An entropy-based measure of hydrologic complexity and its applications

Abstract

Basin response and hydrologic fluxes are functions of hydrologic states, most notably of soil moisture. However, characterization of hillslope-scale soil moisture is challenging since it is both spatially heterogeneous and dynamic. This paper introduces an entropy-based and discretization-invariant dimensionless index of hydrologic complexity math formula that measures the distance of a given distribution of soil moisture from a Dirac delta (most organization) and a uniform distribution (widest distribution). Applying the distributed hydrologic model MOBIDIC to seven test basins with areas ranging 10⁰−10³ km² and representing semiarid and temperate climates, math formula is shown to capture distributional characteristics of soil moisture fields. It can also track the temporal evolution of the distributional features. Furthermore, this paper explores how basin attributes affect the characteristic math formula, and how math formula can be used to explain interbasin variability in hydrologic response. Relationships are found only by grouping basins with the same climate or size. For the semiarid basins, math formula scales with catchment area, topographic wetness, infiltration ratio, and base flow index; while math formula is inversely related to relief ratio.