Draft · 2021. 4. 5. · Draft 26 Abstract 27 Maritime pine (Pinus pinaster Ait.) forests in the...
Transcript of 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]
1
Page 1 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
2
Page 2 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
3
Page 3 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
4
Page 4 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
5
Page 5 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
6
Page 6 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
7
Page 7 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
8
Page 8 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
9
Page 9 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
10
Page 10 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
11
Page 11 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
”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
12
Page 12 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
13
Page 13 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
14
Page 14 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
15
Page 15 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
16
Page 16 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
17
Page 17 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
18
Page 18 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
19
Page 19 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
20
Page 20 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
21
Page 21 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
22
Page 22 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
23
Page 23 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
24
Page 24 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
25
Page 25 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
References636
Achim, A., Ruel, J.C., Gardiner, B.A., Laflamme, G., and Meunier, S. 2005. Modelling the637
vulnerability of balsam fir forests to wind damage. Forest Ecology and Management 204(1):638
35–50.639
Albrecht, A., Hanewinkel, M., Bauhus, J., and Kohnle, U. 2012a. How does silviculture af-640
fect storm damage in forests of south-western Germany? Results from empirical modeling641
based on long-term observations. European Journal of Forest Research 131: 229–247. doi:642
10.1007/s10342-010-0432-x.643
Albrecht, A., Kohnle, U., Hanewinkel, M., and Bauhus, J. 2012b. Storm damage of Douglas-fir644
unexpectedly high compared to Norway spruce. Annals of Forest Science 70(2): 195–207.645
doi:10.1007/s13595-012-0244-x.646
Avery, T.E., and Burkhart, H.E. 2002. Forest Measurements, Fifth edition. McGraw-Hill, New647
York.648
Ballings, M., and den Poel, V. 2014. Package AUC . URL649
http://cran.r-project.org/web/packages/AUC/AUC.pdf [accessed 10 November650
2014].651
Bennett, N.D., Croke, B.F.W., Guariso, G., Guillaume, J.H., Hamilton, S.H., Jakeman,652
A.J., Marsili-Libelli, S., Newham, L.T.H., Norton, J.P., Perrin, C., Pierce, S., Robson,653
B., Seppelt, R., Voinov, A., Fath, B.D., and Andreassian, V. 2013. Characterising per-654
formance of environmental models. Environmental Modelling and Software 40: 1–20. doi:655
10.1016/j.envsoft.2012.09.011.656
26
Page 26 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
Biging, G.S., and Dobbertin, M. 1995. Evaluation of competition indices in individual tree657
growth models. Forest Science 41(2): 360–377.658
Blennow, K., and Sallnas, O. 2004. WINDA - a system of models for assessing the probability659
of wind damage to forest stands within a landscape. Ecological Modelling 175(1): 87–99.660
doi:10.1016/j.ecolmodel.2003.10.009.661
Bruno, E. 2008. Calcul des niveaux trophique et hydrique stationnels a partir du releve floris-662
tique Introduction. Rapport technique de l’IFN.663
Bruno, E., and Bartoli, M. 2001. Premiers enseignements de l’utilisation de logiciel ecoflore664
pour traiter les releves botaniques du l’IFN. 53(3-4), Revue Forestiere Francaise.665
Byrne, K.E., and Mitchell, S.J. 2013. Testing of WindFIRM/ForestGALES BC: A hybrid-666
mechanistic model for predicting windthrow in partially harvested stands. Forestry 86:667
185–199. doi:10.1093/forestry/cps077.668
Colin, A., Meredieu, C., Labbe, T., and Belouard, T. 2010. Etude retrospective et mise a jour669
de la ressource en pin maritime du massif des Landes de Gascogne apres la tempete Klaus670
du 24 janvier 2009. IFN n2010-CER-2-077.671
Commission des affaires economiques 2009. Les consequences de la tempete672
du 24 janvier 2009 das le Sud-Quest. Assemblee Nationale, Paris. URL673
http://www.assemblee-nationale.fr/13/rap-info/i1836.asp [accessed 13674
