Estimation of the high-spatial-resolution variability in extreme wind speeds for forestry applications

The bioeconomy has an increasing role to play in climate change mitigation and the sustainable development of national economies. In Finland, a forested country, over 50 % of the current bioeconomy relies on the sustainable management and utilization of forest resources. Wind storms are a major risk that forests are exposed to and high-spatial-resolution analysis of the most vulnerable locations can produce risk assessment of forest management planning. In this paper, we examine the feasibility of the wind multiplier approach for downscaling of maximum wind speed, using 20 m spatial resolution CORINE land-use dataset and high-resolution digital elevation data. A coarse spatial resolution estimate of the 10-year return level of maximum wind speed was obtained from the ERA-Interim reanalyzed data. Using a geospatial re-mapping technique the data were downscaled to 26 meteorological station locations to represent very diverse environments. Applying a comparison, we find that the downscaled 10-year return levels represent 66 % of the observed variation among the stations examined. In addition, the spatial variation in wind-multiplier-downscaled 10-year return level wind was compared with the WAsP model-simulated wind. The heterogeneous test area was situated in northern Finland, and it was found that the major features of the spatial variation were similar, but in some locations, there were relatively large differences. The results indicate that the wind multiplier method offers a pragmatic and computationally feasible tool for identifying at a high spatial resolution those locations with the highest forest wind damage risks. It can also be used to provide the necessary wind climate information for wind damage risk model calculations, thus making it possible to estimate the probability of predicted threshold wind speeds for wind damage and consequently the probability (and amount) of wind damage for certain forest stand configurations.


