Historical Winter Storm Atlas for Germany (GeWiSA)

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 ($\widetilde{GS}$) 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 $\widetilde{GS}$, 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.

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 [3,4,5,6], and large-scale winter storms mainly occurring from October to March, which are related to intense low-pressure systems [2,7,8,9,10]. 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 [13,14,15], 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 [20,21,22,23]. 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.

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 (Figure 1): (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 ($\widetilde{GS}$), (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 $\widetilde{GS}$ by STF yielding GS.

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 areas: the North German Plain, the Central German Plain, the Alpine Foothills and the Alps in Southern Germany [30]. Germany’s surface is covered by agricultural areas (59%), forests (30%) and 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 (

Table 1. Winter storms included in GeWiSA [1].

ID	Winter Storm	Duration	Losses (US$m)	ID	Winter Storm	Duration	Losses (US$m)
1	-	3 January 81	51	50	Winnie	24–25 October 98	130
2	-	3 February 81	25	51	Lothar	26 December 99	2200
3	-	15–16 December 82	26	52	Anatol	3–4 December 99	410
4	-	9 October 82	13	53	Lara	4–6 February 99	140
5	-	10 December 82	8	54	Ginger	28 May 00	310
6	-	18 January 83	130	55	Kerstin	29–30 January 00	120
7	-	26–28 November 83	130	56	Oratia	29–30 October 00	93
8	-	1 February 83	110	57	-	10–11 December 00	15
9	-	22–24 November 84	220	58	-	9 November 01	31
10	-	3 January 84	58	59	Jeanett	26–28 October 02	1700
11	-	20 October 84	29	60	Anna	26–27 February 02	730
12	-	7–8 February 84	3	61	Jennifer	28–29 January 02	410
13	-	6 December 85	44	62	Calvann	2–3 January 03	360
14	-	6 November 85	29	63	January	21 December 03	120
15	-	19–20 December 86	430	64	Hanne	12–14 January 04	330
16	-	20–23 October86	430	65	-	17 December 04	320
17	-	19–20 January86	430	66	Oralie	20–21 March 04	270
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

). The storms were selected based on the overall losses (inflation-adjusted 2018 $) from Munich Re’s NatCatSERVICE [1]. The first winter storm contained in Munich Re’s NatCatSERVICE occurred in 1981. A maximum number of five severe winter storms per year was selected with overall losses being at least US$ 3.0m. According to the overall losses, the most severe storms were Kyrill (US$ 5100 m), Lothar (US$ 2200m) and Friederike (US$ 1900 m) [1]. A year with several severe winter storms was 1990. In this year, storms Daria, Vivian and Wiebke occurred, causing US$ 1800 m each.

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% (Figure 2). 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].

2.4. Predictor Variables (PV)

A total of 37 PVs that are known to influence GS [22,23,25] 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%), but not always, 10 m above ground level as recommended by the World Meteorological Organization. To consider the large-scale pattern of GS, longitude (lon) and latitude (lat) were used as PVs (

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.

Symbol	Name	Sector (°)	Distance (m)	Data Source	Original Resolution
h	measuring height	-	-	DWD	-
lon	longitude	-	-	-	-
lat	latitude	-	-	-	-
ε	elevation	-	-	EU-DEM v.1	20 m × 20 m
η1000	relative elevation	1–360	1000	EU-DEM v.1	20 m × 20 m
η3000	relative elevation	1–360	3000	EU-DEM v.1	20 m × 20 m
η5000	relative elevation	1–360	5000	EU-DEM v.1	20 m × 20 m
η7500	relative elevation	1–360	7500	EU-DEM v.1	20 m × 20 m
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
z0,25	roughness length	1–360	25	ESM 2012 R 2017	2.5 m × 2.5 m
z0,100	roughness length	1–360	100	ESM 2012 R 2017	2.5 m × 2.5 m
z0,200	roughness length	1–360	200	ESM 2012 R 2017	2.5 m × 2.5 m
z0,400	roughness length	1–360	400	ESM 2012 R 2017	2.5 m × 2.5 m
z0,n	roughness length	337.5–22.4	400	ESM 2012 R 2017	2.5 m × 2.5 m
z0,ne	roughness length	22.5–67.4	400	ESM 2012 R 2017	2.5 m × 2.5 m
z0,e	roughness length	67.5–112.4	400	ESM 2012 R 2017	2.5 m × 2.5 m
z0,se	roughness length	112.5–157.4	400	ESM 2012 R 2017	2.5 m × 2.5 m
z0,s	roughness length	157.5–202.4	400	ESM 2012 R 2017	2.5 m × 2.5 m
z0,sw	roughness length	202.5–247.4	400	ESM 2012 R 2017	2.5 m × 2.5 m
z0,w	roughness length	247.5–292.4	400	ESM 2012 R 2017	2.5 m × 2.5 m
z0,nw	roughness length	292.5–337.4	400	ESM 2012 R 2017	2.5 m × 2.5 m

). Esri’s ArcGIS^® 10.4 software (Redlands, CA, USA) was used for PV building.

