draft · 2021. 4. 5. · draft 26 abstract 27 maritime pine (pinus pinaster ait.) forests in the...

Draft

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-2015-0237.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

https://mc06.manuscriptcentral.com/cjfr-pubs

Canadian Journal of Forest Research

Draft

(1) Title: Mechanistic and statistical approaches to predicting wind damage to individual1

maritime pine (Pinus pinaster Ait.) trees in forests2

3

(2) Authors:4

Kana Kamimuraa,b 15

Barry Gardinera,b6

Sylvain Duponta,b7

Dominique Guyona,b8

Celine Meredieuc,d9

(3) Affiliation and address:10

a INRA UMR 1391 ISPA, F-33140 Villenave d’Ornon, France11

b Bordeaux Sciences Agro, UMR 1391 ISPA, F-33170 Gradignan, France12

c INRA, UMR 1202 BIOGECO, 69 route d’Arcachon, F-33612 Cestas cedex France13

d Univ. Bordeaux, BIOGECO, UMR 1202, F-33615 Pessac, France14

15

Email address16

Kana Kamimura ([email protected]), Barry Gardiner ([email protected]),17

Sylvain Dupont ([email protected]), Dominique Guyon ([email protected]),18

Celine Meredieu ([email protected])19

20

(4) Corresponding author21

Name: Kana Kamimura22

Address: Institute of Mountain Science, Shinshu University, 8304 Minamiminowa, Kamiina,23

Nagano 399-4598, Japan24

Telephone: +81 (0)265 77 1511, Fax: +81 (0)265 77 1511, Email: [email protected]

1Current affiliation and address: Institute of Mountain Science, Shinshu University, 8304 Minamiminowa,Kamiina, Nagano 399-4598, Japan, [email protected]

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Abstract26

Maritime pine (Pinus pinaster Ait.) forests in the Aquitaine region, south-west France,27

suffered catastrophic damage from Storms Martin (1999) and Klaus (2009), and more28

damage is expected in the future due to forest structural change and climate change.29

Thus, developing risk assessment methods is one of the keys to finding forest manage-30

ment strategies to reduce future damage. In this paper we evaluated two approaches to31

calculating wind damage risk to individual trees using data from different damage data32

sets from two storm events. Airflow models were coupled either with a mechanistic model33

(GALES) or a bias-reduced logistic regression model, in order to discriminate between34

damaged and undamaged trees. The mechanistic approach was found to successfully dis-35

criminate the trees for different storms, but only in locations with soil conditions similar36

to where the model parameters were obtained from previous field experiments. The sta-37

tistical approach successfully discriminated the trees only when applied to similar data38

as that used for creating the models, but it did not work at an acceptable level for other39

data sets. One variable, decade of stand establishment, was a significant variable in all40

statistical models, suggesting that site preparation and tree establishment could be a key41

factor related to wind damage in this region.42

Keyword: Tree wind damage, GALES, Logistic regression, Airflow models43

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1 Introduction44

Strong winds during storms can cause catastrophic damage to forests. In the last two decades,45

two storm events caused substantial damage to maritime pine (Pinus pinaster Ait.) planted46

forests in the Aquitaine region, south-west France (specifically in the Landes de Gascogne and47

Dunes atlantiques areas, Fig. 1). Fig. 1Storm Martin, on 27 December 1999, resulted in approxi-48

mately 26 million m3 of timber loss, which was equivalent to the general harvested volume for49

3.5 years in maritime pine forests in south-west France (Cucchi et al., 2004). Ten years later,50

Storm Klaus on 24 January 2009 damaged approximately 37 million m3 of maritime pine trees51

further south in the region (Colin et al., 2010). This led to losses of approximately e1,80052

million in the forestry sector, which was almost 60 % of total economic losses in France that53

year (Commission des affaires economiques, 2009). These storms are predicted by some re-54

searchers to become more intense although less frequent in the future (e.g. Marcos et al., 2011;55

Feser et al., 2015), and further catastrophic damage in these maritime pine forests is likely56

to occur. It is thus important to understand the direct causes leading to damage occurrence57

and to develop methodologies to assess and predict the risk of damage in order to sustainably58

manage the forests.59

There are several key factors associated with wind damage based on previous studies. The60

main biotic factors are tree dimensions, tree species, absence/presence of leaves, and tree accli-61

mation to the new environment, and the main abiotic factors are soil type, terrain conditions,62

and wind speed (e.g. Gardiner and Quine, 2000; Mitchell, 2013). For instance, wind damage63

has been observed to increase with increasing tree height (e.g. Albrecht et al., 2012b; Kamimura64

et al., 2008). The terrain conditions have an important role in the development of root an-65

chorage (Nicoll et al., 2005), and also trees are more likely to have stronger anchorage in areas66

receiving persistently higher wind exposure (Nicoll et al., 2008). Although abiotic factors can-67

not be changed to lower the risk of wind damage, changing key biotic factors through forest68

management actions such as thinning can contribute to mitigating wind damage occurrence.69

Thinning is one of the main forest management actions providing extra or higher net income70

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to forest owners by producing timber before the final cut and more valuable timber at the final71

harvest (e.g. Dorning et al., 2015; Helmes and Stockbridge, 2011). On the other hand, trees are72

often damaged by strong winds within a few years after thinning due to increased aerodynamic73

roughness above the canopy leading to higher levels of turbulence, and through the creation of74

small gaps increased wind penetration between trees (e.g. Cremer et al., 1982; Mitchell, 2013).75

The gaps created following thinning might also act as a trigger point for damage propagation76

during a storm (Dupont et al., 2015). Therefore, selecting the most at risk trees for early77

removal is one of the key ways to reduce wind damage risk. However, currently available78

approaches to predict wind damage risk at the single tree level include uncertainty on whether79

the models represent common storm damage phenomena and can be generalized.80

There are two modelling approaches commonly used for wind damage studies; mechanistic81

and statistical. For the mechanistic approach, a hybrid mechanistic/empirical wind risk assess-82

ment model GALES (Gardiner et al., 2008) has been used to calculate the critical wind speed83

(CWS ) for the start of stand level damage (e.g. Byrne and Mitchell, 2013; Achim et al., 2005).84

The advantage of the mechanistic approach is that it is applicable to different forest environ-85

ments due to the inclusion of the mechanical properties of individual tree species and rooting86

strength for different soil types. Prior studies confirmed the effectiveness of using GALES for87

calculating the CWS at the stand level for a range of stand types (e.g. Blennow and Sallnas,88

2004; Byrne and Mitchell, 2013; Hale et al., 2015; Kamimura et al., 2008; Ruel et al., 2000). On89

the other hand, it is not straightforward to include new factors (findings) into GALES without90

understanding the influence of each component and factor because it is an integrated model of91

the behaviour of trees, forest, and the wind. Recently the model has been modified to calculate92

the CWS for individual trees by including additional factors dealing with tree competition93

from Hale et al. (2012) and Seidl et al. (2014). But the new version of GALES has not been94

fully validated against data from observed damage to trees under a range of conditions such as95

different tree species and storm events.96

For the statistical approach, logistic regression models are often used in wind damage studies97

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to find the probability of damage and the risk factors. In particular logistic regression models98

can directly identify which factors are associated with wind damage occurrence and it is more99

straightforward to include new variables in the models than with the mechanistic approach.100

