Mechanistic and statistical approaches to predicting wind damage to individual maritime pine (Pinus pinaster Ait.

Transcription

1 Mechanistic and statistical approaches to predicting wind damage to individual maritime pine (Pinus pinaster Ait.) trees in forests Journal: Canadian Journal of Forest Research Manuscript ID cjfr r1 Manuscript Type: Article Date Submitted by the Author: 01-Sep-2015 Complete List of Authors: Kamimura, Kana; Shinshu University, Institute of Mountain Science (IMS) Gardiner, Barry; INRA, UMR 1391 ISPA Dupont, Sylvain; INRA, UMR 1391 ISPA Guyon, Dominique; INRA, UMR 1391 ISPA Meredieu, Celine; INRA, UMR 1202 BIOGECO Keyword: Tree wind damage, GALES, Logistic regression, Airflow models, Storms

2 Page 1 of 50 Canadian Journal of Forest Research 1 2 (1) Title: Mechanistic and statistical approaches to predicting wind damage to individual maritime pine (Pinus pinaster Ait.) trees in forests (2) Authors: Kana Kamimura a,b 1 Barry Gardiner a,b Sylvain Dupont a,b Dominique Guyon a,b Céline Meredieu c,d (3) Affiliation and address: a INRA UMR 1391 ISPA, F Villenave d Ornon, France 12 b Bordeaux Sciences Agro, UMR 1391 ISPA, F Gradignan, France c INRA, UMR 1202 BIOGECO, 69 route d Arcachon, F Cestas cedex France d Univ. Bordeaux, BIOGECO, UMR 1202, F Pessac, France address Kana Kamimura (kamimura@shinshu-u.ac.jp), Barry Gardiner (barry.gardiner@bordeaux.inra.fr), Sylvain Dupont (sylvain.dupont@bordeaux.inra.fr), Dominique Guyon (dominique.guyon@bordeaux.inra. Céline Meredieu (celine.meredieu@pierroton.inra.fr) (4) Corresponding author Name: Kana Kamimura Address: Institute of Mountain Science, Shinshu University, 8304 Minamiminowa, Kamiina, Nagano , Japan Telephone: +81 (0) , Fax: +81 (0) , kamimura@shinshu-u.ac.jp 1 Current affiliation and address: Institute of Mountain Science, Shinshu University, 8304 Minamiminowa, Kamiina, Nagano , Japan, kamimura@shinshu-u.ac.jp 1

3 Page 2 of Abstract Maritime pine (Pinus pinaster Ait.) forests in the Aquitaine region, south-west France, suffered catastrophic damage from Storms Martin (1999) and Klaus (2009), and more damage is expected in the future due to forest structural change and climate change. Thus, developing risk assessment methods is one of the keys to finding forest management strategies to reduce future damage. In this paper we evaluated two approaches to calculating wind damage risk to individual trees using data from different damage data sets from two storm events. Airflow models were coupled either with a mechanistic model (GALES) or a bias-reduced logistic regression model, in order to discriminate between damaged and undamaged trees. The mechanistic approach was found to successfully discriminate the trees for different storms, but only in locations with soil conditions similar to where the model parameters were obtained from previous field experiments. The sta- 38 tistical approach successfully discriminated the trees only when applied to similar data as that used for creating the models, but it did not work at an acceptable level for other data sets. One variable, decade of stand establishment, was a significant variable in all statistical models, suggesting that site preparation and tree establishment could be a key factor related to wind damage in this region. 43 Keyword: Tree wind damage, GALES, Logistic regression, Airflow models 2

4 Page 3 of 50 Canadian Journal of Forest Research 44 1 Introduction Strong winds during storms can cause catastrophic damage to forests. In the last two decades, two storm events caused substantial damage to maritime pine (Pinus pinaster Ait.) planted forests in the Aquitaine region, south-west France (specifically in the Landes de Gascogne and Dunes atlantiques areas, Fig. 1). Storm Martin, on 27 December 1999, resulted in approxi- Fig. 1 mately 26 million m 3 of timber loss, which was equivalent to the general harvested volume for 3.5 years in maritime pine forests in south-west France (Cucchi et al., 2004). Ten years later, Storm Klaus on 24 January 2009 damaged approximately 37 million m 3 of maritime pine trees further south in the region (Colin et al., 2010). This led to losses of approximately e1,800 million in the forestry sector, which was almost 60 % of total economic losses in France that year (Commission des affaires économiques, 2009). These storms are predicted by some re- 55 searchers to become more intense although less frequent in the future (e.g. Marcos et al., 2011; Feser et al., 2015), and further catastrophic damage in these maritime pine forests is likely to occur. It is thus important to understand the direct causes leading to damage occurrence and to develop methodologies to assess and predict the risk of damage in order to sustainably manage the forests. There are several key factors associated with wind damage based on previous studies. The main biotic factors are tree dimensions, tree species, absence/presence of leaves, and tree acclimation to the new environment, and the main abiotic factors are soil type, terrain conditions, and wind speed (e.g. Gardiner and Quine, 2000; Mitchell, 2013). For instance, wind damage has been observed to increase with increasing tree height (e.g. Albrecht et al., 2012b; Kamimura et al., 2008). The terrain conditions have an important role in the development of root anchorage (Nicoll et al., 2005), and also trees are more likely to have stronger anchorage in areas receiving persistently higher wind exposure (Nicoll et al., 2008). Although abiotic factors cannot be changed to lower the risk of wind damage, changing key biotic factors through forest management actions such as thinning can contribute to mitigating wind damage occurrence. Thinning is one of the main forest management actions providing extra or higher net income 3