All orographic PVs were derived from the digital elevation model EU-DEM v.1 [35]. The elevation (ε) was rescaled from the original 20 m × 20 m to 25 m × 25 m using ArcGIS’ aggregate tool. Based on ε, the relative elevation (η) was calculated by subtracting the mean elevation of an outer circle of each grid cell from the grid cell-specific ε value [24]. Four η variants with outer-circle radii of 1000 m (η₁₀₀₀), 3000 m (η₃₀₀₀), 5000 m (η₅₀₀₀) and 7500 m (η₇₅₀₀) were built. For the eight main compass directions, η was modeled with a 3000 m radius. Another PV for describing the orography was sheltering (σ), which was also calculated for the eight main compass directions by summing up the angles between grid cell-specific elevation and the visible horizon up to a distance of 1000 m [36].

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 classes. First, a z₀ value was assigned to each land use class (

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

) [38]. Then, the 2.5 m × 2.5 m z₀ grid was aggregated to 25 m × 25 m. For the eight main compass directions effective z₀ was calculated in a 400 m radius to account for non-local roughness-induced modification of GS [25].

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 $\widetilde{GS}$ and the aggregated $\widetilde{GS}$ prediction ($\widehat{GS}$) of B [39,40,41]. The algorithm starts by calculating the median of $\widetilde{GS}$ ($\widetilde{GS}$) of all DS1 stations. Then, the regression trees B₁, …, B_m are combined in a weighted manner [39,40,41] to improve model accuracy. The individual regression trees are a function of selected PV:

$$\widehat{GS}\left(PV\right)=\widetilde{GS}\left(PV\right)+v{\displaystyle \sum }_{m=1}^M{p}_m{B}_m\left(PV\right)$$

(1)

where p_m is the weight for model m, M is the total number of regression trees, and 0 < v ≤ 1 is the learning rate [39,40,41].

The number of PVs available for modeling $\widetilde{GS}$ enabled more than 3400 combinations (PVC), with different number of PVs to be evaluated and sorted in descending order according to the coefficient of determination ($R^2$) related to DS2 ($R_{DS2}^2$). Averaging the three first PVC yielded the overall highest $R_{DS2}^2$. Thus, the first three PVC were used for development of the final $\widetilde{GS}$ map.

2.6. Thin Plate Spline Interpolation (TPS)

The quotient of GS related to a specific storm event to $\widetilde{GS}$ is STF, which describes the gust speed intensity:

$$STF=\frac{GS}{\widetilde{GS}}$$

(2)

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 $\widetilde{GS}$ by STF yielded the storm-related GS.

3. Results and Discussion

3.1. Median Gust Speed

In

Table 4. Predictor variable combinations (PVC) yielding the highest coefficients of determination in DS2 ($R_{DS2}^2$ ).

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

, 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.

The $\widetilde{GS}$ field in h = 10 m related to severe winter storms is presented in Figure 3. Highest $\widetilde{GS}$ values can be found in the northwestern parts of the study area. Close to the North Sea coast and on the offshore islands, $\widetilde{GS}$ is up to 27 m/s. Lowest $\widetilde{GS}$ values occur in the south. There, $\widetilde{GS}$ 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, in southern Germany. There is also a slight decreasing $\widetilde{GS}$ tendency from west to east. While $\widetilde{GS}$ in the west is about 23 m/s, in the east it is close to 20 m/s. Despite the large-scale $\widetilde{GS}$ pattern, very high $\widetilde{GS}$ values occur in low mountain ranges on mountain tops throughout the study area. In some places, $\widetilde{GS}$ even exceeds the $\widetilde{GS}$ values near the coasts. However, this is only the case where η₇₅₀₀ ≥ 350 m and σ_sum ≤ 80°. In contrast, lowest $\widetilde{GS}$ (< 15 m/s) were mainly simulated in the strongly incised valleys where η₇₅₀₀ ≤ −300 m and σ_sum ≥ 300°. The effect of z₀ on $\widetilde{GS}$ is weaker, but it leads to lower $\widetilde{GS}$ in urban and forested areas.

