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

: Routinely collected booking records of salvaged timber from the period 1979–2008 were used to empirically model the (1) storm damage probability; (2) proportions of storm-damaged timber and (3) endemic storm damage risk in the forest area of the German federal state of Baden-Wuerttemberg by applying random forests. Results from cross-validated predictor importance evaluation demonstrate that the relative impact of modeled gust speed ﬁelds on the predictive accuracy of the random forests models was greatest compared to the impact of forest and soil features. Forest areas prone to storm damage occurring within a period of ﬁve years were mainly located in mountainous upland regions where maximum gust speed exceeds 31 m/s in a ﬁve-year return period and conifers dominate the tree species composition. While mean storm damage probability continuously increased with increasing statistical gust speed proportions of storm-damaged timber peaked at a statistical maximum gust speed value of 29 m/s occurring in a ﬁve-year return period. Combining the statistical gust speed ﬁeld with daily gust speed ﬁelds of two exceptional winter storms improved model accuracy and considerably increased the explained variance. Endemic storm damage risk was calculated from endemic storm damage probability and proportions of endemically storm-damaged timber. In combination with knowledge of local experts the storm damage risk modeled in a 50 m ˆ 50 m resolution raster dataset can easily be used to identify areas prone to storm damage and to adapt silvicultural management regimes to make forests more windﬁrm.


Introduction
Storms influence forest ecosystems at multiple levels.They are key factors for forest composition, structure, demography, growth and ecosystem processes [1][2][3].In European forests, storms caused 18.5 million m 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].
Exceptional winter storms that impacted Central Europe during the past decades were "Wiebke" in March 1990 [6], "Lothar" in December 1999 [7] and "Kyrill" in January 2007 [8].With respect to the amount of damaged timber, storm Lothar, which passed Southwest Germany [9] and Switzerland [10] on 26 December 1999, was the most damaging event in these areas.In the aftermath of Lothar, approximately 30 million m 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].
Beside infrequent, catastrophic storms like Wiebke and Lothar, frequent, less intense storm events cause substantial amounts of endemically damaged timber [12] and chronically affect forest ecosystem services [13,14].Endemic damage is damage due to regularly occurring storm events that are part of the local wind climate.An essential prerequisite for analysis and modeling of endemic forest storm damage is thus knowledge about statistical properties of the local wind climate which can be used to establish functional relationships between statistical wind fields and storm damage occurrence.
A variety of factors have an influence on forest storm damage formation.They can basically be differentiated into: weather conditions, orography, human influence, soil conditions and stand conditions [15].Initially, high impact wind conditions may lead to damage and it is believed that in particular wind loads associated with strong gusts cause tree failure [16].
However, the predictive power of modeled storm-related gust speed fields was low in previous empirical storm damage modeling studies [12,[17][18][19][20].One reason for the low predictive power certainly was the coarse (often 1 km ˆ1 km) spatial resolution [12,17,19] which did not realistically represent the small scale nature of gusts.Furthermore, modeled gust speed fields were based on smoothed orography, which did not represent orographically complex terrain in sufficient detail.The combination of coarsely resolved gust speed and orography often resulted in a weak association between gust speed and terrain-related variables like topographic exposure [19,21] and elevation [20,22].In fact, due to the better availability of datasets with a higher spatial resolution of topographic exposure and/or elevation, previous empirical forest storm damage models were often based on terrain-related proxy variables and not on high impact wind conditions [19,21].
The development of empirical forest storm damage models is generally based on a similar conceptual approach [19]: (1) mapping of storm-damaged areas; (2) mapping of environmental factors that might be directly or indirectly associated with forest storm damage; (3) estimation of the relative contribution of these factors to storm damage occurrence and/or storm damage amount and (4) calculation and classification of storm damage into different probability levels.Yet, in most previous studies damage probability calculations were based on only one or two exceptional storm events that led to catastrophic damage [17,19,20,23,24].This means that in these studies results from damage probability modeling were presented and discussed based on the assumption that future storm events will occur under environmental conditions similar to those found for the few investigated exceptional cases, even though it is clear that storm damage events will rarely occur under similar environmental conditions again.
The goals of this study are therefore (1) separating the impact of catastrophic, infrequent storm events in forests from the impact of endemic storm events in the period 1979-2008 in the southwestern German federal state of Baden-Wuerttemberg; (2) quantifying the contribution of environmental factors to forest storm damage probability, proportions of storm-damaged timber for both catastrophic and endemic events as well as endemic storm damage risk and (3) building statistical models that are capable of predicting the five-year storm damage probability, proportions of storm-damaged timber in various periods and endemic storm damage risk on a high spatial resolution (50 m ˆ50 m).
All symbols, abbreviations and acronyms used in the text, are summarized in Table A1.