5 Page 4 of to forest owners by producing timber before the final cut and more valuable timber at the final harvest (e.g. Dorning et al., 2015; Helmes and Stockbridge, 2011). On the other hand, trees are often damaged by strong winds within a few years after thinning due to increased aerodynamic roughness above the canopy leading to higher levels of turbulence, and through the creation of small gaps increased wind penetration between trees (e.g. Cremer et al., 1982; Mitchell, 2013). The gaps created following thinning might also act as a trigger point for damage propagation 77 during a storm (Dupont et al., 2015). Therefore, selecting the most at risk trees for early 78 removal is one of the key ways to reduce wind damage risk. However, currently available approaches to predict wind damage risk at the single tree level include uncertainty on whether the models represent common storm damage phenomena and can be generalized. There are two modelling approaches commonly used for wind damage studies; mechanistic and statistical. For the mechanistic approach, a hybrid mechanistic/empirical wind risk assess- ment model GALES (Gardiner et al., 2008) has been used to calculate the critical wind speed (CWS) for the start of stand level damage (e.g. Byrne and Mitchell, 2013; Achim et al., 2005). The advantage of the mechanistic approach is that it is applicable to different forest environments due to the inclusion of the mechanical properties of individual tree species and rooting strength for different soil types. Prior studies confirmed the effectiveness of using GALES for calculating the CWS at the stand level for a range of stand types (e.g. Blennow and Sallnas, 2004; Byrne and Mitchell, 2013; Hale et al., 2015; Kamimura et al., 2008; Ruel et al., 2000). On the other hand, it is not straightforward to include new factors (findings) into GALES without understanding the influence of each component and factor because it is an integrated model of the behaviour of trees, forest, and the wind. Recently the model has been modified to calculate the CWS for individual trees by including additional factors dealing with tree competition from Hale et al. (2012) and Seidl et al. (2014). But the new version of GALES has not been fully validated against data from observed damage to trees under a range of conditions such as different tree species and storm events. For the statistical approach, logistic regression models are often used in wind damage studies 4

6 Page 5 of 50 Canadian Journal of Forest Research to find the probability of damage and the risk factors. In particular logistic regression models can directly identify which factors are associated with wind damage occurrence and it is more straightforward to include new variables in the models than with the mechanistic approach. For example, Albrecht et al. (2012a) introduced a generalized linear mixed model for a range of environmental conditions and storm events in German forests and found tree species and stand height as the most important factors linked to wind damage occurrence at the stand level. However, there is still uncertainty whether such statistical models provide generalized information and estimation on wind damage or only locally specific information because statistical analysis ignores the actual damage mechanism in the analysis process (Gardiner and Quine, 2000). Hale et al. (2015) found no indication of the advantages of a particular approach for understanding and predicting wind damage in forests by comparing mechanistic and statistical approaches at the stand level. In fact these approaches appear to be very complementary probably due to the mechanistic approach being causal and the statistical approach being incidental. It is therefore beneficial to identify advantages and limitations of both approaches in order to develop wind damage risk assessment tools at the single tree level. In this paper, we focused on evaluating the mechanistic and statistical approaches in order to find suitable methodologies for wind risk assessment at the single tree level. Our objectives were 1) downscaling a mechanistic model and creating statistical models at the single tree level using a detailed and accurate data set, 2) testing the two approaches in order to find the most appropriate models, 3) applying the two approaches using a larger data of damaged trees from a different storm event, 4) evaluating and comparing the performance of the two models and the benefits of the different approaches, and 5) discussing the transferability of the models and the potential of using the different approaches for multiple storm events. Using the two approaches also helps to both understand the general principles of damage occurrence and develop comprehensive assessment approaches for wind damage to maritime pine trees in the Aquitaine region. 5