For example, Albrecht et al. (2012a) introduced a generalized linear mixed model for a range of101

environmental conditions and storm events in German forests and found tree species and stand102

height as the most important factors linked to wind damage occurrence at the stand level. How-103

ever, there is still uncertainty whether such statistical models provide generalized information104

and estimation on wind damage or only locally specific information because statistical analysis105

ignores the actual damage mechanism in the analysis process (Gardiner and Quine, 2000). Hale106

et al. (2015) found no indication of the advantages of a particular approach for understanding107

and predicting wind damage in forests by comparing mechanistic and statistical approaches at108

the stand level. In fact these approaches appear to be very complementary probably due to the109

mechanistic approach being causal and the statistical approach being incidental. It is therefore110

beneficial to identify advantages and limitations of both approaches in order to develop wind111

damage risk assessment tools at the single tree level.112

In this paper, we focused on evaluating the mechanistic and statistical approaches in order113

to find suitable methodologies for wind risk assessment at the single tree level. Our objectives114

were 1) downscaling a mechanistic model and creating statistical models at the single tree115

level using a detailed and accurate data set, 2) testing the two approaches in order to find116

the most appropriate models, 3) applying the two approaches using a larger data of damaged117

trees from a different storm event, 4) evaluating and comparing the performance of the two118

models and the benefits of the different approaches, and 5) discussing the transferability of the119

models and the potential of using the different approaches for multiple storm events. Using the120

two approaches also helps to both understand the general principles of damage occurrence and121

develop comprehensive assessment approaches for wind damage to maritime pine trees in the122

Aquitaine region.123

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2 Material and methods124

2.1 Study site and data125

Fig. 1 shows the location of the study area from which we used data from two field surveys with126

different original objectives. The first data set was a field survey of 29 permanent plots (400127

m2/plot) in the Nezer Forest located in the Aquitaine region (44◦ 34’ 20” N, 1◦ 2’ 20” W; Fig.128

1-(a)). Soil type was wet podzol of more than 55 cm depth and with a single soil texture type129

of sand determined from the classification of the national inventory survey in French forests130

(Bruno and Bartoli, 2001; Bruno, 2008) and a technical report (GISsol, 2011). In the field131

survey, tree size was measured in 1998, and damaged trees were determined after the storm in132

1999. The data consisted of tree height, stem diameter at breast height (dbh), tree location,133

and damage status for almost all trees. This data was also subdivided into two groups by134

area; Nezer I and Nezer II (see also Fig. 1-(a)), in order to first create and adjust models and135

secondly to test them. This is explained in the next section. The second data set was from136

field surveys of the national forest inventory in France (Inventaire Forestier National; NFI) in137

the Landes de Gascogne region (Fig. 1-(b)). The survey plots are located on a 1 km x 1 km138

grid in forests based on a 10-year cycle of inventory plot survey, and there are different plot139

sizes at each location for different diameter classes (Inventaire Forestier National, 2005, 2011).140

We used a total of 235 plots data collected from 2007 to 2008, with more than half of the trees141

in each plot being maritime pine. After Storm Klaus in 2009, damaged trees in the NFI plots142

were identified by an additional field survey. Basic statistics of the data sets are presented in143

Table 1. Table 1144

A number of different pieces of spatial information were included for each plot in the two145

data sets. The distance from the windward stand edge (the westerly direction for both storms)146

was defined as the boundary line between forests and unforested area including roads (> 3 m147

width). While the distance was very precise in Nezer Forest, the distance had to be estimated148

using the coarse plot location in the NFI data in which the exact plot positions were not149

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publically available. The stem spacing in both data sets was the average value calculated from150

the number of stems in the plot. Gap size, defined as the distance in a westerly direction151

between the forest in which the plot was located and the next forest block, was also calculated.152

Furthermore, the NFI plots were identified either within the Landes or Dunes based on the153

designation given by the Inventaire Forestier National (2009). The Nezer Forest is located in154

the Landes area. All spatial information was computed using ArcGIS 10.1 (ESRI. Co., USA).155

2.2 Analysis procedure156

The analysis consisted of three parts; preparation (modelling/adapting), testing, and applica-157

tion (Fig. 2). Fig. 2There were three data sets: Nezer I, Nezer II, and the NFI data. First,the Nezer158

I data was used for calculating detailed wind speeds using the Advanced Regional Prediction159

System (ARPS) (Dupont and Brunet, 2008), for comparison against the CWS s of GALES for160

individual trees, and for use in the logistic regression models. In particular, ARPS was used161

to obtain wind speeds at two different heights for creating/adjusting the models. The area162

of Nezer I was chosen in order to reduce the simulation time taken by ARPS while including163

a sufficient number of plots to develop the models. Second, the GALES settings and logistic164

regression models were tested using the rest of the Nezer data (Nezer II). For Nezer II, another165

wind simulation was carried out at a lower spatial resolution with the Wind Atlas Analysis166

and Application Program (WAsP) (Mortensen et al., 2007). We used this model to reduce167

the computation time because Nezer II had a much larger area than Nezer I (explained in the168

next section). Third, the selected logistic regression models and the GALES model settings169

were applied to the data set from the NFI data in the Aquitaine region to examine how the170

models performed with the different quantity and quality of data from the NFI dataset and171

for a different storm. Additional conditions such as soil type, rooting depth, and the storm172

duration, which were excluded in the Nezer data, were also examined by subsetting the data173

when no discrimination was found in the NFI data. The criteria used to build the subset data174

are presented in Table 2. All models used in this analysis and their usage are explained in the175

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following sections. Table 2176

2.3 Estimation of wind speeds177

2.3.1 Wind data178

There are only 14 meteorological stations in the whole region of the study. For that reason,179

we used the numerically computed wind speeds above the forest canopy from the Systeme180

d’Analyse Fournissant des Renseignements Atmospheriques a la Neige (SAFRAN) in addition181

to the available data at a meteorological station at Cap Ferret (located at the Atlantic coast;182

44◦ 38’ N, 1◦ 15’ W). SAFRAN is a numerical model of Meteo France for estimating meteo-183

rological conditions away from meteorological stations using statistical analysis in addition to184

the observed climate data at the Meteo France forecast network, and terrain information (i.e.185

elevation and slope aspect). It provides hourly mean wind speed at 10 m height as well as186

other atmospheric parameters such as air temperature, humidity, and precipitation (Durand187

et al., 2009). The estimation has an 8 km resolution and is available across France (Vidal et al.,188

2010). In this analysis, we used wind speeds on 27-28 December 1999 (Storm Martin) and 24189

January 2009 (Storm Klaus) extracted from the outputs of SAFRAN. These wind speeds were190

then used as inputs to the detailed airflow models to estimate wind speeds (EWS ) at specific191

locations in the forests. In addition, the maximum hourly wind speed and duration of winds192

(> 10 m/s) during the storm periods were calculated for each grid cell. 10 m/s was used as the193

base wind speed to calculate the duration because it is the lowest maximum wind speed from194

all SAFRAN grid cells in the Aquitaine region (Fig. 1-(b)) during Storm Klaus.195

2.3.2 ARPS (for the Nezer I data)196

ARPS was originally developed at the Center for Analysis and Prediction of Storms at the197

University of Oklahoma for predicting the behaviour of storms based on a three-dimensional198

numerical simulation (Xue et al., 2000, 2001). Subsequently, ARPS was modified by Dupont199

and Brunet (2008) in order to calculate turbulence within and above forest canopies using200

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a large-eddy simulation method, and this version of the model has been validated for use in201

maritime pine forests (Dupont et al., 2011, 2012). Using the modified version of ARPS, wind202

speeds in the Nezer I area (approximately 2 km x 2 km) were estimated for westerly winds203

(main wind direction during Storm Martin). The forest information for the model was the204

maximum stand height and mean stem density of each stand. The maximum stand height was205

calculated as the mean height of the 20 % tallest trees in a plot. The horizontal resolution206

was 6 m and vertical resolution was 2 m. The maximum hourly wind speed at 10 m height207

for the whole Nezer Forest was 15.08 m/s determined from SAFRAN. Thus, all outputs from208

ARPS (velocities in each three-dimensional grid cell) were linearly adjusted in order to ensure a209

maximum wind speed of 15.08 m/s at 10 m height. Subsequently, the estimated wind speeds at210

the maximum stand height and 29 m height (2 m higher than the maximum tree height in the211