Study Area
Storm damage probability, proportions of storm-damaged timber and storm damage risk were simulated in the forests of Baden-Wuerttemberg (Figure 1).Approximately 38% (13,700 km 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].
Atmosphere 2016, 7, 7 3/23 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].

Forest Damage Data
Annual booking records of salvaged timber were used to reconstruct the spatial storm damage pattern that occurred in the state forests during 1979-2008 (P30yr).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 (P1), 1984-1988 (P2), …, 2004-2008 (P6), proportions of storm-damaged timber (DAMemp,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 P1-P6 in order to account for the impact of "Wiebke" and "Lothar" and the subsequent delayed salvage-logging after the two storm events.
The choice of the period length was a trade-off between statistical representativity and the number of periods required to predict storm damage probability.Figure 2 shows the proportions of storm-damaged timber for P30yr (DAMemp,30yr).
As can be seen in Figure 3, DAMemp,i considerably differs between P1 to P6.The high values of DAMemp,3 and DAMemp,5 result from the impact of the catastrophic storm events Wiebke and Lothar on the forests in Baden-Wuerttemberg.Storm Kyrill, which occurred in P6 caused no discernable proportions of storm-damaged timber in the study area.The proportions of endemically

Forest Damage Data
Annual booking records of salvaged timber were used to reconstruct the spatial storm damage pattern that occurred in the state forests during 1979-2008 (P 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.
The choice of the period length was a trade-off between statistical representativity and the number of periods required to predict storm damage probability.Figure 2 shows the proportions of storm-damaged timber for P 30yr (DAM emp,30yr ).
As can be seen in Figure 3, DAM 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 .DAM emp,i , DAM emp,endemic and DAM emp,30yr were interpolated to 50 m ˆ50 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).

Predictor Variables
Predictor variables that were available for random forests (RF) model building are listed in Table 1.Forest type (FOR) which consists of the three classes "conifer forest", "broad-leaved" and "mixed forest", was built from Corine Land Cover data.All soil related predictor variables were obtained from the Water and Soil Atlas of Baden-Wuerttemberg.Slope (SL) was calculated and classified from a digital terrain model.
The variable GS 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.The screening of the results from correlation analysis indicate that GS 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 ˆ50 m.Further descriptions of the predictor variables are given in [19] and [27].
Multicollinearity among the predictor variables was investigated following [17] by assessing the variance inflation and the condition index in combination with variance-decomposition proportions according to [28].However, no collinearity was detected among the predictor variables.

Model Building
To predict empirical storm damage probability (PCmod,j) and empirical proportions of storm-damaged timber (DAMmod) 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].
Bagged classification trees were used to model PCemp,j.Bagged regression trees were used to model DAMemp,i, DAMemp,endemic and DAMemp,30yr.To quantify the impact of Wiebke and Lothar on the RF-modeling results (denoted by * ), GSWiebke and GSLothar were included in the model building process yielding DAMmod,3*, DAMmod,5* and DAMmod,30yr*.A summary of the RF-model outputs for P1-P6 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

Model Building
To predict empirical storm damage probability (PC 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].
Bagged classification trees were used to model PC 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˚a nd 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.
The predictive accuracy of bagged classification trees was evaluated with a receiver operating characteristic (ROC) curve, which is a common measure for quantifying the accuracy of predictions [36,37].For a model with high predictive power, ROC-curves steeply increase and the area under the curve (AUC) approaches a value of 1.0 whereas an AUC-value of 0.5 indicates limited predictive power.Predictive accuracy of regression trees was measured by mean squared error (MSE) and the coefficient of determination (R 2 ). .

