Tree Damage by Ice Accumulation in Norway Spruce ( Picea abies (L.) Karst.) Stands Regarding Stand Characteristics

: Freezing rain is a frequently occurring, but relatively rarely studied disturbance in Europe, although ice accumulation may occasionally cause severe damage for forestry. We aimed to characterize ice-accumulation damage to overstory trees in spruce stands, assess the probability of damage based on the stand and individual tree parameters, and deﬁne the most signiﬁcant parameters that a ﬀ ect the probability of individual tree damage in all stands and in recently thinned stands. Among the studied stands, the proportion of damaged overstory spruce ranged from 1.8% to 60.9% and was higher ( p < 0.001) in recently thinned stands (27.8% ± 1.9%) than in the other stands (20.4% ± 1.6%). Stem breakage was the prevalent (98.5% ± 1.1%) damage type. At the stand level, the probability of damage decreased for older, less dense stands with a larger mean diameter. Within stands, overstory trees were more damaged (23.5% ± 1.2%; p < 0.001) than those in the lower stand layers, but, within overstory, trees with larger dimensions and a higher social position (high relative diameter and low slenderness ratio) and a higher proportion of crown were less damaged. The probability of breakage to overstory trees was most accurately predicted using almost the same variables for all stands and recently thinned stands. The site type, tree height, relative diameter, and crown ratio were common for both, with the addition of mean diameter at breast height for all stands and the stand density for recently thinned stands. Our results indicate the importance of the tree and stand characteristics on the resistance of individual tree to ice accumulation and the need for management practices that balance increased growth and the stability of trees throughout the rotation.


Introduction
Natural disturbances strongly affect forest structure and the dynamics of forest stands with an effect on different types of provided ecosystem services [1], including economic activities [2] and carbon sequestration [3]. Among the disturbance types, wind, insects and fire are studied in the most detail across Europe [4,5] and in the hemiboreal forests [6][7][8][9][10][11], but damage from ice accumulation is relatively rarely studied.
Ice accumulation is most often caused by freezing rain (also called supercooled rain)-a liquid precipitation with a droplet temperature of below 0 • C that may freeze on impact with solid objects [12]. Recently, several climatological studies of freezing rain have been done in Europe [13][14][15], including an estimation of its spatial and temporal occurrence [16]. Freezing rain is a common phenomenon in the region. Currently, central and eastern Europe typically undergo one to two events per year, and the

Materials and Methods
We aimed to characterize ice-accumulation damage in Norway spruce stands, assess the probability of damage concerning the stand and individual tree parameters, and define the most significant parameters that affect the probability of individual tree damage in all stands and recently thinned stands. For this, we studied Norway spruce (Picea abies (L.) Karst.) stands in the eastern part of Latvia (Rēzekne, Baltinava, Balvi and Kārsava municipalities) after freezing rain in December 2012 in unfrozen soil conditions. In Latvia, the season for freezing rain is from September to April, with the peak in December [16]. The studied sites are located in the region of Latvia with the highest frequency of freezing rain events. During the period from 1940/1941 to 2009/2010, the mean number of days per year with ice (>5 mm) on surfaces in December was one in the western regions (Liepāja) and five in the eastern regions (Alūksne) [according to the data from the Latvian Environment, Geology and Meteorology Center]. Under the future emission scenarios of RCP4.5 and RCP8.5, a slight increase may occur [19].
We randomly selected 61 spruce stands where, according to stand inventory data, the proportion of spruce was at least 70% of the stand total growing stock and the area was ≥0.8 ha. No meteorological data are available for these stands at the occurrence of the incidence, but no significant wind was reported during the storm. The intensity of the disturbance is characterized by the amount of ice that increased the pressure on the trees. As an indicator of intensity, icing during the same event increased the tree mass by 1.5 times in nearby pine stands, compared to trees without ice [29].
