96 Egon 12–13 January 17 120 48 Xylia 27–29 October 98 370 97 Friederike 18 January 18 1900 49 - 4–5 March 98 270 98 Burglind 3 January 18 240

2.3. Gust Speed (GS) Data Maximum daily GS including all measurements available from the DWD climate data center in the period 1981–2018 was used for GeWiSA development [32]. Based on the data availability (DA), GS time series were included in the parameterization dataset (DS1) and test dataset (DS2). DS1 contains 135 GS time series with DA > 90.0% (Figure2). DS2 contains 172 GS time series with DA being in the range 25.0–89.9%. Time series where DA < 25.0% were not considered for further analysis. Due to the long measurement period, the metadata revealed numerous GS station relocations, measuring height changes and/or instrument changes [22]. To use homogenous GS time series, a breakpoint analysis was carried out for each GS time series, and, if necessary, the GS time series was corrected by quantile matching [22,33,34]. Atmosphere 20192019, 10, 387x FOR PEER REVIEW 5 of 16 17

111 Figure 2. Gust speedspeed (GS(GS)) measurement measurement stations stations subdivided subdivided into into a parameterization a parameterization dataset dataset (DS1) (DS1) and 112 andtest datasettest dataset (DS2). (DS2).

113 22.4..4. Predictor Predictor Variables Variables (PV) (PV) 114 A total of 37 PV PVss that are known to influence influence GS [22,23,2522,23,25] were developed to model the spatial GS pattern at 25 m 25 m resolution. One PV was the measuring height of GS (h), which is often (47%), 115 GS pattern at 25 m× × 25 m resolution. One PV was the measuring height of GS (h), which is often 116 (but47%) not, but always, not always10 m above, 10 mground above level ground as recommended level as recommended by the World by Meteorological the World Meteorological Organization. 117 OrganizationTo consider the. To large-scale consider patternthe large of-scaleGS, longitude pattern of ( lonGS), andlongitude latitude (lon (lat) and) were latitude used as(lat PVs) were (Table used2). ® 118 asEsri’s PVs ArcGIS (Table 2)10.4. Esri’s software ArcGIS (Redlands,® 10.4 software CA, USA)(Redlands, was used CA, forUSA PV) was building. used for PV building. 119 All orographic orographic PVs PVs were were derived derived from from the digital the digital elevation elevation model model EU-DEM EU v.1-DEM [35]. v.1 The [ elevation35]. The (ε) was rescaled from the original 20 m 20 m to 25 m 25 m using ArcGIS’ aggregate tool. Based on 120 elevation (ε) was rescaled from the original× 20 m × 20 m× to 25 m × 25 m using ArcGIS’ aggregate tool. 121 Basedε, the relativeon ε, the elevation relative (ηelevation) was calculated (η) was bycalculated subtracting by subtracting the mean elevation the mean of anelevation outer circle of an of outer each 122 circlegrid cell of each from grid the grid cell cell-specificfrom the gridε value cell-specific [24]. Four ε valueη variants [24]. withFour outer-circleη variants with radii outer of 1000-circle m (η radii1000), 3000 m (η ), 5000 m (η ) and 7500 m (η ) were built. For the eight main compass directions, 123 of 1,000 m3000 (η1000), 3,000 m5000 (η3000), 5,000 m (η75005000) and 7,500 m (η7500) were built. For the eight main 124 compassη was modeled directions, with η awas 3000 modeled m radius. with Another a 3,000 PVm radius. for describing Another the PV orography for describing was the sheltering orography (σ), 125 waswhich sheltering was also ( calculatedσ), which was for thealso eight calculated main compassfor the eight directions main compass by summing directions up the by angles summing between up 126 thegrid angles cell-specific between elevation grid cell and-specific the visible elevation horizon and upthe tovisible a distance horizon of 1000up to m a distance [36]. of 1,000 m [36]. The z -related predictors originate from the European Settlement Map (ESM) 2012 R 2017 [37]. 127 The z0-related predictors originate from the European Settlement Map (ESM) 2012 R 2017 [37]. The ESM 2012 R 2017 data set contains highly resolved 2.5 m 2.5 m grid cells and their land use 128 The ESM 2012 R 2017 data set contains highly resolved 2.5 m × 2.5 m grid cells and their land use classes. First, a z value was assigned to each land use class (Table3)[ 38]. Then, the 2.5 m 2.5 m z 129 classes. First, a z00 value was assigned to each land use class (Table 3) [38]. Then, the 2.5 m ×× 2.5 m z00 grid was aggregated to 25 m 25 m. For the eight main compass directions effective z was calculated 130 grid was aggregated to 25 m × 25 m. For the eight main compass directions effective z0 was calculated 131 in a 400 m radius to account for non-localnon-local roughness-inducedroughness-induced modificationmodification ofof GSGS [[2525].]. 132 133

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Table 2. Predictor variables (PV) for modeling gust speed (GS) with DWD being the German Meteorological Service, EU-DEM is a digital elevation model and ESM is the European Settlement Map.