7 Page 6 of Material and methods Study site and data Fig. 1 shows the location of the study area from which we used data from two field surveys with different original objectives. The first data set was a field survey of 29 permanent plots (400 m 2 /plot) in the Nezer Forest located in the Aquitaine region ( N, W; Fig. 1-(a)). Soil type was wet podzol of more than 55 cm depth and with a single soil texture type of sand determined from the classification of the national inventory survey in French forests (Bruno and Bartoli, 2001; Bruno, 2008) and a technical report (GISsol, 2011). In the field survey, tree size was measured in 1998, and damaged trees were determined after the storm in The data consisted of tree height, stem diameter at breast height (dbh), tree location, and damage status for almost all trees. This data was also subdivided into two groups by area; Nezer I and Nezer II (see also Fig. 1-(a)), in order to first create and adjust models and secondly to test them. This is explained in the next section. The second data set was from field surveys of the national forest inventory in France (Inventaire Forestier National; NFI) in the Landes de Gascogne region (Fig. 1-(b)). The survey plots are located on a 1 km x 1 km grid in forests based on a 10-year cycle of inventory plot survey, and there are different plot sizes at each location for different diameter classes (Inventaire Forestier National, 2005, 2011). We used a total of 235 plots data collected from 2007 to 2008, with more than half of the trees in each plot being maritime pine. After Storm Klaus in 2009, damaged trees in the NFI plots were identified by an additional field survey. Basic statistics of the data sets are presented in Table 1. Table 1 A number of different pieces of spatial information were included for each plot in the two data sets. The distance from the windward stand edge (the westerly direction for both storms) was defined as the boundary line between forests and unforested area including roads (> 3 m width). While the distance was very precise in Nezer Forest, the distance had to be estimated using the coarse plot location in the NFI data in which the exact plot positions were not 6

8 Page 7 of 50 Canadian Journal of Forest Research 150 publically available. The stem spacing in both data sets was the average value calculated from 151 the number of stems in the plot. Gap size, defined as the distance in a westerly direction between the forest in which the plot was located and the next forest block, was also calculated. Furthermore, the NFI plots were identified either within the Landes or Dunes based on the designation given by the Inventaire Forestier National (2009). The Nezer Forest is located in the Landes area. All spatial information was computed using ArcGIS 10.1 (ESRI. Co., USA) Analysis procedure The analysis consisted of three parts; preparation (modelling/adapting), testing, and applica- tion (Fig. 2). There were three data sets: Nezer I, Nezer II, and the NFI data. First,the Nezer Fig. 2 I data was used for calculating detailed wind speeds using the Advanced Regional Prediction System (ARPS) (Dupont and Brunet, 2008), for comparison against the CWS s of GALES for individual trees, and for use in the logistic regression models. In particular, ARPS was used to obtain wind speeds at two different heights for creating/adjusting the models. The area of Nezer I was chosen in order to reduce the simulation time taken by ARPS while including a sufficient number of plots to develop the models. Second, the GALES settings and logistic regression models were tested using the rest of the Nezer data (Nezer II). For Nezer II, another wind simulation was carried out at a lower spatial resolution with the Wind Atlas Analysis and Application Program (WAsP) (Mortensen et al., 2007). We used this model to reduce the computation time because Nezer II had a much larger area than Nezer I (explained in the next section). Third, the selected logistic regression models and the GALES model settings were applied to the data set from the NFI data in the Aquitaine region to examine how the models performed with the different quantity and quality of data from the NFI dataset and for a different storm. Additional conditions such as soil type, rooting depth, and the storm duration, which were excluded in the Nezer data, were also examined by subsetting the data when no discrimination was found in the NFI data. The criteria used to build the subset data are presented in Table 2. All models used in this analysis and their usage are explained in the 7

9 Page 8 of following sections. Table Estimation of wind speeds Wind data There are only 14 meteorological stations in the whole region of the study. For that reason, we used the numerically computed wind speeds above the forest canopy from the Système d Analyse Fournissant des Renseignements Atmosphériques à la Neige (SAFRAN) in addition to the available data at a meteorological station at Cap Ferret (located at the Atlantic coast; N, 1 15 W). SAFRAN is a numerical model of Météo France for estimating meteorological conditions away from meteorological stations using statistical analysis in addition to the observed climate data at the Météo France forecast network, and terrain information (i.e. 186 elevation and slope aspect). It provides hourly mean wind speed at 10 m height as well as other atmospheric parameters such as air temperature, humidity, and precipitation (Durand et al., 2009). The estimation has an 8 km resolution and is available across France (Vidal et al., 2010). In this analysis, we used wind speeds on December 1999 (Storm Martin) and 24 January 2009 (Storm Klaus) extracted from the outputs of SAFRAN. These wind speeds were then used as inputs to the detailed airflow models to estimate wind speeds (EWS) at specific locations in the forests. In addition, the maximum hourly wind speed and duration of winds (> 10 m/s) during the storm periods were calculated for each grid cell. 10 m/s was used as the base wind speed to calculate the duration because it is the lowest maximum wind speed from all SAFRAN grid cells in the Aquitaine region (Fig. 1-(b)) during Storm Klaus ARPS (for the Nezer I data) ARPS was originally developed at the Center for Analysis and Prediction of Storms at the University of Oklahoma for predicting the behaviour of storms based on a three-dimensional numerical simulation (Xue et al., 2000, 2001). Subsequently, ARPS was modified by Dupont and Brunet (2008) in order to calculate turbulence within and above forest canopies using 8

