Importance of temporal variability for hydrological predictions based on the maximum entropy production principle

Abstract

This work builds on earlier work by Kleidon and Schymanski (2008) who explored the use of the maximum entropy production (MEP) principle for modeling hydrological systems. They illustrated that MEP can be used to determine the partitioning of soil water into runoff and evaporation—which determines hydroclimatic conditions around the Globe—by optimizing effective soil and canopy conductances in a way to maximize entropy production by these fluxes. In the present study, we show analytically that under their assumption of constant rainfall, the proposed principle always yields an optimum where the two conductances are equal, irrespective of rainfall rate, evaporative demand, or gravitational potential. Subsequently, we show that under periodic forcing or periodic variations in one resistance (e.g., vegetation seasonality), the optimal conductance does depend on climatic drivers such as the length of dry spells or the time of closure of stomata.

Energy states of soil water – a thermodynamic perspective on soil water dynamics and storage-controlled streamflow generation in different landscapes

“…4). Both catchments have been extensively characterized in previous studies with respect to their physiographic characteristics, dominant runoff generation mechanisms and available data (Wrede et al, 2015;Martinez-Carreras et al, 2015;Loritz et al, 2017;Angermann et al, 2017). Hence, we focus here exclusively on those system characteristics which determine their respective energy state functions.…”

Unifying catchment water balance models for different time scales through the maximum entropy production principle

“…Equation (4) is a commonly used water balance model in catchment hydrology [L'vovich, 1979;Thomas, 1981;Sivapalan, 2003;Yang et al, 2008;Westhoff et al, 2014]. It should be noted that in this analysis the cross-catchment groundwater flows are assumed to be negligible; they should be introduced as needed when cross-catchment problems are explored.…”

“…In theoretical catchment hydrology, the search for common organizing principles has been a long‐standing research question [ McDonnell et al ., ; Schaefli et al ., ], in view of their promise to simplify the task of scaling up descriptions of hydrologic fluxes governing the water balances to longer time scales (or larger spatial scales) without the need for detailed information [ Kleidon and Schymanski , ]. The organizing principles that have been proposed so far in catchment hydrology include ecological optimality based on minimization of plant water stress [ Eagleson , ], vegetation optimality based on maximization of net carbon profit [ Schymanski et al ., ], minimum energy expenditure [ Rodriguez‐Iturbe et al ., ], maximum energy dissipation [ Zehe et al ., ], and maximum entropy production (MEP) [ Kleidon and Schymanski , ; Paik and Kumar , ; del Jesus et al ., ; Westhoff et al ., ]. The principle of MEP, which states that complex systems are organized in such a way that the rate of entropy production is maximized at steady state, has recently been proposed as a possible basis to understand or represent optimality in hydrology more generally [ Kleidon and Schymanski , ].…”

HESS Opinions: From response units to functional units: a thermodynamic reinterpretation of the HRU concept to link spatial organization and functioning of intermediate scale catchments

“…This implies the possibility of independent predictions either using an optimized bulk resistance (Westhoff et al, 2014) or based on an optimized density of vertical and lateral macropores Kleidon et al, 2013). If conclusive, this might be seen as an argument that at least the potential natural state of a catchment as open terrestrial system functions in accordance with such a principle.…”