Original Symbol Name Sector ( ) Distance (m) Data Source ◦ Resolution h measuring height - - DWD - lon longitude - - - - lat latitude - - - - ε elevation - - EU-DEM v.1 20 m 20 m × η relative elevation 1–360 1000 EU-DEM v.1 20 m 20 m 1000 × η relative elevation 1–360 3000 EU-DEM v.1 20 m 20 m 3000 × η relative elevation 1–360 5000 EU-DEM v.1 20 m 20 m 5000 × η relative elevation 1–360 7500 EU-DEM v.1 20 m 20 m 7500 × ηn relative elevation 337.5–22.4 3000 EU-DEM v.1 20 m 20 m × ηne relative elevation 22.5–67.4 3000 EU-DEM v.1 20 m 20 m × ηe relative elevation 67.5–112.4 3000 EU-DEM v.1 20 m 20 m × ηse relative elevation 112.5–157.4 3000 EU-DEM v.1 20 m 20 m × ηs relative elevation 157.5–202.4 3000 EU-DEM v.1 20 m 20 m × ηsw relative elevation 202.5–247.4 3000 EU-DEM v.1 20 m 20 m × ηw relative elevation 247.5–292.4 3000 EU-DEM v.1 20 m 20 m × ηnw relative elevation 292.5–337.4 3000 EU-DEM v.1 20 m 20 m × σn sheltering 337.5–22.4 1000 EU-DEM v.1 20 m 20 m × σne sheltering 22.5–67.4 1000 EU-DEM v.1 20 m 20 m × σe sheltering 67.5–112.4 1000 EU-DEM v.1 20 m 20 m × σse sheltering 112.5–157.4 1000 EU-DEM v.1 20 m 20 m × σs sheltering 157.5–202.4 1000 EU-DEM v.1 20 m 20 m × σsw sheltering 202.5–247.4 1000 EU-DEM v.1 20 m 20 m × σw sheltering 247.5–292.4 1000 EU-DEM v.1 20 m 20 m × σnw sheltering 292.5–337.4 1000 EU-DEM v.1 20 m 20 m × σsum sheltering 1–360 1000 EU-DEM v.1 20 m 20 m × z roughness length 1–360 25 ESM 2012 R 2017 2.5 m 2.5 m 0,25 × z roughness length 1–360 100 ESM 2012 R 2017 2.5 m 2.5 m 0,100 × z roughness length 1–360 200 ESM 2012 R 2017 2.5 m 2.5 m 0,200 × z roughness length 1–360 400 ESM 2012 R 2017 2.5 m 2.5 m 0,400 × z roughness length 337.5–22.4 400 ESM 2012 R 2017 2.5 m 2.5 m 0,n × z roughness length 22.5–67.4 400 ESM 2012 R 2017 2.5 m 2.5 m 0,ne × z roughness length 67.5–112.4 400 ESM 2012 R 2017 2.5 m 2.5 m 0,e × z roughness length 112.5–157.4 400 ESM 2012 R 2017 2.5 m 2.5 m 0,se × z roughness length 157.5–202.4 400 ESM 2012 R 2017 2.5 m 2.5 m 0,s × z roughness length 202.5–247.4 400 ESM 2012 R 2017 2.5 m 2.5 m 0,sw × z roughness length 247.5–292.4 400 ESM 2012 R 2017 2.5 m 2.5 m 0,w × z roughness length 292.5–337.4 400 ESM 2012 R 2017 2.5 m 2.5 m 0,nw ×

Table 3. Roughness length (z0) assigned to the European Settlement Map (ESM) 2012 R 2017 [37] land use classes with acronyms for non-built up (NBU), built up (BU) and Normalized Diﬀerence Vegetation Index (NDVI).

Name z0 (mm) BU Buildings 1600 BU Area-Street Green NDVI 100 BU Area-Green Urban Atlas 500 BU Area-Green NDVI 500 BU Area-Streets 100 BU Area-Open Space 1 NBU Area-Street Green NDVI 100 NBU Area-Green NDVI 750 NBU Area-Streets 100 NBU Area-Open Space 30 Railways 100 Water 1 Atmosphere 2019, 10, 387 7 of 17