Introduction
The forest-based bioeconomy plays an important role in climate change mitigation (Kilpeläinen et al., 2016), and in a forested country like Finland, over 50 % of the current bioeconomy relies on the sustainable management and utilization of forest resources.In Scandinavia, forest grows relatively slowly, and it takes typically 50-100 years from forest cultivation to final harvesting.During this long period the projected climate change (Ruosteenoja et al., 2016) may largely alter the growing conditions, thus affecting the survival and productivity of forests (Kellomäki et al., 2008;Bärring et al., 2017).For example, according to Bärring et al. (2017) in Scandinavia the vegetative growing period may extent by around 1 month by 2050 compared to current climate.A warming climate is expected to increase the volume of growing stock of Finnish forests due to increasing forest growth (see, e.g., Kellomäki et al., 2008).However, warming is also expected to increase certain risks to forests.Drought may have negative impacts especially in southern Finland for Norway spruce forests (Ruosteenoja et al., 2017;Kellomäki et al., 2008).Related to drought, forest fire danger will increase (Lehtonen et al., 2016b).During winter season heavy snow Published by Copernicus Publications on behalf of the European Geosciences Union.
A. Venäläinen et al.: The high-spatial-resolution variability in extreme wind speed loads will decrease in southern but increase in northern Finland (Lehtonen et al., 2016a).In the past few decades, wind storms have damaged a significant amount of timber and caused large economic and ecological losses in forestry from central to northern Europe (Schelhaas et al., 2003;Gregow, 2013;Gregow et al., 2011;Reyer et al., 2017).In Finland, strong winds have damaged over 24 million m 3 of timber in different winter and summer storms since 2000 (e.g., Gregow et al., 2011;Zubizarreta-Gerendiain et al., 2017).During the coming decades, the risk of wind damage to forests is expected to increase, although the frequency and severity of the storms may not increase (Nikulin et al., 2011;Pryor et al., 2012).This increase is due to the shortening of the frozen soil period, which currently improves tree anchorage during the windiest season of the year from late autumn to early spring (Peltola et al., 1999a;Venäläinen et al., 2001;Kellomäki et al., 2010;Gregow et al., 2011).
In addition to the properties of wind (e.g., speed, direction, gustiness and their duration), the stand and site characteristics affect largely the vulnerability to wind damage (Peltola et al., 1999b;Gardiner et al., 2016).In Finnish conditions, mature stands adjacent to newly clear-cut areas or recently heavily thinned stands are especially vulnerable to wind damage (e.g., Laiho, 1987;Zubizarreta-Gerendiain et al., 2012).Risks to these forests may be decreased by proper forest management and planning for the spatial and temporal patterns of cuttings in forested areas (Tarp and Helles, 1997;Meilby et al., 2001;Zeng et al., 2004Zeng et al., , 2007a;;Heinonen et al., 2009;Zubizarreta-Gerendian et al., 2017).Several mechanistic models that have been built in recent decades allow the prediction of threshold wind speeds that can uproot or break trees under alternative forest stand configurations (e.g., Peltola et al., 1999bPeltola et al., , 2010;;Gardiner et al., 2000Gardiner et al., , 2008;;Byrne and Mitchell, 2013;Seidl et al., 2014;Dupont et al., 2015).Consequently, based on these predicted threshold wind speeds it will be possible to predict the probability (and amount) of wind damage based on local wind characteristics if sufficient knowledge about the local wind climate is available (e.g., Gardiner et al., 2008;Blennow et al., 2010;Zubizarreta-Gerendian et al., 2017).
An estimation of the frequency of extreme weather events, like extreme wind speeds, can be accomplished by utilizing extreme value analysis (EVA) methods.These methods enable to fit their statistical distribution (e.g., Gumbel, Frechet or Weibull distribution) into observations that offer the best estimate of the occurrence probability of the most extreme values of the studied phenomena (e.g., Coles, 2001).The software package, Extremes Toolkit, developed by the National Center of Atmospheric Research (NCAR), is a widely used example of a tool that can be utilized to produce such a statistical distribution (Gilleland and Katz, 2011).For an accurate estimation of the probability of the occurrence of very extreme events with long return periods (e.g., 50 to 100 years), observations over many decades are needed.Additional difficulty to gain an accurate estimation of return levels of extreme wind speeds and wind gusts is caused by a lack of homogeneous wind observation time series due to changes in the measuring conditions and instruments (Laapas and Venäläinen, 2017).One possibility of assessing the return levels of extreme wind speed in coarse resolution is to use reanalyzed datasets (e.g., Dee et al., 2011), which are produced by assimilating all available observations in a systematic way.The benefit of these datasets is that they offer consistent spatial and temporal resolution over several decades (and hundreds of variables).Reanalyzed datasets are also relatively straightforward to handle from a processing standpoint.Although the quality of these data varies from location to location and from variable to variable, the scale of the magnitude of extreme wind for a coarse spatial scale can indeed be estimated based on them (e.g., Brönniman et al., 2012).From the point of local effects, the ERA-Interim dataset has a relatively coarse spatial resolution of about 80 km and detailed spatial variation cannot be taken into account in such a coarse grid.In addition, the continuous change in the availability of reliable observational data creates limitations and must be taken into account, especially if trend analyses of a change in, for example, wind are made (Dee et al., 2011).
The high-resolution spatial variation in extreme wind speed that is affected by topography and surface characteristics (e.g., Wieringa, 1986) can be considered by applying spatial statistical tools (e.g., Etienne et al., 2010;Jung and Schindler, 2015).Additionally, complex airflow models like WAsP (Mortensen, 2015) and WindSim (http://www.windsim.com/),typically applied for wind power potential predictions, can be used for this purpose.One example of exposure estimation is the detailed aspect method of scoring (DAMS), which takes into account the local wind climate, elevation, aspect and topographic exposure (Quine and White, 1993;Hale et al., 2015).DAMS is used in the Forest-GALES (http://www.forestry.gov.uk/forestgales) for estimating the probability of wind speeds that cause damage.GISbased methods for mapping the most wind damage prone areas have also been introduced (e.g., Talkkari et al., 2000;Zeng et al., 2007b;Schindler et al., 2012;Ruel et al., 2002).A pragmatic and computationally very feasible approach to use to estimate the return levels of extreme wind speeds for large geographical areas with very high spatial resolution is the wind multiplier approach.In this approach, regional wind speeds obtained, for example, from the reanalyzed data (or climate change scenario), are downscaled to local wind speeds to consider the local effects of land cover and topography (e.g., Jones et al., 2005;Cechet et al., 2012;Yang et al., 2014).By applying GIS tools to detailed land-use data and digital elevation maps, it is also very straightforward to produce the required multipliers.
In this study, we evaluated the applicability of the wind multiplier approach for an estimation of the highresolution (20 m) variability of extreme wind speeds in Finnish forested landscapes, employing CORINE land-use and high-resolution digital elevation data.First we calculated the return levels of extreme wind speeds using the ERA-Interim reanalyses dataset to each coarse resolution grid box and for eight wind directions (cardinal and sub-cardinal).Based on the elevation data, the wind multiplier depicting the effect of orography on wind speed was processed.Likewise, the multiplier depicting the effect of terrain properties on wind speed was processed for each 20 m grid square.Thereafter, wind multipliers were used to provide quantitative estimates of local wind conditions relative to the regional wind speeds in our 20 km × 20 km test area located in northern Finland and for 26 meteorological observing stations with various surface characteristics in different parts of the country as well.The data processing was done using standard Python, QGIS, and ArcGis software routines.The work was motivated by the fact that fulfilling the increasing needs of forest biomass for the growing forest-based bioeconomy will also require increasing area of thinned and clear-cut areas (Heinonen et al., 2017), thus increasing the wind damage and other risks to these forests.Having reliable high-resolution information on extreme wind speeds expected over forested landscapes will enhance both forest management and planning.The method gives a detailed estimate of the exposure of forest to wind damage.However, it is worth noting that if the coarse resolution data that are been downscaled are biased, then the downscaled data will be biased too.For example, climate scenarios that often contain biases must be bias-corrected prior to downscaling.

