An entropy-based measure of hydrologic complexity and its applications

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 H 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, H 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 H, and how H 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, H scales with catchment area, topographic wetness, infiltration ratio, and base flow index; while H is inversely related to relief ratio