Nezer I data for the year 1999) were extracted to use with the GALES and logistic regression212

models.213

2.3.3 WAsP (for the Nezer II and NFI data)214

WAsP, a computer simulation of a linear airflow model, was developed by the Wind Energy215

and Atmospheric Physics Department, Risø National Laboratory, Denmark (Mortensen et al.,216

2007). WAsP can estimate wind speeds over a large area in a relatively short time period217

using the surface roughness on low hill linear approximation developed by Jackson and Hunt218

(1975). Wind speeds were simulated at 500 m x 500 m horizontal resolution at 29 m height for219

Storm Martin and 29 and 40 m height for Storm Klaus. 40 m was the approximate maximum220

tree height of maritime pine in the Landes and Dunes areas determined from the NFI data.221

A land-use map (0 to 300 m elevation range and 50 m contour interval) plus an aerodynamic222

roughness map (0.003 m for water, 0.01 m for unforested-areas over land, and 1.0 m for forest)223

was prepared in advance for the WAsP simulation. In addition, because WAsP requires wind224

speeds from a known location as input, observed data at the meteorological station at Cap225

Ferret and extracted wind data from SAFRAN near Captieux (located at the center of the226

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maritime pine forests; 44◦ 17’ N, 0◦ 15’ W) were used to model wind speeds during Storms227

Martin and Klaus respectively.228

2.4 Wind damage assessment models229

Two models, GALES and logistic regression, were used to find trees with a high probability of230

damage. The input data and parameters for GALES and independent variables for the logistic231

regression models are presented in Table 3. Table 3232

2.4.1 Mechanistic model: GALES233

The original version of GALES only calculated the stand average CWS s for uprooting and234

stem breakage (Gardiner et al., 2000, 2008; Hale et al., 2015). This is based on the ”roughness235

method”, which uses the drag and drag partitioning on rough surfaces to calculate the mean236

loading on trees (Raupach, 1992; Hale et al., 2015). For this analysis, GALES had to be237

adapted to calculate the CWS s for individual trees. Hale et al. (2012) found a significant linear238

relationship between the maximum hourly turning moment (Nm) at the stem base of individual239

trees, Mmax, and the squared hourly mean wind speed ((m/s)2) at canopy top, referred to as240

uh2, multiplied by a turning moment coefficient, TMC, for each tree (defined as the TMC241

method in this study).242

Mmax = TMC · uh2 = 111.7dbh2h · uh

2 (1)

Subsequently, Seidl et al. (2014) improved the TMC method using an additional factor, a243

competition index CI, which is described as the relationship between a subject tree and neigh-244

bouring trees (distance-dependent competition) in order to estimate the allocation of growth245

resources such as water and light generally limited by the size and number of neighbours (Av-246

ery and Burkhart, 2002). In this paper, we employed the idea of Seidl et al. (2014) but used247

instead a distance-independent competition index from Biging and Dobbertin (1995) because248

distance-dependent competition cannot be calculated without exact tree positions and distance-249

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independent competition with TMC was also significant in the study of Hale et al. (2012). The250

TMC with the distance-independent competition index is referred to as the TMCci method251

in this paper. The maximum turning moment with TMCci, Mmax ci, was calculated from the252

original data used in Hale et al. (2012) as253

Mmax ci = TMCci · uh2 = (0.13CI + 116.3dbh2h− 0.617CI · dbh2h) · uh

2 (2)

and254

CI = Σbai · yi (3)

where bai (m2) is the basal area of the ith neighbouring tree and yi = 1 when the dbh of the255

ith neighbouring tree is larger than that of the subject tree, otherwise yi = 0 (Biging and256

Dobbertin, 1995; Hale et al., 2012). All trees in a plot are treated as potentially neighbouring257

trees. The GALES parameters for maritime pine except Eq. (2) were found from the data258

of field experiments in the Landes de Gascogne region conducted by Cucchi et al. (2004) (see259

Table 2 in Cucchi et al. (2005) for averaged parameter values). The coefficients in Eq. (2) were260

obtained using the data in Hale et al. (2012).261

The GALES model can calculate the CWS s for trees located at any distance from the262

stand edge. For well acclimated trees, it is assumed that the CWS is the same at all distances263

(Gardiner et al., 2000). For a newly created edge the CWS is adjusted depending on the264

change in wind loading from the edge to the interior of the stand (Gardiner et al., 1997).265

This calculation method is effective when we have management records such as harvesting and266

logging road construction. However, no management information was available in the NFI data267

for this study. For this reason, we assumed two conditions; 1) all maritime pine trees were268

assumed to be well acclimated to the wind environment, so the CWS s were not dependent on269

the distance from the edge and gap size (described as assumption ”A”), and 2) all trees were270

not acclimated to their local wind conditions (described as assumption ”N”). For assumption271

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”N”, the calculation of CWS placed the trees at a newly created edge with a large upwind gap272

(10 times mean stand height) in order to give the maximum wind exposure to the trees. These273

settings were applied to both the TMC and TMCci methods. Full descriptions of the model274

settings are presented in Table 4. Table 4Furthermore, CWS s for stem breakage and uprooting were275

averaged in order to consider the average possibility of failure, since both types of damage were276

observed in the region after the storms.277

The maximum hourly wind speeds estimated using ARPS and WAsP were directly used278

to compare the CWS s from the GALES model. GALES converts the wind loading due to279

the hourly wind speed to the extreme wind loading during the hour, which is related to wind280

damage occurrence. This conversion is based on a gust factor established from field observations281

and wind tunnel experiments (Gardiner et al., 1997; Hale et al., 2015).282

2.4.2 Statistical model: Logistic regression283

Logistic regression models were created using the Nezer I data with the input variables in Table284

3 and there were interaction variables such as ratio of tree height to dbh, ratio of tree height285

to stand dominant height, and ratio of tree height to stem spacing. The data was unbalanced286

(i.e. only 11.5 % of trees were damaged out of the total). To avoid misclassification due287

to over-fitting, we used a bias-reduced maximum likelihood estimation method with a model288

calibration. First, Firth’s penalized logistic regression method (Firth, 1993) was applied to289

build a basic logistic regression model using all data from Nezer I. In addition, significant290

independent variables were selected under the backward method, which eliminates variables291

until reaching the best significant level. Next, it is necessary to find the coefficients least affected292

by the particular data balance because statistical models are strongly influenced by data from293

the largest data group when using an unbalanced data set (undamaged trees in this study).294

Therefore model coefficients were calibrated based on a linear shrinkage technique introduced295

by Steyerberg et al. (2001). This technique is useful for model fitting with unbalanced data296

and a part of data from the whole data set was used for creating the original model. More297

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specifically, 1) logits Lo = ln(p/(1− p)), where p was probability of damage, for all trees in the298

Nezer I data were calculated using the logistic regression model created by Firth’s penalized299

method (determined as the original model), 2) 300 new models of logistic regression were created300

using the same coefficients as the original model but with subset data consisting of 70 % of301

the original trees selected by a bootstrapping random selection method (i.e. 70 % of the tree302

data was randomly selected from all the Nezer I data), 3) logits using the subset models, Ls,303

were calculated for each tree, 4) 300 linear slopes (ratio) between Lo and Ls were computed304

respectively, 5) a linear shrinkage factor was calculated by averaging the 300 linear slopes, 6)305

the coefficients of the original models were calibrated by multiplying by the shrinkage factor.306

The computation of the model was carried out using the statistical software R (R Core Team,307

