Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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Probabilistic modelling of water balance at a point: the role of climate, soil and vegetation

I. Rodriguez-Iturbe

I. Rodriguez-Iturbe

Environmental Engineering and Water Resources Program and Princeton Environmental Institute, Princeton, NJ 08544, USA

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A. Porporato

A. Porporato

Dipartimento di Idraulica Trasporti e Infrastrutture Civili, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

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L. Ridolfi

L. Ridolfi

Dipartimento di Idraulica Trasporti e Infrastrutture Civili, Politecnico di Torino, Corso Duca degli Abruzzi, 24, 10129 Torino, Italy

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V. Isham

V. Isham

Department of Statistical Science, University College London, Gower Street, London WC1E 6BT, UK

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D. R. Coxi

D. R. Coxi

Nuffield College, University of Oxford, Oxford OX1 1NF, UK

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    The soil moisture dynamics under seasonally fixed conditions are studied at a point. The water balance is described through the representation of rainfall as a marked Poisson process which in turn produces an infiltration into the soil dependent on the existing level of soil moisture. The losses from the soil are due to evapotranspiration and leakage which are also considered dependent on the existing soil moisture. The steady–state probability distributions for soil moisture are then analytically obtained. The analysis of the distribution allows for the assessment of the role of climate, soil and vegetation on soil moisture dynamics. Further hydrologic insight is obtained by studying the various components of an average water balance. The realistic representation of the processes acting at a site and the analytical tractability of the model make it well suited for further analyses which consider the spatial aspect of soil moisture dynamics.