The wind multiplier approach
The wind multiplier approach used here follows the one presented in AS/NZS 1170.2 (2011) and Yang et al. (2014), where terrain properties are taken into account when assessing local maximum wind speeds (see Eq. 1).The return level of regional maximum wind speed (V R ) in an open terrain at a 10 m height is downscaled into site-specific maximum wind speed (V site ) as follows: where the three wind multipliers used are the terrain/height multiplier (M z ), shielding multiplier (M s ) and topographic (hill-shape) multiplier (M h ).The impact of wind direction is taken into account using a fourth factor (M d ).In our study, we use a 20 m × 20 m grid, which is in line with the CORINE Land Cover 2012 dataset.It provides information on land cover and land use in 2012, and its changes from 2006 to 2012 (based on the European Gioland 2012 project).Our interest is forested landscape (including practically no buildings or other similar obstacles); therefore, the shielding factor was not considered.The return levels of winds speeds (V R ) were also defined separately for the eight cardinal and intercardinal wind directions.Thus, there was no need to calculate the direction multiplier (M d ).
2.2 Estimation of return level for regional maximum wind speeds The regional-scale return levels of maximum wind speeds were calculated using the ERA-Interim dataset (Dee et al., 2011) and the generalized extreme value (GEV) method (e.g., Coles, 2001).This method estimated the 10-year return level of maximum wind speed as, for example, in inland Finland at below 12 m s −1 and on the open sea at even around 24 m s −1 (Fig. 1).The values are given as grid box averages, each covering an area of 0.75 • × 0.75 • , and the time period used for the calculation of return levels covered years 1979-2015.The maximum wind speed dependence on wind direction was estimated by making the calculations wind direction wise (Fig. A1).The parameter we analyzed was 10 min instantaneous wind speed available at 6 h intervals.The GEV distribution is based on the block maxima approach -i.e., we have maximum values for the selected block, in our cases year, and the distribution is fitted to these data (Coles, 2001).In northern Europe, like in Finland, the cause of the high wind speeds varies from season to season.During summer the extreme wind speed values are typically associated with convective weather phenomena, whereas during winter season they are caused by large synoptic-scale wind storms.As we use only the annual maximum wind speed in the return level calculations we have not paid attention to the cause of the extreme wind speed.