2.5. LS-Boost Modeling (LSBoost) The spatial median gust speed pattern at 25 m 25 m was modeled by the LSBoost algorithm [36] × which is implemented in the Matlab® Software Statistics and Machine Learning Toolbox (Release 2018b; The Math Works Inc., Natick, MA, USA). The LSBoost model is a sequence of regression trees (B), i.e., decision trees with binary splits for regression. It aims at reducing the mean squared error (MSE) between GSf and the aggregated GSf prediction (GSc) of B [39–41]. The algorithm starts by calculating the median of GSf (GSf) of all DS1 stations. Then, the regression trees B1, ... , Bm are combined in a weighted manner [39–41] to improve model accuracy. The individual regression trees are a function of selected PV: XM GSc(PV) = GSf(PV) + v pmBm(PV) (1) m=1 where pm is the weight for model m, M is the total number of regression trees, and 0 < v 1 is the ≤ learning rate [39–41]. The number of PVs available for modeling GSf enabled more than 3400 combinations (PVC), with different number of PVs to be evaluated and sorted in descending order according to the coefficient 2 2 of determination (R ) related to DS2 (RDS2). Averaging the three first PVC yielded the overall highest 2 f RDS2. Thus, the first three PVC were used for development of the final GS map.

2.6. Thin Plate Spline Interpolation (TPS)

The quotient of GS related to a speciﬁc storm event to GSf is STF, which describes the gust speed intensity: GS STF = (2) GSf which was modeled by a thin plate spline interpolation [42] in the entire study area. The applied TPS algorithm is implemented in the Matlab® Software Curve Fitting Toolbox (Release 2018b; The Math Works Inc., Natick, MA, USA). Geographic information from lon and lat were used as predictors for STF estimation. Multiplication of modeled GSf by STF yielded the storm-related GS.

3. Results and Discussion

3.1. Median Gust Speed In Table4, three PVC consisting of seven PVs each are listed. Besides lon, lat and h, which were used in all models, PVC from SW and S sectors was used. One reason for including directional information on η, σ and z0 is that the main wind direction during winter storms is southwest [43]. It is striking that elevation was not included in the most informative models.

Table 4. Predictor variable combinations (PVC) yielding the highest coeﬃcients of determination in 2 DS2 (RDS2 ). PVC 1 2 3 4 5 6 7

1 lon lat h η5000 ηsw σne z0,sw 2 lon lat h η7500 ηs σsum z0,400 3 lon lat h η7500 ηs σs z0,sw

The GSf ﬁeld in h = 10 m related to severe winter storms is presented in Figure3. Highest GSf values can be found in the northwestern parts of the study area. Close to the North Sea coast and on the oﬀshore islands, GSf is up to 27 m/s. Lowest GSf values occur in the south. There, GSf is often below 20 m/s. Reasons for the decreasing GS values towards the southern lowlands are the increasing surface roughness, the increasing distance from the coast and the more complex orography, i.e., sheltering, Atmosphere 2019, 10, x FOR PEER REVIEW 8 of 16

167 information on η, σ and z0 is that the main wind direction during winter storms is southwest [43]. It 168 is striking that elevation was not included in the most informative models.

169 Table 4. Predictor variable combinations (PVC) yielding the highest coefficients of determination in 2 170 DS2 (푅퐷푆2). PVC 1 2 3 4 5 6 7 1 lon lat h η5000 ηsw σne z0,sw 2 lon lat h η7500 ηs σsum z0,400 3 lon lat h η7500 ηs σs z0,sw 171 The 퐺푆̃ field in h = 10 m related to severe winter storms is presented in Figure 3. Highest 퐺푆̃ 172 values can be found in the northwestern parts of the study area. Close to the North Sea coast and on 173 the offshore islands, 퐺푆̃ is up to 27 m/s. Lowest 퐺푆̃ values occur in the south. There, 퐺푆̃ is often Atmosphere 2019, 10, 387 8 of 17 174 below 20 m/s. Reasons for the decreasing GS values towards the southern lowlands are the increasing 175 surface roughness, the increasing distance from the coast and the more complex orography, i.e., 176 insheltering, southern in Germany. southern There Germany. is also There a slight is decreasing also a slightGSf decreasingtendency from 퐺푆̃ westtendency to east. from While westGSf toin east. the 177 westWhile is 퐺푆 about̃ in 23the m west/s, in is the about east it23 is m/s, close in to the 20 meast/s. Despiteit is close the to large-scale 20 m/s. DespiteGSf pattern, the large very-scale high GSf퐺푆̃ 178 valuespattern, occur very inhigh low 퐺푆̃ mountain values occur ranges in onlow mountain mountain tops ranges throughout on mountain the study tops throughout area. In some the places, study 179 GSfarea.even In some exceeds places the,GSf 퐺푆̃values even exceeds near the coasts. the 퐺푆̃ However, values near this the is only coast thes. However, case where thisη is only350 the m case and 7500 ≥ 180 σwheresum 80η7500. ≥ In 35 contrast,0 m and lowest σsum ≤ GS8f0 °.(< In15 contrast, m/s) were lowest mainly 퐺푆̃ simulated(< 15 m/s) inwere the stronglymainly simulated incised valleys in the ≤ ◦ 181 wherestronglyη incised300 valleys m and whereσsum η7500300 ≤ −.300 The m eandﬀect σ ofsumz ≥ 300on GSf°. Theis weaker, effect of but z0 on itleads 퐺푆̃ is to weaker lower, GSfbutin it 7500 ≤ − ≥ ◦ 0 182 urbanleads to and lower forested 퐺푆̃ in areas. urban and forested areas.

