The complementary relationship and generation of the Budyko functions

Zhou, Sha; Yu, Bofu; Huang, Yuefei; Wang, Guangqian

doi:10.1002/2015gl063511

Cited by 96 publications

(70 citation statements)

References 20 publications

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“…If the local precipitation is zero, evapotranspiration approaches zero due to no available water; C is zero constant. Note that another form of the BH is also given by Mezentsev (1955) (later, Choudhury, 1999, and Yang et al, 2008, which is, in fact, identical to Fu's equation (Zhou et al, 2015) with the parameters linearly related (R 2 = 0.9997) (Sun, 2007). Water balance analysis in Sect.…”

Section: Budyko Hypothesis Model At Annual and Monthly Scalesmentioning

confidence: 99%

New interpretation of the role of water balance in an extended Budyko hypothesis in arid regions

Sun

et al. 2016

Hydrol. Earth Syst. Sci.

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Abstract. The Budyko hypothesis (BH) is an effective approach to investigating long-term water balance at large basin scale under steady state. The assumption of steady state prevents applications of the BH to basins, which is unclosed, or with significant variations in root zone water storage, i.e., under unsteady state, such as in extremely arid regions. In this study, we choose the Heihe River basin (HRB) in China, an extremely arid inland basin, as the study area. We firstly use a calibrated and then validated monthly water balance model, i.e., the abcd model, to quantitatively determine annual and monthly variations of water balance for the sub-basins and the whole catchment of the HRB, and find that the roles of root zone water storage change and that of inflow from upper sub-basins in monthly water balance are significant. With the recognition of the inflow water from other regions and the root zone water storage change as additional possible water sources to evapotranspiration in unclosed basins, we further define the equivalent precipitation (P e ) to include local precipitation, inflow water and root zone water storage change as the water supply in the Budyko framework. With the newly defined water supply, the Budyko curve can successfully describe the relationship between the evapotranspiration ratio and the aridity index at both annual and monthly timescales, whilst it fails when only the local precipitation being considered. Adding to that, we develop a new Fu-type Budyko equation with two non-dimensional parameters (ω and λ) based on the deviation of Fu's equation. Over the annual timescale, the new Fu-type Budyko equation developed here has more or less identical performance to Fu's original equation for the sub-basins and the whole catchment. However, over the monthly timescale, due to large seasonality of root zone water storage and inflow water, the new Fu-type Budyko equation generally performs better than Fu's original equation. The new Fu-type Budyko equation (ω and λ) developed here enables one to apply the BH to interpret regional water balance over extremely dry environments under unsteady state (e.g., unclosed basins or sub-annual timescales).

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Section: Budyko Hypothesis Model At Annual and Monthly Scalesmentioning

confidence: 99%

New interpretation of the role of water balance in an extended Budyko hypothesis in arid regions

Sun

et al. 2016

Hydrol. Earth Syst. Sci.

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“…2). Diverse authors have derived equations to further develop Budyko's framework (Mezentsev, 1955;Pike, 1964;Fu, 1981;Choudhury, 1999;Yang et al, 2008;Zhou et al, 2015). In particular, Yang et al (2008) mathematically derived a general solution for the set of partial differential equations Figure 1.…”

Section: Published By Copernicus Publications On Behalf Of the Europementioning

confidence: 99%

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

Carmona

Poveda

Sivapalan

et al. 2016

Hydrol. Earth Syst. Sci.

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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.

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“…In light of this parameter independence, recent studies carried out in the original Budyko framework [3,15,[23][24][25], which present statistical correlations between the Fu model parameter w and non-climatic catchment characteristics, may be premature, pending investigation of which catchment characteristics are already incorporated implicitly by considering the complete catchment water balance and including the independent variable, ∆S. Equation (28) offers a case in point, since varying ∆S/P in this equation has the same shape-changing effect on the ET/P versus ET 0 /P curve as does varying w in Equation (30), which neglects vadose-zone water storage.…”

Section: Discussionmentioning

confidence: 99%

“…The Schreiber model is non-parametric, conforming to the boundary conditions in Equations (8) and (9) while interpolating smoothly between them. It is often used as a basis for comparison with parametric models [15].…”

Section: Example: Extending the Schreiber Modelmentioning

confidence: 99%

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Incorporating the Vadose Zone into the Budyko Framework

Sposito

2017

Water

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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 subsurface 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.

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The complementary relationship and generation of the Budyko functions

Cited by 96 publications

References 20 publications

New interpretation of the role of water balance in an extended Budyko hypothesis in arid regions

New interpretation of the role of water balance in an extended Budyko hypothesis in arid regions

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

Incorporating the Vadose Zone into the Budyko Framework

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