The field data collection took place across the summers 2020 and 2021. UAV laser scanning data were collected for the powerline strips. A base station with known GPS coordinates was used for accurate geocoding of the laser returns. The collection was planned based on a 4 or 5 double line pattern along the powerline, at a flight altitude of ∼60 m above ground and with a flight line spacing of ∼10–15 m, resulting in an overlap of the flight lines of ∼85 % in front and ∼75 % side and a scan angle of 0° from nadir, resulting in a ground sampling distance of near 1.41 cm per pixel. Several postprocessing engines were used but Pix4D (© 2025 Pix4D SA) and DroneDeploy (© 2025 DroneDeploy) were the major tools for this (details not shown). The pre-processing of the UAV-LS data yielded a dataset containing the coordinates, species, height and the bounding box of each tree within 25 m of each side of the powerline gate. This pre-processed dataset underwent further processing to calculate the following “landscape” variables: the shortest distance from each tree to the powerline, the distance from each tree to the nearest forest edge (towards and away from the powerline or in the direction parallel to the powerline when an edge existed), the associated size of non-forested gaps (when present). The diameter at breast height (DBH) was estimated using species-specific equations pairing UAV-LS-derived height data and field-based measurements of DBH (see Appendix A, Table A1). The crown radii in the eight cardinal directions were measured to calculate the offset of the crown gravity centre relative to the top of the tree (see below).

The input dataset was then further processed to obtain all necessary variables required to calculate the CWS using ForestGALES. The stem volume and crown depth of each tree was estimated using Norwegian and species-specific equations derived from the National Forest Inventory and described in the Appendix of Merlin et al. (2025) (the stem volume equation are reiterated here in the Appendix A.1.1, Table A2). A measure of the crown asymmetry for each tree was done using the 8 crown radii measured in the previous step by estimating the displacement of the centre of gravity between a right circular cone shape and an irregular cone. Details about the calculation of the displacement of the crown centre of gravity are shown in Appendix A.1.2, Fig. A1. The crown offset was then added in the calculation of the deflection loading factor (DLF) as an additional displacement of the crown weight – thereby increasing the DLF compared to a tree with a symmetrical crown, decreasing the CWS thereby increasing the tree's vulnerability to wind damage (see Eqs. 2 and 3 for the DLF in the CWS calculations, Locatelli et al., 2022).

For each tree, the characteristics of the surrounding trees were aggregated to represent the neighbourhood of each tree using Voronoi diagrams. We considered both the first order and second order neighbouring Voronoi cells – trees – when defining the neighbouring trees (hereafter named “tier 1 & tier 2”). We calculated the mean tree height, DBH, crown depth and width, and distance for the neighbourhood trees and labelled this as stand variables. We calculated two competition indices, i.e. the Hegyi (distance-dependent, Hegyi, 1974) and the BAL (distance independent, Stage, 1973). Both indices are implemented in the single-tree version of ForestGALES.

The distance to the edge of the forest and the associated forest gap size were calculated in four directions – to and from the powerline, and along the powerline direction – using individual tree positions. Three alternatives were retained when calculating the critical wind speed: (i) the “closest largest gap” was defined using the linear optimizer function of the lpSolve package in R (Berkelaar, 2024), (ii) the “minimum” was simply the closest forest edge and (iii) the “mean” the average of the distances to and size of the non-forested gaps in the four considered directions.

We derived soil type and rooting depth from the Geological Survey of Norway (NGU; https://geo.ngu.no/kart/losmasse_mobil/, last access: 29 May 2026) and the ForestGALES classification (Kennedy, 2002) as detailed in the Appendix of Merlin et al. (2025). Finally, we derived the topographic exposure index Topex (Chapman, 2000) from Norwegian elevation models at 10 m resolution across Norway for a horizon distance of 200, 500, and 1000 m averaged across the eight compass directions, hereafter referred to as Topex 200, Topex 500 and Topex 1000. Topex has been successfully used in forest wind damage assessments and modelling in complex terrain (Costa et al., 2023).