10 Page 9 of 50 Canadian Journal of Forest Research a large-eddy simulation method, and this version of the model has been validated for use in maritime pine forests (Dupont et al., 2011, 2012). Using the modified version of ARPS, wind speeds in the Nezer I area (approximately 2 km x 2 km) were estimated for westerly winds (main wind direction during Storm Martin). The forest information for the model was the maximum stand height and mean stem density of each stand. The maximum stand height was calculated as the mean height of the 20 % tallest trees in a plot. The horizontal resolution was 6 m and vertical resolution was 2 m. The maximum hourly wind speed at 10 m height for the whole Nezer Forest was m/s determined from SAFRAN. Thus, all outputs from ARPS (velocities in each three-dimensional grid cell) were linearly adjusted in order to ensure a maximum wind speed of m/s at 10 m height. Subsequently, the estimated wind speeds at the maximum stand height and 29 m height (2 m higher than the maximum tree height in the Nezer I data for the year 1999) were extracted to use with the GALES and logistic regression models WAsP (for the Nezer II and NFI data) WAsP, a computer simulation of a linear airflow model, was developed by the Wind Energy and Atmospheric Physics Department, Risø National Laboratory, Denmark (Mortensen et al., 2007). WAsP can estimate wind speeds over a large area in a relatively short time period using the surface roughness on low hill linear approximation developed by Jackson and Hunt (1975). Wind speeds were simulated at 500 m x 500 m horizontal resolution at 29 m height for Storm Martin and 29 and 40 m height for Storm Klaus. 40 m was the approximate maximum tree height of maritime pine in the Landes and Dunes areas determined from the NFI data. A land-use map (0 to 300 m elevation range and 50 m contour interval) plus an aerodynamic roughness map (0.003 m for water, 0.01 m for unforested-areas over land, and 1.0 m for forest) was prepared in advance for the WAsP simulation. In addition, because WAsP requires wind speeds from a known location as input, observed data at the meteorological station at Cap Ferret and extracted wind data from SAFRAN near Captieux (located at the center of the 9

11 Page 10 of maritime pine forests; N, 0 15 W) were used to model wind speeds during Storms Martin and Klaus respectively Wind damage assessment models Two models, GALES and logistic regression, were used to find trees with a high probability of damage. The input data and parameters for GALES and independent variables for the logistic regression models are presented in Table 3. Table Mechanistic model: GALES The original version of GALES only calculated the stand average CWS s for uprooting and stem breakage (Gardiner et al., 2000, 2008; Hale et al., 2015). This is based on the roughness method, which uses the drag and drag partitioning on rough surfaces to calculate the mean loading on trees (Raupach, 1992; Hale et al., 2015). For this analysis, GALES had to be adapted to calculate the CWS s for individual trees. Hale et al. (2012) found a significant linear relationship between the maximum hourly turning moment (Nm) at the stem base of individual trees, M max, and the squared hourly mean wind speed ((m/s) 2 ) at canopy top, referred to as u h 2, multiplied by a turning moment coefficient, TMC, for each tree (defined as the TMC method in this study). M max = T MC u h 2 = 111.7dbh 2 h u h 2 (1) Subsequently, Seidl et al. (2014) improved the TMC method using an additional factor, a competition index CI, which is described as the relationship between a subject tree and neighbouring trees (distance-dependent competition) in order to estimate the allocation of growth resources such as water and light generally limited by the size and number of neighbours (Avery and Burkhart, 2002). In this paper, we employed the idea of Seidl et al. (2014) but used instead a distance-independent competition index from Biging and Dobbertin (1995) because distance-dependent competition cannot be calculated without exact tree positions and distance- 10

12 Page 11 of 50 Canadian Journal of Forest Research independent competition with TMC was also significant in the study of Hale et al. (2012). The TMC with the distance-independent competition index is referred to as the TMCci method in this paper. The maximum turning moment with TMCci, M max ci, was calculated from the original data used in Hale et al. (2012) as M max ci = T MCci u h 2 = (0.13CI dbh 2 h 0.617CI dbh 2 h) u h 2 (2) 254 and CI = Σba i y i (3) 255 where ba i (m 2 ) is the basal area of the ith neighbouring tree and y i = 1 when the dbh of the ith neighbouring tree is larger than that of the subject tree, otherwise y i = 0 (Biging and Dobbertin, 1995; Hale et al., 2012). All trees in a plot are treated as potentially neighbouring trees. The GALES parameters for maritime pine except Eq. (2) were found from the data of field experiments in the Landes de Gascogne region conducted by Cucchi et al. (2004) (see Table 2 in Cucchi et al. (2005) for averaged parameter values). The coefficients in Eq. (2) were obtained using the data in Hale et al. (2012). The GALES model can calculate the CWSs for trees located at any distance from the stand edge. For well acclimated trees, it is assumed that the CWS is the same at all distances 264 (Gardiner et al., 2000). For a newly created edge the CWS is adjusted depending on the change in wind loading from the edge to the interior of the stand (Gardiner et al., 1997). This calculation method is effective when we have management records such as harvesting and logging road construction. However, no management information was available in the NFI data for this study. For this reason, we assumed two conditions; 1) all maritime pine trees were assumed to be well acclimated to the wind environment, so the CWSs were not dependent on the distance from the edge and gap size (described as assumption A ), and 2) all trees were not acclimated to their local wind conditions (described as assumption N ). For assumption 11