183 f Figure 3. Median gust speed (GS) of all winter storms included in GeWiSA. To illustrate the small-scale GSf variability, two map extracts in complex terrain are presented in Figure4. In the center of the ﬁrst map extract is the southwest-northeast oriented mountain range Taunus located north of the city of Frankfurt (Figure4a). The highest GSf value (32 m/s) is simulated close to a mountaintop due to the exceptional combination of η7500 = 293 m, σsum = 147◦ and z0,sw = 87 mm. In eastern direction, in a distance of less than 2 km from the mountain top, GSf is below 18 m/s which is mainly due to high σsum > 250◦ and z0,sw = 750 mm. The second map extract shows the region around the Brocken (Figure4b). The Brocken (1141 m a.s.l.) is an exposed mountain top, where chronically very high wind speeds occur [30] and GSf = 37 m/s is also very high. This is because of the extraordinary exposure of η7500 > 400 m and z0,sw < 100 mm. However, areas with very low GSf values can be found in close vicinity of the highest GSf values. For example, 800 m east of Brocken’s summit GSf is only 22 m/s. Atmosphere 2019, 10, x FOR PEER REVIEW 9 of 16

184 Figure 3. Median gust speed (퐺푆̃) of all winter storms included in GeWiSA.

185 To illustrate the small-scale 퐺푆̃ variability, two map extracts in complex terrain are presented 186 in Figure 4. In the center of the first map extract is the southwest-northeast oriented mountain range 187 Taunus located north of the city of Frankfurt (Figure 4a). The highest 퐺푆̃ value (32 m/s) is simulated 188 close to a mountaintop due to the exceptional combination of η7500 = 293 m, σsum = 147 ° and z0,sw = 87 189 mm. In eastern direction, in a distance of less than 2 km from the mountain top, 퐺푆̃ is below 18 m/s 190 which is mainly due to high σsum > 250 ° and z0,sw = 750 mm. 191 The second map extract shows the region around the Brocken (Figure 4b). The Brocken (1,141 m 192 a.s.l.) is an exposed mountain top, where chronically very high wind speeds occur [30] and 퐺푆̃ = 37 193 m/s is also very high. This is because of the extraordinary exposure of η7500 > 400 m and z0,sw < 100 mm. 194 However, areas with very low 퐺푆̃ values can be found in close vicinity of the highest 퐺푆̃ values. For Atmosphere 2019, 10, 387 9 of 17 195 example, 800 m east of Brocken’s summit 퐺푆̃ is only 22 m/s.

196 FigureFigure 4. 4. MapMap extracts extracts of of median median gust gust speed speed (퐺푆 (̃GSf) )in in the the regions regions (a (a) )north north of of the the city city of of Frankfurt Frankfurt and and 197 (b(b) )around around the the Brocken. Brocken.

3.2. Storm Field Factor (STF) 198 3.2. Storm Field Factor (STF) In Figure5, STF is presented for four severe storms that caused the highest losses in Germany 199 In Figure 5, STF is presented for four severe storms that caused the highest losses in Germany STF 200 inin the the study study period period.. STF valuesvalues related related to to storm storm Daria Daria (25 (25–26–26 Jan January 90) are 90) high are high (up to (up 2.0) to in 2.0) the in 201 northwestthe northwest of Germany of Germany (Figure (Figure 5a). 5Ina). the In east the eastand andsoutheast southeast of the of study the study area, area, Daria Daria was wasmuch much less STF 202 intenseless intense with withSTF < 1.0.< In1.0. contrast, In contrast, storm storm Lothar Lothar (26 Dec (26 99) December was exceptionally 99) was exceptionally strong in S strongouthern in STF 203 GermanySouthern ( GermanyFigure 5b (Figure) with 5STFb) with values upvalues to 2.2. up Central to 2.2. and Central northern and northern parts of parts the study of the area study were area STF GS 204 notwere hit not by hitLothar by Lothar with STF with < 1.0 over< 1.0 wide over areas wide. Although areas. Although GS associatedassociated with storm with Kyrill storm (18 Kyrill–19 GSf STF 205 Jan(18–19 2007) January is greater 2007) than is greater 퐺푆̃ over than almostover entire almost Germany entire ( GermanyFigure 5c) (Figure, the highest5c), the STF highest values (2.1)values are STF 206 lower(2.1) arecompared lower compared to the highest to the Lothar highest-related Lothar-related STF values. Similarvalues. to storm Similar Lothar, to storm storm Lothar, Friederike storm 207 (18Friederike Jan 18) hit (18 a January compact 18) zone hit awith compact only a zone few withfringes only to athe few south fringes (Figure to the 5d) south. In the (Figure entire5d). north In the of STF STF 208 theentire study north area of, theSTF study < 1.0. area, The stud 1.63. For storm Lothar, STFg = 0.79 and for storm Daria, STFg = 1.29. Comparing the distribution of STF, Kyrill’s storm ﬁeld extends over a much larger area than the storm ﬁelds of all other storms. Atmosphere 2019, 10, x FOR PEER REVIEW 10 of 16