Predictor Importance
The contribution of individual predictor variables to final RF-model outputs was evaluated by the predictor importance (PI) which was measured for OOB.The basic idea behind PI is to identify predictor variables which affect RF-model accuracy only little after being randomly permuted.In contrast, important predictor variables strongly change model accuracy after being randomly permuted.Model accuracy is measured before and after permuting a predictor variable for each tree [29,[38][39][40].
The PI-values thus represent for (1) RF-classification models the relative misclassification increase as compared to the OOB-misclassification; (2) RF-regression models the relative increase in MSE as compared to the OOB-MSE [38].The decision whether to integrate GS stat,Dec or GS stat,Jan in the final RF-models was based on PI.

Risk Modeling
The endemic storm damage risk related to a five-year period without exceptional storm events (RC emp,endemic ) was calculated according to with PC 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.

Damage Probability
Results from PI-evaluation associated with the calculation of PCmod,j demonstrate that the relative impact of GSstat,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 GSstat,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.
According to our knowledge, this is the first time that gust speed was found to be the most important predictor variable to be used in empirical storm damage modeling.In our opinion, this is mainly because the spatial resolution of the available gust speed fields (50 m × 50 m) is far more detailed than the gust speed data available in previous studies [12,[17][18][19].The high-resolution gust speed models incorporate roughness and topographic features, which had to be neglected or considered separately in earlier investigations.
It is clear that the proposed modeling approach does not include all variables that are involved in forest storm damage occurrence.Based on findings from previous studies, it is plausible that variables like tree height [24,47,48], tree species [20,48] or forest management [18,48] are important predictor variables for damage occurrence as well.However, these variables were not available at the landscape scale.
Further indication for the plausibility and importance of GSstat-fields for PCmod,j is the dependence of the proportions of forest area associated with PCemp,j on GSstat,Dec.Results shown in Figure 6a demonstrate that the proportion of forest area associated with PCemp,1, which represents the forest area without damage (binary result: storm damage no) over the entire investigation period, is substantially higher for GSstat,Dec ≤ 16 m/s (6.8%) than for GSstat,Dec ≥ 31 m/s (1.4%).This means that with increasing GSstat,Dec the proportion of undamaged forest area decreases.On the other hand, the proportion of forest area associated with PCemp,7 which represents damage occurrence in all six five-year periods, increases with increasing gust speed from 9.9% for GSstat,Dec  16 m/s to 35.8% for GSstat,Dec ≥ 31 m/s (Figure 6b).

Damage Probability
Results from PI-evaluation associated with the calculation of PC 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.
According to our knowledge, this is the first time that gust speed was found to be the most important predictor variable to be used in empirical storm damage modeling.In our opinion, this is mainly because the spatial resolution of the available gust speed fields (50 m ˆ50 m) is far more detailed than the gust speed data available in previous studies [12,[17][18][19].The high-resolution gust speed models incorporate roughness and topographic features, which had to be neglected or considered separately in earlier investigations.
It is clear that the proposed modeling approach does not include all variables that are involved in forest storm damage occurrence.Based on findings from previous studies, it is plausible that variables like tree height [24,47,48], tree species [20,48] or forest management [18,48] are important predictor variables for damage occurrence as well.However, these variables were not available at the landscape scale.
Further indication for the plausibility and importance of GS 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 ď 16 m/s (6.8%) than for GS stat,Dec ě 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 ď 16 m/s to 35.8% for GS stat,Dec ě 31 m/s (Figure 6b).

