Windthrow risk in many parts of the world has been modeled and assessed. Empirical models are best suited for areas with complex, heterogeneous stand structure and composition (Lanquaye-Opoku and Mitchell 2005, Mitchell and others 2001) like the forests of Maine. This empirical approach typically utilizes regression models relating wind damage to physical stand components. Generally, the models produce a probability value rating or index of damage potential based on the stand’s suite of environmental conditions. Index modeling of spatial phenomena is enhanced with GIS, which allows for the integration of spatially explicit model parameters.

Flow Chart

Logistic regression is a commonly used tool for evaluating these models and isolating highly correlated component variables (Lanquaye-Opoku and Mitchell 2005, Mitchell and others 2001). Rather than using logistic regression, this project produced a generalized model, retaining variables that would not be statistically significant in a logistic regression analysis. This approach is unique because it attempts to create a model that may be applicable regionally and not be limited to the landscape where it was developed.

Eight environmental parameters, (elevation, soil rooting depth, topographic exposure, stand species type, stand height, stand density, stand history, and exposed edges) were used to generate a spatially explicit vulnerability index value. Mitchell (1995, 1998) advocates grouping the factors into three broad categories—exposure, soils, and stand characteristics—to form a windthrow triangle, a conceptual model of the relationships among these interacting factors. For this model, factors were broken down further into site and stand parameters and combined to generate the cumulative windthrow risk index (Figure on the right). Data for model variables, including a spatially referenced database of windthrow history, was acquired from various sources and covered an area of private landholdings in the northern portion of the State.

Topographic exposure is a critical variable in assessing stand vulnerability. Several indices have been created to describe relative topographic exposure or topographic protection. Topex wind exposure index has been used for some time to assess windthrow risk in Great Britain (Miller 1985). The importance of topographic exposure in modeling windthrow risk has been demonstrated in other areas with forest-based economies. According to Ruel and others (2002), this variable accounts for over 77 percent of the British wind hazard rating system’s total score. Distance-limited Topex was chosen for this project because of its relatively easy calculation and strong correlation to wind tunnel simulation (Ruel and others 1997). Topographic exposure rasters were generated using a model developed and provided by The Windthrow Research Group, University of British Columbia, Vancouver, Canada. The scripts calculate an index of exposure that is the summation of the maximum and minimum angles to the skyline within a user-specified distance. The index can be calculated in the eight cardinal directions and weighted according to user preferences. Ten exposure grids were produced for this project, simulating unweighted exposure at two limiting distances (1000m and 1500m) and exposure in the eight cardinal directions (limiting distance of 1000m).

Forest soils are also a major component in understanding susceptibility of a forest stand to wind damage. Soil aeration, ease of soil penetration by roots (rooting depth), and moisture-holding capacity all affect the pattern of root development. Generally, loose dry soils facilitate deeper rooting and spreading than do shallow clayey soils (Mergen 1954). Shallow soils, which limit rooting depth and saturate easily like those commonly found in the spruce flat forest type, are increasingly prone to windthrow when saturated. The mass of soil that roots adhere to for anchorage becomes so wet it no longer adheres to itself, and the tree loses a substantial portion of its basal mass, crucial for resistance to windthrow (Day 1950). To compound the problem on wet soils, the rocking of the root plate can pump mud out from under the tree, further reducing the tree’s stability (Maccurach 1991).

Depth to groundwater was consistently cited by Maine forestland managers as crucial to predicting the likelihood of blowdown in stands. The University of Maine’s Cooperative Forestry Research Unit provided a continuous depth to water table raster for this project. This variable was combined with coarse-scale soil depth data to create a raster selecting the minimum depth of the two available data sources and indexed between 0 and 1.

Elevation was also incorporated into the site component of the model. Elevation values from a 30-meter resolution digital elevation model (DEM) of the study were recalculated into an index between 0 and 1. Elevation had statistically significant correlation with wind damage in cut-block edge vulnerability modeling by Mitchell and others (2001). Studies by Worrall and Harrington (1988) in Crawford Notch, NH, found that gap size from chronic wind stress and windsnap or windthrow increased strongly with elevation from over 60percent of the gap area at 764 m (2521 feet) to almost 85 percent of the gap area at 1130 m (3729 feet). Gap formation led to subsequent mortality from chronic wind stress and windthrow in gap edge trees. This trend was confirmed by Perkins and others (1992) on Camel’s Hump in Vermont. These trends are driven by surface friction acting counter to the force of the wind. Wind speed will increase locally with elevation because surface friction will decrease (Bair 1992).

Variables describing stand composition and characteristics were extracted from the forest landowner GIS database, which contains stand level information to a minimum size of 1 acre. Stand composition is recorded under a three- variable scheme (Table: Three Variable Stand Type Scheme). The database also reports stand history from the present to the mid-1980s including stand damage by wind storms and previous harvest entries. The history records include the year of the event, and the event type or silvicultural prescription. An iterative network of Microsoft Access™ queries was developed and used to isolate prior stand entry and wind damage events and to create vulnerability indices for individual stands based on stand type and the presence or absence of balsam fir, stand height, and stand density.