According to stand inventory data gathered before the icing event, the age of selected stands (Ast) was 20 to 113 years. All measurements were done in winter 2012/2013. In each stand, we established 6 to 8 circular sample plots (200 m 2 ; R = 7.96 m), evenly distributed within the stand and offset at least 10 m from the stand edges. Site type (ST) was noted from the prior inventory data and was grouped according to the classification by Bušs [35] into mesic mineral soils, wet mineral soils and drained peat soils. In each plot, for spruce trees with a diameter at breast height (DBH) of ≥2.1 cm we noted the stand layer (overstory, understory and advance regeneration), incidence of damage and damage type (broken or other ice-caused damage, e.g., bent or uprooted). A tree was classified as 'broken' if the broken top was at least 15% of the tree height. For the overstory spruce, we determined DBH, tree height (H) and height of the crown, with height of the broken trees calculated using a regression equation based on the height/DBH relationships of the undamaged overstory spruce trees in the same stands. In total, 7581 spruce trees were measured on the plots, with 4672 situated in the overstory, 1965 in the understory and 944 in advance growth.
We then used these data to calculate the stand parameters: stand density (number of overstory trees per hectare (Nst)) and the mean DBH (DBHst) and height (Hst) of the overstory spruce. For each tree, the relative diameter (ratio between the individual tree and stand mean diameter (Drel)), crown ratio (ratio between the green crown length (cm) and tree height (m) (CR)) and stem slenderness ratio (ratio of the tree height (m) and DBH (cm) (HD)) were calculated. Based on the stand inventory data, stands were divided into (1) recently thinned-thinning done during the three years before the ice storm and (2) other stands-no thinning or thinning done more than three years before the icing event.
The age of the recently thinned stands was 20 to 75 years (median 53 years) and that of the other stands was 31 to 113 years (median 73 years). Stand parameters showed considerable variation with much overlap between the recently thinned and other stands (Table 1) in their common age range (31 to 75 years). No information on thinning intensity (number of trees, basal area or yield removed) was available to assess the direct effect of recent thinning. Therefore, we first assessed the probability of damaged and broken trees concerning the stand and individual tree parameters of all stands (age 20 to 113 years), and then developed assessment models for all stands and for the recently thinned stands. To assess the probability of breakage of individual spruce tree (binary data), each of the measured tree parameter was divided into levels, and in each level, the proportion of broken spruces was calculated. The generalized linear model based on the binomial distribution was applied to assess the relationship between the stand layer and site type as well as the tree DBH, height, relative diameter, crown ratio and slenderness ratio on the proportions of damaged and broken trees. The one-way analysis of variance was used to assess the differences in the proportion of damaged and broken trees among the levels for each factor. The effect of stand density, mean DBH, and mean height on the proportion of broken trees were assessed using the generalized linear model based on the binomial distribution. The relation between these parameters was assessed using Spearman's rank correlation.
We used a cluster dendrogram to group mutually related factors with a height larger than 0.5. The layout of the dendrogram of all stands (Figure 1) was similar to that of the recently thinned stands. In both, the factors were divided into the same five groups. The probability of breakage was assessed using equations compiled with all possible combinations of one to five factors (one from each cluster). In total, 125 equations for each data set (all stands and the recently thinned stands) were evaluated. The selection of the best performing models was based on the comparison of the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the residual deviance between the models and the null model. All tests were performed at α = 0.05, and the mean values and their confidence intervals are shown. All calculations were done in R 3.5.1 [36]. diameter, crown ratio and slenderness ratio on the proportions of damaged and broken trees. The one-way analysis of variance was used to assess the differences in the proportion of damaged and broken trees among the levels for each factor. The effect of stand density, mean DBH, and mean height on the proportion of broken trees were assessed using the generalized linear model based on the binomial distribution. The relation between these parameters was assessed using Spearman's rank correlation. We used a cluster dendrogram to group mutually related factors with a height larger than 0.5. The layout of the dendrogram of all stands (Figure 1) was similar to that of the recently thinned stands. In both, the factors were divided into the same five groups. The probability of breakage was assessed using equations compiled with all possible combinations of one to five factors (one from each cluster). In total, 125 equations for each data set (all stands and the recently thinned stands) were evaluated. The selection of the best performing models was based on the comparison of the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the residual deviance between the models and the null model. All tests were performed at α = 0.05, and the mean values and their confidence intervals are shown. All calculations were done in R 3.5.1 [36].

