# The Role of Highly-Resolved Gust Speed in Simulations of Storm Damage in Forests at the Landscape Scale: A Case Study from Southwest Germany

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}of damaged timber per year over the period 1950–2000 [4]. At least 65% of all forest storm damage is caused by winter storms associated with the passage of high-impact low pressure fronts over Europe during the months November to January [5].

^{3}of storm-damaged timber had to be salvaged in the German southwestern federal state Baden-Wuerttemberg corresponding to a monetary loss estimated at 770 million € [9,11].

## 2. Material and Methods

#### 2.1. Study Area

^{2}) of the area of Baden-Wuerttemberg are covered with forests. The share of state-owned forests is 24%. The commercial forests in the study area are managed according to the guidelines of the state forest administration. According to Corine Land Cover data from the year 2000, close to half (45%) of the forest area was covered by conifer-dominated forests. Mixed forests covered 35% and broad-leaved forests covered 20% [25]. The proportions of the forest types are very similar between state forests and non-state forests. A map showing the distribution of forest types in the study area can be found in [17]. The largest contiguous forest area is found in the low mountain range Black Forest with the highest elevations Feldberg (1496 m) in the south and Hornisgrinde (1164 m) in the north. A further prominent low mountain range is the Swabian Alb (highest elevations < 1020 m). To the west, the study area is bounded by the broad, flat Rhine Valley. A detailed summary of roughness and orographic features of the study area is given in [26].

#### 2.2. Forest Damage Data

_{30yr}). The booking records contained information on the amount of storm-damaged timber and the total amount of harvested timber attributed to 15.871 forest compartments (average size ~20 ha). For the six five-year periods 1979–1983 (P

_{1}), 1984–1988 (P

_{2}), …, 2004–2008 (P

_{6}), proportions of storm-damaged timber (DAM

_{emp,i}, i = 1, …, 6) were calculated by dividing the cumulative amount of storm-damaged timber by the amount of all harvested timber for each compartment. Proportions of storm-damaged timber were compiled and analyzed for P

_{1}–P

_{6}in order to account for the impact of “Wiebke” and “Lothar” and the subsequent delayed salvage-logging after the two storm events.

_{30yr}(DAM

_{emp,30yr}).

_{emp,i}considerably differs between P

_{1}to P

_{6}. The high values of DAM

_{emp,3}and DAM

_{emp,5}result from the impact of the catastrophic storm events Wiebke and Lothar on the forests in Baden-Wuerttemberg. Storm Kyrill, which occurred in P

_{6}caused no discernable proportions of storm-damaged timber in the study area. The proportions of endemically storm-damaged timber (DAM

_{emp,endemic}) were calculated by averaging DAM

_{emp,1}, DAM

_{emp}

_{,2}, DAM

_{emp,4}and DAM

_{emp,6}.

**Figure 2.**Map of proportions of storm-damaged timber in the period 1979–2008 (DAM

_{emp,30yr}). The legend values are highest class values. Grey areas indicate non-state forest areas for which no booking records are available. Blue arrow captions denote high mountain tops in the Black Forest.

**Figure 3.**Boxplots of proportions of storm-damaged timber (DAM

_{emp}) in six five-year periods. Boxplot style: red lines indicate medians; boxes indicate interquartile ranges; whiskers indicate 1.5-times interquartile ranges.

_{emp,i}, DAM

_{emp,endemic}and DAM

_{emp,30yr}were interpolated to 50 m × 50 m resolution raster datasets. The number of storm damage occurrences during P

_{1}–P

_{6}is the raster cell-specific empirical classified storm damage probability (PC

_{emp,j}, j = 1, …, 7) with PC

_{emp,1}indicating that storm damage did not occur during the entire investigation period; PC

_{emp,7}indicates that storm damage occurred in all six five-year periods. All datasets were prepared with the ArcGIS

^{®}10.2 software (ESRI, Redlands, CA, USA).

#### 2.3. Predictor Variables

_{stat}, which represents the statistical properties of the near-surface gust speed field from the period 1979–2013 in the study area in either December (GS

_{stat,Dec}) or January (GS

_{stat,Jan}), is available from the study of [27]. It is a function of elevation, topographic exposure, roughness, aspect and reanalyzed wind speed at the 850 hPa pressure level. The GS

_{stat}-values used in this study, were calculated for a return period of five years. All variables that were included in the gust speed modeling process were excluded from storm damage model building.