A simple summary of the differences between the standing and damaged trees was performed for tree height, DBH, D/H ratio, the ratio of the estimated crown depth to tree height, species mix (whether the tree of interest was in a stand of the same species (coded 0), of a different species and a conifer species (coded 1), or of a different species and broadleaf (coded 2)), tree status (whether the tree of interest was taller or thinner than the neighbouring trees). Considering the large imbalance in the sample sizes between the damaged and standing trees, we used a repeated random subsampling approach for N=100 simulations. In each of the simulations, all 180 damaged trees were combined with a randomly selected subset of 180 standing trees drawn without replacement to produce balanced datasets. The differences in the characteristics between the standing and damaged trees were evaluated in each simulation, and the results were summarized across the 100 simulations. This approach assumes independence among trees and treats each random subsample of standing trees as an equally plausible representation of the undamaged population. Similar results were obtained when performing the analysis on the complete unbalanced dataset. The significance of the difference was tested using the Mann–Whitney–Wilcoxon (MWW) test foregoing assumptions about the underlying distribution. The statistics of the test were then averaged across the 100 repeated assessments. Similarly, a 2-sample test for equality of proportions was used to test whether damaged trees were different from standing trees in the type of trees in their surroundings (same species, different species with conifers or broadleaves).

The maximum wind speed at 10 m above ground was obtained from the hourly meteorological data from the long-term stable post-processed products of the Norwegian Meteorological Institute MET (available for download here: https://thredds.met.no/thredds/metno.html, last access: 29 May 2026) on a 1km×1km spatial grid across Norway. Since all damage was recorded during the winter of 2020–2021, corresponding to the period when tree falls occur most frequently in Norway, the search for the maximum observed wind speed was restricted between October 2020 and April 2021. The maximum wind speed for the winter 2020–2021 in the centroid of each of the 25 powerline strips and for each location of the 180 damaged trees was extracted. Some of the sites belonged to the same 1 km raster cell from the meteorological data, hence the final 2020–2021 maximum wind speed dataset contained 97 different locations for the 205 sites (25 powerline strips and 180 recorded individual tree damage events). The wind climate during this period (winter 2020–2021) was relatively mild, with a mean wind speed of approximately 3 to 4 ms-1 and a 95th percentile between 4 and 5 ms-1. The maximum observed wind speed itself reflected a mild winter, with values around 10 ms-1 for all locations considered here (see Fig. A2).

The Global Wind Atlas (https://globalwindatlas.info/en, last access: 29 May 2026) provides a worldwide description of the mean wind climate via the two Weibull distribution parameters A and k. Both parameters are available at a 250 m resolution (at the equator) and were downloaded for Norway. The value of the two parameters in the centroid of each of the 25 powerline strips and for each location of the 180 damaged trees were extracted. The maximum wind speeds described by a Weibull distribution converge to a Gumbel (GEV type I distribution – see below) distribution. The A and k parameters of the Weibull mean wind distribution can then be transformed into the two Gumbel parameters following Quine (2000) to describe the extreme wind climate based on information from the mean wind climate.

Since the extreme (maximum) wind speed climate is theoretically more relevant for assessing the probability of damage than the mean wind climate, it would be logical to use a model describing the extreme wind climate across Norway. Generalized Extreme Value (GEV) distribution models are well-established and widely used in extreme value statistics (Palutikof et al., 1999). The GEV distribution was first introduced by Jenkinson (1955), describing three possible types of extreme value distributions for the block maxima of a given variable: type I – Gumbel, type II – Fréchet and type III – Weibull (Beirlant et al., 2004). The GEV distribution is a three-parameter distribution of the form: 1G(X≤x)=e-1+ξ×z-μσ1ξ,forξ≠0e-e-z-μσ,forξ=0 where μ is the location, σ is the scale, and ξ is the shape parameter. The shape parameter determines one of the three previously mentioned types: type I is when ξ=0, type II is when ξ>0 and type III when ξ<0. For an accurate parameter estimation of the GEV distribution at each site, the time series sample must be sufficiently long; a minimum of ten years of observations is recommended, but the longer the more accurate the estimates of wind extremes will be (Palutikof et al., 1999). There is however no published map of the three GEV parameters for Norway, therefore a GEV model was fitted on a long-term dataset of yearly maximum wind speed for each of the sites. The long-term extreme wind speed dataset contained the yearly maximum wind speed for 47 years (1975–2021) extracted from the same data source as for the maximum wind speed observed in the winter 2020–2021 (i.e. the long-term stable post-processed products of the Norwegian Meteorological Institute MET). Similarly to this other dataset, it contained the time series of maximum wind speed for the 97 locations corresponding to the 205 sites.

