The complementary relationship and generation of the Budyko functions

• Published in: Geophysical research letters Vol. 42; no. 6; pp. 1781 - 1790
• Main Authors: Zhou, Sha, Yu, Bofu, Huang, Yuefei, Wang, Guangqian
• Format: Journal Article
• Language: English
• Published: Washington John Wiley & Sons, Inc 28.03.2015
• Subjects: Atmospheric precipitations; Budyko functions; Climate; Climate change; complementary relationship; Constraining; Elasticity; Energy; Evapotranspiration; generating function; Geophysics; Hydrology; Mathematical analysis; Meteorology; Methods; Potential evapotranspiration; Precipitation; Properties; Runoff; Sensitivity analysis; Unity; Watersheds
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1002/2015GL063511

The Budyko hypothesis states that the ratio of the actual evapotranspiration over precipitation (E/P) is fundamentally related to the ratio of the potential evapotranspiration over precipitation (E0/P). A number of Budyko functions have been proposed to describe such a relationship between E0/P and E/P. There is, however, no simple method to generate Budyko functions that meet the water and energy constraints. This study showed analytically that for any Budyko function, the sum of elasticity of evapotranspiration with respect to potential evapotranspiration and that with respect to precipitation is equal to unity. This complementary relationship for sensitivity of evapotranspiration has important implications for evaluating hydrologic impact of change in climate and/or catchment characteristics. More importantly, this study found a function that is monotonically increasing with simple limiting properties. This function can be used to generate numerous valid Budyko functions and can also be used to test the validity of the existing Budyko functions. Key Points A complementary relationship for sensitivity of evapotranspiration or runoff A methodology was developed to generate and validate Budyko functions The existing Budyko functions are special cases to meet Budyko requirements