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

Abstract

The prediction of hydrologic conditions in watersheds has manifold applications, ranging from flood disaster preparedness to water supply and environmental flow management. In watersheds with scarce or no flow data, it is difficult to make accurate hydrologic predictions. Past work has used similarity in single-valued properties of the terrain (for example, drainage area, mean slope) as the basis to relate flow conditions in gauged watersheds to the ungauged ones. The resulting predictions show modest accuracy and have a weak physical basis. In this study, we develop a physics-informed machine learning approach to extract features that represent the hydrologic dynamics — width function and hypsometric curve. These two geomorphometric measures are computed using functional forms fitted to estimates derived from digital elevation data. Furthermore, dynamically-similar groups are identified based on results from unsupervised clustering and divergence measures. Our approach paves the way towards a flexible and scalable machine learning approach that can be used to assess hydrologic similarity and improve prediction, one informed by physics of surface flow generation and transport in watersheds. A case study involving 72 sub-watersheds in the Narmada River Basin (India) is used to illustrate the new methodology.