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

Abstract

Abstract. The present study confirms that a thermodynamic perspective on soil water is well suited to distinguishing the typical interplay of gravity and capillarity controls on soil water dynamics in different landscapes. To this end, we express the driving matric and gravity potentials by their energetic counterparts and characterize soil water by its free energy state. The latter is the key to defining a new system characteristic determining the possible range of energy states of soil water, reflecting the joint influences of soil physical properties and height over nearest drainage (HAND) in a stratified manner. As this characteristic defines the possible range of energy states of soil water in the root zone, it also allows an instructive comparison of top soil water dynamics observed in two distinctly different landscapes. This is because the local thermodynamic equilibrium at a given HAND and the related equilibrium storage allow a subdivision of the possible free energy states into two different regimes. Wetting of the soil in local equilibrium implies that free energy of soil water becomes positive, which in turn implies that the soil is in a state of storage excess, while further drying of the soil leads to a negative free energy and a state of storage deficit. We show that during 1 hydrological year the energy states of soil water visit distinctly different parts of their respective energy state spaces. The two study areas compared here exhibit furthermore a threshold-like relation between the observed free energy of soil water in the riparian zone and observed streamflow, while the tipping points coincide with the local equilibrium state of zero free energy. We found that the emergence of a potential energy excess/storage excess in the riparian zone coincides with the onset of storage-controlled direct streamflow generation. While such threshold behaviour is not unusual, it is remarkable that the tipping point is consistent with the underlying theoretical basis.

A topographic index explaining hydrological similarity by accounting for the joint controls of runoff formation

“…The same leading author Gao et al (2019) further exploited the role surface topography plays when rainfall becomes runoff and used HAND to infer model parameters of a conceptual hydrological model, showing that their developed runoff generation module performed almost as well as fully calibrated models. Finally, Zehe et al (2019) used HAND as a proxy for the gravitational potential for calculating potential energy of soil water and showed that their approach is "well suited to distinguishing the typical interplay of gravity and capillarity controls on soil water dynamics in different landscapes".…”

“…However, a thermodynamic perspective can be much more general and is by no means limited to the explanation of optimal drainage densities. As examples, Zehe et al (2013) showed that a thermodynamic optimum density of macropores maximizing dissipation of free energy during recharge events allowed an acceptable prediction of the rainfall-runoff response of a lower-mesoscale catchment; Hildebrandt et al (2016) used an energy-centered approach to explain how plants extract water from the soil, Zhang and Savenije (2018) showed how salt and fresh water mixing in estuaries can be described in energetic terms, and finally Zehe et al (2019) discussed how an energetic perspective on soil water movement can improve our general understanding of catchment hydrology.…”

Surface water and groundwater: unifying conceptualization and quantification of the two “water worlds”

“…We note, too, that the CTRW framework also simplifies (e.g. Berkowitz et al, 2006Berkowitz et al, , 2016 to specialized subsets of non-Fickian transport behaviour embodied within, for example, multirate mass transfer (Haggerty and Gorelick, 1995) and fractional derivative (Zhang et al, 2009) formulations. It is important to recognize, too, that specification of a pure exponential form for ψ(t), namely ψ(t) = λ exp(−λt), with mean 1/λ, and/or choice of β > 2, reduces the CTRW transport in Eq.…”

“…More recent applications demonstrated, in line with this asset, new ways to simplify distributed models without lumping, which allowed the successful simulation of the water balance of a 19 km 2 large catchment using a single effective hillslope model (Loritz et al, 2017). The key to this was to respect energy conservation during the aggregation procedure, specifically through derivation of an effective topography that conserved the average distribution of potential energy along the average flow path length to the stream, and through a macro-scale effective soil water retention curve that conserved the relation between the average soil water content and matric potential energy using a set point-scale retention experiments (Jackisch, 2015;Zehe et al, 2019).…”

Reply to Hongkai Gao

“…However, a thermodynamic perspective can be much more general and is by no means limited to the explanation of optimal drainage densities. As examples, Zehe et al (2013) showed that a thermodynamic optimum density of macropores maximizing dissipation of free energy during recharge events allowed an acceptable prediction of the rainfall-runoff response of a lower-mesoscale catchment; Hildebrandt et al (2016) used an energy-centered approach to explain how plants extract water from the soil, Zhang and Savenije (2018) showed how salt and fresh water mixing in estuaries can be described in energetic terms, and finally Zehe et al (2019) discussed how an energetic perspective on soil water movement can improve our general understanding of catchment hydrology.…”