13 Page 12 of N, the calculation of CWS placed the trees at a newly created edge with a large upwind gap (10 times mean stand height) in order to give the maximum wind exposure to the trees. These settings were applied to both the TMC and TMCci methods. Full descriptions of the model settings are presented in Table 4. Furthermore, CWS s for stem breakage and uprooting were Table 4 averaged in order to consider the average possibility of failure, since both types of damage were observed in the region after the storms. The maximum hourly wind speeds estimated using ARPS and WAsP were directly used 279 to compare the CWSs from the GALES model. GALES converts the wind loading due to the hourly wind speed to the extreme wind loading during the hour, which is related to wind damage occurrence. This conversion is based on a gust factor established from field observations and wind tunnel experiments (Gardiner et al., 1997; Hale et al., 2015) Statistical model: Logistic regression Logistic regression models were created using the Nezer I data with the input variables in Table 3 and there were interaction variables such as ratio of tree height to dbh, ratio of tree height to stand dominant height, and ratio of tree height to stem spacing. The data was unbalanced (i.e. only 11.5 % of trees were damaged out of the total). To avoid misclassification due to over-fitting, we used a bias-reduced maximum likelihood estimation method with a model 289 calibration. First, Firth s penalized logistic regression method (Firth, 1993) was applied to build a basic logistic regression model using all data from Nezer I. In addition, significant independent variables were selected under the backward method, which eliminates variables until reaching the best significant level. Next, it is necessary to find the coefficients least affected by the particular data balance because statistical models are strongly influenced by data from the largest data group when using an unbalanced data set (undamaged trees in this study). Therefore model coefficients were calibrated based on a linear shrinkage technique introduced by Steyerberg et al. (2001). This technique is useful for model fitting with unbalanced data and a part of data from the whole data set was used for creating the original model. More 12

14 Page 13 of 50 Canadian Journal of Forest Research specifically, 1) logits Lo = ln(p/(1 p)), where p was probability of damage, for all trees in the Nezer I data were calculated using the logistic regression model created by Firth s penalized method (determined as the original model), 2) 300 new models of logistic regression were created using the same coefficients as the original model but with subset data consisting of 70 % of the original trees selected by a bootstrapping random selection method (i.e. 70 % of the tree data was randomly selected from all the Nezer I data), 3) logits using the subset models, Ls, were calculated for each tree, 4) 300 linear slopes (ratio) between Lo and Ls were computed respectively, 5) a linear shrinkage factor was calculated by averaging the 300 linear slopes, 6) the coefficients of the original models were calibrated by multiplying by the shrinkage factor. The computation of the model was carried out using the statistical software R (R Core Team, 2013) and the package logistf (Heinze et al., 2014) Evaluating settings and models 310 The CWS from the GALES model does not take account of any uncertainty in the wind speed 311 causing damage to a tree (i.e. it calculates only exact values of wind speed) and logistic 312 regression models do not provide dichotomous outputs (predicted damaged/undamaged trees 313 in this study) but only gives probabilities. One method for estimating damage is to use a threshold (cutpoint) value. The cutpoint is varied to see how the model predictions change in order to evaluate their overall performance and to determine the optimum cutpoint to give the highest model accuracy (Hale et al., 2015). First, the CWS s from each GALES model setting were systematically altered by multiplying the CWS by a value between 0 and 200 % (defined as the multiplier ). Second, the adjusted CWSs were compared with the EWS s from ARPS or WAsP to discriminate between damaged and undamaged trees and multipliers giving the optimal accuracy were determined (Bennett et al., 2013). This method of systematically multiplying the CWS has been used by Hale et al. (2015), but in that paper it was used to test ForestGALES (GALES + WAsP and GALES + windiness score) at the stand level. For the logistic regression models, the cutpoints for the probability of damage were changed between 0 13

15 Page 14 of and 1 and each tree was classified as either damaged or undamaged. The comparison between estimated and observed damaged and undamaged maritime pine trees were then classified into four groups (see Fig. 4 in Bennett et al. (2013)): TP (true positive: correctly predicted damaged trees), FP (false positive: incorrectly predicted damaged trees), FN (false negative: incorrectly predicted undamaged trees), and TN (true negative: correctly predicted undamaged trees). Using the four groups, three rates were computed as T P R = T P T P + F N (4) T NR = T N T N + F P (5) F P R = 1 T NR (6) where TPR is the true positive rate, TNR is the true negative rate, and FPR is the false positive rate. Then receiver operating characteristics, ROC, and area under the ROC curves (AUC ) were used to test the model fit (effectiveness of discrimination) in terms of the imposed changes in the CWS and cutpoint. The ROC curve is obtained by plotting FPR against TPR, and generally the ROC shows a convex curve. For models to be regarded as classifying the tree data successfully into either damaged or undamaged groups, the AUC should be greater than 0.7 (Hosmer and Lemeshow, 2000). Thus, GALES settings and logistic regression models with AUC > 0.7 were regarded as having an acceptable discrimination level between damaged or undamaged trees. AUC in this study was calculated with the R package, AUC (Ballings and den Poel, 2014). If n denotes total number of data, the model accuracy = (T P + T N)/n and depends on the modified CWS values and the cutpoints. Optimal accuracy is found when T P R T NR (Hosmer and Lemeshow, 2000). 14