218 Atmosphereand STF 2019enables, 10, 387 a simplified model building for GS associated with future storms, because only10 ofSTF 17 219 needs to be modeled. Using this approach, synthetic GS fields can easily be produced.

220 FigureFigure 5.5.Storm Storm field field factor factor (STF (STF) of) the of winter the winter storms storms (a) Daria; (a) (bDaria;) Lothar; (b) ( cLothar;) Kyrill and(c) Kyrill (d) Friederike. and (d) 221 Friederike. The shape of SF related to storm Lothar differs greatly from most other SFs. On the upper tail 222 of SF,Since where STF the is exceedance derived as probabilitya deviation isfrom below the 0.05,common storm reference Lothar ( STF퐺푆̃ for= 1.76) all storms is very, it exceptional. is possible 223 Into theconsistently same exceedance determine probability and compare range, theSTF shareof of storm the study Daria area is 1.62. where In contrast,STF exceedsSTF avalues certain related value. 224 toHere, storm the Friederike comparison are of much all analyzed smaller (stormSTFg = events1.01). Theis presented great amount by survival of damage functions caused (SF) by of storm STF 225 Friederike(Figure 6). can Survival be explained functions by the represent fact that itsthe storm exceedance field hit probability several densely of STF populated in the regions. study area. 226 Accordingly, storm Kyrill exceeds 퐺푆̃ on the largest part of the study area. The median STF (푆푇퐹̃ ) 227 for Kyrill is 1.38. On 5% of the study area, Kyrill-specific STF > 1.63. For storm Lothar, 푆푇퐹̃ = 0.79 228 and for storm Daria, 푆푇퐹̃ = 1.29. Comparing the distribution of 푆푇퐹, Kyrill’s storm field extends over 229 a much larger area than the storm fields of all other storms. 230 The shape of SF related to storm Lothar differs greatly from most other SFs. On the upper tail of 231 SF, where the exceedance probability is below 0.05, storm Lothar (STF = 1.76) is very exceptional. In 232 the same exceedance probability range, STF of storm Daria is 1.62. In contrast, STF values related to

Atmosphere 2019, 10, x FOR PEER REVIEW 11 of 16

푆푇퐹̃ 233 Atmospherestorm Friederike2019, 10, 387 are much smaller ( = 1.01). The great amount of damage caused by 11storm of 17 234 Friederike can be explained by the fact that its storm field hit several densely populated regions.