**Table 1.**List of predictor variables [19].

Predictor | Acronym | Scale | Classes | Data Source |
---|---|---|---|---|

Forest type | FOR | Categorical | 3 | LUBW^{1} |

Soil type | SOIL | Categorical | 20 | WSA^{2} |

Soil depth | DEPTH | Categorical | 5 | WSA^{2} |

Soil substrate | SUB | Categorical | 17 | WSA^{2} |

Soil acidification | ACID | Categorical | 13 | WSA^{2} |

Soil moisture regime | MOIST | Categorical | 21 | WSA^{2} |

Groundwater affected soils | GRD | Categorical | 4 | WSA^{2} |

Geology | GEOL | Categorical | 14 | WSA^{2} |

Slope | SL | Ordinal | 7 | LUBW^{1} |

Gust speed of December | GS_{stat,Dec} | Continuous | - | [27] |

Gust speed of January | GS_{stat,Jan} | Continuous | - | [27] |

Gust speed of 1 March 1990 | GS_{Wiebke} | Continuous | - | According to [27] |

Gust speed of 26 December 1999 | GS_{Lothar} | Continuous | - | According to [27] |

^{1}LUBW: State Institute for Environmental Protection Baden-Wuerttemberg;

^{2}WSA: Water and Soil Atlas of Baden-Wuerttemberg.

_{stat,Dec}and GS

_{stat,Jan}were most strongly associated with storm damage. This is plausible since the highest gust speed values for a return period of five years occur in December and January in the study area [27]. Therefore, these gust speed fields were used for storm damage modeling. Focusing on GS

_{stat,Dec}and GS

_{stat,Jan}is in accordance with [5], who identified December and January as the months in which by far the highest amounts of storm-damaged timber occur in European forests. In Figure 4, GS

_{stat,Dec}is mapped over the forest area. The strong variations of GS

_{stat,Dec}on a small spatial scale, especially in the Black Forest, are due to the complex orography in the study area. The spatial resolution of all predictor variables is 50 m × 50 m. Further descriptions of the predictor variables are given in [19] and [27].

**Figure 4.**Map of statistical gust speed of December for a return period of five years (GS

_{stat,Dec}) covering the forest area.

#### 2.4. Model Building

_{mod,j}) and empirical proportions of storm-damaged timber (DAM

_{mod}) in the entire study area, the ensemble learning method random forests implemented in the Matlab

^{®}Statistics and Machine Learning Toolbox (The Math Works Inc., Natick, MA, USA, Release 2015a) was applied. The principle of RF is to combine many binary decision trees using bootstrap samples each containing 66% of the learning sample and randomly choosing a subset of predictors at each tree node [29]. The remaining 34% data left out are the out-of-bag (OOB) samples, which are used for cross-validation [30,31].

_{emp,j}. Bagged regression trees were used to model DAM

_{emp,i}, DAM

_{emp,endemic}and DAM

_{emp,30yr}. To quantify the impact of Wiebke and Lothar on the RF-modeling results (denoted by

^{*}), GS

_{Wiebke}and GS

_{Lothar}were included in the model building process yielding DAM

_{mod,3*}, DAM

_{mod,5*}and DAM

_{mod,30yr*}. A summary of the RF-model outputs for P

_{1}–P

_{6}and the corresponding gust speed fields used for RF-model building is shown in Table 2. The RF-models were applied to simulate storm damage probability and proportions of storm-damaged timber for the entire forest area. From the modeled data, maps of classified storm damage probability and proportions of storm-damaged timber were produced.

^{2}).

**Table 2.**Summary of random forests (RF) model outputs for different periods (1–6, 30 year) and gust speed fields used to build the RF-models.

Periods | Gust Speed Field | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

RF-Model Output | 1 | 2 | 3 | 4 | 5 | 6 | 30 Year | Wiebke | Lothar | Stat,December | Stat,January |

DAM_{mod,30yr} | ● | ● | |||||||||

DAM_{mod,1} | ● | ● | |||||||||

DAM_{mod,2} | ● | ● | |||||||||

DAM_{mod,3} | ● | ● | |||||||||

DAM_{mod,4} | ● | ● | |||||||||

DAM_{mod,5} | ● | ● | |||||||||

DAM_{mod,6} | ● | ● | |||||||||

DAM_{mod,endemic} | ● | ● | ● | ● | ● | ||||||

DAM_{mod,30yr*} | ● | ● | ● | ● | |||||||

DAM_{mod,3*} | ● | ● | ● | ||||||||

DAM_{mod,5*} | ● | ● | ● |

#### 2.5. Predictor Importance

_{stat,Dec}or GS

_{stat,Jan}in the final RF-models was based on PI.