Damage Proportions
As has already been reported for PCmod,j, gust speed was the most important predictor variable for modeling of proportions of storm-damaged timber (Table 3).Not only for DAMmod,endemic and DAMmod,30yr, but also for DAMmod,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.
The GSstat-values as well as the GSWiebke-and GSLothar-values were higher than all other PI-values related to DAMmod,3* and DAMmod,5*.The great importance of GSWiebke and GSLothar 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.

Damage Proportions
As has already been reported for PC 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.
The GS stat -values as well as the GS Wiebke -and GS Lothar -values were higher than all other PI-values related to DAM mod,3˚a nd 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.The results from the PI-evaluation for DAM mod,30yr˚d emonstrate 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 .
Atmosphere 2016, 7, 7 10/23 The results from the PI-evaluation for DAMmod,30yr* demonstrate that GSstat,Dec, GSWiebke and GSLothar 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 GSLothar is higher than for GSWiebke.

Damage Risk
The importance of the risk factors for RF-model output RCmod,endemic is similar to the importance of predictor variables for PCmod,j and DAMmod,endemic (Figure 8).The most important risk factor was GSstat,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 RCmod,endemic (PI < 10).

Mapping of Damage Probability
Results from ROC-curve evaluation of the OOB-samples of PCmod,j (PCOOB,j) show that the cross-validated AUC-value for PCOOB,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

Damage Risk
The importance of the risk factors for RF-model output RC 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).
Atmosphere 2016, 7, 7 10/23 The results from the PI-evaluation for DAMmod,30yr* demonstrate that GSstat,Dec, GSWiebke and GSLothar 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 GSLothar is higher than for GSWiebke.

Damage Risk
The importance of the risk factors for RF-model output RCmod,endemic is similar to the importance of predictor variables for PCmod,j and DAMmod,endemic (Figure 8).The most important risk factor was GSstat,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 RCmod,endemic (PI < 10).

Mapping of Damage Probability
Results from ROC-curve evaluation of the OOB-samples of PCmod,j (PCOOB,j) show that the cross-validated AUC-value for PCOOB,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

Mapping of Damage Probability
Results from ROC-curve evaluation of the OOB-samples of PC 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.It is very likely that the accuracy of the obtained modeling results would improve when damage data, which are at the moment associated with forest compartments, become available as a raster dataset at a higher spatial resolution.
As an example for RF-model performance, Figure 10 compares PCemp (Figure 10a,d) with PCmod (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.It is very likely that the accuracy of the obtained modeling results would improve when damage data, which are at the moment associated with forest compartments, become available as a raster dataset at a higher spatial resolution.
As an example for RF-model performance, Figure 10 compares PC 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.It is very likely that the accuracy of the obtained modeling results would improve when damage data, which are at the moment associated with forest compartments, become available as a raster dataset at a higher spatial resolution.
As an example for RF-model performance, Figure 10 compares PCemp (Figure 10a,d) with PCmod (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.The functional dependence of the averaged probability classes of the OOB-samples (PC 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 ď 16 m/s to 0.93 at GS stat,Dec ě 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].

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The functional dependence of the averaged probability classes of the OOB-samples (PCOOB,mean) on GSstat,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 PCOOB,mean and GSstat,Dec is strong.PCOOB,mean increases from 0.66 at GSstat,Dec  16 m/s to 0.93 at GSstat,Dec ≥ 31 m/s.The steeper increase of the polynomial at higher values of GSstat,Dec might be the result of the basically quadratic relationship between near-surface wind field properties and wind loading on trees [50].The evaluation of PCmod,j exhibits that 67% of all PCmod,j-classes are assigned to PCmod,5-PCmod,7 (PCmod,1: 8%; PCmod,2: 8%; PCmod,3: 12%; PCmod,4: 5%; PCmod,5: 12%; PCmod,6: 28%; PCmod,7: 27%).A map of PCmod (Figure 12) illustrates that in large parts of the forest area PCmod-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 GSstat,Dec-values, dry soils and the predominance of broad-leaved and mixed forests.Highest PCmod-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 GSstat,Dec is high, soils are fresh or temporarily fresh and conifers predominate.The evaluation of PC 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.