235 236 Figure 6. Survival functions (SF) of the winter storm storm-related-related storm field field factor ( STF) representing the 237 share of study area.area. The eight most severe winter storms are labeled with their ID. The two winter 238 storms (ID: 77, Kyrill; ID: 51: Lothar) which caused the greatest losses are colored red. The six next 239 severe winter storms are colored blue.blue. The grey lines indicate all other winterwinter storms.storms. 3.3. Winter Storm-Related Gust Speed 240 3.3. Winter Storm-Related Gust Speed The GS maps created from multiplying GSf by STF are displayed in Figure7. For storm Daria, 241 The GS maps created from multiplying 퐺푆̃ by STF are displayed in Figure 7. For storm Daria, a a clear northwest-southeast gradient of GS was modeled (Figure7a). In large parts of Northwestern 242 clear northwest-southeast gradient of GS was modeled (Figure 7a). In large parts of Northwestern Germany, GS is in the range 30–40 m/s. Apart from exposed mountain tops, GS 20 m/s in the 243 Germany, GS is in the range 30–40 m/s. Apart from exposed mountain tops, GS ≈ 20 m/s in the southeast. During storm Lothar, GS in Northern Germany is often below 15 m/s (Figure7b) whereas in 244 southeast. During storm Lothar, GS in Northern Germany is often below 15 m/s (Figure 7b) whereas a clearly defined area in Southern Germany GS often exceeds 25 m/s. In some areas, GS even exceeds 245 in a clearly defined area in Southern Germany GS often exceeds 25 m/s. In some areas, GS even 50 m/s. Storm Kyrill hit Germany with an extensive high-impact gust speed field (Figure7c) with 246 exceeds 50 m/s. Storm Kyrill hit Germany with an extensive high-impact gust speed field (Figure 7c) GS > 30 m/s frequently occuring in the study area and GS > 40 m/s over large areas in the west and 247 with GS > 30 m/s frequently occuring in the study area and GS > 40 m/s over large areas in the west southeast. The GS field of storm Friederike is most pronounced in Central Germany (Figure7d). There, 248 and southeast. The GS field of storm Friederike is most pronounced in Central Germany (Figure 7d). GS often exceeds 30 m/s. Also in the south, GS values are often at 20 m/s. In the north, GS values are 249 There, GS often exceeds 30 m/s. Also in the south, GS values are often at 20 m/s. In the north, GS relatively low (< 15 m/s). In contrast to the other three presented storms, there is no contiguous area 250 values are relatively low (< 15 m/s). In contrast to the other three presented storms, there is no where GS > 40 m/s. 251 contiguous area where GS > 40 m/s. SFs of GS are presented in Figure8. For storm Kyrill, the median is highest (29.7 m /s). A similarly high median value was modeled for storm Daria (27.9 m/s). In contrast, the median GS of Lothar is initially clearly lower (17.9 m/s). From the median on, however, SF belonging to Lothar cuts all other SFs. At exceedance probability 0.05 GS related to Lothar is 38.0 m/s. Moreover, for storm Daria GS is very high (37.0 m/s). Somewhat lower GS values occur for storm Kyrill (35.4 m/s) and especially storm Friederike (32.5 m/s). During storm Friederike, GS values of more than 34.4 m/s occur on 1% in the study area. The only storm where GS > 40 m/s at exceedance probability 0.01 is Lothar (42.8 m/s). The corresponding GS values for storms Daria (39.9 m/s), Kyrill (35.4 m/s) and Friederike (34.4 m/s) are considerably lower.

AtmosphereAtmosphere 20120199, 10, 10, x, 387FOR PEER REVIEW 1212 of of16 17

252 FigureFigure 7. 7.GustGust speed speed (GS (GS) fields) ﬁelds of ofthe the winter winter storm stormss (a ()a Daria;) Daria; (b ()b Lothar;) Lothar; (c) ( cKyrill) Kyrill and and (d ()d Friederike.) Friederike.

253 SFIns of general, GS are SFspresented for GS andin FigureSTF are 8. For very storm similar. Kyrill, However, the median the comparison is highest (29.7 of SFs m/s). for AGS similarlyand STF 254 highrelated median to a certain value winterwas modeled storm allows for storm to draw Daria conclusions (27.9 m/s). aboutIn contrast, the absolute the medianGS level GS andof Lothar about is the 255 initiallyGS level clearly in comparison lower (17.9 to m/s).GSf. For From instance, the median winter on, storm however, Lothar’s SF belonging STF survival to Lothar function cuts is well all other above 256 SFalls. At other exceedance SF for an probability exceedance 0.05 probability GS related< 0.20.to Lothar In contrast, is 38.0 m/s. the SFMoreover, for GS in for the storm same Daria exceedance GS is 257 veryprobability high (37.0 range m/s is). Somewhat only slightly lower above GSthe values other occur SF. Thisfor storm means Kyrill that (35.4 Lothar’s m/s)GS andintensity especially was storm more 258 Friederikeextreme than(32.5 itsm/s). absolute DuringGS stormlevel. Friederike, GS values of more than 34.4 m/s occur on 1% in the 259 study area. The only storm where GS > 40 m/s at exceedance probability 0.01 is Lothar (42.8 m/s). The 260 corresponding GS values for storms Daria (39.9 m/s), Kyrill (35.4 m/s) and Friederike (34.4 m/s) are 261 considerably lower. 262 In general, SFs for GS and STF are very similar. However, the comparison of SFs for GS and STF 263 related to a certain winter storm allows to draw conclusions about the absolute GS level and about

Atmosphere 2019, 10, x FOR PEER REVIEW 13 of 16

264 the GS level in comparison to 퐺푆̃ . For instance, winter storm Lothar’s STF survival function is well 265 above all other SF for an exceedance probability < 0.20. In contrast, the SF for GS in the same 266 exceedance probability range is only slightly above the other SF. This means that Lothar’s GS

267 Atmosphereintensity2019 was, 10 more, 387 extreme than its absolute GS level. 13 of 17

268

269 FigureFigure 8. 8Survival. Survival functions functions (SF) (SF) of of the the winter winter storm storm related related gust gust speed speed (GS (GS) representing) representing the the share share 270 ofof study study area. area. The The eight eight mostmost severesevere winter storms are are labeled labeled with with their their ID. ID. The The two two winter winter storms storms (ID: 271 (ID:77, 77,Kyrill; Kyrill; ID: ID:51: 51:Lothar) Lothar) which which caused caused the greatest the greatest losses losses are colored are colored red. The red. six The next six severe next severe winter 272 winterstorms storms are colored are colored blue. blue.The grey The lines grey indicate lines indicate all other all otherwinter winter storms. storms.