Estimation of the impact of terrain roughness on maximum wind speeds
In AS/NZS 1170.2 (2011) for elevations below 50 m, 1000 m fetch was used when the surface roughness impact was estimated.In this study, we applied a somewhat different approach.First, each CORINE land-use class was interpreted to roughness lengths following the technique applied in the production of the Finnish Wind Atlas (Tammelin et al., 2013).We were interested in this work in very high-resolution spatial variation in wind speed in typically highly variable terrain mosaic composed of forests, fields, lakes, clear-cut areas etc.The detailed structure of wind flow in this kind of heterogeneous terrain is very complex (e.g., Dupont and Brunet, 2008).One dominant feature is rapid deceleration of wind when wind encounters a forest edge.In Finnish conditions the main wind damages are found typically within one to two mean stand heights from the upwind forest edge (Peltola et al., 1999b).When estimating the impacts of upwind conditions on wind speed in the location that was of interest, we used 500 m fetch to calculate the effective roughness (z eff ).As the conditions close to the place of interest have a larger importance than the values at a further distance, each 20 m grid cell had a weighting factor (we), which was presumed to follow normal distribution (Eq.2) having variance of 150 m.With these assumptions the weighting of each grid is as demonstrated in Fig. A2.The weight of the closest grid square is about 11 % and the furthest grid square located 500 m upwind has a weight of only 0.04 %.This formula is doubtless a simplification of a very complex issue as the exact impact of roughness elements on wind flow depend, beside terrain properties also on the characteristics of prevailing air flow.However, when we want to have an application that is computationally so light that it can be utilized easily, all these issues cannot be taken into account and the approach selected here gives a realistic interpretation of the complicated issue.
where σ defines the shape of distribution and, in our case (150), x is the fetch and µ the location, in this case zero.Thus, z eff was calculated as where z oi is the surface roughness length of ith 20 m grid cell.The final step to calculate the surface-roughness-dependent multiplier (M z ) was to use the estimates given in Tables 3.2 and 3.3 by Yang et al. (2014).This step led to an estimate given in Eq. ( 4).
The multipliers were defined for eight directions (cardinal and intercardinal), using the GDAL raster utility programs.
In ERA-Interim analyses, a roughness length for each grid cell is presumed.To normalize the roughness length of the ERA-Interim data into a reference roughness, we multiplied the ERA-Interim wind speed values by 1/M z (Eq.4), using the ERA-Interim grid cell roughness length as the value of z eff .
The values of z 0 , z eff and M z in the case of sharp roughness change between forest and lake are demonstrated in Fig. 2. When the wind comes from an open lake (z 0 = 0.0004 m) to dense forest (z 0 = 1.4 m), the multiplier M z changes from 1.21 to 0.75 within a distance of 300 m and to 0.80 within a distance of 80 m.The change is very rapid, demonstrating the strong slowing of wind speed within a dense forest during the first tens of meters.This rapid change is demonstrated in the case where the most vulnerable forest edges are studied; the wind-throw risk is largest within approximately 20-30 m from the upwind edge of a clear-cut area (e.g., Peltola et al., 1999b).The acceleration of wind speed from forest to open water surface is not as rapid as the slowing; the change in M z from the minimum value of 0.75 to maximum takes about 500 m (Fig. 2).This rate of acceleration is quite close to the values introduced by Venäläinen et al. (1998).The land-use map and the values of Z eff and M z for the Pyhtätunturi Fell area for northwesterly winds are given in Figs.A3 and A4, respectively.

