Entropy theory-based approach to derive equivalent GIUH

Abstract

Flood hydrographs are desirable at various hotspots in river basins for a wide range of applications such as hydrologic design and risk assessment of water resources systems. However, determining the hydrographs at ungauged locations has always been challenging. Among various approaches available for simulating a flood hydrograph, the synthetic UH (unit hydrograph) approach has attracted the attention of hydrologists for use in ungauged catchments. The approach involves the derivation of UH for the target location’s catchment and convoluting it with an excess rainfall hyetograph specified for the catchment to arrive at a flood hydrograph. The UH can be derived using Geomorphological Instantaneous UH (GIUH). Recently, there has been growth in interest to consider Horton–Strahler (HS) ratio-based equivalent GIUH (E-GIUH) derived using the self-similarity hypothesis for ungauged catchments, owing to its advantages in overcoming uncertainty in HS ratios arising from uncertainty in the choice of a source DEM. The E-GIUH is constructed using a PDF (probability distribution function) that provides an adequate fit to salient points determined from the E-GIUH characteristics (peak flow, time to peak, and base time). The characteristics are derived using empirical relationships considering the catchment’s geomorphology (equivalent HS ratios, length of the highest order stream) and characteristic flow velocity. An issue in analysis with E-GIUH is that its construction involves uncertainty in the choice of PDF. Furthermore, the empirical relationships used with E-GIUH lack a physical basis. This paper proposes an entropy theory-based methodology to account for the uncertainty in the choice of a PDF for the E-GIUH construction. The efficacy of the proposed methodology in simulating flood hydrographs at ungauged sites is illustrated for typical rainfall-runoff events from 10 unregulated catchments ranging in size from 107 – 2000 km2 and located in two river basins along the west coast of India. The hydrographs are compared with those simulated using conventional EGIUH in terms of several performance measures to illustrate the improvement noted with the entropy theory-based methodology.