Statistical analysis of drainage density from digital terrain data

Drainage density (D-d), defined as the total length of channels per unit ar ea, is a fundamental property of natural terrain that reflects local climat e, relief, geology, and other factors. Accurate measurement of D-d is impor tant for numerous geomorphic and hydrologic applications, yet it is a surpr isingly difficult quantity to measure, particularly over large areas. Here, we develop a consistent and efficient method for generating maps of D-d us ing digital terrain data. The method relies on (i) measuring hillslope flow path distance at every unchanneled site within a basin, and (ii) analyzing this field as a random space function. As a consequence, we measure not on ly its mean (which is half the inverse of the traditional definition of dra inage density) but also its variance, higher moments, and spatial correlati on structure. This yields a theoretically sound tool for estimating spatial variability of drainage density. Averaging length-to-channel over an appro priate spatial scale also makes it possible to derive continuous maps of D- d and its spatial variations. We show that the autocorrelation length scale provides a natural and objective choice for spatial averaging. This mappin g technique is applied to a region of highly variable D-d in the northern A pennines, Italy. We show that the method is capable of revealing large-scal e patterns of variation in D-d that are correlated with lithology and relie f. The method provides a new and more general way to quantitatively define and measure D-d to test geomorphic models, and to incorporate D-d variation s into regional-scale hydrologic models. (C) 2001 Elsevier Science B.V. All rights reserved.