Results
Among the studied stands, the proportion of damaged overstory spruce ranged from 1.8% to 60.9% (mean 22.9 ± 3.4%). Overstory spruce was damaged significantly more (both p < 0.001) than that in the understory and advance regeneration ( Table 2). Most the damaged overstory spruce was broken, ranging from 72.7% to 100% (mean 98.5% ± 1.1%) among the stands. Within 13 out of 61 stands, all damaged spruces were broken. A similar proportion (p > 0.05) of broken spruce was found in the overstory and understory, and in both stand layers this proportion was significantly larger (both p < 0.01) than that for the advance regeneration layer ( Table 2). The proportion of damaged overstory spruce trees was similar (p > 0.05) on mesic mineral soil and drained peat soil, and for both, the proportion was slightly, but significantly (both p < 0.05) higher than among stands on wet mineral soil. Yet, among all damaged spruces, the proportion with broken tops was similar (all p > 0.05) among site types (Table 2). In the recently thinned stands, the proportion of overstory spruce with some type of damage was significantly (p < 0.001) higher than that in the other stands, yet the proportion of damaged spruce trees with broken top was similar (p > 0.05).
We further analyzed the probability of breakage among individual overstory spruce in all stands (pooled recently thinned and other stands). Stand parameters (except the stand height, p > 0.05) had a significant effect on the probability of breakage. The proportion of the broken spruce was significantly lower in older stands (rho = −0.56, p < 0.01) and in stands with a larger DBH for the overstory spruce (rho = −0.50, p < 0.001). The degree of breakage increased with higher stand density (rho = 0.48, p < 0.001; Figure 2).

Results
Among the studied stands, the proportion of damaged overstory spruce ranged from 1.8% to 60.9% (mean 22.9 ± 3.4%). Overstory spruce was damaged significantly more (both p < 0.001) than that in the understory and advance regeneration ( Table 2). Most the damaged overstory spruce was broken, ranging from 72.7% to 100% (mean 98.5% ± 1.1%) among the stands. Within 13 out of 61 stands, all damaged spruces were broken. A similar proportion (p > 0.05) of broken spruce was found in the overstory and understory, and in both stand layers this proportion was significantly larger (both p < 0.01) than that for the advance regeneration layer ( Table 2). The proportion of damaged overstory spruce trees was similar (p > 0.05) on mesic mineral soil and drained peat soil, and for both, the proportion was slightly, but significantly (both p < 0.05) higher than among stands on wet mineral soil. Yet, among all damaged spruces, the proportion with broken tops was similar (all p > 0.05) among site types (Table 2). In the recently thinned stands, the proportion of overstory spruce with some type of damage was significantly (p < 0.001) higher than that in the other stands, yet the proportion of damaged spruce trees with broken top was similar (p > 0.05).
We further analyzed the probability of breakage among individual overstory spruce in all stands (pooled recently thinned and other stands). Stand parameters (except the stand height, p > 0.05) had a significant effect on the probability of breakage. The proportion of the broken spruce was significantly lower in older stands (rho = −0.56, p < 0.01) and in stands with a larger DBH for the overstory spruce (rho = −0.50, p < 0.001). The degree of breakage increased with higher stand density (rho = 0.48, p < 0.001; Figure 2).   In addition, the crown ratio, DBH, height, relative diameter and slenderness ratio-all had a significant effect (all p < 0.001) on the probability of breakage among overstory spruce trees. Spruce with a crown length of less than 30% had the highest proportion of broken trees (35.4% ± 7.5%) and were significantly more damaged than trees with a crown length greater than 40% (differences among groups 0.01 < p < 0.001, Figure 3a). In addition, significantly fewer spruce trees with a crown length greater than 80% of the tree height were broken (11.8% ± 3.4%, all differences 0.01 < p < 0.001) than those with lower crown proportions.