Estimation of the impact of topography on maximum wind speeds
The topographic multiplier M h was taken as the larger of the two estimates M h1 and M h2 (Eq.5).
M h1 simulates the impact of small-scale topographic variation that is typical in Finland.H eff is calculated as the difference between the place of interest and the median elevation of 1000 m distance upwind from the location of interest (see Fig. 3).The logarithmic shape follows that of logarithmic wind law in the case of surface roughness of 1 m that is typical for a forest and wind speed 15 m s −1 at an elevation of 10 m.The other multiplier, M h2 , simulates the general increase of wind speed as a function of elevation.The shape of Eq. ( 5b) is based on an estimate of the dependence of a 50-year return level of maximum wind speed on elevation, defined by using wind measurements made at observing stations located at different elevations (not published).Finland is a rather flat country, and most of the country is located below an elevation of 200 m a.s.l (above sea level).Multiplier M h2 is thus larger than M h1 at only very rare locations in the entire country.The topographic wind multiplier M h was calculated using the digital elevation data obtained from the Finnish National Data Survey.The data were 25 m spatial resolution raster data re-sampled to 20 m resolution.The data were first smoothed by replacing each pixel with the average of its 3 × 3 neighborhood to filter out the very small-scale noisy features the data might contain.The processing was done by utilizing the R package "raster".H eff was then calculated in the eight directions of the wind, using Python and the GDAL routine.
An example of the change in topographic multiplier in the case of a transection reaching over the roughly 500 m high Pyhätunturi Fell (Fig. 5) in northern Finland in the case of northwesterly wind is given in Figs. 4 and A5.As this place is located at a relatively high elevation, the purely on elevation-dependent M h2 dominates, and only in the case of a steep hill slope around the location interval 11 655-13 405 m (Fig. 4) does the multiplier M h1 get larger values than M h2 .The approach used in this study is also simpler than the one described in AS/NZS 1170.2 (2011).Still, as the terrain in Finland is relatively flat, the main impact of these relatively small-scale topographic variations can be taken into account even with the schema utilized here., A3).In addition to the forests, other terrain types included open tundra, agricultural fields, lakes, and ski slopes.The test area had both larger topographic variation and spatial variation in wind speeds than the typical Finnish landscape and in that sense represented more challenging conditions than those expected in most of the rest of the country.This Pyhätunturi Fell test area was also used in the EU-funded MOWIE project, where three 10 m tall wind-measuring masts were installed at a range of elevations above the mean sea level: 470 m (MM1), 419 m (MM2) and 408 m (MM3).In addition, there was a permanent observing mast (FMI station number 7708) on the telecommunication mast (TM) at an elevation of 61 m above the surface at the top of the hill (see Fig. 5).All wind speed measurements were corrected to 10 m high values by applying the logarithmic wind law.Wind climate simulations for this same area have earlier been made utilizing the Karlsruhe Mesoscale Model (KAMM) and WAsP by Frank et al. (1999).An airborne detailed photograph of the area is available, for example, from the Finnish Land Survey's map service (https: //asiointi.maanmittauslaitos.fi/karttapaikka/?lang=en).
Based on the measurements made at the observing stations, 10-year return levels of maximum wind speeds were calculated for each location and compared with return period values obtained for the station locations using the wind multiplier approach and the ERA-Interim maximum wind speed estimates.The return levels were calculated using the same GEV approach as in the case of ERA-Interim data.The observations were 10 min winds speed measured after every 3 h and the annual maximum values was filtered from these data.In this sense the observational values are not exactly the same as reanalyzed data, and this may create some systematic difference.However, when using the annual maximum values as the bases for fitting the distribution this may reduce the bias.For stations MM1, MM2 and MM3, there was only 2 years of data available, a short period to estimate even 10-year return levels.Therefore, to have the extreme value analysis be as robust as possible, for these stations, we applied the block maxima approach (e.g., Coles, 2001) to the monthly maximum values, using the R package extRemes (Gilleland and Katz, 2016).For most of the other station locations, the data used for the extreme value analyses covered the years 1979-2015, which is the same period as used in the case of ERA-Interim data.
For the Pyhätunturi Fell area, we also compared a spatial variation in high wind speed as simulated by the WAsP package with a wind multiplier downscaled wind.The area was slightly smaller (Fig. 5) due to the availability of terrain information needed for a WAsP simulation.In the WAsP simulation, the geostrophic wind speed was expected to be 39 m s −1 from northwest.This geostrophic wind speed leads to approximately 26 m s −1 winds at the top of the Pyhätunturi Fell, which is roughly the 10-year return level maximum wind speed (see Table 1).For a comparable wind multiplier downscaling, the coarse-scale northwesterly wind 12.7 m s −1 was used as the basis in the calculation.In this way the maximum wind speed was the same in both simulations.

