Catchments as Organised Systems

[F] Linking landscape structure and rainfall runoff behaviour in a thermodynamic optimality context

Our main objective is to explore an alternative thermodynamic perspective on rainfall-runoff generation on the hillslope and headwater scale. From a thermodynamic perspective any water mass flux is equal to a “potential gradient” divided by a “resistance”, and fluxes deplete due to the second law of thermodynamics their driving gradients.

Flux equation

Eq 1. General flux equation

Relevant potentials controlling rainfall-runoff are soil water potentials, piezometric heads and surface water levels and their gradients are associated with spatial differences in associated forms of free energy. Rainfall-runoff processes thus are associated with conversions of capillary binding energy (in fact chemical energy of soil water), potential energy and kinetic energy. These conversions reflect energy conservation and irreversibility as they imply small amounts of dissipation of free energy into heat and thus production of entropy. Energy conversions during rainfall-runoff transformation are, though being small, nevertheless of key importance, because they are related to the partitioning of incoming rainfall mass into runoff components and storage dynamics.

Catchments as thermodynamic systems

Fig 1. Deviations around a local thermodynamic equilibrium during wetting and drying cycles

This splitting and the subsequent subsurface dynamics is strongly controlled by preferential flow paths, which in turn largely influence hydrologically relevant resistance fields in larger control volumes. The field of subsurface flow resistances depends for instance on soil hydraulic conductivity, its spatial covariance and soil moisture. Apparent preferential pathways reduce, depending on their density, topology and spatial extent, subsurface flow resistances along their main extent, resulting in accelerated fluxes against the driving gradient. This implies an enlarged power in the subsurface flux thereby either an enlarged free energy export from the control volume or an increased depletion of internal driving gradients, and thus a faster relaxation back towards local thermodynamic equilibrium.

Thermodynamic optimality principles allow for a priory optimization of the resistance field at a given gradient, not in the sense how they exactly look like but in the sense how they function with respect to export and dissipation of free energy associated with rainfall-runoff processes. We will thus explore the possibility of independent predictions of rainfall-runoff in this project, in the sense that the a-priory optimum model structures should match independent observations at the hillslope and headwater scale. We also explore whether an apparent disequilibrium in landscape structure (reflected in topography, vegetation pattern, soil catena and apparent preferential pathways) implies temporally persistent patterns of soil moisture states in the sense that they coincide with local thermodynamic equilibria. This might offer the opportunity for useful backward predictions of distributed state dynamics by using observed dynamics of stream and ground water levels as boundary conditions characterizing the levels of relevant minima in geo-potential and zero matric potential in the subsurface. Last not least we test the feasibility to define hydrological similarity with respect to free energy stocks and conversions related to rainfall-runoff (instead of focusing directly on the mass balance) with respect to classify catchments and hillslopes with respect to similar behavior.