Analytical derivation of the Budyko curve based on rainfall characteristics and a simple evaporation model
Tóm tắt
The Budyko curve is often used to estimate the actual evaporation as a function of the aridity index in a catchment. Different empirical equations exist to describe this relationship; however, these equations have very limited physical background. The model concept presented in this paper is physically based and uses only measurable parameters. It makes use of two types of evaporation: interception and transpiration. It assumes that interception can be modeled as a threshold process on a daily time scale. If multiplied with the rainfall distribution function, integrated, and multiplied with the expected number of rain days per month, the monthly interception is obtained. In a similar way, the monthly interception can be upscaled to annual interception. Analogous to the interception process, transpiration can be modeled as a threshold process at a monthly time scale and can be upscaled by integration and multiplication with the expected number of rain months. The expected rain days per month are modeled in two ways: as a fixed proportion of the monthly rainfall and as a power function based on Markov properties of rainfall. The latter is solved numerically. It appears that on an annual basis the analytical model does not differ much from the numerical solution. Hence, the analytical model is used and applied on 10 locations in different climates. This paper shows that the empirical Budyko curve can be constructed on the basis of measurable parameters representing evaporation threshold values and the expected number of rain days and rain months and, in addition, a monthly moisture carryover amount for semiarid zones.
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Tài liệu tham khảo
Baird A. J., 1999, Eco‐hydrology: Plants and Water in Terrestrial and Aquatic Environments
Budyko M. I., 1974, Climate and Life
de Groen M. M., 2002, Modelling Interception and Transpiration at Monthly Time Steps: Introducing Daily Variability Through Markov Chains
Gerrits A. M. J., 2009
Mazvimavi D.(1998) Water resources management in the water catchment board pilot areas phase 1: Data collection technical report Cent. for Appl. Social Sci. Univ. of Zimbabwe Harare.
Ol'dekop E. M., 1911, On evaporation from the surface of river basins, Trans. Meteorol. Obs., 4, 200
Rodríguez‐Iturbe I., 2004, Ecohydrology of Water‐Controlled Ecosystems
Rutter A. J., 1971, A predictive model of rainfall interception in forests. I. Derivation of the model and comparison with observations in a plantation of Corsican pine, Agric. Meteorol., 9, 367, 10.1016/0002-1571(71)90034-3
Schreiber P., 1904, Über die Beziehungen zwischen dem Niederschlag und der Wasserführung der Flüsse in Mitteleuropa, Z. Meteorol., 21, 441
Shuttleworth W. J., 1993, Handbook of Hydrology, 4.1
Turc L., 1954, Le bilan d'eau des sols. Relation entre la précipitation, l'évaporation et l'écoulement, Ann. Agron., 5, 491