16 Page 15 of 50 Canadian Journal of Forest Research Results Modelling/Adapting and Testing (Nezer data) Mechanistic approach All results calculated at the maximum stand height did not show any acceptable discrimination, while the non-acclimated settings (TMC-N and TMCci-N) calculated at 29 m height success- fully discriminated between damaged and undamaged trees (i.e. AUC > 0.7) (Fig. 3). At both heights, AUCs of the model assuming acclimation were lower than those assuming no acclimation, which suggested that the trees in Nezer I had in general not acclimated to the wind. The best GALES settings (TMC-N and TMCci-N) were subsequently used for the Nezer Fig. 3 II data with the EWSs from WAsP. Table 5 presents a comparison of AUC s, multipliers of the CWSs at the optimal accuracy, and the optimal accuracy of the two settings in Nezer I and II. The AUC s for the calculation of Nezer II had an acceptable level (> 0.7); however, the optimal accuracies decreased compared with those from Nezer I. In addition, a multiplier of more than 1.0 indicated that the CWS s were always slightly underestimated (i.e. a calibration factor of was required for the highest optimal accuracy). Table Statistical approach Only one independent variable, Y (decade of establishment) was selected in the most significant logistic regression model using the backward method. However, since it is obvious that the local wind speed is one of the important triggers of wind damage occurrence, logistic regression models were created always including the wind variable (wind speed at 29m height). Significant independent variables were chosen by gradually removing variables except the wind variable until the model significance exceeded a p-value = As a result, seven significant logistic regression models were found containing eight independent variables in total (Table 6). The Table 6 AUC s of these seven models decreased in the Nezer II data (Fig. 4), but four models, LRs 1, 2, 6, and 7 had an AUC value of more than 0.7. Fig. 4 15

17 Page 16 of Application (NFI data) Mechanistic approach Both model simulations assuming no acclimation (TMC-N and TMCci-N) with three different calculations of the EWS s (different heights and input meteorological stations) did not satisfy the acceptable level (AUC > 0.7) (Fig. 5-(1)). Using the settings with the EWS s at 29 m height calculated using the Cap Ferret wind data as input to WAsP (these gave the highest discrimination), AUC s were also calculated for the two environmental areas, Landes and Dunes (Fig. 5-(2)). AUC values for Landes were higher than those of the Dunes area for both settings. Also the ROC curves of Landes looked more stable with change of TPR and FPR while those of Dunes sometimes rapidly changed depending on the cutpoints. Subsequently, the AUC s were again calculated using subsetted data (see Table 2) in order to examine whether the specific 378 environmental condition in the NFI data might have reduced the calculation accuracy. Only for subset data L-10, consisting of hydromorphic podzol, deep soil texture, and trees less than 29 m height, did the mechanistic approach successfully discriminate between damaged and undamaged trees with an AUC of (Table 7). A soil type of hydromorphic podzol was always required to improve the AUC s. Table Statistical approach All four logistic regression models (1, 2, 6 and 7), which showed the highest acceptable discrimination for the Nezer data, did not show any acceptable discrimination for the NFI data (AUC < 0.51). Again, AUC s were calculated for the two different environmental areas (Landes and Dunes). For the Dunes data LR7 showed the highest AUC (0.531) and the highest AUC in Landes was found with LR1 (0.586), but both did not reach an acceptable level. Therefore, AUC s were calculated for the subset data (see also Table 2) to find out whether additional variables would be required in the logistic regression models for the region. AUC s of LR1 were always higher than the other three models (LRs 2, 6, and 7) and LR1 had the highest AUC s in all of the subset data. Fig. 6 presents the ROCs of the LR1 model (wind speed + decade 16

18 Page 17 of 50 Canadian Journal of Forest Research of establishment) with the Landes and subset data. All of these subset data consisted of the Fig. 6 same soil type, hydromorphic podzol, which was the same soil type as in the Nezer Forest. Thus, although LR1 was not at acceptable level, soil type could be one of the important vari- ables required to improve the discrimination of damage in the region. In addition, since some characteristics of the Nezer Forest were likely to be unique (e.g. wind duration and soil type), new logistic regression models were created so as to confirm whether additional conditions (dif- ferent from the conditions of Nezer) would affect the model performance (Table 8). For these Table 8 models, one categorical parameter, soil depth (available information in the NFI data), was included in order to describe the detailed soil conditions. Three new models; LR all, LR Landes, and LR Landes Nezer, had more than 0.7 for AUC and approximately 70 % of optimal accuracy (Table 8). LR all and LR Landes Nezer indicated that storm duration and soil depth < 54 cm in creased the probability of damage. Compared with the models from Nezer I (See Table 6), the same trends (negative or positive) of coefficients were found only for Y 3 (established between and 1970) and Y 4 (established between 1970 and 1980). The probability of damage on the trees established between 1960 and 1980 increased compared with the baseline period (Y 1, established between 1940 and 1950) Discussion 410 This paper presents two approaches for estimating wind damage at the tree level with a special 411 focus on coupling airflow models with either a mechanistic or statistical model. First we discussed the uncertainty of data in the study and second the performance of each modelling approach. One of the difficulties for wind damage studies is to obtain forest (tree) and wind climate data, which are satisfactory in terms of quality and quantity for the specific analysis. In particular, wind climate data over forests can hardly ever be obtained because of the limited number of meteorological stations. In this study, we used observed wind speeds at a meteorological 17