Comparison of measurement-based return levels to those based on a wind multiplier approach
A comparison of the ERA-Interim and wind-multiplier-based assessment of 10-year return levels of wind speed to the estimates based on measurements for the test locations (Table 1, Fig. 6) revealed that for these locations, and representing different kinds of terrain and elevations, the wind multiplier approach improved the local wind speed return level estimates remarkably (R 2 = 0.66).There was a small bias in the estimates, the mean difference being −1.2 m s −1 and the RMSE 4.09 m s −1 .According to the comparison, the wind multiplier approach tends to underestimate the wind speed on station located at small Baltic Sea islands -i.e., according to the measurements there is less deceleration of wind speed on these islands than predicted by the method (Fig. 6).This indicates that the method exaggerates the impact of change in surface roughness on wind speed in these rather specific conditions.As we are interested in inland and mainly forested landscape, this is not a crucial issue.However, further development of the method is needed in order to also be able to simulate the coastal and island conditions.The largest differences were found in the case of station no.9004, which is located at an elevation of 1004 m a.s.l., i.e., almost at the highest point in Finland.The anemometer at this station is also located at the Wind multiplier ERA-Interim Small island stations Figure 6.Comparison of 10-year return levels of maximum wind speeds, as calculated, based on observations and by utilizing the wind multiplier method (Eq. 1) and the ERA-Interim dataset for the 26 measuring sites (Fig. 5).Return levels taken directly from the ERA-Interim dataset with no wind multiplier correction are included in the visualization.The shaded areas are 95 % confidence levels for the linear trend lines depicting the dependence between the datasets.The diamond shape symbols indicate that the station is located on small Baltic Sea islands.edge of a steep slope, thus leading to a high topographic multiplier value.
At the four Pyhätunturi Fell stations, the wind multiplier estimates were close to the measurement-based estimates with the exception of station MM1.The estimate based on measurements made at MM1 (29.6 m s −1 ) was about 5 m s −1 higher than the return level estimate calculated for the telecom mast at the same height.The difference between MM1 and MM2 was about 3 m s −1 .The return level estimates for stations MM1, MM2 and MM3 were based on 2 years of measurements and also led to a high degree of uncertainty.For example, for station MM1, the estimated 95 % confidence levels were 23.1 to 36.1 m s −1 .The corresponding estimate of the telecom tower based on 19 years of measurements was more robust with 95 % confidence levels, i.e., 21.5 to 27.6 m s −1 .

Spatial variation in maximum wind speeds
The spatial variation in 10-year return levels of wind speeds within the roughly 4000 km 2 Pyhätunturi test area was large.The lowest values for the 10-year return level were around 9.2 m s −1 and the highest on top of the Pyhätunturi Fell were approximately 26.5 m s −1 (Fig. 7).A crude approximation indicates that mean 10 min wind speed exceeding 12 m s −1 can uproot or break a tree during unfrozen soil conditions (Peltola et al., 1999b;Zubizarreta-Gerendiain et al., 2012).
Table 1.Ten-year return levels of maximum wind speed (m s −1 ) as estimated directly from ERA-Interim data, downscaled to station locations using the wind multiplier approach, and calculated based on measurements for the station locations given in Fig. 5 When we looked at the spatial variation in a 10-year return level of wind speed inside the test area, we can see areas having wind speeds higher than the threshold of 12 m s −1 found on local topographic formations, at the edges of open terrain, and at high-elevation locations.At a total 23.8 % of grid squares, the 10-year return level wind speed reaches the threshold, and if we look only at the forested area, then we end up with 22.8 %.This statistic means that approximately 20 % of the area is exposed to wind speeds that can lead to forest damage.The exact value depends, however, on several factors, including tree and stand characteristics.The next step is to use a wind-throw risk model like HWIND (Peltola et al., 1999b) to simulate the threshold wind speeds needed for wind damage and further to estimate the probability of occurrence of such winds and the amount of damage, respectively.Unfortunately, in this work we do not have the needed forest inventory data available for the test area enabling the simulations.However, this work will be done in future studies using forested areas with sufficient data.In a qualitative comparison, the wind multiplier approach and a WAsP simulation produced the same dominant features of spatial variation in maximum wind speed; maximum val- Ten-year return levels of maximum wind speed (A) calculated using the wind multiplier method (Eq. 1) and the ERA-Interim dataset for the Pyhätunturi test area (Fig. 5).The values where wind speed exceeded 12 m s −1 are indicated by a black dotted line.ues were found at treeless fell-top areas (Fig. 8).One interesting feature was the case of the WAsP simulation for the acceleration of wind at the forest-lake edge; it was immediate, and so was the deceleration on the opposite shore.In such a case of wind multiplier simulation, the impact of roughness change is reflected over a longer distance, as can be seen in the case of the Lake Pyhäjärvi.On top of the fell, the wind speed was adjusted to approximately the same 26 m s −1 .On the lee side of the top of the fell, the wind multiplier simulations indicated a more rapid deceleration of wind speed than WAsP, while on the side to windward, the wind multiplier gave higher wind speeds.With no proper measurements, we could not decide which reflected the real conditions better.
In the case of canyons like Pyhäkuru and Pikkukuru (Fig. 8) WAsP is more capable of predicting higher wind speed values than the wind multiplier and obviously reflect the prevailing conditions better.For most of the lower elevation areas, the difference between the two simulations was small, and with these input wind speeds, the prevailing difference is on the scale of 1 m s −1 , with the wind multiplier giving systematically higher wind speeds (Fig. A6).By scaling wind multiplier input wind speed lower, the bias could have been adjusted to zero.

