Table 1. Bayesian binary logistic generalized linear mixed-effect model estimates of tree- and stand-scale variables on the probability of wind damage for birch. For the variables with several levels, the estimate is the difference from the reference level. Data obtained from National Forest Inventory in Latvia.
Variable Estimate Est.error CI
Min Max
Intercept −5.03 0.27 −5.68 −4.62
Stand age (years)* 0.39 0.07 0.26 0.53
Dominant tree species (reference level: birch)*:
   Pine −0.45 0.17 −0.78 −0.13
   Spruce 0.08 0.16 −0.25 0.39
   Black alder 0.22 0.23 −0.25 0.69
   Aspen 0.17 0.21 −0.24 0.57
   Grey alder −0.13 0.45 −1.08 0.69
   Oak 0.08 0.77 −1.54 1.47
   Ash 0.06 0.70 −1.42 1.31
   Goat willow −0.39 1.31 −3.48 1.71
Stand density (trees ha–1)* −0.70 0.11 −0.92 −0.50
Overstory basal area (m2 ha–1)* 0.21 0.07 0.08 0.34
Management (reference level: not thinned in the last 5 years):
   Thinned in the last 5 years 0.17 0.17 −0.16 0.49
Site type (reference level: dry mineral soil)*:
   Wet mineral soil 0.00 0.20 −0.41 0.40
   Peat soil 0.75 0.20 0.36 1.14
   Drained wet mineral soil 0.32 0.15 0.03 0.60
   Drained peat soil 0.94 0.15 0.65 1.24
Slenderness ratio* 0.39 0.04 0.30 0.47
Prior damage (reference level: not damaged)*:
   Damaged 1.46 0.15 1.18 1.79
Est.error – standard deviation of posterior distribution; CI – 95% credible interval; * – significant effect according to 95% credible interval; Birch – Betula pendula and B. pubescens; Pine – Pinus sylvestris; Spruce – Picea abies; Black alder – Alnus glutinosa; Aspen – Populus tremula; Grey alder – Alnus incana; Oak – Quercus robur; Ash – Fraxinus excelsior; Goat willow – Salix caprea
Table 2. The tested tree- and stand-scale variables used to determine the probability of wind damage on birch by Bayesian binary logistic generalized linear mixed. The number of observations is noted for categorical variables and mean ± standard deviation (SD) is noted for continuous variables. Data obtained from National Forest Inventory in Latvia.
Variable Description Classes/ Range Number of observations/ Mean ± SD
2004–2008 2009–2013
Age Stand age, years 11–216 56.6 ± 20.9 58.1 ± 21.8
Growing stock Mean standing volume, m3 ha–1 16–850 270 ± 127 281 ± 136
Species Dominant tree species Birch 6639 7161
Pine 1825 1869
Spruce 1333 1334
Black alder 627 657
Aspen 793 787
Grey alder 398 341
Oak 47 47
Ash 63 25
Goat willow 36 52
Stand density Overstory number of trees, trees ha⁻¹) 100–11 520 1145 ± 875 1112 ± 906
Basal area Overstory basal area, m2 ha–1 3–67 27.2 ± 9.9 27.8 ± 10.2
Management Harvesting operations in the last five years Thinned 1800 721
Not thinned 9974 11 571
Site type Site types grouped according to soil conditions Dry mineral soil 4718 4804
Wet mineral soil 1374 1370
Peat soil 1058 1345
Drained mineral soil 2462 2434
Drained peat soil 2162 2339
Slenderness ratio Height (m) to diameter at breast height (cm) ratio 0.3–1.9 1.0 ± 0.2 1.0 ± 0.2
Prior damage Stem or root-stump damage in the previous measuring period Not damaged 11 303 11 572
Damaged 471 720
Birch – Betula pendula and B. pubescens; Pine – Pinus sylvestris; Spruce – Picea abies; Black alder – Alnus glutinosa; Aspen – Populus tremula; Grey alder – Alnus incana; Oak – Quercus robur; Ash – Fraxinus excelsior; Goat willow – Salix caprea
1

Fig. 1. The probability of wind damage to birch (Betula pendula and B. pubescens) in relation to the slenderness ratio (height (m) to the diameter at breast height (cm) ratio, HD–1), based on Latvian National Forest Inventory data. The 95% credible interval is represented by the grey area.

2

Fig. 2. The probability of wind damage to birch (Betula pendula and B. pubescens) in relation to the age of dominant tree species in a stand, based on Latvian National Forest Inventory data. The 95% credible interval is represented by the grey area.

3

Fig. 3. The relative snapping height of birch (Betula pendula and B. pubescens) in relation to the slenderness ratio (height (m) to the diameter at breast height (cm) ratio, HD–1), based on Latvian National Forest Inventory data. The 95% confidence interval is represented by the grey area.

Table 3. Generalized linear mixed-effects model estimates of slenderness ratio (HD–1), prior damage, and crown height (h-crown) effects on relative snapping height for birch. Data obtained from National Forest Inventory in Latvia.
Variable Estimate SE t-value p-value
Intercept 0.532 0.048 10.98 <0.001
HD–1 −0.097 0.044 −2.18 0.03
h-crown (m) 0.001 0.003 −0.49 0.06
Prior damage (Damaged vs Not damaged) −0.090 0.030 −2.98 0.003
SE = standard error
4

Fig. 4. The proportion of snapped birch trees (Betula pendula and B. pubescens) according to relative snapping height groups for previously damaged (black bars) and previously undamaged (light grey bars) trees, based on Latvian National Forest Inventory data.