Mapping of Damage Proportions
Results from OOB-evaluation of DAMmod-model performance are presented in Table 4 (DAMOOB).The MSE-values for the RF-model outputs DAMOOB,30yr and DAMOOB,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]

Mapping of Damage Proportions
Results from OOB-evaluation of DAM 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.Figure 13a,b compare DAM 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.
Atmosphere 2016, 7, 7 Figure 13a,b compare DAMemp,30yr with DAMmod,30yr for the region around the Hornisgrinde in the northern Black Forest.The region is characterized by a pronounced variability of GSstat,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 DAMmod,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 DAMmod,30yr in complex terrain; (2) the portability of DAMmod,30yr to all types of forest ownership and (3) the dependency of DAMmod,30yr on GSstat,Dec and FOR.The functional relationships between GSWiebke, GSLothar and GSstat,Dec and OOB-samples of modeled proportions of storm-damaged timber are shown in Figures 14a-c.From this it is clear that an increase of median DAMOOB 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 DAMOOB,3* take values ranging from 0.16 at GSWiebke = 12 m/s to 0.60 at GSWiebke = 51 m/s.The DAMOOB,5*-median values associated with Lothar increase from 0.32 (GSLothar = 15 m/s) to 0.81 (GSLothar = 57 m/s) with interquartile ranges of DAMOOB,5* for GSLothar  48 m/s being considerably lower than for GSLothar < 48 m/s.This finding leads to the conclusion that for very high GSLothar-values the proportions of storm-damaged timber is exceptionally high, regardless of other factors influencing proportions of-storm-damaged timber.The functional relationships between GS 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˚t ake 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˚f or GS Lothar ě 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˚a nd 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 .
Highest GS 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 ď 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 .
The reasons for the decrease of DAM 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.
The relationships between FOR and DAM OOB are presented in Figure 14d-f.The variability of DAM OOB,3˚, DAM OOB,5˚a nd 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].

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DAMOOB as a function of FOR which is interpreted to mean that the variability of gust speed is more informative for the explanation of DAMOOB than FOR.The median values of DAMOOB are always lowest for mixed forests (between DAMOOB,30yr = 0.15 and DAMOOB,5* = 0.24) and highest for conifers (between DAMOOB,30yr = 0.26 and DAMOOB,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].A map of the modeled proportions of endemically storm-damaged timber (Figure 15) shows that the highest DAM 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 (ď5%) 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].
Although it is clear that the proportions of endemically storm-damaged timber is rather small in the entire study area compared to the catastrophic proportions of storm-damaged timber, endemic storm events can regionally be an important disturbance factor.According to our calculations, endemic storm events can cause up to 55% of the total amount of salvaged timber.This is particularly the case when forest composition is dominated by conifers and GS stat,Dec -values are in the range 25-30 m/s.
On the other hand, endemic storm damage is of minor importance when the forest composition is a mixture of conifers and broad-leaved tree species and GS 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.
In order to localize and quantify the exceptional nature of storm Lothar in connection with forest storm damage, the difference between DAM mod,5˚a nd DAM mod,endemic is mapped in Figure 16.A map of the modeled proportions of endemically storm-damaged timber (Figure 15) shows that the highest DAMmod,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, DAMmod,endemic-values higher than 20% do not occur over wide areas (7%).Lowest DAMmod,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].Although it is clear that the proportions of endemically storm-damaged timber is rather small in the entire study area compared to the catastrophic proportions of storm-damaged timber, endemic storm events can regionally be an important disturbance factor.According to our calculations, endemic storm events can cause up to 55% of the total amount of salvaged timber.This is particularly the case when forest composition is dominated by conifers and GSstat,Dec-values are in the range 25-30 m/s.
On the other hand, endemic storm damage is of minor importance when the forest composition is a mixture of conifers and broad-leaved tree species and GSstat,Dec-values are below 20 m/s.Thus, it Atmosphere 2016, 7, 7 can be stated that these results provide a valuable basis for a first assessment of forest areas generally prone to endemic storm damage.
In order to localize and quantify the exceptional nature of storm Lothar in connection with forest storm damage, the difference between DAMmod,5* and DAMmod,endemic is mapped in Figure 16.The difference between both models is remarkable.Especially, in parts of the deep Rhine Valley DAMmod,5*-values are up to 96% higher than DAMmod,endemic-values.This might be the result of low GSstat,Dec-values which indicate low chronic wind loading on trees and thus limited acclimative tree growth.However, in this area, GSLothar-values often exceeded 35 m/s causing catastrophic proportions of storm-damaged timber.Other parts of the study area, where DAMmod,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 DAMmod,5* and DAMmod,endemic was higher than 50%.
In contrast to the severely damaged parts of the study area, the northern part remained virtually undamaged because GSLothar ≤ 20 m/s.In some parts of this region (4%), DAMmod,5*-values

