Abstract
The Budyko framework provides a quantitative description of long-term average annual evapotranspiration at catchment scales in terms of macro-climatic variables. This framework, however, makes no reference to the vadose zone because it neglects changes in ubsurface storage in the catchment water balance. Recent studies have shown clearly that vadose-zone water storage cannot be neglected at sub-catchment or sub-annual space and time scales, resulting in numerous model attempts to extend the original Budyko framework to incorporate the full water balance equation. Here we apply the approach taken in a companion paper on the original Budyko framework to show that it can be generalized rigorously to include changes in vadose-zone water storage in a manner that is both parsimonious in hypotheses and broad in scope.
Highlights
The Budyko framework [1] is the name given to an implicit mathematical relationship between catchment evapotranspiration (ET) and two macro-climatic variables, precipitation (P) and potential evapotranspiration (ET0 ), originally put forth by Budyko [2]
That is derived from P if ∆S < 0 and (2) while the entirety of P is available for ET in the original Budyko framework, only the portion (P − ∆S) is available for ET in the extended Budyko framework if ∆S > 0. This line of reasoning, based solely on the complete water balance, can be summarized in the following two hypotheses: (1) For ∆S < 0, the portion of ET that is derived from precipitation, (ET + ∆S), has the same functional relationship to (ET0 + ∆S) in the extended Budyko framework as ET does to ET0 in the original Budyko framework, i.e., if
The two principal elements of the extended Budyko framework under the assumption of homogeneity are: Equation (6), the extended Budyko equation, which relates ET/P to the scaled variables, ET0 /P and ∆S/P and implies hydrologic similarity/space-time symmetry [9], and Equation (12), the Euler relation, which implies that the calculation of ET/P requires only a knowledge of the two climate elasticities, (
Summary
The Budyko framework [1] is the name given to an implicit mathematical relationship between catchment evapotranspiration (ET) and two macro-climatic variables, precipitation (P) and potential evapotranspiration (ET0 ), originally put forth by Budyko [2] (pp. 322–323). The Budyko framework was developed under the assumption of steady-state water balance, which equates precipitation to the sum of evapotranspiration and runoff, implying negligible changes in subsurface water storage [2,3,4]. This assumption has been validated in observations of long-term average annual ET from large catchments, but it is known to fail at smaller temporal and spatial scales [3]. It will be shown that, by making a single physically-relevant hypothesis about the functional relationship in Equation (4), the Budkyo framework can be extended to include changes in vadose-zone water storage in a manner broad enough to include all extant models [1,3,6] as special cases, while offering a rigorous approach to the specific modeling of Equation (4) that does not require adjustable parameters
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