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 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 10 0 210 3 km 2 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.

Assessing Catchment Resilience Using Entropy Associated with Mean Annual Runoff for the Upper Vaal Catchment in South Africa

“…South Africa, specifically the Upper Vaal catchment depends on this yield for several activities (economic, social, industrial, etc.). This is similar to several other parts of the world [37,65]. The required yield/draft is necessary and vital but not sufficient for managing water resources in the catchment.…”

“…It was argued that hydrological resilience was related more to vulnerability/sustainability than the reliability of water resources such as reservoir systems (e.g., [17]). Real hydrological systems (e.g., catchments) are complex [10,37,69] and have multiple attractors (steady states), which may inform how these systems may respond to and recover from perturbations such as droughts, floods, or groundwater pumping but determining multiple attractors is very challenging [20,21,33]. Selected factors (variables of concern) are often used indirectly to define or measure the resilience of hydrological systems.…”

“…Since resilience is associated with sustainability or vulnerability of a system [7,17,25], which enables the link between entropy and resilience [17], entropy of MAR can be suggested as a surrogate measure of catchment resilience. This could also be supported from catchment resilience being associated with streamflow/runoff as hydrological response [13] or catchment hydrological flux [37,38] and this flux is always associated with a degree of uncertainty or entropy in space and/or in time [4,5,39]. Measuring systems' resilience holistically using entropy could be appealing, however very challenging for hydrological systems, due to the complex interaction of variables, the occurrences of the different states and the selection of different thresholds.…”

Geological entropy and solute transport in heterogeneous porous media

“…The proposed indicator of geological entropy is based on the concept of Shannon information entropy [ Shannon , ], which has been used in the past to quantify complexity and randomness in various scientific fields including statistical mechanics and fluid dynamics [ Jaynes , ; Ottino , ], hydrology [ Martina and Entekhabi , ; Singh , ; Castillo et al ., ], image processing [ Barba et al ., ; Wu et al ., ], geography and spatial statistics [ Batty et al ., ; Leibovici et al ., ], and landscape ecology [ Vranken et al ., ], just to name a few. Information entropy concepts have also been applied to quantify the uncertainty of geological models [ Elfeki and Dekking , ; Huang et al ., ; Wellmann and Regenauer‐Lieb , ; Bianchi et al ., ], and to describe the spatial and temporal variability of solute plumes [ Woodbury and Ulrych , ; Kitanidis , ; Gotovac et al ., ; Chiogna et al ., ], as well as of infiltration processes in unsaturated heterogeneous soils [ Mays et al ., ].…”

“…Water Resources Research 10.1002/2016WR020195 and Entekhabi, 2006Singh, 2011;Castillo et al, 2015], image processing [Barba et al, 1989;Wu et al, 2013], geography and spatial statistics [Batty et al, 2014;Leibovici et al, 2014], and landscape ecology [Vranken et al, 2015], just to name a few. Information entropy concepts have also been applied to quantify the uncertainty of geological models [Elfeki and Dekking, 2005;Huang et al, 2012;Wellmann and Regenauer-Lieb, 2012;Bianchi et al, 2015], and to describe the spatial and temporal variability of solute plumes [Woodbury and Ulrych, 1993;Kitanidis, 1994;Gotovac et al, 2010;Chiogna et al, 2012], as well as of infiltration processes in unsaturated heterogeneous soils [Mays et al, 2002].…”