The species risk index assigns ranks for the four potential forest types (H=0.3; S=0.7; HS=0.45; SH=0.55). The forest type rank is combined additively with an adjustment factor for the presence of balsam fir in the overstory because high rates of root rot predispose fir to wind damage (Whitney 1989). The balsam fir adjustment considers the relative abundance of balsam fir in the overstory as the primary, secondary, or tertiary overstory species.

The stand height risk grid was built directly from the landowner database. The stand type height code was rasterized, creating a raster with five potential data values (0-nonforest; and 1 through 4 representing the height classes found in Table: Three Variable Stand Type Scheme). The values were divided by 4, the maximum value, to create the desired index range between 0 and 1.

The density grid captures the overstory density of the stands in the study area. Access queries determined the height and density of the most dominant or two most dominant species in each stand, if more than one species were present. Queries assigned values corresponding to the original alphabetical density codes of the most dominant overstory species. Density of the primary overstory species was collected and modified if the secondary species was also in the same canopy strata.

Stands are more vulnerable to windthrow following thinning for two reasons. First, the increase in spacing resulting from thinning creates more canopy roughness, which, in turn, increases turbulence of the wind at the canopy level. Increased turbulence and wind penetration result in reduced tree stability (Blackburn and others 1988, Maccurach 1991). Second, high initial stand density produces unfavorable height-to-diameter (H:D) ratios (Wilson and Oliver 2000). This is less of a problem if stand density remains high; however, thinning removes the support of neighboring stems, dramatically increasing stand vulnerability. This period of vulnerability may last from a few years to over a decade.

Due to the prominence of partial removal harvests in the State, it was determined that a binary variable would best capture risk associated with stand entry from thinning and partial harvesting. A binary index raster of stand treatments was created from the records of stand entry in the landowner database. All prior entries that involved incomplete removal of the overstory and occurred in the decade preceding the most recent wind event (2001) were classified as thinned. Clearcuts and uncut stands were classified as unthinned. Thinned stands were assigned a value of 1, and unthinned stands a value of 0.

The edge raster variable represents the percentage of the stand classified as edge. For this project, edge is defined as a 2 height-class difference between stands. Production of this data layer was a multistep procedure. First a raster of stand height was produced. Topex scripts were run on this raster with a limiting distance of 30 m, or 1 pixel. This identified all height-class differences between stands across the landscape. Positive values indicated edges of shorter stands, and negative values indicated edges of taller stands. The original height grid was also analyzed with Arc9’s zonal range statistics tool. Range statistics defined all edges classified by the height differences between the two adjacent stands. This raster was recoded to display only edges greater than 2 height-class differences. The Topex-generated edge raster and range statistics raster were combined to identify the edges of the taller stands (negative Topex scores) when the height difference between adjacent stands was greater than 2 height classes (range statistic greater than 2). Stands delineated in the GIS database were used as zones to calculate the percentage of edge within the individual stands, and the index was generated directly from these values.

Cumulative Wind Damage

The cumulative risk grid is composed in two stages. In the first stage, the three individual site and five individual stand components are combined additively to form separate composite site and composite stand grids. The second stage combines the composite site risk grid and composite stand risk grid additively to form a cumulative windthrow risk grid. The figure on the right displays the cumulative windthrow risk grid. Ten separate cumulative windthrow risk grids were produced, one for each unique exposure input grid (described in Site: Exposure). All grid combinations were performed with the single output map algebra tool in Arc9’s spatial analyst toolbox.

To avoid problems associated with spatial autocorrelation, the wind damage vulnerability model was analyzed with a comparison of means from a random sample of polygons within the study area. Hawth’s analysis tools (Beyer 2006) were used to maintain a minimum distance between sampled points. To ensure consistent results, 10 separate random samples of polygons were drawn from the study area. These 10 samples are analyzed individually and the results pooled to measure consistency between the samples. Approximately 560 polygons are sampled in each iteration of random sampling, accounting for roughly 14 percent of the study area in each sample.

The analysis used either a two-sample t-test or a Mann-Whitney test to detect differences between the population means. Mann-Whitney was chosen as the default test because this nonparametric test is justified in all situations where the t-test is applicable and in situations where the assumptions of the two-sample t-test are not met (Zar 1984). The two-sample t-test was used for Mann-Whitney results indicating near statistical significance when variables met the assumptions of this test. Tests used an alpha of 0.05 to test the null hypothesis, which is that the two population means are equal: H_o: 1= 2. Results from the analysis of the 10 samples were tested for consistency with a t-test. Significant results from the Mann-Whitney and two-sample t-tests were coded either one, positive correlation with the model, or negative one, negative correlation with the model. Non-significant results were coded as a 0.

The t-test procedure tested for statistically significant differences between the responses of the individual model variables across the 10 samples. A mean that was statistically not equal to 0 indicated consistent significance, reflecting either positive or negative correlation with the model. Tests used an alpha of 0.05 to test the null hypothesis that the means for the two populations are equal: H_o: 1= 2.