A 3-D Generalization of the Budyko Framework Captures the Mutual Interdependence Between Long-Term Mean Annual Precipitation, Actual and Potential Evapotranspiration
Abstract
We study the behavior of the 3-D parameter space defined by Φ =PET/P (so-called Aridity Index), Ψ =AET/P, and Ω =AET/PET, where P denotes mean annual precipitation, and PET and AET denote mean annual potential and actual evapotranspiration, respectively. Using information from the CLIMWAT 2.0 database (www.fao.org/nr/water/infores_databases_climwat.html) for P and PET, we estimate AET using both Budyko's and Turc's equations. Our results indicate that the well-known Budyko function that relates Φ vs.Ψ corresponds to a particular bi-dimensional cross-section of a broader coupling existing between Φ, Ψ and Ω (Figure 1a), and in turn of the mutual interdependence between P, PET and AET. The behavior of the three bi-dimensional projections are clearly parameterized by the remaining ortogonal parameter, such that: (i) the relation Φ vs. Ψ is defined by physically consistent varying values of Ω (Figure 1b); (ii) the relation Ω vs. Ψ is defined by physically consistent varying values of the Aridity Index,Φ (Figure 1c), and (iii) the relation Ω vs. Φ is defined by physically consistent varying values of Ψ (Figure 1d). Interestingly, we show that Φ and Ω are related by a power law, Φ~Ω-θ, with scaling exponent θ=1.15 (R2=0.91, n=3420) for the whole world (Figure 1d). Mathematical functions that model the three bi-dimensional projections and the surface defining the interdependence between Φ, Ψ and Ω will be presented. Our results provide a new framework to understand the coupling between the long-term mean annual water and energy balances in river basins, and the hydrological effects brought about by climate change, while taking into account the mutual interdependence between the three non-dimensional parameters Φ, Ψ and Ω, and in turn between P, PET and AET. Figure 1. (a) Three-dimensional rendering of sample values of Φ =PET/P (so-called Aridity Index), Ψ =AET/P, and Ω=AET/PET. Bi-dimensional projections of: (b) relation Φ vs. Ψ parameterized by Ω; (c) relation Ω vs. Ψ parameterized by the Aridity Index,Φ; and (d) relation Ω vs. Φ parameterized by Ψ. The red lines define the respective functions with AET estimated with Budyko's original equation.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2012
- Bibcode:
- 2012AGUFM.H31D1134C
- Keywords:
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- 1814 HYDROLOGY / Energy budgets;
- 1818 HYDROLOGY / Evapotranspiration;
- 1839 HYDROLOGY / Hydrologic scaling;
- 1876 HYDROLOGY / Water budgets