November 2014].675
Cremer, K.W., Borough, C.J., McKinnell, F.H., and Carter, P.R. 1982. Effects of stocking and676
thinning on wind damage in plantations. New Zealand Journal of Forestry Science 12(2):677
244–268.678
Cucchi, V., Meredieu, C., Stokes, A., de Coligny, F., Suarez, J., and Gardiner, B.A. 2005.679
Modelling the windthrow risk for simulated forest stands of Maritime pine (Pinus pinaster680
Ait.). Forest Ecology and Management 213(1-3): 184–196. doi:10.1016/j.foreco.2005.03.019.681
27
Page 27 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
Cucchi, V., Meredieu, C., Stokes, A., Berthier, S., Bert, D., Najar, M., Denis, A., and Lastennet,682
R. 2004. Root anchorage of inner and edge trees in stands of Maritime pine (Pinus pinaster683
Ait.) growing in different podzolic soil conditions. Trees 18(4): 460–466. doi:10.1007/s00468-684
004-0330-2.685
Danjon, F., Fourcaud, T., and Bert, D. 2005. Root architecture and wind-firmness of mature686
Pinus pinaster. New Phytologist 168: 387–400. doi:10.1111/j.1469-8137.2005.01497.x.687
Dorning, M., Smith, J.W., Shoemaker, D., and Meentemeyer, R.K. 2015. Changing decisions in688
a changing landscape: How might forest owners in an urbanizing region respond to emerging689
bioenergy markets? Land Use Policy 49: 1–10. doi:10.1016/j.landusepol.2015.06.020.690
Dorval, A.D. 2015. Architecture racinaire et stabilite chez le pin maritime (Pinus pinaster Ait.)691
au stade jeune. Ph.D. thesis, UMR BIOGECO - INRA / Universite de Bordeaux.692
Dupont, S., Bonnefond, J.M., Irvine, M.R., Lamaud, E., and Brunet, Y. 2011. Long-693
distance edge effects in a pine forest with a deep and sparse trunk space: In situ and694
numerical experiments. Agricultural and Forest Meteorology 151(3): 328–344. doi:695
10.1016/j.agrformet.2010.11.007.696
Dupont, S., and Brunet, Y. 2008. Influence of foliar density profile on canopy flow: A697
large-eddy simulation study. Agricultural and Forest Meteorology 148: 976–990. doi:698
10.1016/j.agrformet.2008.01.014.699
Dupont, S., Irvine, M.R., Bonnefond, J.M., Lamaud, E., and Brunet, Y. 2012. Turbulent700
structures in a pine forest with a deep and sparse trunk space: stand and edge regions.701
Boundary-Layer Meteorology 143(2): 309–336. doi:10.1007/s10546-012-9695-8.702
Dupont, S., Pivato, D., and Brunet, Y. 2015. Wind damage propagation in forests. Agricultural703
and Forest Meteorology 214–215: 243–251. doi:10.1016/j.agrformet.2015.07.010.704
Durand, Y., Giraud, G., Laternser, M., Etchevers, P., Merindol, L., and Lesaffre, B. 2009.705
Reanalysis of 47 Years of Climate in the French Alps (1958 - 2005): Climatology and Trends706
28
Page 28 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
for Snow Cover. Journal of Applied Meteorology and Climatology 48(12): 2487–2512. doi:707
10.1175/2009JAMC1810.1.708
Feser, F., Barcikowska, M., Krueger, O., Schenk, F., Weisse, R., and Xia, L. 2015. Storminess709
over the North Atlantic and northwestern Europe-A review. Quarterly Journal of the Royal710
Meteorological Society (141): 350–382. doi:10.1002/qj.2364.711
Firth, D. 1993. Bias reduction of maximum likelihood estimates. Biometrika 80(1): 27–38.712
Gardiner, B., Byrne, K., Hale, S., Kamimura, K., Mitchell, S.J., Peltola, H., and Ruel, J.C.713
2008. A review of mechanistic modelling of wind damage risk to forests. Forestry 81(3):714
447–463. doi:10.1093/forestry/cpn022.715
Gardiner, B., Peltola, H., and Kellomaki, S. 2000. Comparison of two models for predicting716
the critical wind speeds required to damage coniferous trees. Ecological Modelling 129(1):717
1–23. doi:10.1016/S0304-3800(00)00220-9.718
Gardiner, B.A. 1995. The interactions of wind and tree movement in forest canopies. In Wind719
and Trees. Edited by M.P. Coutts and J. Grace, Cambridge University Press, Cambridge,720
pp. 41–59.721
Gardiner, B.A., and Quine, C.P. 2000. Management of forests to reduce the risk of abiotic722
damage - a review with particular reference to the effects of strong winds. Forest Ecology723
and Management 135(1-3): 261–277. doi:10.1016/S0378-1127(00)00285-1.724
Gardiner, B.A., Stacey, G.R., Belcher, R.E., and Wood, C.J. 1997. Field and wind tunnel725
assessments of the implications of respacing and thinning for tree stability. Forestry 70(3):726
233–252. doi:10.1093/forestry/70.3.233.727
GISsol 2011. L’etat des sols de France. Nancy. URL728
http://www.gissol.fr/rapports/Rapport HD.pdf [accessed 4 August 2015].729
29
Page 29 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
Gude, J., Mitchell, M.S., Ausband, D.E., Sime, C., and Bangs, E.E. 2009. Internal Validation of730