2013) and the package ”logistf” (Heinze et al., 2014).308

2.5 Evaluating settings and models309

The CWS from the GALES model does not take account of any uncertainty in the wind speed310

causing damage to a tree (i.e. it calculates only exact values of wind speed) and logistic311

regression models do not provide dichotomous outputs (predicted damaged/undamaged trees312

in this study) but only gives probabilities. One method for estimating damage is to use a313

threshold (cutpoint) value. The cutpoint is varied to see how the model predictions change314

in order to evaluate their overall performance and to determine the optimum cutpoint to give315

the highest model accuracy (Hale et al., 2015). First, the CWS s from each GALES model316

setting were systematically altered by multiplying the CWS by a value between 0 and 200 %317

(defined as the ”multiplier”). Second, the adjusted CWSs were compared with the EWS s from318

ARPS or WAsP to discriminate between damaged and undamaged trees and multipliers giving319

the optimal accuracy were determined (Bennett et al., 2013). This method of systematically320

multiplying the CWS has been used by Hale et al. (2015), but in that paper it was used to test321

ForestGALES (GALES + WAsP and GALES + windiness score) at the stand level. For the322

logistic regression models, the cutpoints for the probability of damage were changed between 0323

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and 1 and each tree was classified as either damaged or undamaged. The comparison between324

estimated and observed damaged and undamaged maritime pine trees were then classified into325

four groups (see Fig. 4 in Bennett et al. (2013)): TP (true positive: correctly predicted damaged326

trees), FP (false positive: incorrectly predicted damaged trees), FN (false negative: incorrectly327

predicted undamaged trees), and TN (true negative: correctly predicted undamaged trees).328

Using the four groups, three rates were computed as329

TPR =TP

TP + FN(4)

TNR =TN

TN + FP(5)

FPR = 1− TNR (6)

where TPR is the true positive rate, TNR is the true negative rate, and FPR is the false330

positive rate. Then receiver operating characteristics, ROC, and area under the ROC curves331

(AUC ) were used to test the model fit (effectiveness of discrimination) in terms of the imposed332

changes in the CWS and cutpoint. The ROC curve is obtained by plotting FPR against TPR,333

and generally the ROC shows a convex curve. For models to be regarded as classifying the334

tree data successfully into either damaged or undamaged groups, the AUC should be greater335

than 0.7 (Hosmer and Lemeshow, 2000). Thus, GALES settings and logistic regression models336

with AUC > 0.7 were regarded as having an acceptable discrimination level between damaged337

or undamaged trees. AUC in this study was calculated with the R package, AUC (Ballings338

and den Poel, 2014). If n denotes total number of data, the model accuracy = (TP + TN)/n339

and depends on the modified CWS values and the cutpoints. Optimal accuracy is found when340

TPR ≈ TNR (Hosmer and Lemeshow, 2000).341

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3 Results342

3.1 Modelling/Adapting and Testing (Nezer data)343

3.1.1 Mechanistic approach344

All results calculated at the maximum stand height did not show any acceptable discrimination,345

while the non-acclimated settings (TMC-N and TMCci-N) calculated at 29 m height success-346

fully discriminated between damaged and undamaged trees (i.e. AUC > 0.7) (Fig. 3). At347

both heights, AUCs of the model assuming acclimation were lower than those assuming no348

acclimation, which suggested that the trees in Nezer I had in general not acclimated to the349

wind. Fig. 3The best GALES settings (TMC-N and TMCci-N) were subsequently used for the Nezer350

II data with the EWS s from WAsP. Table 5 presents a comparison of AUC s, multipliers of the351

CWS s at the optimal accuracy, and the optimal accuracy of the two settings in Nezer I and II.352

The AUC s for the calculation of Nezer II had an acceptable level (> 0.7); however, the optimal353

accuracies decreased compared with those from Nezer I. In addition, a multiplier of more than354

1.0 indicated that the CWS s were always slightly underestimated (i.e. a calibration factor of355

1.03-1.08 was required for the highest optimal accuracy). Table 5356

3.1.2 Statistical approach357

Only one independent variable, Y (decade of establishment) was selected in the most significant358

logistic regression model using the backward method. However, since it is obvious that the359

local wind speed is one of the important triggers of wind damage occurrence, logistic regression360

models were created always including the wind variable (wind speed at 29m height). Significant361

independent variables were chosen by gradually removing variables except the wind variable362

until the model significance exceeded a p-value = 0.01. As a result, seven significant logistic363

regression models were found containing eight independent variables in total (Table 6). Table 6The364

AUC s of these seven models decreased in the Nezer II data (Fig. 4), but four models, LRs 1,365

2, 6, and 7 had an AUC value of more than 0.7. Fig. 4366

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3.2 Application (NFI data)367

3.2.1 Mechanistic approach368

Both model simulations assuming no acclimation (TMC-N and TMCci-N) with three different369

calculations of the EWS s (different heights and input meteorological stations) did not satisfy370

the acceptable level (AUC > 0.7) (Fig. 5-(1)). Using the settings with the EWS s at 29 m371

height calculated using the Cap Ferret wind data as input to WAsP (these gave the highest372

discrimination), AUC s were also calculated for the two environmental areas, Landes and Dunes373

(Fig. 5-(2)). AUC values for Landes were higher than those of the Dunes area for both settings.374

Also the ROC curves of Landes looked more stable with change of TPR and FPR while those of375

Dunes sometimes rapidly changed depending on the cutpoints. Subsequently, the AUC s were376

again calculated using subsetted data (see Table 2) in order to examine whether the specific377

environmental condition in the NFI data might have reduced the calculation accuracy. Only378

for subset data L-10, consisting of hydromorphic podzol, deep soil texture, and trees less than379

29 m height, did the mechanistic approach successfully discriminate between damaged and380

undamaged trees with an AUC of 0.709 (Table 7). A soil type of hydromorphic podzol was381

always required to improve the AUC s. Table 7382

3.2.2 Statistical approach383

All four logistic regression models (1, 2, 6 and 7), which showed the highest acceptable discrim-384

ination for the Nezer data, did not show any acceptable discrimination for the NFI data (AUC385

< 0.51). Again, AUC s were calculated for the two different environmental areas (Landes and386

Dunes). For the Dunes data LR7 showed the highest AUC (0.531) and the highest AUC in387

Landes was found with LR1 (0.586), but both did not reach an acceptable level. Therefore,388

AUC s were calculated for the subset data (see also Table 2) to find out whether additional389

variables would be required in the logistic regression models for the region. AUC s of LR1 were390

always higher than the other three models (LRs 2, 6, and 7) and LR1 had the highest AUC s391

in all of the subset data. Fig. 6 presents the ROCs of the LR1 model (wind speed + decade392

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of establishment) with the Landes and subset data. Fig. 6All of these subset data consisted of the393

same soil type, hydromorphic podzol, which was the same soil type as in the Nezer Forest.394

Thus, although LR1 was not at acceptable level, soil type could be one of the important vari-395

ables required to improve the discrimination of damage in the region. In addition, since some396

characteristics of the Nezer Forest were likely to be unique (e.g. wind duration and soil type),397

new logistic regression models were created so as to confirm whether additional conditions (dif-398

ferent from the conditions of Nezer) would affect the model performance (Table 8). Table 8For these399

models, one categorical parameter, soil depth (available information in the NFI data), was400

included in order to describe the detailed soil conditions. Three new models; LRall, LRLandes,401

and LRLandes−Nezer, had more than 0.7 for AUC and approximately 70 % of optimal accuracy402

(Table 8). LRall and LRLandes−Nezer indicated that storm duration and soil depth < 54 cm in-403

creased the probability of damage. Compared with the models from Nezer I (See Table 6), the404

same trends (negative or positive) of coefficients were found only for Y 3 (established between405

