Identifying Spatially Inhomogeneous Relationships Between Drainage Density and Its Controlling Variables

Spatial variation of the value of drainage density (D) is observed on variety of scales. It is attributed to a nonuniform distribution of variables that exert control over D. Comprehensive understanding of the dependence of D on its controlling factors is lacking because of complex, nonlinear character of such dependence. This study presents the use of the regression tree technique to identify different relationships between D and its controlling variables across the conterminous United States. Local drainage density (response variable) is calculated on a 4 km-size regular grid from high resolution stream network data from the National Hydrographic Dataset. Explanatory variables pertaining to geology, soil, terrain, climate, land cover, and vegetation density are also calculated on the same grid. The resulting grids are fed to a GUIDE algorithm to build a regression tree. The algorithm performs "regression by parts" - it hierarchically partitions the dataset so as to increase the accuracy of linear regression in each partition. Each final partition (a terminal node of the tree) contains entries in the dataset (cells in a grid) for which a good-fit linear relation between D and its controlling variables can be established. Ranges of explanatory variables in each node are determined by the path in the tree, and spatial extent (footprint of relationship) of the node is mapped. Collection of all such relations and their footprints provides comprehensive understanding of dependence of D on its controlling factors.