For each of the 97 time-series, the GEV fitting procedure was as follows: (1) the Augmented Dickey–Fuller (ADF) and the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) stationary tests were performed and stationarity of the time series was ensured (for α=0.05); (2) the GEV distribution was fitted using the Maximum Likelihood Estimation (MLE); (3) each model fit was checked using two diagnostic plots: (i) the empirical versus model quantiles plot with confidence bands, (ii) the model density compared with the histogram of the empirical data; (4) both the Kolmogorov–Smirnov and Anderson–Darling tests were performed to confirm the empirical data and a randomly generated sample from a GEV model with the estimated parameters originated from the same distribution. During step (2), initial estimates were supplied, in the form of the mean observed maximum wind speed across the time series for the location parameter, a scale value of 1 and a shape value of 0.1. The use of good initial estimates – especially for the location parameter – was important in ensuring convergence of the model. The final parameter estimates for the 97 fitted models were on average 10.5 (SD =1.96) for the location parameter, 0.894 (SD =0.241) for the scale parameter and -0.213 (SD =0.130) for the shape parameter. The majority (94 out of 97) of the models showed a negative shape parameter, indicating a GEV model of type III. Traditionally, extreme wind speeds in temperate latitudes have been fitted to a Type I (Gumbel) distribution, as was done when using the Weibull distribution parameters in this study. However several published studies (Li et al., 2022; Palutikof et al., 1999; Soukissian and Tsalis, 2015) have shown that the Type III distribution is appropriate.

Note that the wind direction or seasonality of the extreme wind speed were not accounted for in this study.

The CWS equations for breakage Eq. (2) and overturning Eq. (3) are shown below (Hale et al., 2015; Locatelli et al., 2022): 2CWSbreakage=π⋅MOR⋅D03⋅fknot32⋅TC⋅TMC_Ratio⋅fEdge+Gap⋅DLF3CWSoverturning=Creg⋅WstemTC⋅TMC_Ratio⋅fEdge+Gap⋅DLF where π: pi mathematical constant. The Wstem is the total stem weight defined as the total stem volume multiplied by the stem density. The stem volume was estimated using species-specific models defined and routinely used by the Norwegian National Forest Inventory (kg). The equations are detailed in the Appendix A, Table A2. TC is the turning moment coefficient, a dimensionless parameter representing the wind-induced turning moment acting on an individual tree, accounting for tree size and competitive environment. Further details on the calculation of TC can be found in the fgr R package (Locatelli et al., 2022). The TC can be further modified following recent (less than 5 years) thinning operations via the TMC_Ratio accounting for differences in the spacing between trees before and after thinning operations. Since the model was run at a single point in time with no thinning operations conducted in the 5 years prior, the TMC_Ratio was set to 1.0. The diameter at base D0 was derived from DBH, tree height and crown depth using the ForestGALES default equation (m). The wood parameters MOR: modulus of rupture (MPa), MOE: modulus of elasticity (Pa) were extracted from Fischer et al. (2016) and Høibø and Vestøl (2010) for spruce and pine growing in Norway and from Peltola et al. (2000) for birch. The spruce and pine values were obtained from dry boards (spruce) and logs (pine) at 12 % moisture content. The conversion to green wood values used in the ForestGALES model was made following the method of Unterwieser and Schickhofer (2011) used by Locatelli et al. (2016). The new values are summarized in the Appendix A, Table A3, along with the equations for the dry to greenwood conversion. The parameter fknot is a species-specific factor accounting for the reduction in wood strength due to the presence of knots. The default value from the ForestGALES model for each of the species considered was used here, namely 0.9 for Norway spruce, 0.85 for Scots pine and 1.0 for birch. The parameter fEdge+Gap: the combined effect of the tree position relative to the upwind stand edge and the size of the upwind gap, and DLF is the deflection loading factor accounting for the added bending moment due to the displaced crown and stem (Locatelli et al., 2022). Finally, the Creg is the species-specific overturning coefficient empirically describing the root anchorage for different soil and rooting depth combinations (Nmkg-1) (Nicoll et al., 2006). See Hale et al. (2012, 2015) and Locatelli et al. (2022) among others for more in-depth information and definitions of the different parts of the ForestGALES model for the individual tree version.