Reliability of tested method
The wind multiplier method has been used earlier to estimate the design values of buildings and other constructions (AS/NZS 1170.2, 2011) and assessment of wind damage risk (Yang et al., 2014).Based on our study, the wind multiplier method is very capable of identifying the locations having the highest extreme wind speeds in Finnish conditions.This is true despite the fact that this approach is much simpler than the dynamical models.The method seem to underestimate wind speeds at small islands located on the open sea and this issue has to be taken into account if high-spatialresolution assessment of extreme wind speeds is calculated to such conditions.The wind multiplier approach is also easily transferable to any location with needed terrain information and is an interesting and easily applicable alternative to use to assess the exposure of terrain.How precise each grid square estimate is depends on several external factors.First, we must have an estimate of the coarse-scale return levels of the extreme wind speeds.Reanalyzed data give such a coarse estimate.If the reanalyzed data are compared to in situ measurements in certain wind storm event, it is easy to find large differences between them.In addition, the return levels of wind speed calculated using ERA-Interim grid values can be quite different from the value based on point measurements, but downscaling the grid value to the point using the wind multiplier approach improves the estimate substantially, as we demonstrated in Fig. 6.It is also good to remember that, although the wind measurements made at meteorological stations can go through several quality control steps, they may still contain erroneous values.FMI has a three-stage quality control system.The first check is done at the observation station site checking the main instrument malfunctions.The next check is done before storing the data in the database.This check includes, for example, comparison with the extreme values and temporal and spatial consistency.The final step is the manual quality control for those values that did not pass earlier steps.The quality control ensures that the values stored in database are realistic and can have occurred.However, quality control does not guarantee that the measurements are exactly correct.In addition, quality control does not ensure the homogeneity of observations.The changes at measuring site and changes in instrumentation as well as the changes in the height of anemometer installation can lead to discontinuations, i.e., break points, in observational time series.These break points are relatively common also in wind observational time series like studied by Laapas and Venäläinen (2017).In that sense the return periods based on measured values (Table 1, Fig. 6) contain uncertainties that are wise to remember when the comparison is fully valued.
The simple visualization and comparison of the spatial variation in wind speed at Pyhätunturi Fell was done by ap-plying WAsP and, in addition, by applying wind multipliers.These demonstrate that the main features of spatial variation in an extreme wind field produced by these two different methods are very similar.A profound analysis on the exact accuracy of the simulations is not possible, however, based on the available measurements; it would require much more detailed and reliable wind measurement data.However, by fine tuning the wind multipliers, it is possible to achieve results that are closer to the WAsP simulation.Pyhätunturi is not a typical Finnish forested landscape due to its high topographic variation.In those parts of the test area that exemplify a more typical landscape with only relatively small topographic features and found at elevations below 300 m, these two methods give quite similar results.It is also good to remember that, as we are summarizing all wind directions (Fig. 7), the importance of lee-side wind simulation accuracy is not as crucial as having accuracy for the windward size having the highest wind speeds.
The wind multiplier method itself is also relatively easy to apply.The calculation of surface roughness and topographic multipliers can be done using routine GIS tools, and these calculations can be done for large areas, such as the whole country.Similarly, this method could be used to assess the risks to forests that are related to forest management and planning with relatively little extra effort.Further, climate change impact assessments can be done with high spatial resolution when the return levels of maximum wind speed are calculated using climate scenarios instead of only reanalyzed data.
One challenge of the method is the accuracy of surface roughness information in the CORINE dataset; it is updated approximately every 6 years and thus does not represent real-time land-use conditions for all locations.For example, forest clear-cutting changes the roughness conditions very dramatically.Thinning affects it less.More frequent updates to surface conditions could be obtained from satellite measurements.As an example, the European Space Agency's (ESA) satellite Sentinel-2 (http://www.esa.int/Our_Activities/Observing_the_Earth/Copernicus/Sentinel-2) is producing high-spatial-resolution (at best 10 m) data describing the earth surface properties.Because of the development of satellite-measured data handling methods, the data can provide new possibilities for updating the surface state with a higher frequency than, for example, the CORINE data are updated.Use of up-to-date airborne laser scanning data, if available (e.g., Kotivuori et al., 2016), can also offer a viable means to provide very detailed information on forest properties and thus also offer information on surface roughness conditions.