#### 2.6. Risk Modeling

_{emp,endemic}) was calculated according to

_{emp,endemic}being calculated and classified based on storm damage occurrence in P

_{1}, P

_{2}, P

_{4}and P

_{6}. Based on the RC

_{emp,endemic}-values a risk matrix (Figure 5) was produced according to [41]. The DAM

_{emp,endemic}-values were assigned to five classes (0%–6%, 7%–14%, 15%–24%, 25%–37%, 38%–55%) using natural breaks yielding severity (negligible, minor, moderate, extensive, serious). Storm damage risk was divided into the four risk indexes low, moderate, high and very high. To provide easily accessible information on RC

_{emp,endemic}, it was modeled in the entire study area using a RF-model (RC

_{mod,endemic}). The importance of the predictor variables (risk factors) for RC

_{mod,endemic}was evaluated by PI.

**Figure 5.**Combinations of severity and empirical probability of endemic storm damage events (PC

_{emp,endemic}) used to classify empirical endemic storm damage risk (RC

_{emp,endemic}).

## 3. Results and Discussion

#### 3.1. Predictor Importance

#### 3.1.1. Damage Probability

_{mod,j}demonstrate that the relative impact of GS

_{stat,Dec}on the predictive accuracy of the RF-model was greatest (PI = 19.1). A predictor variable nearly equally important for RF-model accuracy as GS

_{stat,Dec}was FOR (PI = 18.3) which is in good agreement with findings reported for the study area in previous investigations [17,19]. Also important for the RF-modeling performance was MOIST (PI = 11.9). The soil moisture regime is known to have great influence on windfirmness of trees. In moist soils, root development is often hampered [42,43] and root anchorage is lower as compared with drier soils [44,45]. In this study, all other predictor variables that have been shown to be of importance for storm damage occurrence like soil type [17,19] or soil acidification [46] are of minor importance (PI < 10) for classification of storm damage probability.

_{stat}-fields for PC

_{mod,j}is the dependence of the proportions of forest area associated with PC

_{emp,j}on GS

_{stat,Dec}. Results shown in Figure 6a demonstrate that the proportion of forest area associated with PC

_{emp,1}, which represents the forest area without damage (binary result: storm damage no) over the entire investigation period, is substantially higher for GS

_{stat,Dec}≤ 16 m/s (6.8%) than for GS

_{stat,Dec}≥ 31 m/s (1.4%). This means that with increasing GS

_{stat,Dec}the proportion of undamaged forest area decreases. On the other hand, the proportion of forest area associated with PC

_{emp,7}which represents damage occurrence in all six five-year periods, increases with increasing gust speed from 9.9% for GS

_{stat,Dec}≤ 16 m/s to 35.8% for GS

_{stat,Dec}≥ 31 m/s (Figure 6b).

**Figure 6.**(

**a**) Proportion of forest area associated with empirical storm damage probability class 1 (PC

_{emp,1}) and (

**b**) proportion of forest area associated with empirical storm damage probability class 7 (PC

_{emp,7}) as a function of statistical gust speed of December for a return period of five years (GS

_{stat,Dec}). The red dashed line is the best-fit curve; the black dashed lines indicate the 95% regression parameter confidence intervals.

#### 3.1.2. Damage Proportions

_{mod,j}, gust speed was the most important predictor variable for modeling of proportions of storm-damaged timber (Table 3). Not only for DAM

_{mod,endemic}and DAM

_{mod,30yr}, but also for DAM

_{mod,i}, permutation of gust speed deteriorated MSE most. Other predictor variables that had a distinct effect on proportions of storm-damaged timber were FOR, MOIST and SL.

_{stat}-values as well as the GS

_{Wiebke}- and GS

_{Lothar}-values were higher than all other PI-values related to DAM

_{mod,3*}and DAM

_{mod,5*}. The great importance of GS

_{Wiebke}and GS

_{Lothar}for modeling proportions of storm-damaged timber is a display of the uniqueness of the gust speed field properties during the exceptional storm events that can only in part be represented by the statistical gust speed fields.

