Imputation of Continuous Tree Suitability over the Continental United States from Sparse Measurements Using Associative Clustering

Up-scaling from sparse measurements to a continuous raster of estimated values is a common problem in Earth System Science. We present a new general-purpose empirical imputation method based on associative clustering, which associates sparse measurements of dependent variables with particular multivariate clustered combinations of the independent variables, and then uses several methods to estimate values for unmeasured clusters, based on directional proximity in multidimensional data space, at both the cluster and map cell levels of resolution. We demonstrate this new imputation tool on tree species range distribution maps, which describe the suitable extent and expected growth performance of a particular tree species over a wide area. Range maps having continuous estimates of tree growth performance are more useful than more classical tree range maps that simply show binary occurence suitability. The USDA Forest Service Forest Inventory Assessment (FIA) plots provide information about the occurence and growth performance for various tree species across the US, but such measurements are limited to FIA plots. Using Associative Clustering, we scale up the discontinuous FIA Inventory growth measurements into continuous maps that show the expected growth and suitabilty for individual tree species covering the Continental United States. A multivariate cluster analysis was applied to global output from a General Circulation Model (GCM) consisting of 17 variables downscaled to 4km2 resolution. Present global growing conditions were divided into 30 thousand relatively homogeneous ecoregions describing climatic and topographic conditions. At every mapcell a multi-linear regression was applied in 17 dimensional hyperspace to derive the suitability of a tree species where not measured using the forest inventory data. The continuous species distribution maps obtained were compared and validated against existing tree range suitability maps. Associative Clustering is intended to be a general-purpose imputation tool, is model-free, and can be used to derive tree growth for future conditions that have no present-day analog.