Thermodynamics and Optimality of the Water Budget on Land: A Review

Authors:

Axel Kleidon and Stan Schymanski

Abstract:

The water balance on land plays a critical role in connecting key hydrological processes with climate and ecology. Over the last few years, several advances have been made in applying thermodynamic and optimality approaches to better describe Earth system processes in general, and the water balance on land in particular. Both concepts relate to the proposed principle of Maximum Entropy Production (MEP), which states that complex systems far from thermodynamic equilibrium organize in a way such that the rate of entropy production -- a measure of irreversibility -- is maximized in steady state. MEP provides a foundation to understand optimality in hydrology at a fundamental, thermodynamic level that is applicable across a wide range of Earth systems beyond hydrology. This review describes the foundation of the water balance far from thermodynamic equilibrium and potential applications of MEP. Some of the objections to optimality and thermodynamics are discussed as well as its potential implications.

Reference:

  • Geophysical Research Letters, Vol. 35, L20404, doi:10.1029/2008GL035393.
  • Weblink to publisher's web page.
  • Postprint of this manuscript (accepted version of the paper formatted by author).
  • BibTex entry.

Figure 1: Schematic diagram illustrating the land surface as a thermodynamic system, with boundaries shown as dotted lines. The arrows show the mass fluxes across system boundaries in terms of their rates and chemical potentials mu (with subscripts: P = precipitation, S = soil, V = vegetation, A = atmosphere, O = ocean) and the boxes denote dissipative processes.

Figure 2: Diagram to illustrate a MEP state for poleward heat transport. a: Temperature difference as a function of heat flux. b: Entropy production associated with poleward heat transport and the increase in planetary entropy production as a function of poleward heat transport. After Kleidon and Lorenz (2005).

Figure 3: Simplified representation of the land system of Fig. 1 in terms of an electric circuit analogy. The solid lines represent flow of liquid water, the dashed line flow of water vapor.

Figure 4: Existence of an MEP state as a result of flux-force trade-off associated with evapotranspiration E and conductivity k_e (cf. eqn. 8). For demonstration, values shown have been normalized by their maximum value.