**Table 3.**Predictor importance (PI) of random forests model outputs for proportions of storm damaged timber (DAM

_{mod}) Top three important predictor variables are marked bold.

DAM_{mod} | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Predictor | 1 | 2 | 3 | 4 | 5 | 6 | Endemic | 30 year | 3^{*} | 5^{*} |

FOR | 14.2 | 12.0 | 11.9 | 12.3 | 12.2 | 11.3 | 8.6 | 14.9 | 11.9 | 14.3 |

SOIL | 4.0 | 6.1 | 8.3 | 6.9 | 4.8 | 5.2 | 5.8 | 5.2 | 7.1 | 5.4 |

DEPTH | 3.0 | 2.5 | 3.2 | 3.1 | 2.9 | 3.1 | 2.9 | 2.9 | 2.8 | 3.1 |

SUB | 3.9 | 6.1 | 5.0 | 4.5 | 4.6 | 6.0 | 4.6 | 4.1 | 5.8 | 4.7 |

ACID | 2.6 | 3.2 | 3.7 | 3.0 | 3.0 | 3.4 | 3.0 | 3.6 | 4.0 | 2.9 |

MOIST | 9.1 | 14.0 | 13.1 | 12.6 | 12.5 | 8.5 | 11.4 | 13.3 | 15.1 | 12.1 |

GRD | 1.7 | 2.1 | 2.5 | 1.4 | 2.4 | 1.7 | 2.1 | 3.0 | 2.0 | 2.1 |

GEOL | 6.3 | 7.9 | 11.0 | 7.3 | 9.7 | 5.9 | 7.8 | 5.9 | 10.4 | 8.9 |

SL | 11.1 | 11.4 | 12.7 | 13.5 | 18.6 | 13.1 | 12.1 | 10.3 | 13.1 | 12.8 |

GS_{stat,Dec} | 15.6 | 20.0 | 16.6 | 21.2 | 21.2 | 20.6 | 19.1 | |||

GS_{stat,Jan} | 21.8 | 15.6 | 19.7 | |||||||

GS_{Wiebke} | 23.2 | |||||||||

GS_{Lothar} | 20.1 |

_{mod,30yr*}demonstrate that GS

_{stat,Dec}, GS

_{Wiebke}and GS

_{Lothar}are the most important predictor variables (Figure 7). In agreement with the empirical proportions for storm-damaged timber that were presented in Figure 3, the PI-value for GS

_{Lothar}is higher than for GS

_{Wiebke}.

**Figure 7.**Predictor Importance (PI) of random forests model output for modeled proportions of storm-damaged timber in the period 1979–2008 with Wiebke and Lothar gust speed fields being included in model building.

#### 3.1.3. Damage Risk

_{mod,endemic}is similar to the importance of predictor variables for PC

_{mod,j}and DAM

_{mod,endemic}(Figure 8). The most important risk factor was GS

_{stat,Dec}(PI = 19.0) followed by MOIST (PI = 15.7) and FOR (PI = 12.5). All other risk factors were only of minor importance for RC

_{mod,endemic}(PI < 10).

**Figure 8.**Predictor Importance (PI) of random forests model output for modeled endemic storm damage risk.

#### 3.2. Mapping of Damage Probability

_{mod,j}(PC

_{OOB,j}) show that the cross-validated AUC-value for PC

_{OOB,1}, which represents the damage probability class “no damage”, is higher (AUC = 0.86) than in previous studies [12,17,19,49] (Figure 9). The AUC-values that are associated with PC

_{OOB,2}–PC

_{OOB,7}vary between 0.74 and 0.81. PC

_{OOB,2}–PC

_{OOB,7}define more precisely the probability of damage occurrence in P

_{30yr}. The more precise division of PC

_{mod,j}was enabled by the inclusion of highly-resolved gust speed fields into the RF-model building process.

**Figure 9.**Receiver operating curves for modeled classified storm damage probability and the associated area under curve (AUC) values.

_{emp}(Figure 10a,d) with PC

_{mod}(Figure 10b,e) for two small parts of the state forest area. Results presented in Figure 10c,f illustrate the application of the RF-model to all types of forest ownership found in the presented map extracts.