To illustrate the small-scale $\widetilde{GS}$ variability, two map extracts in complex terrain are presented in Figure 4. In the center of the first map extract is the southwest-northeast oriented mountain range Taunus located north of the city of Frankfurt (Figure 4a). The highest $\widetilde{GS}$ value (32 m/s) is simulated close to a mountaintop due to the exceptional combination of η₇₅₀₀ = 293 m, σ_sum = 147° and z_0,sw = 87 mm. In eastern direction, in a distance of less than 2 km from the mountain top, $\widetilde{GS}$ is below 18 m/s which is mainly due to high σ_sum > 250° and z_0,sw = 750 mm.

The second map extract shows the region around the Brocken (Figure 4b). The Brocken (1141 m a.s.l.) is an exposed mountain top, where chronically very high wind speeds occur [30] and $\widetilde{GS}$ = 37 m/s is also very high. This is because of the extraordinary exposure of η₇₅₀₀ > 400 m and z_0,sw < 100 mm. However, areas with very low $\widetilde{GS}$ values can be found in close vicinity of the highest $\widetilde{GS}$ values. For example, 800 m east of Brocken’s summit $\widetilde{GS}$ is only 22 m/s.

3.2. Storm Field Factor (STF)

In Figure 5, STF is presented for four severe storms that caused the highest losses in Germany in the study period. STF values related to storm Daria (25–26 January 90) are high (up to 2.0) in the northwest of Germany (Figure 5a). In the east and southeast of the study area, Daria was much less intense with STF < 1.0. In contrast, storm Lothar (26 December 99) was exceptionally strong in Southern Germany (Figure 5b) with STF values up to 2.2. Central and northern parts of the study area were not hit by Lothar with STF < 1.0 over wide areas. Although GS associated with storm Kyrill (18–19 January 2007) is greater than $\widetilde{GS}$ over almost entire Germany (Figure 5c), the highest STF values (2.1) are lower compared to the highest Lothar-related STF values. Similar to storm Lothar, storm Friederike (18 January 18) hit a compact zone with only a few fringes to the south (Figure 5d). In the entire north of the study area, STF < 1.0. The study area-wide maximum STF value is 1.6 occurring in Central Germany. Overall, STF values in the study area are lower than those related to the other displayed winter storms.

If a large STF variability occurs at a small spatial distance, it is likely that two or more measuring stations in the immediate vicinity have a very different gust speed intensity. In such a case, the great stochastic component of gusts becomes apparent.

The representation of storm-related GS intensity by STF makes it very clear that GS is highly storm-specific. On the other hand, the common reference, i.e., $\widetilde{GS}$, allows a consistent (1) assessment across all analyzed storm events, (2) comparison of the gust speed intensity of all analyzed storm events and (3) delimitation of all analyzed storm events. Furthermore, the separation of GS into $\widetilde{GS}$ and STF enables a simplified model building for GS associated with future storms, because only STF needs to be modeled. Using this approach, synthetic GS fields can easily be produced.

Since STF is derived as a deviation from the common reference $\widetilde{GS}$ for all storms, it is possible to consistently determine and compare the share of the study area where STF exceeds a certain value. Here, the comparison of all analyzed storm events is presented by survival functions (SF) of STF (Figure 6). Survival functions represent the exceedance probability of STF in the study area. Accordingly, storm Kyrill exceeds $\widetilde{GS}$ on the largest part of the study area. The median STF ($\widetilde{STF}$) for Kyrill is 1.38. On 5% of the study area, Kyrill-specific STF > 1.63. For storm Lothar, $\widetilde{STF}$ = 0.79 and for storm Daria, $\widetilde{STF}$ = 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.

The shape of SF related to storm Lothar differs greatly from most other SFs. On the upper tail of SF, where the exceedance probability is below 0.05, storm Lothar (STF = 1.76) is very exceptional. In the same exceedance probability range, STF of storm Daria is 1.62. In contrast, STF values related to storm Friederike are much smaller ($\widetilde{STF}$ = 1.01). The great amount of damage caused by storm Friederike can be explained by the fact that its storm field hit several densely populated regions.