1960 and 1970) and Y 4 (established between 1970 and 1980). The probability of damage on406

the trees established between 1960 and 1980 increased compared with the baseline period (Y 1,407

established between 1940 and 1950).408

4 Discussion409

This paper presents two approaches for estimating wind damage at the tree level with a special410

focus on coupling airflow models with either a mechanistic or statistical model. First we411

discussed the uncertainty of data in the study and second the performance of each modelling412

approach.413

One of the difficulties for wind damage studies is to obtain forest (tree) and wind climate414

data, which are satisfactory in terms of quality and quantity for the specific analysis. In partic-415

ular, wind climate data over forests can hardly ever be obtained because of the limited number416

of meteorological stations. In this study, we used observed wind speeds at a meteorological417

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station and computed wind speeds from SAFRAN as input wind data for the airflow models,418

ARPS and WAsP. ARPS is a three-dimensional grid base simulation model allowing calculation419

of horizontal and vertical wind velocities, and has been well evaluated by Dupont and Brunet420

(2008). For this reason, we used ARPS with confidence of representing realistic wind condi-421

tions over the forest canopy in the Nezer Forest, although it is not straightforward to use this422

model for large areas. On the other hand, WAsP has been shown to have a lowered accuracy423

when used in forested area by Suarez et al. (1999), who compared several airflow models in424

complex forested terrain. They demonstrated that WAsP had the largest variation amongst425

the models with both over- and under-predictions of up to 20 %. Although WAsP has benefits426

for estimating wind speeds over a large area, it is important to take account uncertainty in427

the modelled outputs. SAFRAN, which provides the input wind data to ARPS and WAsP,428

generally estimates wind speeds 10 % lower than actual wind speeds (Quintana-Seguı et al.,429

2008). As a result, the wind speeds used in this study will have a bias leading to decreased430

accuracy of the results. Therefore, especially for the mechanistic approach, it is necessary to431

consider this uncertainty for comparison between the critical and estimated wind speeds.432

The mechanistic approach, i.e. GALES with ARPS or WAsP, was able to discriminate433

between damaged and undamaged trees in the Nezer Forest only under specific conditions. In434

Nezer I (GALES + ARPS), better discrimination was found using the estimated wind speed435

at 29 m height (approximately 10 % above the maximum tree height in the Nezer Forest) than436

at maximum stand height. It suggests that choosing the correct height above the canopy is437

very important for comparing the critical and estimated wind speeds because of two possible438

reasons. It is obvious that wind gust speeds above canopy surface lead to damage to trees (e.g.439

Usbeck et al., 2012) and such wind (airflow) varies spatially over the canopy during a storm440

due to the quasi-stochastic nature of turbulence in strongly sheared flows (Dupont et al., 2011).441

Thus using a large-eddy simulation model like ARPS is beneficial for describing the detailed442

wind characteristics over a canopy. In contrast, the critical wind speeds from GALES are443

averaged wind speeds (hourly mean wind speed) which vary according to the stand conditions444

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and tree locations relative to the upwind edge and gap size. Therefore, wind speeds from the445

GALES model are temporal (one hour) and spatial (≈ one tree height) averages. This might446

lead to disagreement between the critical wind speeds from GALES and estimated wind speeds447

from ARPS close to the canopy top (e.g. at the maximum stand height) where the actual448

wind speed varies the most due to the local maxima in wind shear and the close presence of449

individual trees. On the other hand, wind speeds at 10 % above the maximum tree height450

should be less affected by very local variations. This height was also effective in Nezer II,451

although the resolution of estimated wind speeds from WAsP was lower. From the results, it452

is necessary to find a suitable height in advance for a comparison between calculated critical453

wind speeds and estimated wind speeds in order to use the mechanistic approach. This requires454

that wind speeds for comparisons between critical and estimated wind speeds should not be455

too strongly influenced by very local canopy characteristics, but must in addition represent the456

winds affecting individual trees. This height should be neither very close to the canopy top457

nor too far from the canopy and 10 % above the maximum stand height appears to be a good458

compromise based on this study.459

Including assumptions of tree acclimation to their wind environment is another key to460

improve the classification of damaged and undamaged trees in the mechanistic approach. In461

Nezer I, TMC-N and TMCci-N discriminated the trees whereas TMC-A and TMCci-A did not.462

TMC-N and TMCci-N also satisfactorily discriminated the trees in Nezer II. This could be463

due to GALES not correctly calculating the change in wind loading back from edges in these464

maritime pine forests in which wind penetrates a long distance from the edge (Dupont et al.,465

2012). Also in GALES the calculation is based on data from spruce forests with high leaf areas,466

deep crowns at the edge, and with very little penetration of wind into the edge of the stand467

(Gardiner, 1995; Irvine et al., 1998). Dupont et al. (2015) point out that current mechanistic468

models could have a bias to estimating wind damage due to ignoring the dynamics of tree469

motion and damage propagation caused by the wind during a storm (Byrne and Mitchell,470

2013). In particular, when the sudden loss of trees occurs during a strong wind it creates471

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an effectively new edge. The downwind trees at the new gap then receive an increased wind472

loading without any time to acclimate to their new environment. It could potentially lead to473

further damage propagation especially to trees located close to the original damage (Dupont474

et al., 2015). Therefore, the non-acclimated setting in GALES might be better at capturing475

the condition of trees during a storm when there is damage propagation through the forest.476

Some of the logistic regression models created using the Nezer I data were able to discrim-477

inate the damaged and undamaged trees in Nezer II, but model behaviour changed between478

the two data sets (Fig. 4). The models containing a small number of variables rapidly changed479

the true positive rate for an increasing false positive rate. It meant that the model accuracy480

depended highly on which cutpoint was chosen to classify damaged and undamaged trees.481

Moreover, a particular variable, decade of establishment, was always significantly selected in482

the models. This variable integrates several factors such as tree age, tree height (older decades483

of establishment will on average have taller trees), and different establishment methods applied484

in the Landes de Gascogne and Dunes atlantiques areas. A lot of previous research has shown485

that increasing stand (tree) height and age are important indicators to identify stands and trees486

liable to be damaged (e.g. Cucchi et al., 2005; Albrecht et al., 2012a; Hale et al., 2015). How-487

ever, age was not a significant variable and tree height had a negative coefficient in the logistic488

regression models (i.e. smaller trees had higher probability of damage). This discrepancy of489

age and tree height does not provide an explanation of why the decade of establishment was a490

significant variable in Nezer Forest. Probably it is necessary to consider the variable not only491

along with tree characteristics, but also with detailed descriptions and records of management492

in the Nezer Forest (e.g. planting choice, ground preparation, thinning, etc.).493

Using the whole NFI data set, both the mechanistic and statistical approaches did not494

discriminate between damaged and undamaged trees. This may be due to the uncertainty and495

variation of the NFI data plots including the number of trees, plot size which depends on tree496

size, differences in management, and differences in tree species composition. In addition, tree497

growth and root systems are variable in different parts of the forest and in particular there498

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are big differences between the Landes and the Dunes areas (e.g. Lemoine and Decourt, 1969).499

More importantly, the models probably do not contain enough variables to cover the range of500

environmental growing conditions in the NFI data. In the mechanistic approach, some of the501

AUC s improved when using only the data from the Landes area. This is probably because the502

maritime pine parameters in GALES were obtained from only the Landes area (Cucchi et al.,503

2004). In addition, the AUC s of the TMC method were better than the TMCci (including the504

distance-independent competition index). TMC is directly influenced by tree size only (dbh2h),505

whereas TMCci is influenced by the average forest condition due to the inclusion of a distance-506

independent competition index based on a unit of one ha. In other words, competition index507

may be more effective for stands of high complexity as examined by Seidl et al. (2014), who508

found better agreement of TMC with a distance-dependent competition index using stand data509

including three different tree species. Hale et al. (2012) also found that the turning moment510

coefficient was related to a number of tree competition indices for some specific forest locations,511

but no clear relationship was found in other forests. Competition index could therefore be512

beneficial to improve wind damage estimation for specific forest conditions.513

In addition, the critical wind speeds of damaged trees growing on hydromorphic podzol514