**Figure 10.**Two examples of (

**a**,

**d**) PC

_{emp}; (

**b**,

**e**) PC

_{mod}for the state forest; (

**c**,

**f**) PC

_{mod}for all types of forest ownership in the presented map extract.

_{OOB,mean}) on GS

_{stat,Dec}is quantified by a second order polynomial in Figure 11. The high value of the coefficient of determination (R

^{2}= 0.96) indicates that the relationship between PC

_{OOB,mean}and GS

_{stat,Dec}is strong. PC

_{OOB,mean}increases from 0.66 at GS

_{stat,Dec}≤ 16 m/s to 0.93 at GS

_{stat,Dec}≥ 31 m/s. The steeper increase of the polynomial at higher values of GS

_{stat,Dec}might be the result of the basically quadratic relationship between near-surface wind field properties and wind loading on trees [50].

**Figure 11.**Out-of-bag samples of averaged probability class of modeled classified storm damage probability (PC

_{OOB,mean}) as a function of statistical gust speed of December for a return period of five years (GS

_{stat,Dec}).

_{mod,j}exhibits that 67% of all PC

_{mod,j}-classes are assigned to PC

_{mod,5}–PC

_{mod,7}(PC

_{mod,1}: 8%; PC

_{mod,2}: 8%; PC

_{mod,3}: 12%; PC

_{mod,4}: 5%; PC

_{mod,5}: 12%; PC

_{mod,6}: 28%; PC

_{mod,7}: 27%). A map of PC

_{mod}(Figure 12) illustrates that in large parts of the forest area PC

_{mod}-values are higher than 50% which means that storm damage is likely for a return period of 5 years. Only large parts of the Swabian Alb and the Rhine Valley are less threatened by high-impact storm events. The lower storm damage probability in these two parts of the study area mainly results from low GS

_{stat,Dec}-values, dry soils and the predominance of broad-leaved and mixed forests. Highest PC

_{mod}-values occur in large parts of the Black Forest, in the northern part of the Alpine Foothills and in the northern parts of Baden-Wuerttemberg where GS

_{stat,Dec}is high, soils are fresh or temporarily fresh and conifers predominate.

#### 3.3. Mapping of Damage Proportions

_{mod}-model performance are presented in Table 4 (DAM

_{OOB}). The MSE-values for the RF-model outputs DAM

_{OOB,30yr}and DAM

_{OOB,endemic}are MSE = 0.02 and MSE = 0.01. The explained variance as quantified by R

^{2}equals to 0.30 and 0.28 which is better than analogous results from previous studies [12,18]. RF-Model accuracy clearly increased for DAM

_{OOB,3}and DAM

_{OOB,5}from MSE = {0.08, 0.10} and R

^{2}= {0.25, 0.22} to MSE = {0.07, 0.07} and R

^{2}= {0.36, 0.41} when GS

_{Wiebke}(DAM

_{OOB,3*}) and GS

_{Lothar}(DAM

_{OOB,5*}) are included into RF-model development. Highest model accuracy (R

^{2}= 0.53 and MSE = 0.01) was achieved when GS

_{stat,Dec}, GS

_{Wiebke}and GS

_{Lothar}are used in combination to model proportions of storm-damaged timber from 1979 to 2008 (DAM

_{OOB,30yr*}). The clear increase of R

^{2}suggests that the gust speed fields related to Wiebke and Lothar substantially differ from the statistical gust speed field and thus explain an additional large part of variance in DAM

_{emp,30yr}-data.

RF-Model Output | |||||||
---|---|---|---|---|---|---|---|

DAM_{OOB,3} | DAM_{OOB,5} | DAM_{OOB,endemic} | DAM_{OOB,30yr} | DAM_{OOB,3*} | DAM_{OOB,5*} | DAM_{OOB,30yr*} | |

MSE | 0.08 | 0.10 | 0.01 | 0.02 | 0.07 | 0.07 | 0.01 |

R^{2} | 0.25 | 0.22 | 0.28 | 0.30 | 0.36 | 0.41 | 0.53 |

_{emp,30yr}with DAM

_{mod,30yr}for the region around the Hornisgrinde in the northern Black Forest. The region is characterized by a pronounced variability of GS

_{stat,Dec}-values (Figure 13c,f). This variability is caused by orographically complex terrain and large variations in elevation across all forest types (Figure 13d). The transfer of DAM

_{mod,30yr}to all types of forest ownership found in the Corine data-based map extract also gives plausible values (Figure 13e). It is therefore concluded that this example demonstrates (1) appropriate accuracy of DAM

_{mod,30yr}in complex terrain; (2) the portability of DAM

_{mod,30yr}to all types of forest ownership and (3) the dependency of DAM

_{mod,30yr}on GS

_{stat,Dec}and FOR.