19 Page 18 of station and computed wind speeds from SAFRAN as input wind data for the airflow models, ARPS and WAsP. ARPS is a three-dimensional grid base simulation model allowing calculation of horizontal and vertical wind velocities, and has been well evaluated by Dupont and Brunet (2008). For this reason, we used ARPS with confidence of representing realistic wind conditions over the forest canopy in the Nezer Forest, although it is not straightforward to use this model for large areas. On the other hand, WAsP has been shown to have a lowered accuracy when used in forested area by Suárez et al. (1999), who compared several airflow models in complex forested terrain. They demonstrated that WAsP had the largest variation amongst the models with both over- and under-predictions of up to 20 %. Although WAsP has benefits for estimating wind speeds over a large area, it is important to take account uncertainty in the modelled outputs. SAFRAN, which provides the input wind data to ARPS and WAsP, generally estimates wind speeds 10 % lower than actual wind speeds (Quintana-Seguí et al., 2008). As a result, the wind speeds used in this study will have a bias leading to decreased accuracy of the results. Therefore, especially for the mechanistic approach, it is necessary to consider this uncertainty for comparison between the critical and estimated wind speeds. 433 The mechanistic approach, i.e. GALES with ARPS or WAsP, was able to discriminate between damaged and undamaged trees in the Nezer Forest only under specific conditions. In Nezer I (GALES + ARPS), better discrimination was found using the estimated wind speed at 29 m height (approximately 10 % above the maximum tree height in the Nezer Forest) than at maximum stand height. It suggests that choosing the correct height above the canopy is very important for comparing the critical and estimated wind speeds because of two possible reasons. It is obvious that wind gust speeds above canopy surface lead to damage to trees (e.g. Usbeck et al., 2012) and such wind (airflow) varies spatially over the canopy during a storm due to the quasi-stochastic nature of turbulence in strongly sheared flows (Dupont et al., 2011). Thus using a large-eddy simulation model like ARPS is beneficial for describing the detailed 443 wind characteristics over a canopy. In contrast, the critical wind speeds from GALES are 444 averaged wind speeds (hourly mean wind speed) which vary according to the stand conditions 18

20 Page 19 of 50 Canadian Journal of Forest Research and tree locations relative to the upwind edge and gap size. Therefore, wind speeds from the GALES model are temporal (one hour) and spatial ( one tree height) averages. This might lead to disagreement between the critical wind speeds from GALES and estimated wind speeds 448 from ARPS close to the canopy top (e.g. at the maximum stand height) where the actual wind speed varies the most due to the local maxima in wind shear and the close presence of individual trees. On the other hand, wind speeds at 10 % above the maximum tree height 451 should be less affected by very local variations. This height was also effective in Nezer II, although the resolution of estimated wind speeds from WAsP was lower. From the results, it is necessary to find a suitable height in advance for a comparison between calculated critical wind speeds and estimated wind speeds in order to use the mechanistic approach. This requires that wind speeds for comparisons between critical and estimated wind speeds should not be too strongly influenced by very local canopy characteristics, but must in addition represent the winds affecting individual trees. This height should be neither very close to the canopy top nor too far from the canopy and 10 % above the maximum stand height appears to be a good compromise based on this study. Including assumptions of tree acclimation to their wind environment is another key to improve the classification of damaged and undamaged trees in the mechanistic approach. In Nezer I, TMC-N and TMCci-N discriminated the trees whereas TMC-A and TMCci-A did not. TMC-N and TMCci-N also satisfactorily discriminated the trees in Nezer II. This could be due to GALES not correctly calculating the change in wind loading back from edges in these maritime pine forests in which wind penetrates a long distance from the edge (Dupont et al., 2012). Also in GALES the calculation is based on data from spruce forests with high leaf areas, deep crowns at the edge, and with very little penetration of wind into the edge of the stand (Gardiner, 1995; Irvine et al., 1998). Dupont et al. (2015) point out that current mechanistic models could have a bias to estimating wind damage due to ignoring the dynamics of tree motion and damage propagation caused by the wind during a storm (Byrne and Mitchell, 2013). In particular, when the sudden loss of trees occurs during a strong wind it creates 19