273 3.4.3.4. Model Model Comparison Comparison 2 274 ResultsResults from from comparing comparing measured measured and and modeled modelGSed GSaccording accordin togR toare R2 presentedare presented in Figure in Figure9a for 9a 2 275 DS1for andDS1 DS2and (pleaseDS2 (please note thenote di thefferent different scaling scaling of the of y-axes). the y-axes) For DS1. For mean DS1,R meanof all R events2 of all isevents 0.998. is 2 276 The0.998.R standardThe R2 standard deviation deviation in DS1 isin very DS1 lowis very (0.001). low For(0.001) DS2,. For which DS2 is, which used tois validateused to thevalidate model, the R2 2 277 meanmodel,DS mean2 is 0.786. 푅퐷푆2 Ais Mann-Kendall 0.786. A Mann trend-Kendall test trend revealed test arevealed significant a significant (significance (significance level: 0.05) level: trend 0.05) of the R2 values.2 The increasing model accuracy towards the end of the investigation period can be 278 trendDS of2 the 푅퐷푆2 values. The increasing model accuracy towards the end of the investigation period 279 explainedcan be explained by the increasing by the increas numbering of GSnumbertime series of GS available time series for modelavailable validation. for model The validation average data. The 280 availabilityaverage data of DS2 availability before 1999 of DS2is 50%. before From 1999 1999, isit 50%. is on From average 1999 61%., it The is on data average available 61%. for The model data 281 parameterizationavailable for model in DS1 parameterization is about 97% for in theDS1 entire is about period. 97% for the entire period. 2 2 2 R 2 R 2 R 2 282 TheThe highest highest Rvalues values ( (푅DS퐷푆11= =1.000, 1.000, DS푅퐷푆2 2= =0.939) 0.939 were) were calculated calculated for for storm storm Lothar. Lothar One. One reason reason R2 2 283 forfor this this is is the the spatially spatially clearly clearly defined defined storm storm field. field. For For all all other other storms, storms the, the deviation deviation between between DS푅퐷푆1 1 R2 2 R2 2 R2 2 284 andand DS푅퐷푆2 is2 clearlyis clearly greater, greater, e.g., for e.g. storm, for storm Kyrill KyrillDS1 = 0.997푅퐷푆1 and= 0.997DS 2and= 0.678. 푅퐷푆2 Based = 0.678 on. allBased simulated on all 285 GSsimulatedfields, there GS fields, is an indication there is an that indication the standard that the deviation standard of deviationGS in the of study GS in area the is study an important area is an 2 2 286 factorimportant for storm factor event-related for storm eventR ,- correlationrelated 푅2, coecorrelationfficient between coefficient standard between deviation standard of deviationGS and R of isGS 287 0.61and (significance 푅2 is 0.61 (significance level: < 0.00001), level: and < 0.00001 thus for), and model thus accuracy. for model Starting accuracy with. Starting storm Lotharwith storm (ID: 51)Lothar in R2 R2 2 2 R2 2 288 1999,(ID: 51)DS1 andin 1999,DS2 푅have퐷푆1 veryand similar푅퐷푆2 have variations, very similar with mean variations,being with the only mean distinctive 푅 being feature. the only 289 distinctiveThe second feature. model accuracy measure is mean absolute error (MAE) (Figure9b). For DS1, mean 290 MAEDSThe1 is second 0.17 m /models, which accuracy is within measure the typical is meanGS absolutemeasurement error ( accuracy.MAE) (Figure Moreover, 9b). For there DS1, is mean no 291 temporalMAEDS1 trendis 0.17 in m/s,MAE whichDS1. This is within does notthe applytypical for GS DS2, measurement where mean accuracy.MAEDS2 Moreover,for all events there before is no 292 stormtemporal Lothar trend is 2.2 in m MAE/s. AfterDS1. This 1999 doesMAE notDS2 apply= 1.7 m for/s. DS2, where mean MAEDS2 for all events before 293 stormFrom Lothar thepresented is 2.2 m/s. errorAfter measures 1999 MAE itD isS2 = concluded 1.7 m/s. that the simulated GS fields very reasonably reconstruct historical GS fields.