**Figure 13.**Map extract showing (

**a**–

**c**) DAM

_{emp,30yr}, DAM

_{mod,30yr}, GS

_{stat,Dec}for state forests; (

**d**–

**f**) FOR, DAM

_{mod,30yr}and GS

_{stat,Dec}over all types of forest ownership in the northern Black Forest. The black dots indicate the locations of meteorological stations in this area used to build the gust speed model. The legend values indicate highest class values.

_{Wiebke}, GS

_{Lothar}and GS

_{stat,Dec}and OOB-samples of modeled proportions of storm-damaged timber are shown in Figure 14a–c. From this it is clear that an increase of median DAM

_{OOB}can be linked to an increase of gust speed. In the range of gust speed values measured during the passage of Wiebke, the medians of DAM

_{OOB,3*}take values ranging from 0.16 at GS

_{Wiebke}= 12 m/s to 0.60 at GS

_{Wiebke}= 51 m/s. The DAM

_{OOB,5*}-median values associated with Lothar increase from 0.32 (GS

_{Lothar}= 15 m/s) to 0.81 (GS

_{Lothar}= 57 m/s) with interquartile ranges of DAM

_{OOB,5*}for GS

_{Lothar}≥ 48 m/s being considerably lower than for GS

_{Lothar}< 48 m/s. This finding leads to the conclusion that for very high GS

_{Lothar}-values the proportions of storm-damaged timber is exceptionally high, regardless of other factors influencing proportions of-storm-damaged timber. The differences in DAM

_{OOB,3*}and DAM

_{OOB,5}

_{*}between corresponding GS

_{Wiebke}- and GS

_{Lothar}-classes result from damage that was caused by the passage of storms other than Wiebke and Lothar in P

_{3}and P

_{5}.

_{stat,Dec}-values are clearly lower than GS

_{Wiebke}- and GS

_{Lothar}-values. The corresponding DAM

_{OOB,30yr}-median values nonetheless increase from 0.16 at GS

_{stat,Dec}≤ 16 m/s to 0.29 at GS

_{stat,Dec}= 29 m/s. However, DAM

_{OOB,30yr}-median values are clearly lower than DAM

_{OOB}-values dependent on GS

_{Wiebke}and GS

_{Lothar}.

_{OOB,30yr}-median values at highest GS

_{stat,Dec}-values are open to speculation. One reason might be that by far the largest proportion of highest GS

_{stat,Dec}-values occurs at highest elevations in the southern Black Forest around the Feldberg. Therefore, decreasing proportions of storm-damaged timber at these elevations might be due to acclimative tree growth in response to recurrently high wind loading that increases tree stability against excessive wind exposure [20,51,52,53,54]. Another reason might be the limited predictive accuracy of the applied gust speed model at elevations higher than 1200 m a.s.l. due to finite availability of meteorological stations at which gust speed is measured [27]. Furthermore, in the applied gust speed model airflow is parameterized to be more laminar at highest elevations, like the Feldberg region, which reach the top of the atmospheric boundary layer.

_{OOB}are presented in Figure 14d–f. The variability of DAM

_{OOB,3*}, DAM

_{OOB,5*}and DAM

_{OOB,30yr}as a function of gust speed is greater than the variability of DAM

_{OOB}as a function of FOR which is interpreted to mean that the variability of gust speed is more informative for the explanation of DAM

_{OOB}than FOR. The median values of DAM

_{OOB}are always lowest for mixed forests (between DAM

_{OOB,30yr}= 0.15 and DAM

_{OOB,5*}= 0.24) and highest for conifers (between DAM

_{OOB,30yr}= 0.26 and DAM

_{OOB,5}

_{*}= 0.47). This effect might be due to higher drag of evergreen conifers in winter when most high-impact storms occur in the study area [55] while broad-leaved tree species are leafless [46,56,57].