A higher proportion of spruce trees with a DBH of 10 to 15 cm and a height of 15 to 17 m were broken (31.5% ± 3.4% and 32.4% ± 4.3%, respectively), and damage gradually decreased for trees of larger dimensions (Figure 3b,c). A sharp decrease in the proportion of broken trees was observed for spruce larger than 25 cm. The low proportion of broken trees with a DBH of ≤10 cm and a height of ≤13 m was largely (59% and 78% of the trees in the corresponding level of diameter and height, respectively) formed by two stands (20-and 31-year-old stands with a mean crown length of 85.8% and 70.8%) having only 7.8% and 18.8%, respectively, of broken trees.
The proportion of broken individual trees was also assessed in relation to the social status within a stand (i.e., in relation to the relative diameter and slenderness ratio). Spruce trees smaller than the stand-wide mean DBH (relative diameter of 0.71 to 1.00) showed the highest proportion of broken tops, ranging from 28.7% ± 3.1% to 31.9% ± 3.4% (Figure 3d). That was significantly higher (0.01 < p < 0.001) than among the spruce trees with a larger relative diameter. Similarly, the highest proportion of broken trees was 36.3% ± 3.0% for slenderness ratio 1.01%-1.10% and 35.7% ± 3.9% for slenderness ratio 1.11-1.20 (Figure 3e). That was significantly higher (all p < 0.001) than among the tress with lower slenderness ratio. The lower proportions of broken tops among trees with a relative diameter of ≤0.7 and slenderness ratio ≥1.3 was due to their significantly shorter (for both all p < 0.001) heights In addition, the crown ratio, DBH, height, relative diameter and slenderness ratio-all had a significant effect (all p < 0.001) on the probability of breakage among overstory spruce trees. Spruce with a crown length of less than 30% had the highest proportion of broken trees (35.4% ± 7.5%) and were significantly more damaged than trees with a crown length greater than 40% (differences among groups 0.01 < p < 0.001, Figure 3a). In addition, significantly fewer spruce trees with a crown length greater than 80% of the tree height were broken (11.8% ± 3.4%, all differences 0.01 < p < 0.001) than those with lower crown proportions.
A higher proportion of spruce trees with a DBH of 10 to 15 cm and a height of 15 to 17 m were broken (31.5% ± 3.4% and 32.4% ± 4.3%, respectively), and damage gradually decreased for trees of larger dimensions (Figure 3b,c). A sharp decrease in the proportion of broken trees was observed for spruce larger than 25 cm. The low proportion of broken trees with a DBH of ≤10 cm and a height of ≤13 m was largely (59% and 78% of the trees in the corresponding level of diameter and height, respectively) formed by two stands (20-and 31-year-old stands with a mean crown length of 85.8% and 70.8%) having only 7.8% and 18.8%, respectively, of broken trees.