Mapping of Damage Risk
ROC-curve based evaluation of the OOB-samples of RC 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.

Conclusions
The presented statistical modeling approach allows for the analysis of storm damage probability and proportions of storm-damaged timber at the landscape scale at very high spatial resolution (50 m × 50 m).It is based on five-year aggregated booking records and enables the distinction between endemic and catastrophic storm damage proportions for the period 1979-2008.This means that the proposed methodology opens up the possibility to embed damage caused by exceptional storms like Wiebke and Lothar into the regional chronic damage pattern.In the context of empirical-statistical storm damage modeling this is an important achievement, because consideration of single storm events might bias the assessment of storm damage predictor importance since every storm event is unique concerning intensity, spatial extent and duration [23].Including high-resolution statistical gust speed fields [27] into storm damage modeling process clearly improves model accuracy in comparison to previous studies when only lower resolution gust speed fields were available [17,19].The results obtained for the probability and proportions of endemically storm-damaged timber can be regarded as estimates of endemic storm damage risk.
Given that predictor variables similar to the predictor variables that have been used in this study are available, the methodology can easily be transferred to other areas.An important task for the future will be the inclusion of convective, localized storm events which mainly occur during summertime in the study area [58][59][60].
In combination with knowledge of local experts, the modeling approach can then be used to identify areas prone to storm damage and to initiate the adaption of silvicultural management

Conclusions
The presented statistical modeling approach allows for the analysis of storm damage probability and proportions of storm-damaged timber at the landscape scale at very high spatial resolution (50 m ˆ50 m).It is based on five-year aggregated booking records and enables the distinction between endemic and catastrophic storm damage proportions for the period 1979-2008.This means that the proposed methodology opens up the possibility to embed damage caused by exceptional storms like Wiebke and Lothar into the regional chronic damage pattern.In the context of empirical-statistical storm damage modeling this is an important achievement, because consideration of single storm events might bias the assessment of storm damage predictor importance since every storm event is unique concerning intensity, spatial extent and duration [23].Including high-resolution statistical gust speed fields [27] into storm damage modeling process clearly improves model accuracy in comparison to previous studies when only lower resolution gust speed fields were available [17,19].The results obtained for the probability and proportions of endemically storm-damaged timber can be regarded as estimates of endemic storm damage risk.
Given that predictor variables similar to the predictor variables that have been used in this study are available, the methodology can easily be transferred to other areas.An important task for the future will be the inclusion of convective, localized storm events which mainly occur during summertime in the study area [58][59][60].
In combination with knowledge of local experts, the modeling approach can then be used to identify areas prone to storm damage and to initiate the adaption of silvicultural management regimes to make forests more windfirm in high and very high storm damage risk areas.Based on our findings an effective measure could be the conversion of coniferous forests to either broad-leaved or mixed forests.