**Figure 14.**Boxplot of DAM

_{OOB,3*}as a function of GS

_{Wiebke}(

**a**); DAM

_{OOB,5*}as a function of GS

_{Lothar}(

**b**); DAM

_{OOB,30yr}as a function of GS

_{stat,Dec}(

**c**); DAM

_{OOB,3*}(

**d**); DAM

_{OOB,5*}(

**e**) and DAM

_{OOB,30yr}as a function of FOR (

**f**).

_{mod,endemic}-values (up to 55%) occur mostly in the northern Black Forest in exposed areas at high elevations. Other areas prone to endemic storm damage are in the Forests of Odes and the northern Alpine Foothills. Apart from these regions, DAM

_{mod,endemic}-values higher than 20% do not occur over wide areas (7%). Lowest DAM

_{mod,endemic}-values (≤5%) can be found in 16% of the forest area. These areas, which are not prone to storm damage, are mainly located in the deep Rhine Valley and in narrow valleys of the Swabian Alb where statistical wind speed values are low [26].

_{stat,Dec}-values are in the range 25–30 m/s.

_{stat,Dec}-values are below 20 m/s. Thus, it can be stated that these results provide a valuable basis for a first assessment of forest areas generally prone to endemic storm damage.

_{mod,5*}and DAM

_{mod,endemic}is mapped in Figure 16.

**Figure 15.**Map of modeled proportions of endemically storm-damaged timber (DAM

_{mod,endemic}). The legend values indicate highest class values.

**Figure 16.**Difference map of modeled proportions of storm-damaged timber in the period 1999–2003 with Lothar gust speed field being included in model building (DAM

_{mod,5*}) and modeled proportions of endemically storm-damaged timber DAM

_{mod,endemic}. The legend values indicate highest class values.

_{mod,5*}-values are up to 96% higher than DAM

_{mod,endemic}-values. This might be the result of low GS

_{stat,Dec}-values which indicate low chronic wind loading on trees and thus limited acclimative tree growth. However, in this area, GS

_{Lothar}-values often exceeded 35 m/s causing catastrophic proportions of storm-damaged timber. Other parts of the study area, where DAM

_{mod,5*}-values were also considerably higher (40%–50%) after the passage of Lothar, are located in the northern Black Forest and Virngrund. Overall, in 10% of the forest area the difference between DAM

_{mod,5*}and DAM

_{mod,endemic}was higher than 50%.

_{Lothar}≤ 20 m/s. In some parts of this region (4%), DAM

_{mod,5*}-values were even below DAM

_{mod,endemic}-values.

_{mod,endemic}, highest DAM

_{mod,30yr*}-values occur in the northern Black Forest, in the Forests of Odes, Virngrund and parts of the Rhine Valley reaching up to 91%.

**Figure 17.**Map of modeled proportions of storm-damaged timber in the period 1979–2008 with Wiebke and Lothar gust speed fields being included in model building (DAM

_{mod,30yr*}). The legend values indicate highest class values.

#### 3.4. Mapping of Damage Risk

_{mod,endemic}(RC

_{OOB,endemic}) exhibits that RF-model accuracy is best for low (AUC = 0.83) and very high (AUC = 0.82) storm damage risk. For moderate and high storm damage risk RF-model accuracy is slightly lower (AUC = 0.72 and AUC = 0.76). The observed risk-relaed AUC-value pattern corresponds to results that were presented in Figure 14. They indicate that at very low gust speed, storm damage risk is low, while at very high gust speed, storm damage risk is very high. In the moderate and high storm damage risk indexes, the influence of gust speed is superimposed by other environmental factors like forest type and soil moisture. Prominent, extended areas exposed to very high storm damage risk are located in parts of the northern Black Forest and the north-eastern part of Baden-Wuerttemberg (Figure 18). Forested areas at low storm damage risk are the Rhine Valley and the valleys of the Swabian Alb.

## 4. Conclusions

## Author Contributions

## Conflicts of Interest

## Appendix

Symbols, Acronyms | Description |

ACID | Soil acidification |

AUC | Area under curve |

DAM_{emp} | Empirical proportions of storm-damaged timber |

DAM_{emp,30yr} | Empirical proportions of storm-damaged timber in the period 1979–2008 |

DAM_{emp,endemic} | Empirical proportions of endemically storm-damaged timber |

DAM_{emp,i} | Empirical proportions of storm-damaged timber in P_{i} |

DAM_{mod} | Modeled proportions of storm-damaged timber |

DAM_{mod,3*} | Modeled proportions of storm-damaged timber in P_{3} with GS_{Wiebke} being included in model building |

