Entropy Budget of the Soil Hydrological Cycle
Authors:
Abstract:
The analysis and the modelling of the soil hydrological cycle on a global scale is a challenging task, since a complete description of soil water dynamics is very dificult to achieve. The reason for this is the large variety of processes which are involved in the movement of water through the soil combined with spatial heterogeneity on many scales. This leads to the question, if there are simple principles allowing for the prediction of hydrological features without knowing every single detail of the soil hydrologic system under consideration. The subject of this essay is the testing of such a principle, the principle of Maximum Entropy Production (MEP), with respect to soil hydrology. MEP is a simple optimality approach which seems to be suitable to explain a large range of earth system phenomena [17], [15], [25]. Hence, it could be useful with regard to a better understanding of mechanisms in soil hydrology. The assumption behind MEP is that a few constraints on a system are suficient to predict its behaviour, although they do not directly describe its state. Constraints like the waterbalance in case of soil hydrology, for instance, can be met by many possible partitionings between the particular hydrological ows and subsequently do not allow for their exact specification. According to MEP, however, this uncertainty can be interpreted as degrees of freedom which result in the emergence of a state of the system where its entropy production is maximised [5], [4], [6]. In this way, MEP predicts a specific state of a system, like a certain partitioning of ows in the soil hydrological cycle, given some basic constraints like the waterbalance. The production of entropy is a universal property of many parts of the earth system, resulting from the dissipation of free energy into heat by numerous irreversible natural processes. Considering runoff, for example, the potential energy of water is transformed into kinetic energy and then dissipated into heat by friction, which corresponds to entropy production. Since soil hydrological processes take place far away from thermodynamic equilibrium, the quantification of their entropy production requires methods from non-equilibrium thermodynamics. Having drawn up an entropy budget of the soil hydrological cycle, it is possible to implement and test MEP. The chapters 1 to 6 of this essay deal with the application of non - equilibrium thermodynamics and MEP to the soil hydrological system. First, the irreversible thermodynamic nature of the hydrological cycle is illustrated. Then, methods for the calculation of the entropy production of important hydrological processes are presented, followed by some estimates in this respect. Finally, MEP is tested and the results and limits of this approach are discussed. Readers who are only familiar with classical thermodynamics may still feel uncomfortable with the idea that thermodynamic methods are used to analyse systems like the soil. For this reason, the basic principles of non - equilibrium thermodynamics are shortly reviewed in chapter 7 of this essay, showing their applicability to the earth system. Subsequently, the principle of Maximum Entropy Production is explained in detail in chapter 8 with the aid of conceptual models. The chapters 7 and 8 represent a general introduction into the subject. They are placed at the end of the essay, because the first 6 chapters are going to be published as a journal article and therefore belong together as a unit. Eventually, a short discussion about the universality of MEP can be found in chapter 9.
Reference:
- P Porada, 2010. Thesis: Entropy Budget of the Soil Hydrological Cycle. Supervisors: Prof. Dr. W Lucht, Humboldt University Berlin, Dr. A Kleidon, MPI Biogeochemistry Jena.
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