Entropy production of soil hydrological processes and its maximisation

Abstract

Abstract. Hydrological processes are irreversible and produce entropy. Hence, the framework of non-equilibrium thermodynamics is used here to describe them mathematically. This means flows of water are written as functions of gradients in the gravitational and chemical potential of water between two parts of the hydrological system. Such a framework facilitates a consistent thermodynamic representation of the hydrological processes in the model. Furthermore, it allows for the calculation of the entropy production associated with a flow of water, which is proportional to the product of gradient and flow. Thus, an entropy budget of the hydrological cycle at the land surface is quantified, illustrating the contribution of different processes to the overall entropy production. Moreover, the proposed Principle of Maximum Entropy Production (MEP) can be applied to the model. This means, unknown parameters can be determined by setting them to values which lead to a maximisation of the entropy production in the model. The model used in this study is parametrised according to MEP and evaluated by means of several observational datasets describing terrestrial fluxes of water and carbon. The model reproduces the data with good accuracy which is a promising result with regard to the application of MEP to hydrological processes at the land surface.

Maximum entropy production: can it be used to constrain conceptual hydrological models?

“…The reason for this is that none of the parameters influenced the gradient driving E a and no feedback between the flux (E a ) and its driving gradient (∇ E a ) was implemented in the used model set-up. In contrary to the model of Porada et al (2011), conceptual models do not account for the capillary rise and the associated power in this flux.…”

“…7). If the approach of Porada et al (2011) works here, the intersect of the two ridges should coincide with a closed water balance for the unsaturated zone and maximum NSE for the fast runoff reservoir.…”

“…However, this approach means that only one parameter per submodule can be constrained with the maximum power principle while the other parameters should be chosen in another manner. Porada et al (2011) proposed a method to be able to constrain two parameters with respect to entropy production. They created surface plots with on the x and y axis the two parameters and on the z axis the entropy produced by the two fluxes that were controlled by the two parameters.…”

“…Another example was illustrated by Porada et al (2011), who used MEP to constrain parameters for a physically based model based on multiple 1-D columns to simulate the water balance of the largest 35 catchments on Earth. Two parameters were constrained with respect to MEP; namely, resistance for root water uptake by maximizing entropy produced by rootwater uptake and hydraulic conductivity by maximizing entropy produced by baseflow.…”

Technical note: Inference in hydrology from entropy balance considerations

“…For example, Porada et al (2011) performed a detailed entropy production analysis of the land surface hydrologic cycle including the shallow vadose zone assuming vertical equilibrium of the soil bucket model. Applying linear bucket models without considering internal gradients, Kleidon and Schymanski (2008) showed that if the natural system possesses enough degrees of freedom, in case of steady state, the system will tend towards a certain exchange coefficient, when entropy production is maximized.…”