Atmosphere 2019, 10, x FOR PEER REVIEW 14 of 16

294 AtmosphereFrom2019 the, 10 presented, 387 error measures it is concluded that the simulated GS fields very reasonably14 of 17 295 reconstruct historical GS fields.

296 FigureFigure 9.9. StormStorm event-relatedevent-related ((aa)) coecoefficientﬃcient ofof determinationdetermination ((RR22)) and (b)) meanmean absoluteabsolute errorerror ((MAE)) 297 ofof thethe parameterizationparameterization datasetdataset (DS1)(DS1) andand thethe testtest datasetdataset (DS2).(DS2). PleasePlease notenote thethe didifferentﬀerent scalingscaling ofof 298 thethe y-axes.y-axes.

299 InIn general,general, itit cancan bebe assumedassumed thatthat modelmodel accuracyaccuracy isis veryvery highhigh inin areasareas withwith highhigh measurementmeasurement 300 stationstation density.density. ToTo testtest ifif atat aa lowerlower stationstation densitydensity modelmodel accuracyaccuracy decreases,decreases, thethe DS2DS2 station-relatedstation-related 301 meanmean absoluteabsolute percentage percentage error error (MAPE (MAPE) of) ofGS GSover over all all storm storm events events was was calculated calculated (Figure (Figure 10 ).10).MAPE MAPEis 302 usedis used here here to compensateto compensate for for the the spatial spatial diﬀ differenceserences in GS in levelGS level in the in studythe study area. area. It was It was found fou thatnd that the 303 medianthe median of all ofMAPE all MAPEvalues values is 7.34%. is No7.34%. clear No spatial clearMAPE spatialpattern MAPE occurs. pattern Furthermore, occurs. Furthermore, no correlation no 304 betweencorrelation station between density station and MAPEdensitywas and found, MAPE indicating was found, that indicating the model that accuracy the model does notaccuracy depend does on 305 thenot stationdepend density. on the station It is therefore density. assumed It is therefore that the assumedGS model that can the be GS reliably model applied can be reliably throughout applied the 306 studythroughout area. the study area.

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307 Figure 10. Number of parameterization dataset (DS1) stations in a 100 km radius and mean absolute Figure 10. Number of parameterization dataset (DS1) stations in a 100 km radius and mean absolute 308 percentage error (MAPE) related to DS2 measurement stations. percentage error (MAPE) related to DS2 measurement stations.

309 4. Conclusions 310 In this study, itit couldcould bebe shownshown that on the basis of a large number of storms,storms, it isis possiblepossible to 311 separate individual storm events from the median storm field field over Germany. This enables both the 312 probabilistic and spatially explicit quantificationquantification of the (1) storm hazard associated with the median 313 gust speed fieldfield and (2)(2) stormstorm hazardhazard associatedassociated withwith singlesingle catastrophiccatastrophic stormstorm events.events. The results 314 from the simulation clearlyclearly demonstratedemonstrate thatthat eacheach stormstorm eventevent leadsleads toto uniqueunique gustgust speedspeed fields.fields. 315 It isis obviousobvious thatthat thethe storm-specificstorm-specific gust gust speed speed fields fields show show completely completely di ffdifferenterent characteristics characteristics in 316 thein the study study area. area. A good A good example example of their of their variability variability is the is comparison the comparison of storm of storm Lothar Lothar with storm with storm Kyrill. 317 DueKyrill. to theDue event-specific to the event- characteristicsspecific characteristics of their gust of their speed gust fields, speed the two fields, storms the tledwo to storms significantly led to 318 disignificantlyfferent damage different patterns. damage The catastrophic patterns. The damage catastrophic caused damage by storm caused Lothar by can storm be explained Lothar can by the be 319 explained by the fact that its gust speed field intensity deviates most strongly from the median gust

Atmosphere 2019, 10, 387 16 of 17 fact that its gust speed field intensity deviates most strongly from the median gust speed field in a narrowly defined area where many objects such as forests and buildings, which could not withstand the extreme wind loads connected with the gusts, occurred. This is also expressed by the unique shape of the survival function associated with storm Lothar. The simulated gust speed fields now make it possible to explicitly assign the damage caused by individual storm events to a specific gust speed intensity. Due to the probabilistic modeling approach, one is no longer bound to the analysis of individual storm events, but can make spatially high-resolution statements about the storm hazard independent of storm events, which can ultimately lead to better risk management. Moreover, the probabilistic structure of the model enables the development of storm event scenarios under climate change in future studies.

Author Contributions: C.J. and D.S. developed the research idea, carried out data analysis and wrote the manuscript. Funding: This work was supported by the Federal Ministry for the Environment, Nature Conservation and Nuclear Safety within the framework of the Forest Climate Fund (MiStriKli 28W-K-4-166-01). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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