(saturated for long periods) with non-wind acclimated settings were in better agreement with515

the estimated wind speeds during Storm Klaus than other trees in the NFI data. Maritime516

pine trees on wet soil have less anchorage (Danjon et al., 2005), so we assumed that they517

might be less fully acclimated (or very slow to acclimate). Another variable leading to better518

discrimination was to exclude taller trees (i.e. ≥ 29m). It raises the question whether the519

relationship between the maximum turning moment and stem weight obtained from Cucchi520

et al. (2004) also holds for taller trees. In their experiments, the mean tree height was less than521

25 m, so it is uncertain if we should use the same parameter values in GALES for taller trees.522

However, it is difficult to confirm this possible difference in parameters based on tree height523

from this study because only 4 % of the total number of trees exceeded 29 m in height. Thus,524

it will be necessary to test the parameters of maritime pine trees over a wider range of tree525

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heights.526

The original logistic regression models could successfully discriminate between damaged and527

undamaged trees in the Nezer Forest (Fig. 4) and worked better than the mechanistic method.528

This is the same results found by Hale et al. (2015). However, when applied to the NFI data529

they did not show acceptable discrimination. Additionally, the models with the subset data530

did not present much improvement in the discrimination (see Fig. 6). These results indicate531

the limitations of these statistical approaches if they are to be used to predict damage caused532

by future storms. Steyerberg et al. (2004) pointed out that there are more difficulties of re-533

calibrating logistic regression models than recreating a new model mainly because of the change534

of intercept. Gude et al. (2009) also suggested that several techniques for validating logistic535

regression models in order to apply them to other events are effective when internal model536

validation and shrinkage techniques are used, but this modification only works for the same537

sample population. Thus, it would be difficult to directly apply the original models developed538

using the Nezer data to the NFI data.539

Nevertheless, the statistical approach in this study suggested important variables associated540

with wind damage occurrence. First, the AUC s were always better when the subset data541

included only the soil type hydromorphic podzol (same soil type as in Nezer Forest). This542

soil type also improved the discrimination in the mechanistic analysis. Soil type together with543

soil moisture is associated with root-soil anchorage (Nicoll and Ray, 1996; Yang et al., 2014),544

so a similar stability against wind is observed on the same soil type. Second, different trends545

were observed in the coefficients between the original Nezer model and the new models (LRall,546

LRLandes, LRLandes−Nezer) except for the establishment decades from 1960 to 1980. In addition,547

higher values of coefficients were found after 1980 and lower before 1960 in the NFI data. These548

characteristics of establishment decades could not be explained only by tree height and age.549

In particular the coefficients of tree height showed a contradiction between the models created550

using the Nezer I data and the models created using the NFI data, although the establishment551

decade (tree age) and tree height are generally related. In other words, tree height could be an552

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important variable (e.g. Schmidt et al., 2010), but its influence might be a function of storm type553

and the exact forest conditions at the time of the storm. The mechanistic model when linked554

with a growth model for maritime pine forests in Aquitaine also showed increasing vulnerability555

to wind with increasing stand height (Cucchi et al., 2005), and stand stability was also reduced556

by thinning and upwind felling of stands . One possible reason why the establishment decade557

was a better variable at discriminating between damaged and undamaged trees than the other558

variables is that this variable integrates various information about a stand including planting559

methods. In this region, different planting methods were applied in each decade, in particular560

a different ploughing method was used in the 1960s (pers. comm. Dominique Guyon and Jean-561

Michel Carnus in INRA, 2014). Before 1960 trees were sown along 2 m rows, between 1960 and562

1990 sowing was along a line, and after 1990 planting of nursery trees along lines tended to be563

used. It is not clear from this study whether the establishment methods directly affected tree564

stability or more variation in tree stability was introduced by different establishment methods565

(Dorval, 2015). But it could suggest the importance of including management information and566

history in order to improve wind risk assessment at the single tree level.567

It is also important to consider that the discrimination might be affected by the storm char-568

acteristics. Storm Klaus crossed southern France with long periods of strong winds and heavy569

rain (Liberato et al., 2011), whereas Storm Martin crossed central France and was of shorter570

duration. While both of the approaches discriminated between the damaged and undamaged571

trees in the Nezer Forest caused by Storm Martin, poor discrimination was found when used572

with the damaged tress in the NFI data after Storm Klaus. Additionally, less improvement of573

discrimination was found even if subsets of data with different stand heights and height of wind574

speed prediction were used (see Fig. 5). This contrast in results from the two storms might be575

due to the different importance between wind characteristics and tree characteristics. When576

the maximum wind speeds are not extremely high, tree characteristics, especially tree height,577

would be a key factor for predicting damage. However, under the conditions of an intense and578

prolonged wind such as during Storm Klaus, a lot of trees could be blown down in a short579

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period because of rapid damage propagation. In this case, tree characteristics would be less580

effective for predicting wind damage than wind characteristics because damage can propagate581

from vulnerable to less vulnerable trees. In other words the differences between vulnerability of582

trees are overwhelmed by the dynamics of damage propagation. This suggests that both static583

and dynamic phenomena associated with storm damage need to be included for the optimal584

discrimination of wind damage.585

In short, our study clarified the advantages and disadvantages of two approaches to predict-586

ing wind damage to single trees in a uniform pine forest (Table 9). Table 9Both approaches showed587

good discrimination with the original data (Nezer I), but it is more problematic to use these588

models with other data set. In particular the statistical approach provided no discrimination589

with the larger data set. Although the mechanistic approach gave improved discrimination with590

several subsets of the larger data set, there are still issues concerning the availability of empirical591

model parameters for a range of site conditions. The statistical approach is not recommended592

for predicting future wind damage because these models tend to explain only damage from the593

single storm event used for building them. However, when multiple data sets are available,594

the approach can help to identify the specific factors associated with wind damage. Thus, it595

is important to choose the appropriate approaches based on the available data sets (including596

data quality and quantity) and the primary purpose of the analysis (e.g. building forecasting597

models, identifying critical factors, etc.).598

5 Conclusions599

Wind damage to individual trees caused by two storms was examined using two different mod-600

elling approaches, mechanistic and statistical, with a variety of data in the Aquitaine region,601

south-west France. Four GALES settings and seven logistic regression models were examined602

using the detailed data in the Nezer Forest located within the region in order to find whether603

they could discriminate damaged and undamaged trees. Some settings and models successfully604

discriminated the trees, but did not work well when applied to the French national inventory605

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data which was obtained over the whole region. Using subset data to reduce the variability606

from the NFI data was partly successful in improving the discrimination using the mechanistic607

modelling approach, but it was not helpful in improving discrimination using the statistical608

approach. Our results suggested that the current GALES model used at the single tree level609

was able to identify wind damage risk only to trees growing on particular soils, probably due610

to the strong reliance on empirical parameters for rooting resistance. Thus, more effort is re-611

quired to collect parameters for maritime pine from tree-pulling experiments on different soil612

types and rooting depths in addition to the currently available tree-pulling experiment data613

obtained by Cucchi et al. (2005) in this region. The statistical approach only requires the tree614

characteristics and observed damage history, but it proved difficult to generalize the models for615

the region even for the same tree species. Therefore, while the statistical approach is able to be616

applied only to the damage events used to create the model, the mechanistic approach could be617

more widely used for different storm events due to taking into account as much as possible the618

actual damage mechanisms during storms and minimizing the number of empirical relationships619

(Gardiner et al., 2000). In summary, this study revealed the effectiveness and limitations of620

both approaches at the single tree level, but also pointed to possibilities of improving wind risk621

assessment by coupling the two approaches in order to add new parameters identified by the622

statistical approach into the mechanistic wind risk model.623

624

Acknowledgement625

We are grateful to Yves Brunet in INRA-Bordeaux for supporting this work and to Thierry626

Belouard (IGN) who kindly provided the national forest inventory data in the Landes de627

Gascogne region, and we also want to thank Gaston Courrier and Didier Garrigou in INRA-628

Bordeaux, who conducted the field surveys in the Nezer Forest. We would also like to thank629

Sebastien Lafont, Tovo Rabemanantsoa and Christophe Moisy at INRA-Bordeaux who pro-630

vided us with important data for our analysis. Finally we would like to thank to Jean-Michel631

Carnus at INRA-EFPA who provided information on silviculture in the Landes de Gascogne632

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and Dunes atlantiques areas. This work was founded by an INRA scientific package awarded to633

Barry Gardiner and by grant ANR-12-AGRO-0007-04 (ANR, Agrobiosphere, France, Project634

”FOR-WIND”).635

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Table 1: Number of maritime pine trees, number of research plots, number of damaged treesand ratio to total number of trees, and mean and standard deviation (parenthesis) of dbh, treeheight, tallest tree height and tree age in the study sites.

