*2.1. Soil Frost Modelling*

Soil frost conditions were modelled by using an extended version of the original soil temperature model [30]. It was derived from the law of conservation of energy and mass assuming constant water content in the soil. Model was further developed to take into account the heat flow below soil layer of consideration [42]. Following [42], soil temperature at depth *ZS* (m) can be calculated as follows:

$$T\_{\rm Z}^{t+1} = T\_{\rm Z}^{t} + \frac{\Lambda t \ast \bar{\mathbf{K}}\_{\rm T}}{(\mathbb{C}\_{\rm S} + \mathbb{C}\_{\rm d\mathcal{K}}) \ast (\mathbb{2} \times \mathbb{Z}\_{\rm S})^{2}} \ast \left[T\_{\rm AIR}^{t} - T\_{\rm Z}^{t}\right] \ast \left[\mathbb{e}^{-f\_{\rm S} \cdot \mathbf{D}\_{\rm S}}\right] + \frac{\Lambda t \ast \bar{\mathbf{K}}\_{\rm T,LOW}}{\left(\mathbb{C}\_{\rm S,LOW} + \mathbb{C}\_{\rm d\mathcal{K}}\right) \ast \mathbf{2} \ast \left(\mathbb{Z}\_{\rm I} - \mathbb{Z}\_{\rm S}\right)^{2}} \ast \left[T\_{\rm LOW} - T\_{\rm Z}^{t}\right],\tag{1}$$

where *T<sup>t</sup> Z* ( ◦C) is the soil temperature on a previous day, *TAIR* ( ◦C) is the air temperature, Δ*t* is the length of a time step (s), *KT* (W m−<sup>1</sup> ◦C−1) is the thermal conductivity of the soil above *ZS*, *CS* (J m−<sup>3</sup> ◦C<sup>−</sup>1) is the specific heat capacity of the soil above *ZS*, *CICE* (J m−<sup>3</sup> ◦C−1) is the specific heat capacity due to freezing and thawing, *fS* (m−1) is an empirical damping parameter due to snow cover, *DS* (m) is snow depth, *KT,LOW* (W m−<sup>1</sup> ◦C<sup>−</sup>1) is the thermal conductivity of the soil below *ZS*, *CS,LOW* (J m−<sup>3</sup> ◦C<sup>−</sup>1) is specific heat capacity of the soil below *ZS*, and *TLOW* ( ◦C) is soil temperature at the depth of Zl. Following to [31], *Zl* was set to 6.8 m.

By using soil temperature observations from several stations across Finland, the soil temperature model was parametrized for three different soil types: clay or silt soil, sandy soil, and peatlands [31]. Between the depths of 20 and 100 cm, the parametrized model explained approximately 90–99% of the observed variability in soil temperatures.

In a study by [31], also a snow depth model (based largely on the work of [43]) was used to simulate the snow depth, using daily temperature and precipitation observations [44], for different forest conditions in addition to open areas. In this study, we used the soil frost data calculated by [31] for different combinations of forest and soil types, based on combined use of soil temperature and snow depth model. The soil frost data in 0.1◦ × 0.2◦ grid has been calculated for dense spruce stands on clay or silt soil (hereafter CSS), pine stands on sandy soil (hereafter SP) and pine stands on peatlands (hereafter PP), respectively. Calculations for each of the forest and soil types were performed on every grid cell. The soil was assumed to be frozen and provide sufficient anchorage for trees when the modelled soil frost extended at least to a depth of 20 cm continuously from the surface and unfrozen otherwise. The expectation of the sufficient anchorage was based on the typical rooting depth of main boreal tree species, see e.g., [21,24,27,28].

#### *2.2. Estimation of the 10-Year Return Levels of Wind Speed*

The 10-year return levels, corresponding to an annual probability of exceeding the 90th percentile, of maximum wind speeds were calculated using the ERA-Interim dataset [32] covering years 1979–2014 and the generalized extreme value method (GEV) [45]. We used the block maxima approach, in this case for seasonal maximum wind speeds of both frozen and unfrozen soil season, with the

maximum-likelihood fitting of GEV distribution [46,47]. We analysed 10-minute instantaneous wind speeds available at 6-hour intervals given as grid box averages, each covering an area of 0.75◦ × 0.75◦.

The maximum wind speed dependence on wind direction was estimated by making the calculations wind direction wise, i.e., the 10-year return levels were estimated separately for cardinal and intercardinal wind direction sectors. For comparison and validation purposes, 10-year return levels were also calculated for 40 weather stations (Figure 1a) across Finland (on mainland) using wind speed observations covering the same period of 1979–2014 as in the ERA-Interim dataset. Observational data consisted of synoptic observations of 10-minute average wind speed with 3-hour measurement interval.

Compared to our data period of 1979–2014, the 10-year return level estimates can be expected to be quite robust. Estimated 10-year return level, i.e., wind speed equalled or exceeded on average once every 10 years, is relatively short period compared to our data period of 35 years. However, in coastal regions of southern and southwestern Finland, uncertainties related to the statistical estimation of return level is somewhat increased. This applies particularly for PP as, based on soil frost calculations by [31], mild winters with no soil frost, or at least not exceeding 20 cm in depth, are quite common (not shown). In these cases, the dataset from which soil frost season return levels are calculated is smaller, leading to a wider return level estimate confidence intervals. Also, regions with only short soil frost period, when the window for seasons maximum wind speed can often be only e.g., 1–2 months, have larger variability in the used dataset for return level estimation, therefore increasing uncertainty even if totally frost-free years are rare.

Considering normal approximation 95% confidence intervals of calculated 10-year return level estimates for weather stations, range is on average +/−1 m/s over all 1920 return level calculations consisting of 40 stations, eight wind directions, three forest soil types, and distinction between frozen and unfrozen soil season, respectively.