The proportion of broken individual trees was also assessed in relation to the social status within a stand (i.e., in relation to the relative diameter and slenderness ratio). Spruce trees smaller than the stand-wide mean DBH (relative diameter of 0.71 to 1.00) showed the highest proportion of broken tops, ranging from 28.7% ± 3.1% to 31.9% ± 3.4% (Figure 3d). That was significantly higher (0.01 < p < 0.001) than among the spruce trees with a larger relative diameter. Similarly, the highest proportion of broken trees was 36.3% ± 3.0% for slenderness ratio 1.01%-1.10% and 35.7% ± 3.9% for slenderness ratio 1.11-1.20 (Figure 3e). That was significantly higher (all p < 0.001) than among the tress with lower slenderness ratio. The lower proportions of broken tops among trees with a relative diameter of ≤0.7 and slenderness ratio ≥1.3 was due to their significantly shorter (for both all p < 0.001) heights (0.81 and 0.89 ratios to the stand mean height, respectively) than for all other levels of relative diameter and slenderness ratio.   Regression analyses integrated these separate factors to show how they interacted to determine the susceptibility of individual spruce trees to damage from ice loading. In all stands combined, the probability of individual tree breakage was most accurately predicted using the site type, mean DBH (stand parameters), tree height, relative diameter and crown ratio (individual tree parameters). All factors were significant (0.036 < p < 0.001; Table 3). The second-most accurate model did not include tree height and showed all the other significant factors included in the best performing model. The third best model included only DBH and the crown ratio of the individual tree.
Among the recently thinned stands, the best performing model for predicting the probability of individual spruce tree breakage included the site type and stand density (stand parameters) and the tree height, relative diameter and crown ratio (individual tree parameters). All factors were significant (0.015 < p < 0.001; Table 4). Hence, four out of five factors for thinned stands are the same as those in the best performing model for all stands. The second-most accurate model for the recently thinned stands included all the same factors except site type. The third best model included four out of five factors compared to the best performing model, but with tree DBH instead of the tree height.

Discussion
Freezing rain and the consequent damage due to ice accumulation is rarely studied in European boreal and hemiboreal forests, yet it may occur as a high-impact hazardous event both for infrastructure [37] and forestry [27]. We observed a large variation in damage levels among the studied stands, ranging from 2% to 61% of trees damaged by ice accumulation. Accordingly, several studies have reported on the heterogeneity of the damage severity among and within stands (e.g., [26,38,39]), which is determined by complex interactions between the intensity of disturbance and the stand and tree parameters.
The ice-accumulation thickness is the major explanatory variable of the damage severity [27,40], with the importance of tree and stand parameters decreasing with the increasing storm intensity [27]. Perhaps for that reason, studies have found diverse responses or ones of different magnitudes between the tree or stand characteristics and damage, although several general trends appear. Other external aggravating factors, such as wind and snow during or after the freezing rain can increase the total damage in forests [41][42][43]. However, strong wind or accumulating snow were not reported during the freezing rain event at our study stands. Thus, we assume that these did not contribute to the damage that we assessed. However, both ice and snow accumulation form a static load on the tree crowns with a similar mechanical effect; thus, we also refer to studies of damage caused by snow, where appropriate. Most studies also include the effects of wind to some extent.
Among physical site conditions, elevation and slope are the primary characteristics affecting damage severity [27], likely due to influence of these features on wind direction and intensity and crown asymmetry of trees growing on slopes. However, the flat topography of the studied sites suggests a negligible effect of these factors. Furthermore, the soil texture and depth affect the tree susceptibility [41]. We found slight, but significant differences in proportion of damaged spruce trees among soil types, with a higher proportion on mesic mineral and drained peat soils compared to the wet mineral soils. Contrarily, stands on undrained mineral soils were more damaged by snow than stands on organic soils [44], yet no direct relation was suggested to explain these differences. However, unexpectedly (see [41]), no effect on damage type was found regardless of the differences in the soil (root anchorage strength on different soils) among site types.
Damage to individual trees is largely determined by the biomechanics of ice loading and tree parameters [23], with the damage type (uprooting, breakage or bending) related to the wood structural strength and tree stem and root properties [45]. Nearly all damaged trees in our study were broken (mean 99%), as commonly happens with snow loading in middle-aged and mature stands [46]. In the absence of strong wind, ice and snow primarily accumulates on the top of a tree where the vertical force of gravity [41] causes breakage if the bending strength is lower than the root anchorage strength [45].