Categories Unit Data I (Nezer) Data II (Nezer) NFIN of trees - 252 829 1705N of plots - 11 17 235N of damaged trees - 29 105 566Damage ratio % 11.5 12.7 33.2dbh cm 19.9 (10.9) 18.2 (11.4) 29.7 (14.4)Tree height m 12.9 (6.4) 11.6 (6.6) 17.7 (6.9)Tallest tree height m 26.7 26.7 38.6Age year 21.2 (13.7) 17.9 (12.5) 35.8 (22.2)

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Table 2: Criteria used to select the subset data from the entire NFI data set in terms of soiltype, soil depth, soil humidity, storm duration during Storm Klaus, and tree height. SubsetL-12 has similar condition to the Nezer Forest.Subsetdata

n Ratio ofdamage(%)

Area type Soil type Soildepth(cm)

Soil hu-midity

Duration(hrs)

Treeheight(m)

D-0 328 6 Dunes All All All All AllL-0 1377 40 Landes All All All All AllL-1 728 48 Landes Hydro. P.* All All All AllL-2 448 26 Landes Podzol All All All AllL-3 1094 39 Landes All ≥ 85 All All AllL-4 970 46 Landes All All Wet** All AllL-5 984 43 Landes All All All 10-11 AllL-6 561 50 Landes Hydro. P. ≥ 85 All All AllL-7 659 50 Landes Hydro. P. All Wet** All AllL-8 592 49 Landes Hydro. P. All All 10-11 AllL-9 703 49 Landes Hydro. P. All All All < 29L-10 536 50 Landes Hydro. P. ≥ 85 All All < 29L-11 546 51 Landes Hydro. P. All Wet** 10-11 AllL-12 533 52 Landes Hydro. P. All Wet** 10-11 < 29∗Hydromorphic podzol∗∗Slightly wet

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Table 3: Input variables for the mechanistic method of GALES and the airflow models andindependent variables for building the logistic regression models. The variables were obtainedfrom the field surveys, the tree-pulling experiments by Cucchi et al. (2004), and airflow models(SAFRAN, ARPS, and WAsP). Categorical variables were set only for establishment decade(Y ) due to planting methods in the region changing with time.

Variables Unit Data level Description UsageTree Plot

h m Yes — Tree height ME∗, LR∗∗

dbh cm Yes — Stem diameter at breast height (1.3 m) ME, LRA Year — Yes Tree age LRY Unitless — Yes Decade of establishment, 1: <1950, 2:

1950-1960, 3: 1960-1970, 4: 1970-1980,5: 1980-1990, 6: ≥1990

LR

CI Unitless Yes — Distance independent competition in-dex

ME, LR

sp m — Yes Mean stem spacing calculated fromstem density in a plot

ME, LR

hmax Unitless — Yes Maximum stand height calculated fromthe mean height of 20 % of the tallesttrees in a plot

ME, LR

D m Yes Yes Distance from the stand edge to thewest

ME, LR

G m — Yes Distance between forested area ME, LRMOE Pa — — Modulus of elasticity MEMOR Pa — — Modulus of rupture MECreg Nm/kg — — Resistance to uprooting as function of

stem weightME

Wm, W29, W40 m/s Yes Yes Maximum hourly wind speed at themaximum stand height, 29 and 40 mheight for westerly wind estimated us-ing ARPS (Wm and W29) and WAsP(W29 and W40). Only W29 was used forthe logistic regression models.

ME, LR

∗ Mechanistic model∗∗Logistic regression model

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Table 4: The settings for GALES based on tree acclimation to the wind environment, which isdependent on the distance from the windward stand edge (west) and gap size. TMC is basedon Eq. (1), and TMCci is based on Eq. (2.)

Tree condition Assumption Setting nameAcclimated Tree is located within the stand at its actual

distance from the westerly edge with the cor-rect upwind gap size.

TMC-A TMCci-A

Non-acclimated Tree is artificially located at a newly creatededge and the upwind gap size is set at 10times the mean tree height.

TMC-N TMCci-N

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Table 5: AUC, multiplier of the CWS, and optimal accuracy of the TMC-N and TMCci-Nsettings for calculation made at 29 m height in the Nezer I and II data

Model Nezer I Nezer IIAUC Multiplier Accuracy (%) AUC Multiplier Accuracy (%)

TMC-N 0.710 1.08 88.4 0.765 1.04 72.4TMCci-N 0.703 1.08 87.6 0.763 1.03 71.9

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Table 6: Coefficients of logistic regression models (p-value < 0.01) from the Nezer I data

Variables LR 1 LR 2 LR 3 LR 4 LR 5 LR 6 LR 7Intercept -4.49 -3.39 -2.78 -2.51 -1.19 -4.23 -5.22W29 0.09 0.08 0.03 0.03 0.02 0.02 0.02Y 3 (1960-70) 0.12 0.11 0.24 0.19 0.18 0.42 0.31Y 4 (1970-80) 0.94 1.02 1.38 1.32 1.36 1.46 1.33Y 5 (1980-90) -0.28 -0.43 -0.26 -0.35 -0.26 -0.25 -0.21Y 6 (≥1990) -3.22 -3.60 -3.02 -3.26 -3.13 -2.84 -2.63h -0.04 -0.14 -0.13 -0.13 -0.38 -0.39h/sp 0.57 0.55 0.72 1.60 2.00CI -0.02 -0.03 -0.03 -0.05h/hmax -1.99 -1.87 -2.60sp 0.85 1.32dbh -0.06

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Tab

le7:

FivehighestAUCsforTMC-N

from

theGALESmodelforthesubsetLan

des

data.

Optimal

accuracy

andthemultiplier

oftheCWSarealso

presented.

