Hydrologic similarity based on width function and hypsometry: An unsupervised learning approach

In ungauged or data-scarce watersheds, systematic analyses of a set of proximate watersheds (for example, selected based on locational proximity or similarity in climate, morphometry, lithology, soils, and vegetation) have been shown to lend significant insights regarding hydrologic response and prediction. Current approaches often rely on: (a) statistical regression models that use measurable watershed attributes, such as area, slope, and stream length; and (b) comparative hydrology that considers watershed characteristics to assess hydrologic similarity to select analogous gauged watersheds as proxies. Newer conceptions regarding hydrologic similarity focus on hydrologic response and therefore emphasize the use of dynamical measures of the stream network and watershed terrain. For example, the width function and hypsometric curve can be readily estimated using the available global digital terrain datasets and represented as functional forms involving a small set of parameters, thus achieving significant data reduction. In this study, a new approach to hydrological similarity in watersheds, one that utilizes these functional forms to identify dynamically similar watersheds, is presented. Dissimilarity matrices are created based on divergence measures, and watersheds are classified using hierarchical clustering. The joint analysis of watershed width functions and hypsometric curves allows for the classification of watersheds into a reduced number of dynamically-similar groups. An illustrative case study for the Narmada River, with 72 sub-watersheds, is presented.