Estimation of watershed width function: a statistical approach using LiDAR data

Abstract

Terrain variability and channel network characteristics critically influence the hydrologic response of watersheds. Width function represents this response under idealized flow conditions of constant velocity and absence of losses, and can be estimated solely using the terrain data. However, the width function, in its graphical form, is less tractable for further analytical applications such as in the derivation of link-based geomorphological instantaneous unit hydrograph. In this study, we systematically redress these issues in the following manner: (a) develop a framework for the functional estimation of width functions using a mixture of truncated skew-normal distributions that captures a wide variety of distribution shapes, (b) provide a basis for model selection based on the Bayesian Information Criterion, (c) demonstrate the utility of a functional estimation approach by identifying hydrologically similar watersheds based on divergence measures applied to the width function estimates, and (d) illustrate the utility of efficient statistical estimation of geomorphic functions and metrics, which affords data reduction and can be scaled to very-large terrain datasets.