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

Abstract

Abstract. This paper studies a 3-D state space representation of Budyko's framework designed to capture the mutual interdependence among long-term mean actual evapotranspiration (E), potential evapotranspiration (E p ) and precipitation (P ). For this purpose we use three dimensionless and dependent quantities: = E/P , = E p /P and = E/E p . This 3-D space and its 2-D projections provide an interesting setting to test the physical soundness of Budyko's hypothesis. We demonstrate analytically that Budyko-type equations are unable to capture the physical limit of the relation between and in humid environments, owing to the unfeasibility of E p /P = 0 when E/E p → 1. Using data from 146 sub-catchments in the Amazon River basin we overcome this inconsistency by proposing a physically consistent power law: = k e , with k = 0.66, and e = 0.83 (R 2 = 0.93). This power law is compared with two other Budyko-type equations. Taking into account the goodness of fits and the ability to comply with the physical limits of the 3-D space, our results show that the power law is better suited to model the coupled water and energy balances within the Amazon River basin. Moreover, k is found to be related to the partitioning of energy via evapotranspiration in terms of . This suggests that our power law implicitly incorporates the complementary relationship of evapotranspiration into the Budyko curve, which is a consequence of the dependent nature of the studied variables within our 3-D space. This scaling approach is also consistent with the asymmetrical nature of the complementary relationship of evapotranspiration. Looking for a physical explanation for the parameters k and e, the interannual variability of individual catchments is studied. Evidence of space-time symmetry in Amazonia emerges, since both between-catchment and between-year variability follow the same Budyko curves. Finally, signs of co-evolution of catchments are explored by linking spatial patterns of the power law parameters with fundamental characteristics of the Amazon River basin. In general, k and e are found to be related to vegetation, topography and water in soils.

Variability of soil moisture proxies and hot days across the climate regimes of Australia

“…1. Contrary to recent studies [Greve et al, 2014[Greve et al, , 2016Carmona et al, 2016], large parts of the temperate, semiarid, and savanna climate regions in Australia enter the transitional regime and are neither strongly moisture nor radiation limited (Figures 1a and 1b). 2.…”

“…A significant negative relationship between various SM indices and Tx90 has been observed for large parts of Australia, in particular the southeast and north of the country coinciding with the identification of the transitional regime. The main conclusions of this study are the following: Contrary to recent studies [ Greve et al , , ; Carmona et al , ], large parts of the temperate, semiarid, and savanna climate regions in Australia enter the transitional regime and are neither strongly moisture nor radiation limited (Figures a and b). Arid and semiarid regions of Australia exhibit the strongest increase in the quantile regression slopes (from low to high percentiles), indicating that months with low SM is highly likely to experience a large number of Tx90 (Figure ). API appears to best represent patterns seen with the AWAP SM and has the largest anticorrelations with Tx90 in the transitional zone (Figure ). …”

“…Using the AWAP data set, this was applied to each Köppen climate regime for each year during the extended period: 1950 and 2015 (Figure a). As mentioned, the transitional regime occurs between the field capacity and the wilting point [ Seneviratne et al , ; Greve et al , , ; Carmona et al , ], with the field capacity (PET/ P < 1) and the wilting point (PET/ P > 3), depending on vegetation and root zone [ Rouholahnejad and Kirchner , ]. Typically, semiarid regions are defined as being within the transitional regime [ Seneviratne et al , ; Greve et al , ].…”

Changing the retention properties of catchments and their influence on runoff under climate change

“…The Budyko framework was proposed six decades ago, but new datasets have motivated a recent use of this integrated, elegant and intuitive framework to analyze changes in the land hydrological cycle (e.g. Berghuijs et al 2014, Greve et al 2014, Carmona et al 2016. The Budyko framework distills complex systems to a key effective lumped parameter, which helps to understand and quantify measurements and model features.…”

Conjoint Analysis of Surface and Atmospheric Water Balances in the Andes‐Amazon System

“…The basin plays a fundamental hydroclimatological role in Earth's climate and exhibits various stability characteristics associated with land cover types and extent (Hirota et al, ; Keller et al, ; Lenton et al, ; Nobre & Borma, ). Understanding the dynamics of the hydrological cycle of the Amazon River basin has been the focus of many previous studies, some interested in individual branches of the hydrological cycle (Costa & Foley, ; Getirana et al, ; Marengo, ; Zeng, ), others in one particular variable of the hydrological budget over the Amazon River basin, such as precipitation in particular seasons (Carlo et al, ; Costa & Foley, ; Liebmann et al, ; Liebmann & Marengo, ; Satyamurty et al, ), runoff (Azarderakhsh et al, ; Coe et al, ; Syed et al, ), evapotranspiration (Carmona et al, ; Hasler & Avissar, ; Mallick et al, ), and wind divergence (Liebmann et al, ; Zeng, ).…”