Earth System Dynamics Discussions www.earth-syst-dynam-discuss.net 2190-4995 2 1 2011 10.5194/esdd-2-105-2011 http://www.earth-syst-dynam-discuss.net/2/105/2011/ http://www.earth-syst-dynam-discuss.net/2/105/2011/esdd-2-105-2011.html http://www.earth-syst-dynam-discuss.net/2/105/2011/esdd-2-105-2011.pdf 105 132 2011-01-28 Entropy production of soil hydrological processes and its maximisation P. Porada pporad@bgc-jena.mpg.de A. Kleidon S. J. Schymanski Max Planck Institute for Biogeochemistry, P.O. Box 10 01 64, 07701 Jena, Germany 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. Atkins, P W.: Physical Chemistry, Sixth edition, Oxford University Press, Oxford, 1998. Budyko, M.: Climate and life, Academic Press, New York, 1974. Carsel, R F. and Parrish, R S.: Developing Joint Probability Distributions of Soil Water Retention Characteristics, Water Resour. Res., 24, 755–769, doi:10.1029/WR024i005p00755, 1988. Cramer, W., Kicklighter, D W., Bondeau, A., Moore~III, B., Churkina, G., Nemry, B., Ruimy, A., and Schloss, A.: Comparing global models of terrestrial Net Primary Productivity~(NPP): overview and key results, Global Change Biol., 5, 1–15, doi:10.1046/j.1365-2486.1999.00009.x, 1999. Dai, A. and Trenberth, K E.: Estimates of Freshwater Discharge from Continents: Latitudinal and Seasonal Variations, J. Hydrometeorol., 3, 660–687, doi:10.1175/1525-7541(2002)003<0660:EOFDFC>2.0.CO;2, 2002. Dewar, R C.: Maximum Entropy Production as an Inference Algorithm that Translates Physical Assumptions into Macroscopic Predictions: Dont Shoot the Messenger, Entropy, 11, 931–944, doi:10.3390/e11040931, 2009. Edlefsen, N E. and Anderson, A. B C.: Thermodynamics of Soil Moisture, Hilgardia, 15, 31–298, 1943. IGBP-DIS: SoilData(V.0), A program for creating global soil-property databases, IGBP Global Soils Data Task, France, 1998. Kleidon, A. and Schymanski, S.: Thermodynamics and optimality of the water budget on land: A review, Geophys. Res. Lett., 35, L20404, doi:10.1029/2008GL035393, 2008. Kleidon, A., Schymanski, S J., and Stieglitz, M.: Thermodynamics, Irreversibility, and Optimality in Land Surface Hydrology, in: Bioclimatology and Natural Hazards, edited by: Stelcov, K., Mtys, C., Kleidon, A., Lapin, M., Matejka, F., Blaenec, M., Kvarenina, J., and Holcy, J., Springer, Berlin, Germany, 107–118, doi:10.1007/978-1-4020-8876-6_9, 2009. Kondepudi, D. and Prigogine, I.: Modern thermodynamics – from heat engines to dissipative structures, Wiley, Chichester, 1998. Leopold, L B. and Langbein, W L.: The concept of entropy in landscape evolution, US Geol. Surv. Prof. Pap., 500-A, 20, 1962. Martyushev, L M. and Seleznev, V D.: Maximum entropy production principle in physics, chemistry and biology, Phys. Rep., 426, 1–45, doi:10.1016/j.physrep.2005.12.001, 2006. McNaughton, K G. and Jarvis, P G.: Predicting effects of vegetation changes on transpiration and evaporation, in: Water Deficits and Plant Growth, edited by: Kozlowski, T L., Academic Press, New York, 7, 1–47, 1983. Mualem, Y.: A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res., 12, 513–522, doi:10.1029/WR012i003p00513, 1976. Ozawa, H., Ohmura, A., Lorenz, R D., and Pujol, T.: The second law of thermodynamics and the global climate system – a review of the maximum entropy production principle, Rev. Geophys., 41, 1018, doi:10.1029/WR012i003p00513, 2003. Porada, P., Arens, S., Buend\'ia, C., Gans, F., Schymanski, S J., and Kleidon, A.: A simple global land surface model for biogeochemical studies, Technical Reports, Max-Planck-Institut für Biogeochemie, Jena, Germany, 18, 2010. Roderick, M L. and Canny, M J.: A mechanical interpretation of pressure chamber measurements – what does the strength of the squeeze tell us?, Plant Physiol. Biochem., 43, 323–336, doi:10.1016/j.plaphy.2005.02.014, 2005. Schymanski, S J.: Transpiration as the Leak in the Carbon Factory: A Model of Self-Optimising Vegetation, Ph.D thesis, The University of Western Australia, Perth, Australia, 2007. Schymanski, S J., Kleidon, A., and Roderick, M L.: Ecohydrological Optimality, in: Encyclopedia of Hydrological Sciences, edited by: Anderson, M G. and McDonnell, J J., John Wiley & Sons, Ltd, New York, USA, doi:10.1002/0470848944.hsa319, 2009. Schymanski, S J., Kleidon, A., Stieglitz, M., and Narula, J.: Maximum Entropy Production allows simple representation of heterogeneity in arid ecosystems, Philos. T. Roy. Soc B, 365, 1449–1455, doi:10.1098/rstb.2009.0309, 2010. Sheffield, J., Goteti, G., and Wood, E F.: Development of a 50-yr high-resolution global dataset of meteorological forcings for land surface modeling, J. Climate, 19, 3088–3111, doi:10.1175/JCLI3790.1, 2006. Sivapalan, M.: Pattern, Process and Function: Elements of a Unified Theory of Hydrology at the Catchment Scale, in: Encyclopedia of Hydrological Sciences, edited by: Anderson, M G., John Wiley & Sons, Ltd, New York, USA, 193–219, doi:10.1002/0470848944.hsa012, 2005. van Genuchten, M T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Sci. Soc. Am. J., 44, 892–898, 1980. Vörösmarty, C., Fekete, B., Meybeck, M., and Lammers, R.: Geomorphometric attributes of the global system of rivers at 30-minute spatial resolution, J. Hydrol., 237, 17–39, doi:10.1016/S0022-1694(00)00282-1, 2000. Zehe, E., Blume, T., and Blöschl, G.: The principle of maximum energy dissipation: a novel thermodynamic perspective on rapid water flow in connected soil structures, Philos. T. Roy. Soc B, 365, 1377–1386, doi:10.1098/rstb.2009.0308, 2010.