Predictive Logistic Regression Models for Decision-Making in Wildlife Management. Wildlife731
Biology 15(4): 352–369. doi:10.2981/08-057.732
Hale, S., Gardiner, B., Peace, A., Nicoll, B., Taylor, P., and Pizzirani, S. 2015. Comparison733
and validation of three versions of a forest wind risk model. Environmental Modelling and734
Software 68(27-41). doi:10.1007/s10342-010-0448-2.735
Hale, S.E., Gardiner, B.A., Wellpott, A., Nicoll, B.C., and Achim, A. 2012. Wind loading736
of trees: influence of tree size and competition. European Journal of Forest Research 131:737
203–217. doi:10.1007/s10342-010-0448-2.738
Heinze, G., Ploner, M., Dunkler, D., and Southworth, H. 2014. Package ’logistf’ (July 2, 2014).739
URL http://cran.r-project.org/web/packages/logistf/logistf.pdf [accessed 8740
October 2014].741
Helmes, K.L., and Stockbridge, R.H. 2011. Thinning and harvesting in stochastic forest models.742
Journal of Economic Dynamics and Control 35(1): 25–39. doi:10.1016/j.jedc.2010.10.007.743
Hosmer, D.W., and Lemeshow, S. 2000. Applied Logistic Regression, Second Edition. John744
Wiley & Sons, Inc., New York.745
Inventaire Forestier National 2005. IMOT Instruction pour les mesures et observations de746
terrain Version 2005.747
Inventaire Forestier National 2009. Les sylvoecoregions (SER)748
de France metropolitaine Etude de definition. Paris. URL749
http://inventaire-forestier.ign.fr/spip/spip.php?rubrique79 [accessed 11750
June 2015].751
Inventaire Forestier National 2011. La foret francaise - Les resultats issus des campagnes752
d’inventaire.753
30
Page 30 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
URL http://inventaire-forestier.ign.fr/spip/spip.php?article709 [accessed754
27 August 2014].755
Irvine, M.R., Gardiner, B.A., and Morse, A.P. 1998. Energy partitioning influenced by tree756
spacing. Agroforestry Systems 39(3): 211–224.757
Jackson, P., and Hunt, J. 1975. Turbulent wind flow over a low hill. Quarterly Journal of the758
Royal Meteorological Society 101(430): 929–955.759
Kamimura, K., Gardiner, B., Kato, A., Hiroshima, T., and Shiraishi, N. 2008. Devel-760
oping a decision support approach to reduce wind damage risk: a case study on sugi761
(Cryptomeria japonica (L.f.) D.Don) forests in Japan. Forestry 81(3): 429–445. doi:762
10.1093/forestry/cpn029.763
Lemoine, B., and Decourt, N. 1969. Tables de production pour le pin maritime dans le Sud-764
Ouest de la France. Revue forestiere francaise 1: 5–16. doi:10.4267/2042/20235.765
Liberato, M.L.R., Pinto, J.G., Trigo, I.F., and Trigo, R.M. 2011. Klaus - An exceptional766
winter storm over northern Iberia and southern France. Weather 66(January): 330–334.767
doi:10.1002/wea.755.768
Marcos, M., Jorda, G., Gomis, D., and Perez, B. 2011. Changes in storm surges in southern769
Europe from a regional model under climate change scenarios. Global and Planetary Change770
77: 116–128. doi:10.1016/j.gloplacha.2011.04.002.771
Mitchell, S.J. 2013. Wind as a natural disturbance agent in forests: a synthesis. Forestry 86:772
147–157. doi:10.1093/forestry/cps058.773
Mortensen, N.G., Heathfield, D.N., Myllerup, L., Landberg, L., and Rathmann, O. 2007. Get-774
ting Started with WAsP 9. June. URL www.mku.edu.tr/getblogfile.php?keyid=2829775
[accessed 22 December 2014].776
31
Page 31 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
Nicoll, B.C., Achim, A., Mochan, S., and Gardiner, B.A. 2005. Does steep terrain influence tree777
stability? A field investigation. Canadian Journal of Forest Research 35(10): 2360–2367.778
Nicoll, B.C., and Ray, D. 1996. Adaptive growth of tree root systems in response to wind action779
and site conditions. Tree Physiology 16: 891–898.780
Nicoll, B.C., Gardiner, B.A., and Peace, A.J. 2008. Improvements in anchorage pro-781
vided by the acclimation of forest trees to wind stress. Forestry 81(3): 389–398. doi:782
10.1093/forestry/cpn021.783
Quintana-Seguı, P., Le Moigne, P., Durand, Y., Martin, E., Habets, F., Baillon, M., Canellas,784
C., Franchisteguy, L., and Morel, S. 2008. Analysis of Near-Surface Atmospheric Variables:785
Validation of the SAFRAN Analysis over France. Journal of Applied Meteorology and Cli-786
matology 47(1): 92–107. doi:10.1175/2007JAMC1636.1.787
R Core Team 2013. R : A Language and Environment for Statistical Computing. Vienna. URL788
http://www.r-project.org/ [accessed 10 November 2014].789
Raupach, M. 1992. Drag and drag partition on rough surfaces. Boundary-Layer Meteorology790
60: 375–395.791
Ruel, J.C., Quine, C.P., Meunier, S., and Suarez, J. 2000. Estimating windthrow risk in792
balsam fir stands with the ForestGales model. The Forestry Chronicle 76(2): 329–337. doi:793