The CWS for damage – the minimum between the CWS for breakage and overturning – was calculated for each tree under three different seasonal scenarios:

A “summer” scenario, where birch trees have a full crown and without any snow loading

Finally, the CWS is elevated to a reference height of 10 m. The reference height of 10 m was chosen to (i) ensure consistency with standard meteorological wind products and (ii) to avoid integrating the increasing influence of forest and other ground cover further away from the site of interest tied with calculating the CWS at higher heights.

The CWS values on their own offer a broad view into which trees are structurally more vulnerable to damage than others, but this does not account for the wind climate of the area. The probability of damage can be calculated in different ways depending on the wind data and model(s) available and chosen. In this study, we tested three methods based on the probability of exceeding the CWS:

Using a logistic function (Gardiner et al., 2024): the maximum wind speed observed during the actual winter 2020–2021 (ws_20.21) at each location was compared with the calculated CWS. The wind speed was either kept as is or further adjusted by the local Topex value. The equation for predicting the probability of damage is below:4ProbWS2021=11+exp-ws20.21×1-TopexTopexmax-CWSS-11+expCWSSThe factor S is a slope factor, and set to 6 as in (Chen et al., 2018; Gardiner et al., 2024). The value Topex_max is taken as the maximum Topex value across all considered locations and for the horizon chosen (i.e. 200, 500 or 1000 m).

Machine learning (ML) methods can provide a complementary approach to mechanistic models such as ForestGALES. The ML models are purely data-driven and can provide predictive power based on complex multivariate relationships that may not be captured in the models or not yet discovered. By combining ForestGALES with an ML model on a multivariate dataset, the calculated CWS and characteristics from the wind climate and landscape exposure to wind may prove to generate better predictions of individual tree fall (Hart et al., 2019). Moreover, ML models can be used as proxy models, approximating the behaviour of a mechanistic model while speeding up the computation time. An ML surrogate using all tree, soil, landscape and wind data bypassing the calculation of CWS could provide a quicker wind risk assessment in decision-support systems for individual tree management for forest stakeholders (e.g. powerline and railway companies). The training of ML algorithms requires however large datasets. The sample of 180 damaged trees in this study is at the low end of sample sizes for fitting ML algorithms. We explored this method nonetheless to assess its potential and set up a precedent for future studies combining ML and ForestGALES. For this reason, no distinction was made between species when running the ML algorithms; only the best global model previously selected was used in determining the CWS used in the input dataset for the ML algorithm.

The ML algorithm used in this study was the eXtreme Gradient Boosting algorithm (XGBoost), an efficient and reliable method for regression and classification (Chen and Guestrin, 2016). The algorithm is a tree-based incremental learning process. At each iteration, a new weak learner is trained based on the error of the decision tree previously learned. Gradient boosting iteratively adjusts the predictions of the decision trees by minimizing the loss function (based on the error between the predicted and observed values), splitting and removing less significant tree nodes. Then, all decision trees are combined, and the predictions from each tree are weighted based on their importance. The iterative process is repeated until either a specific number of iterations are completed, or a predefined criterion is met. Many of the hyperparameters of the XGBoost algorithm can be modified and tuned. To keep it simple, we did not tune the hyperparameters and we used a set of default hyperparameters following the documentation of the xgboost R package. The values used for the main hyperparameters of the XGBoost algorithm are summarised in the Appendix A, Table A4.

Two types of datasets were used in the XGBoost algorithm. The first dataset – hereafter referred to as the “ForestGALES-ML” dataset – contained the individual tree CWS value calculated by ForestGALES, the exposure index Topex at 200 m, and a variable describing the local wind climate: either the maximum observed wind speed during the winter 2020–2021 (“max_ws”), the 1-year return level (i.e. the location parameter) of either the GEV model (“return_gev”) or the Weibull model (“return_weib”). By using this first dataset, we assessed the potential in combining a mechanistic model (ForestGALES) to obtain a vulnerability index (CWS) and then a ML algorithm to obtain better damage predictions. The second dataset – hereafter referred to as the “TreeChar-ML” dataset – contained the same individual tree information used as input to the ForestGALES model (tree height, DBH, crown width and depth, crown offset, stand mean DBH, crown width and depth, and stand top height) as well as the ForestGALES soil and rooting depth classes, the exposure index Topex at 200 m and one of the three available variables describing the local wind as in the “ForestGALES-ML” dataset.