Figure 1 .
Figure 1.Extent of the study area Baden-Wuerttemberg in the southwest of Germany (red polygon).

Figure 1 .
Figure 1.Extent of the study area Baden-Wuerttemberg in the southwest of Germany (red polygon).

Figure 2 .
Figure 2. Map of proportions of storm-damaged timber in the period 1979-2008 (DAMemp,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 2 .
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 2 .
Figure 2. Map of proportions of storm-damaged timber in the period 1979-2008 (DAMemp,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 .
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.

Figure 4 .
Figure 4. Map of statistical gust speed of December for a return period of five years (GSstat,Dec) covering the forest area.

Figure 4 .
Figure 4. Map of statistical gust speed of December for a return period of five years (GS stat,Dec ) covering the forest area.

Figure 5 .
Figure 5. Combinations of severity and empirical probability of endemic storm damage events (PCemp,endemic) used to classify empirical endemic storm damage risk (RCemp,endemic).

Figure 5 .
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 ).

Figure 6 .
Figure 6.(a) Proportion of forest area associated with empirical storm damage probability class 1 (PCemp,1) and (b) proportion of forest area associated with empirical storm damage probability class 7 (PCemp,7) as a function of statistical gust speed of December for a return period of five years (GSstat,Dec).The red dashed line is the best-fit curve; the black dashed lines indicate the 95% regression parameter confidence intervals.

Figure 6 .
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.

Figure 7 .
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.

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

Figure 7 .
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.

Figure 7 .
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.

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

Figure 8 .
Figure 8. Predictor Importance (PI) of random forests model output for modeled endemic storm damage risk.
with PCOOB,2-PCOOB,7 vary between 0.74 and 0.81.PCOOB,2-PCOOB,7 define more precisely the probability of damage occurrence in P30yr.The more precise division of PCmod,j was enabled by the inclusion of highly-resolved gust speed fields into the RF-model building process.

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

Figure 10 .
Figure 10.Two examples of (a,d) PCemp; (b,e) PCmod for the state forest; (c,f) PCmod for all types of forest ownership in the presented map extract.

Figure 9 .
Figure 9. Receiver operating curves for modeled classified storm damage probability and the associated area under curve (AUC) values.
with PCOOB,2-PCOOB,7 vary between 0.74 and 0.81.PCOOB,2-PCOOB,7 define more precisely the probability of damage occurrence in P30yr.The more precise division of PCmod,j was enabled by the inclusion of highly-resolved gust speed fields into the RF-model building process.

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

Figure 10 .
Figure 10.Two examples of (a,d) PCemp; (b,e) PCmod for the state forest; (c,f) PCmod for all types of forest ownership in the presented map extract.

Figure 10 .
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.

Figure 11 .
Figure 11.Out-of-bag samples of averaged probability class of modeled classified storm damage probability (PCOOB,mean) as a function of statistical gust speed of December for a return period of five years (GSstat,Dec).

Figure 11 .
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 ).

Figure 13 .
Figure 13.Map extract showing (a-c) DAMemp,30yr, DAMmod,30yr, GSstat,Dec for state forests; (d-f) FOR, DAMmod,30yr and GSstat,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.

Figure 13 .
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.

Figure 14 .
Figure 14.Boxplot of DAM OOB,3˚a s a function of GS Wiebke (a); DAM OOB,5˚a s 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).

Figure 15 .
Figure 15.Map of modeled proportions of endemically storm-damaged timber (DAM mod,endemic ).The legend values indicate highest class values.

Figure 16 .
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 (DAMmod,5*) and modeled proportions of endemically storm-damaged timber DAMmod,endemic.The legend values indicate highest class values.

Figure 16 .
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.

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.

Table 3 .
Predictor importance (PI) of random forests model outputs for proportions of storm damaged timber (DAMmod) Top three important predictor variables are marked bold.

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.