A scaling approach to Budyko’s framework and the complementary relationship of evapotranspiration in humid environments: case study of the Amazon River basin.

Abstract:

We study a 3-D generalization of Budyko’s framework that involves the complementary relationship between long-term mean actual evapotranspiration (E) and potential evapotranspiration (Ep), and that captures the mutual interdependence among E, Ep, and mean annual precipitation (P). For this purpose we use three dimensionless and dependent quantities: Ψ=E/P, Φ=Ep/P and Ω=E/Ep. We demonstrate analytically that Budyko-type equations are unable to capture the physical limit of the relation between Ω and Φ in humid environments, owing to the unfeasibility of Ep/P→0 at E/Ep=1. Using independent datasets from 146 sub-catchments in the Amazon River basin we overcome this physical inconsistency by proposing a physically consistent power law Ψ=kΦ ^e with pre-factor k=0.66 and scaling exponent e=0.83 (R²=0.93). The proposed power law is compared with other Budyko-type equations, namely those by Yang et al (2008) and Cheng et al (2011). Taking into account the goodness of fits with confidence bounds set at 95% level and the ability to comply with the physical limits of the 3-D space, our results show that the power law works better to model the long-term water and energy balances within the Amazon River basin. At the interannual time scale, parameters from the three studied equations are estimated for each catchment using 27 years of information and interesting regional patterns emerge, as well as evidence of space-time symmetry. In addition, results show that within individual catchments the parameters from the linear relationship by Cheng et al (2011) and from the power law resemble and are related to the partitioning of energy via evapotranspiration in terms of Ω. Finally, signs of co-evolution of catchments are explored by linking the emerging spatial patterns of the parameters with landscape properties that represent some of the main features of the Amazon River basin, including topography, water in soils and vegetation.