Subset

IDn

Dam

age

ratio

Soiltype

Soil

mois-

ture

Soil

depth

Duration

Tree

heigh

tEstab

lishment

decad

eAUC

Accuracy

Multiplier

L-10

536

50%

Hydro.P.*

all

deep

all

<29m

all

0.709

63%

1.05

L-9

703

49%

Hydro.P.

all

all

all

<29m

all

0.694

63%

0.99

L-6

561

50%

Hydro.P.

all

deep

all

all

all

0.690

62%

1.07

L-1

728

48%

Hydro.P.

all

all

all

all

all

0.682

62%

1.01

L-8

592

49%

Hydro.P.

all

all

10-11hrs.

all

all

0.664

61%

1.00

∗ Hydromorphic

podzol

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Table 8: Coefficients, AUC and optimal accuracy of newly created logistic regression mod-els with the subset data. LRall was based on all of the NFI data with the variables usedfor creating the Nezer model and the external variables (i.e. soil type, duration, soil depth,and Dunes/Landes), LRLandes was based on the Landes data with soil type podzol or hydro-morphic podzol (approximately 85 % of the Landes data) with the same variables as LRall

except Dunes/Landes, and LRLandes−Nezer was based on the same environmental condition andvariables as the original Nezer model. Blank means the variables were not significant in themodels.Variables LRall LRLandes LRLandes−Nezer

n 1705 1176 533

Intercept -18.89 -21.01 1.04W29 -0.12 -0.11 -0.18dbh 0.07 0.08h 0.23 0.25 0.35CI 0.01 0.02 0.02h/hmax -2.03 -0.03Y 2 (1950-1960) -0.25 0.04 0.21Y 3 (1960-1970) 0.33 0.56 1.79Y 4 (1970-1980) 1.37 1.89 2.52Y 5 (1980-1990) 2.42 2.61 2.89Y 6 (1990-2000) 2.72 2.82 3.50Y 7 (≥2000) 2.38 2.43 4.07D 0.00 0.00 0.00G 0.00 0.00 0.00h/sp -0.27 -0.53 -0.55dbh2h -0.26 -0.25h/dbhsp -0.18 -0.27Duration 0.16 0.26 n.i.Soil depth (45-54 cm) 1.36 1.32 n.i.Soil depth (55-65 cm) 16.10 15.76 n.i.Soil depth (65-74 cm) 16.66 16.50 n.i.Soil depth (75-84 cm) 15.72 15.49 n.i.Soil depth (≥84 cm) 15.28 15.28 n.i.Dunes* -1.26 n.i.** n.i.

AUC 0.791 0.738 0.727Optimal accuracy (%) 71.7 69.6 67.9*Dunes=1, Landes=0** not included for creating the model

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Table 9: Advantages and disadvantages of mechanistic and statistical approaches in terms ofmodel goodness of fit to the different data including model generalization and identifying factorsrelated to wind damage. ”+” and ”-” indicate advantage and disadvantage respectively andsymbol size the relative importance.Model goodness Mechanistic StatisticalFit to original data + +Generalization + -Identification of factors - +

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Figure captions828

Fig. 1: Location of study site; (a) boundary of two data sets and survey plots in the Nezer829

Forest and (b) forest area in the region with the location of the Nezer Forest and national830

inventory plots (with more than half of the trees in a plot being maritime pine) and also831

identifying the Dunes or Landes area. Wind speed data at two locations, Cap Ferret and832

Captieux, were used to estimate wind speeds with the WAsP airflow model.833

Fig. 2: Analysis flow consisted of 1) modelling and adapting, 2) testing, and 3) applying to the834

logistic regression (LR) models and GALES using the Nezer and NFI plot data. CWS is the835

critical wind speed (m/s) calculated in GALES and EWS is the estimated wind speed (m/s)836

calculated in ARPS and WAsP.837

Fig. 3: ROC curves of Nezer I for the GALES settings (acclimated or non-acclimated with838

TMC and TMCci methods) at two different heights of estimated wind speeds, (1) at 29 m839

height and (2) at maximum stand height. The values in parentheses are the AUC values.840

Fig. 4: ROC curves for the logistic regression models using the (1) Nezer I and (2) Nezer II841

data. The values in parentheses show the AUC values.842

Fig. 5: ROC curves with TMC-N (solid line) and TMCci-N (dotted line) using (1) all NFI843

data for three different wind speed estimations using WAsP and (2) sub-setted data for Dunes844

and Landes areas with wind speed at 29 m height based on Cap Ferret input wind speeds. The845

values in parentheses are the AUC values.846

Fig. 6: ROC curves of a logistic regression model (LR1) for subset data in the Landes area847

having the five highest AUC values. Descriptions of the subset data are described in Table 2.848

The values in parentheses are the AUC values.849

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Aquitaine region

0 4 82 Kilometers

Data type

Nezer II

Nezer I

Survey plot

(a) Nezer Forest

NFI plots (2007-2008) (Subject plots only)

Landes

Dunes

Nezer Forest

Forested area

²

0 70 14035 Kilometers

Cap Ferret

Captieux

(b) Landes de Gascogne

& Dunes atlantiques

Figure 1: Location of study site; (a) boundary of two data sets and survey plots in the NezerForest and (b) forest area in the region with the location of the Nezer Forest and nationalinventory plots (with more than half of the trees in a plot being maritime pine) and alsoidentifying the Dunes or Landes area. Wind speed data at two locations, Cap Ferret andCaptieux, were used to estimate wind speeds with the WAsP airflow model.

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Nezer Forest data

NFI data

Nezer I

Nezer II

Nezer Forest data (Storm Martin) NFI data of Landes de Gascogne(Storm Klaus)

ARPS

CWS

WAsP

1) Modelling & Adapting 2) Testing 3) Application

WAsP

GALES

LRs

EWS

EWS

GALES

settings

GALES

EWS

Modelling

Adapting

Selected LRs

SelectedGALESsettings

Testing

Applying

Model

Data

Model setting

Calculated value

Created model

Validating

Wind data from SAFRAN

Wind data from met. station

Wind data from met. station

Wind data from SAFRAN

Figure 2: Analysis flow consisted of 1) modelling and adapting, 2) testing, and 3) applyingto the logistic regression (LR) models and GALES using the Nezer and NFI plot data. CWSis the critical wind speed (m/s) calculated in GALES and EWS is the estimated wind speed(m/s) calculated in ARPS and WAsP.

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Draft0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00FPR

TPR

TMC−A (0.561)

TMC−N (0.630)

TMCci−A (0.509)

TMCci−N (0.622)

(2) Wind speed at maximum stand height

0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00FPR

TPR

TMC−A (0.636)

TMC−N (0.710)

TMCci−A (0.611)

TMCci−N (0.703)

(1) Wind speed at 29 m height

Figure 3: ROC curves of Nezer I for the GALES settings (acclimated or non-acclimated withTMC and TMCci methods) at two different heights of estimated wind speeds, (1) at 29 mheight and (2) at maximum stand height. The values in parentheses are the AUC values.

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Draft0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00

FPR

TPR

LR 1 (0.709)

LR 2 (0.716)

LR 3 (0.683)

LR 4 (0.698)

LR 5 (0.695)

LR 6 (0.707)

LR 7 (0.743)

(2) Nezer II

0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00

FPR

TPR

LR 1 (0.763)

LR 2 (0.768)

LR 3 (0.769)

LR 4 (0.770)

LR 5 (0.778)

LR 6 (0.773)

LR 7 (0.768)

(1) Nezer I

Figure 4: ROC curves for logistic regression models using the (1) Nezer I and (2) Nezer II data.The values in parentheses show the AUC values.

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Draft0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00

FPR

TPR

Cap Ferret 29m (0.572)


Catieux 40m (0.554)



Catieux 40m (0.553)

(1) All data

0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00

FPR

TPR

Dune (0.557)

Dune (0.570)

Landes (0.613)

Landes (0.609)

(2) Dune and Landes (Wind speed measurement at Cap Ferret 29 m)

Figure 5: ROC curves with TMC-N (solid line) and TMCci-N (dotted line) using (1) all NFIdata for three different wind speed estimations using WAsP and (2) sub-setted data for Dunesand Landes areas with wind speed at 29 m height based on Cap Ferret input wind speeds. Thevalues in parentheses are the AUC values.

49

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Draft

0.00

0.25

0.50

0.75

1.00

0.00 0.25 0.50 0.75 1.00

FPR

TPR

L-0 (0.586)

L-9 (0.645)

L-1 (0.639)

L-2 (0.622)

L-10 (0.621)

L-6 (0.613)

Figure 6: ROC curves of a logistic regression model (LR1) for subset data in the Landes areahaving the five highest AUC values. Descriptions of the subset data are described in Table 2.The values in parentheses are the AUC values.

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draft · 2021. 4. 5. · draft 26 abstract 27 maritime pine (pinus pinaster ait.) forests in the...

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