The tallest, dominant trees were damaged more frequently than trees in overtopped canopy positions, probably because most of the icing is captured by the highest part of the canopy and exterior branches [47]. Ice has a strong attachment to the surface, and is not shed onto trees of a lower canopy position. More damage to overstory trees than to overtopped trees was observed in broadleaf and mixed forests in the leafless state [38,48,49], but could be even more pronounced for evergreen tree species because foliated trees have a greater surface area to hold more ice [41]. Yet, Abies alba was more resistant to ice damage than other coniferous (including Norway spruce) and broadleaf species, regardless of the leafless season [27].
Contrary to our findings, a higher probability of damage for understory trees was observed among mixed central European forests [27] and is related to secondary damage caused by falling trees and branches. These differences between studies may also be related to species composition, with the overstory of pure spruce stands catching greater ice load than the overstory of mixed broadleaf coniferous stands. That reduces the amount of ice reaching the understory. Yet, both lower primary damage (the sheltering effect) and the increased secondary damage (from falling debris) may both occur [50], resulting in a similar proportion of damaged trees between stand layers [51].
With our study, the proportion of damaged spruce was significantly lower in the older stands (Figure 2a). Similarly, among other studies with stand ages ranging from 20 to 80 years, the incidence of snow damage was highest for stands at the age of 30 years [44], and those damaged by snow and wind were significantly younger than the undamaged stands [52]. Likewise, a higher snow load was required to cause breakage in older spruce stands [53], likely due to the larger dimension trees. Yet, older trees may also be more susceptible to damage due to the higher occurrence of wood structural defects, as spruce is susceptible to stem cracks [54], bark-stripping [55] and root and butt rot [56].
Generally, resistance to stem breakage is a function of the cube of the stem DBH [41] and a larger stem diameter results in a greater structural rigidity (a higher modulus of rupture) and a higher resistance to ice accumulation before failure [23,32,52,57]. Hence, even, while trees from the upper stand layer in our study were damaged more than ones in lower canopy layers, about 30% of those overstory trees with a DBH from 10 to 15 cm were broken, compared to 3% of trees with a DBH greater than 40 cm. In other studies, after a moderate intensity ice-storm, the probability of damage ranged from about 0.13 to 0.03 for trees with a DBH of 10 to 100 cm, respectively. With ice accumulation >20 mm, the cumulative damage ranged from about 0.75 for trees with a DBH of 10 cm to about 0.35 for trees with a DBH of 100 cm [27]. In unmanaged stands with large trees, about 25% of spruces with a DBH of 15 cm was damaged, while larger trees were damaged about three times less frequently [26]. For snow damage, trees with a DBH of 10 to 60 cm had similar amounts of damage [44], though for snow and wind damage models predicted a slight, nonsignificant increase in probability of breakage with an increasing mean plot DBH [58].
With individual trees in our study, resistance to breakage increased with tree height (Figure 3c), partly due to the intercorrelation with the DBH. Other analyses revealed that both the mean and dominant stand height had a statistically insignificant effect on the proportion of damaged trees [59], but for trees with similar stem taper the resistance increased with tree height [41]. Likewise, for a given diameter or height, trees with a lower slenderness ratio are more stable [41,52,58,[60][61][62]. Overall, tree slenderness is among the main single-tree parameters affecting resistance to loading [41,46,50,60]. Likewise, our analyses revealed increased damage to slenderer and relatively thin trees, with a significantly higher proportion of damaged trees for each succeeding slenderness ratio group up to 1.10 ( Figure 3e). This is consistent with findings for several coniferous species, where the slenderness ratio of 0.8 was the threshold for damage occurrence [63].
Another factor that largely determines tree stability is the crown characteristics [46]. Trees with a larger crown are more vigorous due to better growth efficiency [64]. Smaller tree crowns are typically associated with crown asymmetry that increases the risk of damage due to unbalanced ice loading [40,65]. Similarly, we found less frequent damage among trees with a larger crown (Figure 3a), likely because the larger crown depth ensures more evenly distributed weight and lowers the center of gravity of the loading and increases the resistance to breakage [66]. However, a larger crown may have a heavier ice load due to the larger surface area of the canopy area.