DAM_{mod,30yr} | Modeled proportions of storm-damaged timber in the period 1979–2008 |

DAM_{mod,30yr*} | Modeled proportions of storm-damaged timber in the period 1979–2008 with GS_{Wiebke} and GS_{Lothar} being included in model building |

DAM_{mod,5*} | Modeled proportions of storm-damaged timber in P_{5} with GS_{Lothar} being included in model building |

DAM_{mod,endemic} | Modeled proportions of endemically storm-damaged timber |

DAM_{mod,i} | Modeled proportions of storm-damaged timber in P_{i} |

DAM_{OOB} | OOB samples of modeled proportions of storm-damaged timber |

DAM_{OOB,i} | OOB samples of modeled proportions of storm-damaged timber in P_{i} |

DAM_{OOB,3*} | OOB samples of modeled proportions of storm-damaged timber in P_{3} with GS_{Wiebke} being included in model building |

DAM_{OOB,30yr} | OOB samples of modeled proportions of storm-damaged timber in the period 1979–2008 |

DAM_{mod,30yr*} | OOB samples of modeled proportions of storm-damaged timber in the period 1979–2008 with GS_{Wiebke} and GS_{Lothar} being included in model building |

DAM_{OOB,5*} | OOB samples of modeled proportions of storm-damaged timber in P_{5} with GS_{Lothar} being included in model building |

DAM_{OOB,endemic} | OOB samples of modeled proportions of endemically storm-damaged timber |

DEPTH | Soil depth |

FOR | Forest type |

GEOL | Geology |

GRD | Groundwater affected soils |

GS_{stat} | Statistical gust speed for a return period of five years |

GS_{stat,Dec} | Statistical gust speed of December for a return period of five years |

GS_{stat,Jan} | Statistical gust speed of January for a return period of five years |

GS_{Lothar} | Gust speed of 26 December 1999 |

GS_{Wiebke} | Gust speed of 1 March 1990 |

MOIST | Soil moisture regime |

MSE | Mean squared error |

PC_{emp,endemic} | Empirical probability of endemic storm damage events |

PC_{emp,j} | Empirical classified storm damage probability: (j = 1, …, 7) |

PC_{mod} | Modeled storm damage probability in percentages |

PC_{mod,j} | Modeled classified storm damage probability: (j = 1, …, 7) |

PC_{OOB,j} | OOB samples of modeled classified storm damage probability: (j = 1, …, 7) |

PC_{OOB,mean} | OOB samples of averaged modeled classified storm damage probability |

PI | Predictor Importance |

R^{2} | Coefficient of determination |

RC_{emp,endemic} | Empirical endemic storm damage risk |

RC_{mod,endemic} | Modeled endemic storm damage risk |

RC_{OOB,endemic} | OOB samples of modeled endemic storm damage risk |

SL | Slope |

SOIL | Soil type |

SUB | Soil substrate |

Abbreviations | Description |

OOB | Out-of-bag |

P_{30yr} | Period from 1979–2008 |

P_{i} | Five-year period i: 1979–1983 (P_{1}), 1984–1988 (P_{2}), …, 2004–2008 (P_{6}) |

RF | Random forests |

ROC | Receiver operating curve |

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**MDPI and ACS Style**

Jung, C.; Schindler, D.; Albrecht, A.T.; Buchholz, A.
The Role of Highly-Resolved Gust Speed in Simulations of Storm Damage in Forests at the Landscape Scale: A Case Study from Southwest Germany. *Atmosphere* **2016**, *7*, 7.
https://doi.org/10.3390/atmos7010007

**AMA Style**

Jung C, Schindler D, Albrecht AT, Buchholz A.
The Role of Highly-Resolved Gust Speed in Simulations of Storm Damage in Forests at the Landscape Scale: A Case Study from Southwest Germany. *Atmosphere*. 2016; 7(1):7.
https://doi.org/10.3390/atmos7010007

**Chicago/Turabian Style**

Jung, Christopher, Dirk Schindler, Axel Tim Albrecht, and Alexander Buchholz.
2016. "The Role of Highly-Resolved Gust Speed in Simulations of Storm Damage in Forests at the Landscape Scale: A Case Study from Southwest Germany" *Atmosphere* 7, no. 1: 7.
https://doi.org/10.3390/atmos7010007