21 Page 20 of an effectively new edge. The downwind trees at the new gap then receive an increased wind loading without any time to acclimate to their new environment. It could potentially lead to further damage propagation especially to trees located close to the original damage (Dupont et al., 2015). Therefore, the non-acclimated setting in GALES might be better at capturing the condition of trees during a storm when there is damage propagation through the forest. Some of the logistic regression models created using the Nezer I data were able to discriminate the damaged and undamaged trees in Nezer II, but model behaviour changed between the two data sets (Fig. 4). The models containing a small number of variables rapidly changed the true positive rate for an increasing false positive rate. It meant that the model accuracy depended highly on which cutpoint was chosen to classify damaged and undamaged trees. Moreover, a particular variable, decade of establishment, was always significantly selected in the models. This variable integrates several factors such as tree age, tree height (older decades of establishment will on average have taller trees), and different establishment methods applied in the Landes de Gascogne and Dunes atlantiques areas. A lot of previous research has shown that increasing stand (tree) height and age are important indicators to identify stands and trees liable to be damaged (e.g. Cucchi et al., 2005; Albrecht et al., 2012a; Hale et al., 2015). However, age was not a significant variable and tree height had a negative coefficient in the logistic regression models (i.e. smaller trees had higher probability of damage). This discrepancy of age and tree height does not provide an explanation of why the decade of establishment was a significant variable in Nezer Forest. Probably it is necessary to consider the variable not only along with tree characteristics, but also with detailed descriptions and records of management in the Nezer Forest (e.g. planting choice, ground preparation, thinning, etc.). Using the whole NFI data set, both the mechanistic and statistical approaches did not discriminate between damaged and undamaged trees. This may be due to the uncertainty and variation of the NFI data plots including the number of trees, plot size which depends on tree size, differences in management, and differences in tree species composition. In addition, tree growth and root systems are variable in different parts of the forest and in particular there 20

22 Page 21 of 50 Canadian Journal of Forest Research are big differences between the Landes and the Dunes areas (e.g. Lemoine and Decourt, 1969). More importantly, the models probably do not contain enough variables to cover the range of environmental growing conditions in the NFI data. In the mechanistic approach, some of the AUC s improved when using only the data from the Landes area. This is probably because the maritime pine parameters in GALES were obtained from only the Landes area (Cucchi et al., 2004). In addition, the AUC s of the TMC method were better than the TMCci (including the distance-independent competition index). TMC is directly influenced by tree size only (dbh 2 h), whereas TMCci is influenced by the average forest condition due to the inclusion of a distanceindependent competition index based on a unit of one ha. In other words, competition index may be more effective for stands of high complexity as examined by Seidl et al. (2014), who found better agreement of TMC with a distance-dependent competition index using stand data including three different tree species. Hale et al. (2012) also found that the turning moment coefficient was related to a number of tree competition indices for some specific forest locations, 512 but no clear relationship was found in other forests. Competition index could therefore be beneficial to improve wind damage estimation for specific forest conditions. In addition, the critical wind speeds of damaged trees growing on hydromorphic podzol (saturated for long periods) with non-wind acclimated settings were in better agreement with the estimated wind speeds during Storm Klaus than other trees in the NFI data. Maritime pine trees on wet soil have less anchorage (Danjon et al., 2005), so we assumed that they might be less fully acclimated (or very slow to acclimate). Another variable leading to better discrimination was to exclude taller trees (i.e. 29m). It raises the question whether the relationship between the maximum turning moment and stem weight obtained from Cucchi et al. (2004) also holds for taller trees. In their experiments, the mean tree height was less than 25 m, so it is uncertain if we should use the same parameter values in GALES for taller trees. However, it is difficult to confirm this possible difference in parameters based on tree height from this study because only 4 % of the total number of trees exceeded 29 m in height. Thus, it will be necessary to test the parameters of maritime pine trees over a wider range of tree 21

23 Page 22 of heights. The original logistic regression models could successfully discriminate between damaged and undamaged trees in the Nezer Forest (Fig. 4) and worked better than the mechanistic method. This is the same results found by Hale et al. (2015). However, when applied to the NFI data they did not show acceptable discrimination. Additionally, the models with the subset data did not present much improvement in the discrimination (see Fig. 6). These results indicate the limitations of these statistical approaches if they are to be used to predict damage caused by future storms. Steyerberg et al. (2004) pointed out that there are more difficulties of recalibrating logistic regression models than recreating a new model mainly because of the change of intercept. Gude et al. (2009) also suggested that several techniques for validating logistic regression models in order to apply them to other events are effective when internal model validation and shrinkage techniques are used, but this modification only works for the same sample population. Thus, it would be difficult to directly apply the original models developed using the Nezer data to the NFI data. Nevertheless, the statistical approach in this study suggested important variables associated 541 with wind damage occurrence. First, the AUC s were always better when the subset data 542 included only the soil type hydromorphic podzol (same soil type as in Nezer Forest). This soil type also improved the discrimination in the mechanistic analysis. Soil type together with soil moisture is associated with root-soil anchorage (Nicoll and Ray, 1996; Yang et al., 2014), so a similar stability against wind is observed on the same soil type. Second, different trends were observed in the coefficients between the original Nezer model and the new models (LR all, LR Landes, LR Landes Nezer ) except for the establishment decades from 1960 to In addition, higher values of coefficients were found after 1980 and lower before 1960 in the NFI data. These characteristics of establishment decades could not be explained only by tree height and age. In particular the coefficients of tree height showed a contradiction between the models created using the Nezer I data and the models created using the NFI data, although the establishment decade (tree age) and tree height are generally related. In other words, tree height could be an 22