We trained the XGBoost algorithm in the same way for both datasets. The input dataset was biased towards a uniform class distribution as described in Sect. 2.5, selecting an equal number of damaged and standing trees, N=180, 100 times. For each of the 100 datasets, the XGBoost algorithm was trained and tested using a 10-folds cross-validation procedure. The data was randomly partitioned into 10 subsamples (folds) of equal size. Nine folds are combined to train the algorithm, and the last fold is used to test the algorithm. The procedure was repeated by leaving out each of the 10 folds in turn. The AUC value, accuracy and feature (variable) importance (measured with the gain – the fractional contribution of each variable to the model) were measured as the mean from their respective values for each of the 10 repetitions from the cross-validation procedure. The AUC, accuracy and feature importance reported hereafter are their mean (and standard deviation “SD”) values across the 100 repetitions.

The XGBoost algorithm returned a probability of damage. The discrimination threshold between damaged and standing trees used was 0.5, such that a probability equal or greater than 0.5 resulted in the damaged classification.

A summary figure of the methodological approach and entire process is described in Fig. 2.

Several options were tested for calculating the CWS and probability of damage: the use of a crown offset, neighbour level, competition index, seasonal scenarios, type of CWS in terms of gap and edge definition, wind data/model type and the use of multipliers for CWS and the wind speeds (summarized in Fig. 2). All models were assessed for their discrimination power – defined by the AUC – based on the calculated probability of damage using 100 repeated assessments with a balanced sample of damaged and standing trees (see Sect. 2.5). Only 20 % (global models) and 23 % (species-specific models) of all tested models yielded an AUC above 0.6. The mean AUC across the different alternatives for all the tested models an AUC above 0.6 are presented in Appendix B, Fig. B1. Among the models with an AUC above 0.6, the models with the BAL competition index significantly outperformed the alternative for the global and species-specific models except for Norway spruce. The models using the tier 1 & tier 2 or tier 2 neighbour levels had higher AUC values than the alternative neighbour level. There were no clear differences in performance among the alternatives for the inclusion of the crown offset and CWS type across all the tested global and the species-specific models. The different seasonal scenarios performed similarly for the global models, but the AUC values for the winter scenario were lower for birch (significant difference) and Norway spruce (non-significant difference) and higher for Scots pine than the fall and summer scenarios. Surprisingly, the use of the GEV wind model performed the worst: only 9 % of all models using the GEV wind model yielded an AUC value above 0.6. Despite representing the extreme wind climate at each location, it performed worse than the Weibull model which described the mean wind climate (Appendix B, Fig. B2). Using a logistic probability function with the actual observed maximum wind speed for the winter 2020–2021 (“Actual WS”, Eq. 4) yielded the highest AUC across the different wind data/model options for the global and species-specific models except for Norway spruce where the use of the Weibull model outperformed it (by 0.05 AUC units, Appendix B, Fig. B2). Overall, including a Topex correction did not improve the performance of the models under the “Actual WS” alternative (Appendix B, Fig. B2).

The best global and species-specific models – the ones achieving the highest AUC values under the 100 repeated assessments – were selected and presented in Table 2. None of the global models achieved an AUC value above 0.7. The best global model yielded an AUC of 0.676. The best species-specific models all achieved AUC values at or above 0.7. The cutpoint (for converting the damage probability predictions to binary Damaged/Standing predictions) was generally quite low across the selected best global and species-specific models, indicating that the ForestGALES model overestimates the CWS, therefore overestimating of the damage probability.

The ROC curve for the best global and species-specific models selected is presented in Fig. 3, using all samples. The overall accuracy of the best global and species-specific models was ∼64 %, meaning that about 64 % of the damaged and standing trees were correctly identified by the models.