Our results showed almost the same factors for the best explanatory models for all stands compared with the recently thinned stands. The site type, tree height, relative diameter, and crown ratio were common for both, with the additional parameters of the stand mean DBH for all stands and the stand density for recently thinned stands (Tables 3 and 4). Stem development and crown morphology are strongly affected by stand density [31,32,67]. Moreover, while our results revealed an increased proportion of broken spruce with a higher stand density (Figure 2c), other findings about how the stand density affects the damage severity are conflicting [23] and should be viewed in context with the tree slenderness ratio (as a measure of individual tree stability) and the initial stand density and effects of past thinning.
Within high-density stands, individual trees with a high slenderness ratio may be less susceptible than a similar tree in more open stands [52,68]. For a level of slenderness, the probability of wind and snow damage decreases with the increasing stand basal area, probably due to mutual support and collective stability, as has also been observed in stands with a basal area greater than about 20 m 2 ha −1 [59]. In very closely spaced stands, more damage may occur when a tree falls into neighboring trees due to intertwined crowns [69]. Moreover, in dense stands, the crowns of the trees tend to be shorter and more asymmetrical than in sparse stands [46] and trees are slenderer [53]. These characteristics may account for the damage in spruce sites where 95% of the snow damage occurred in stands with the first thinning delayed [44].
Overall, thinning reduces competition among trees, increases diameter growth, reduces slenderness [70] and increases the stability of individual trees. Moreover, while stands with a lower basal area are less damaged [39,58], during the first few years, they have increased sensitivity [46,61,71]. Our stands that were thinned during the three years before the ice loading were significantly more damaged than other stands, likely due to lost support from the neighboring trees [71] and the higher wind speed through the more open canopy [46]. Past studies have shown different results regarding the time needed to regain stand stability, but it seems strongly related to the proportion of basal area removed [34]. Heavily thinned spruce stands affected by several storms (the first was three years after thinning) had 10 times greater proportion of damaged basal area (7% and 74%, respectively) than the unthinned stands [34]. In contrast, as soon as two years after thinning, in 22-year-old spruce stands, the damage from snow loading was lower in thinned plots than unthinned plots [72]. Both the stands thinned 6 to 25 years prior to the damage and unmanaged stands have also shown a similar severity of damage [39].
Generally, thinning should strive to increase the stability of the trees to ice loading, similar to recommendations to increase resistance against other more frequently occurring abiotic damage by wind and snow [4]. Different strategies include: a silvicultural regime with no thinning [34], planting at wide spacing and thinning during early stand development [63], removing of high-risk trees [73] and thinning to promote crop trees [71]. However, the implications for financial return should be carefully assessed, while also considering the probability of icing events during a rotation. For instance, using a wide initial spacing and no subsequent thinning may reduce the total revenue before the final felling [34]. Nonetheless, initially sparse spruce stands at the age of 80 years may result in similar production to those with a commonly used higher initial density [31].

Conclusions
This study aimed to identify stand-and tree-level parameters affecting the probability of damage from ice accumulation in Norway spruce stands. We found considerable variation in damage severity among the studied stands, with overstory trees being most affected in comparison to those in understory or the advance regeneration. Nearly all damaged overstory trees had broken tops. Stands thinned less than three years before icing event were more susceptible than other stands. At the stand level, the probability of damage was less for older, less dense stands with a greater mean diameter, although the variation of these parameters suggests the need to evaluate other explanatory factors that may provide more accurate estimations. At the individual tree level, all measured parameters had a significant effect on damage occurrence. Among them, tree height, relative diameter and crown ratio were the best explanatory variables for both all stands and recently thinned stands. Overall, management practices that increase stability of individual trees should be promoted to reduce the risk of losses during occasional severe ice loading in Norway spruce stands. Financial implications should be considered when evaluating strategies that may reduce the chance of damage.