3.3. Winter Storm-Related Gust Speed

The GS maps created from multiplying $\widetilde{GS}$ by STF are displayed in Figure 7. For storm Daria, a 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 southeast. During storm Lothar, GS in Northern Germany is often below 15 m/s (Figure 7b) whereas in a clearly defined area in Southern Germany GS often exceeds 25 m/s. In some areas, GS even exceeds 50 m/s. Storm Kyrill hit Germany with an extensive high-impact gust speed field (Figure 7c) with GS > 30 m/s frequently occuring in the study area and GS > 40 m/s over large areas in the west and southeast. The GS field of storm Friederike is most pronounced in Central Germany (Figure 7d). There, GS often exceeds 30 m/s. Also in the south, GS values are often at 20 m/s. In the north, GS values are relatively low (< 15 m/s). In contrast to the other three presented storms, there is no contiguous area where GS > 40 m/s.

SFs of GS are presented in Figure 8. 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.

In general, SFs for GS and STF are very similar. However, the comparison of SFs for GS and STF related to a certain winter storm allows to draw conclusions about the absolute GS level and about the GS level in comparison to $\widetilde{GS}$. For instance, winter storm Lothar’s STF survival function is well above all other SF for an exceedance probability < 0.20. In contrast, the SF for GS in the same exceedance probability range is only slightly above the other SF. This means that Lothar’s GS intensity was more extreme than its absolute GS level.

3.4. Model Comparison

Results from comparing measured and modeled GS according to R² are presented in Figure 9a for DS1 and DS2 (please note the different scaling of the y-axes). For DS1 mean R² of all events is 0.998. The R² standard deviation in DS1 is very low (0.001). For DS2, which is used to validate the model, mean $R_{DS2}^2$ is 0.786. A Mann-Kendall trend test revealed a significant (significance level: 0.05) trend of the $R_{DS2}^2$ values. The increasing model accuracy towards the end of the investigation period can be explained by the increasing number of GS time series available for model validation. The average data availability of DS2 before 1999 is 50%. From 1999, it is on average 61%. The data available for model parameterization in DS1 is about 97% for the entire period.

The highest R² values ($R_{DS1}^2$ = 1.000, $R_{DS2}^2$ = 0.939) were calculated for storm Lothar. One reason for this is the spatially clearly defined storm field. For all other storms, the deviation between $R_{DS1}^2$ and $R_{DS2}^2$ is clearly greater, e.g., for storm Kyrill $R_{DS1}^2$ = 0.997 and $R_{DS2}^2$ = 0.678. Based on all simulated GS fields, there is an indication that the standard deviation of GS in the study area is an important factor for storm event-related $R^2$, correlation coefficient between standard deviation of GS and $R^2$ is 0.61 (significance level: < 0.00001), and thus for model accuracy. Starting with storm Lothar (ID: 51) in 1999, $R_{DS1}^2$ and $R_{DS2}^2$ have very similar variations, with mean $R^2$ being the only distinctive feature.

The second model accuracy measure is mean absolute error (MAE) (Figure 9b). For DS1, mean MAE_DS1 is 0.17 m/s, which is within the typical GS measurement accuracy. Moreover, there is no temporal trend in MAE_DS1. This does not apply for DS2, where mean MAE_DS2 for all events before storm Lothar is 2.2 m/s. After 1999 MAE_DS2 = 1.7 m/s.

From the presented error measures it is concluded that the simulated GS fields very reasonably reconstruct historical GS fields.

In general, it can be assumed that model accuracy is very high in areas with high measurement station density. To test if at a lower station density model accuracy decreases, the DS2 station-related mean absolute percentage error (MAPE) of GS over all storm events was calculated (Figure 10). MAPE is used here to compensate for the spatial differences in GS level in the study area. It was found that the median of all MAPE values is 7.34%. No clear spatial MAPE pattern occurs. Furthermore, no correlation between station density and MAPE was found, indicating that the model accuracy does not depend on the station density. It is therefore assumed that the GS model can be reliably applied throughout the study area.

4. Conclusions

In this study, it could be shown that on the basis of a large number of storms, it is possible to separate individual storm events from the median storm field over Germany. This enables both the probabilistic and spatially explicit quantification of the (1) storm hazard associated with the median gust speed field and (2) storm hazard associated with single catastrophic storm events. The results from the simulation clearly demonstrate that each storm event leads to unique gust speed fields.

It is obvious that the storm-specific gust speed fields show completely different characteristics in the study area. A good example of their variability is the comparison of storm Lothar with storm Kyrill. Due to the event-specific characteristics of their gust speed fields, the two storms led to significantly different damage patterns. The catastrophic damage caused by storm Lothar can be explained by the 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.