10.5558/tfc76329-2.794
Schmidt, M., Hanewinkel, M., Kandler, G., Kublin, E., and Kohnle, U. 2010. An inventory-795
based approach for modelling single-tree storm damage - experiences with the winter storm796
of 1999 in southwestern Germany. Canadian Journal of Forest Research 40: 1636–1652.797
Seidl, R., Rammer, W., and Blennow, K. 2014. Simulating wind disturbance impacts on forest798
landscapes: Tree-level heterogeneity matters. Environmental Modelling & Software 51: 1–11.799
doi:10.1016/j.envsoft.2013.09.018.800
32
Page 32 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
Steyerberg, E.W., Eijkemans, M.J.C., and Habbema, J.D.F. 2001. Application of shrinkage801
techniques in logistic regression analysis: a case study. Statistica Neerlandica 55(1): 76–88.802
doi:10.1111/1467-9574.00157.803
Steyerberg, E.W., Borsboom, G.J.J.M., van Houwelingen, H.C., Eijkemans, M.J.C., and804
Habbema, J.D.F. 2004. Validation and updating of predictive logistic regression mod-805
els: a study on sample size and shrinkage. Statistics in Medicine 23(16): 2567–86. doi:806
10.1002/sim.1844.807
Suarez, J.C., Gardiner, B.A., and Quine, C.P. 1999. A comparison of three methods for pre-808
dicting wind speeds in complex forested terrain. Meteorological Applications 6(4): 329–342.809
Usbeck, T., Waldner, P., Dobbertin, M., Ginzler, C., Hoffmann, C., Sutter, F., Steinmeier,810
C., Volz, R., Schneiter, G., and Rebetez, M. 2012. Relating remotely sensed forest damage811
data to wind data: Storms Lothar (1999) and Vivian (1990) in Switzerland. Theoretical and812
Applied Climatology 108: 451–462. doi:10.1007/s00704-011-0526-5.813
Vidal, J.P., Martin, E., Franchisteguy, L., Baillon, M., and Soubeyroux, J.M. 2010. A 50-year814
high-resolution atmospheric reanalysis over France with the Safran system. International815
Journal of Climatology 30(11): 1627–1644. doi:10.1002/joc.2003.816
Xue, M., Droegemeier, K.K., and Wong, V. 2000. The Advanced Regional Prediction System817
(ARPS) - A multi-scale nonhydrostatic atmospheric simulation and prediction model . Part818
I : Model dynamics and verification. Meteorology and Atmospheric Physics 75: 161–193.819
doi:10.1007/s007030070003.820
Xue, M., Droegemeier, K.K., Wong, V., Shapiro, A., Brewster, K., Carr, F., Weber, D., Liu, Y.,821
and Wang, D. 2001. The Advanced Regional Prediction System (ARPS) - A multi-scale non-822
hydrostatic atmospheric simulation and prediction tool. Part II: Model physics and applica-823
tions. Meteorology and Atmospheric Physics 76(1-4): 143–165. doi:10.1007/s007030170027.824
33
Page 33 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
Yang, M., Defossez, P., Danjon, F., and Fourcaud, T. 2014. Tree stability under wind : simu-825
lating uprooting with root breakage using a finite element method. Annals of Botany 114:826
695–709. doi:10.1093/aob/mcu122.827
34
Page 34 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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)
35
Page 35 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
36
Page 36 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
37
Page 37 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
38
Page 38 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
39
Page 39 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
40
Page 40 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
41
Page 41 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
42
Page 42 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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 - +
43
Page 43 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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
44
Page 44 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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.
45
Page 45 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
Draft
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.
46
Page 46 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
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.
47
Page 47 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
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.
48
Page 48 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
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)
Cap Ferret 40m (0.567)
Catieux 40m (0.554)
Cap Ferret 29m (0.545)
Cap Ferret 40m (0.561)
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
Page 49 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research
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.
50
Page 50 of 50
https://mc06.manuscriptcentral.com/cjfr-pubs
Canadian Journal of Forest Research