Stochastically Generating Tree Diameter Lists to Populate Forest Stands Based on the Linkage Variables Forest Type and Stand Age

Forest inventory data were used to develop a standage-driven, stochastic predictor of unit-area, frequencyweighted lists of breast high tree diameters (DBH). The average of mean statistics from 40 simulation prediction sets of an independent 78-plot validation dataset differed from the observed validation means by 0.5 cm for DBH, and by 12 trees/h for density. The 40simulation average of standard deviation, quartile range, maximum value and minimum value differed from the validation dataset, respectively, by 0.3, 1.3, 0.6 and 1.5 cm for DBH, and 10, 42, 29, and 54 trees/h for density. In addition, test statistics were also computed individually for each of the 40 single simulations of the 78-plot validation dataset. In all cases, the test statistics supported the null hypothesis of no difference between simulated and observed DBH lists. When power of these hypothesis test statistics was set to 80%, the calculated minimum detectable differences were still reasonably small at 2.7 cm for mean DBH and 90 trees/h for stocking. Also, the shape and dispersion of simulated mean-DBH/density scatter graphs were similar to the same scatter graph from the observed, validation dataset. Introduction Sample inventories are a relatively abundant data source that routinely contains multi-variable forest attribute information useful to GIS analyses. However, the spatial density of plots in sample inventories is, by design, generally too sparse to directly populate databases associated with most GIS layers of forest stand boundaries. Moeur and Stage (1995) used canonical correlation theory on a set of variables common to both the inventory and the existing GIS databases (hereafter referred to as linkage variables) to assign intact, unmodified plot-level data from the inventory database to a GIS database that is linked to a stand polygon layer. This research has a similar goal, except the focus here is on using the linkage variables and the inventory database to parameterize a stochastic predictor of within-polygon variation of unit-area, frequency-weighted breast high tree diameters (DBH). The application potential of this research is illustrated by the methodological role it played in a larger project. The objective of the larger project was to simulate, over time, the effects of alternative location-specific partial-cut and clearcut-regeneration harvesting on the amount of suitable Red-cockaded Woodpecker (RCW) (Picoides borealis Vieillot) habitat available from some forested area. This required predicting frequency-weighted DBH lists for assignment to GIS pixels representing land areas of a given size, and then approximating stand polygons by grouping contiguous pixels that fall within the polygons. These DBH lists were subsequently used to calculate wood product yields from simulated harvesting, to identify stands suitable for RCW nesting sites, to spatially delimit RCW foraging areas around nesting sites, and to serve as input to a forest growth and mortality simulator (Teck et al. 1996). The forest growth and mortality simulator, in conjunction with the GIS database, provided a dynamic and spatially specific description of vegetation charge over a 20to 30-year period. Alternative, temporaland location-specific silvicultural treatment scenarios were then applied to the simulated forest structure, and their cumulative affects over time on wood product outputs and the forest-wide suitability RCW habitat were evaluated. A Generalized Predictor Model fitting starts by forming relative-size-based subsets made up of individual records of the pth ranked DBH (and associated plot-level linkage variables) from each plot. For notation purposes, the subset of trees made up of the largest DBH from each plot was assigned the rank p = 1, the subset made up of the second largest trees was assigned rank p = 2, etc. The linear model for the relationship between DBH and the vector of linkage variables (λ ) is ; 1, 2, , ; 1, 2, , pi p i pi d p q i s ′ = + ε = = β λ K K (1) where the linkage variables are made up of plot/standlevel attributes such as stand age, stocking, and site productivity, or other surrogate measures of these variables, pi d is the DBH of the pth size-ranked tree from the ith plot, p β is a k-element vector of regression coefficients for the pth subset, pi ε is the error term for the ith tree in the pth subset (where [ ] 0 pi E ε = and 2 Var [ ] pi p ε = σ ), s is the number of plots in the inventory database that contain p sampled trees (s decreases as p increases), and q is the largest 2003 Joint Statistical Meetings Section on Statistics & the Environment