Conclusions
The rapidly growing, forest-based bioeconomy calls for increasing wood harvesting intensity, which means an increase in thinning and a final felling area.This will increase the wind damage risks to forests, especially at the upwind edges of new clear-felling areas and in recently thinned stands that have not yet been acclimated to increasing wind loading.Thus, proper risk assessment is a clear pre-condition for a sustainable forest-based bioeconomy.This study demonstrated a useful tool to use for forest management and planning.
The tested wind multiplier method is very capable of identifying the locations (at high resolution) having the highest extreme wind speeds and could well support the precise assessment of wind damage risks to forests.It can also be used to provide needed wind climate information for wind damage risk model calculations.Thus, it would make it possible to estimate the probability of predicted threshold wind speeds for wind damage, and consequently the probability (and amount) of wind damage under certain forest stand configurations.Accurate estimations of the spatial variation in the return levels of extreme wind speed with very high spatial resolution over the whole country or even over larger areas like Fennoscandia are possible in the future using this approach.A high-resolution estimation of climate change impacts on wind damage risks to forests is also feasible using this approach.

Figure A6.
Histogram depicting the difference between the wind speed as estimated using the wind multiplier approach and as calculated using the WAsP programme (see Fig. 8).

532A.Figure 1 .
Figure 1.Ten-year return level of maximum wind speed calculated using ERA-Interim 1979-2015 data and the GEV analysis approach.

Figure 2 .
Figure 2. The value of surface roughness lengths z 0 and z eff and the surface-roughness-dependent wind multiplier (M z ) in cases where wind is from lake to forest (a) and from forest to lake (b).

Figure 3 .
Figure 3.A visualization of the calculation of the topographic multiplier M h .

Figure 4 .
Figure 4. Variations in elevation (H msl ), median elevation (H med ), and the effective elevation (H eff ) (left axis) and topographic multipliers Mh1 and Mh2 (Eq. 5, Fig. 3) (right axis) along a transection from northwest to southeast (the black line in Fig. 5) crossing the Pyhätunturi Fell in northern Finland.

Figure 5 .
Figure 5.The meteorological stations used in the analyses (see Table 1, Fig. 6) and the topography of the Pyhätunturi area located in northern Finland.The black northwest direction line in the Pyhätunturi figure indicates the transection analyzed in Fig. 4; the black square indicates the border of the WAsP simulation.
level (m s ) ERA−Interim and wind multiplier -1 Figure7.Ten-year return levels of maximum wind speed (A) calculated using the wind multiplier method (Eq. 1) and the ERA-Interim dataset for the Pyhätunturi test area (Fig.5).The values where wind speed exceeded 12 m s −1 are indicated by a black dotted line.

Figure 8 .
Figure8.Comparison of the spatial variation in wind speed as estimated, using the wind multiplier approach, calculated using the WAsP program.The last figure depicts the difference between the two methods.Wind direction is from the northwest and in the case of the wind multiplier it is 12.7 m s −1 .For the WAsP simulation a geostrophic northwesterly wind of 39.2 m s −1 was assumed.

Figure A1 .
Figure A1.Box plot depicting measured 10 min wind speed values at the Pyhätunturi telecom mast station during years 1997-2016 and as taken from the ERA-Interim.The values measured at an elevation of 61 m were corrected to represent 10 m by applying logarithmic wind law.Only values that are 11.4 m s −1 (corresponding value 15 m s −1 at elevation of 61 m) are included into the analyses.

Figure A2 .Figure A3 .
Figure A2.The weight of each grid square's roughness on the effective roughness (z eff ) as a function of upwind distance as calculated using Eq.(2) in the main text.

Figure A4 .
Figure A4.Effective roughness (z eff , Eq. 4) and roughness-dependent wind multiplier (M z ) calculated for the Pyhätunturi Fell area for northwesterly winds.
. The observations are corrected to represent 10 m wind speed by applying logarithmic wind profile.Station elevation a.s.l.(m) has been included in the table.