Hydrological Basis of Different Budyko Equations: The Spatial Variability of Available Water for Evaporation

Yao, Lili; Wang, Dingbao

doi:10.1029/2021wr030921

Cited by 11 publications

(4 citation statements)

References 84 publications

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“…When the net effect of groundwater flux across the watershed boundary and human impacts are negligible, WAI becomes the climate aridity index. The Budyko‐type curve corresponding to Gamma distribution for describing the spatial distribution of available water for ET (Yao & Wang, 2022) is illustrated as follows:

\frac{\mathrm{E}\mathrm{T}}{\mathrm{A}\mathrm{W}\mathrm{E}\mathrm{T}}=\frac{1}{{\Gamma }(k)}\left[{k}^{-1}\gamma \left(k+1,k\frac{{\mathrm{E}\mathrm{T}}_{P}}{\mathrm{A}\mathrm{W}\mathrm{E}\mathrm{T}}\right)+\frac{{\mathrm{E}\mathrm{T}}_{P}}{\mathrm{A}\mathrm{W}\mathrm{E}\mathrm{T}}{\Gamma }\left(k,k\frac{{\mathrm{E}\mathrm{T}}_{P}}{\mathrm{A}\mathrm{W}\mathrm{E}\mathrm{T}}\right)\right]

where

{\Gamma }(k)

is the gamma function;

\gamma \left(k+1,\frac{k}{P}{E}_{p}\right)

is the lower incomplete gamma function, and

{\Gamma }\left(k,\frac{k}{P}{E}_{p}\right)

is the upper incomplete gamma function; and

k

is catchment‐specific parameter relating to factors other than WAI that affect GWET ratio. The functional forms for Budyko curves are dependent on the distribution functions for the spatial variability of available water to ET (Wang, 2018; Yang et al., 2008).…”

Section: Methodsmentioning

confidence: 99%

Climatic Control on Mean Annual Groundwater Evapotranspiration in a Three‐Stage Precipitation Partitioning Framework

Zhang

Yao

Geurink³

et al. 2023

Water Resources Research

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Groundwater evapotranspiration (GWET) is the principal component of groundwater budgets of arid basins with shallow aquifers (Loheide, 2008;Nichols, 2000), and plays an important role in the watershed-scale water balance when water table depth is comparable with the rooting depth of plants (Yeh & Famiglietti, 2009). Capillary forces move groundwater upward from the water table. Groundwater contributes to evapotranspiration (ET) through direct evaporation when the capillary zone intersects the land surface and through transpiration by root water uptake from plants (Lam et al., 2011). With the combined impacts of climate change (Mukherjee & Mishra, 2021) and increased anthropogenic groundwater withdrawal (Wada et al., 2014), the quantification of GWET becomes more crucial for sustainable groundwater management.GWET is usually estimated based on observed hydrologic variables such as streamflow and water table elevation since there is no direct measurement of GWET (Orellana et al., 2012). Daily GWET has been estimated based on base flow recession from observed streamflow (Daniel, 1976) and diurnal water table fluctuations (WTF) from observed groundwater level in unconfined aquifer (White, 1932). Particularly, the WTF method has been applied for estimating groundwater consumption by phreatophytic vegetation with shallow water table in the riparian zone of arid and semi-arid regions (e.g., Carlson Mazur et al., 2014;Diouf et al., 2020;Gribovszki et al., 2008). Besides the observed groundwater level, the WTF method requires specific yield of unconfined aquifer which depends on soil properties and water table depth, and therefore varies spatially and temporally (Orellana et al., 2012;Parajuli et al., 2019Parajuli et al., , 2020Sophocleous, 1985). The WTF method has been improved by capturing robust, diurnal WTF (Soylu et al., 2012) and by accounting for the dependence of specific yield on depth to water table (DWT;Nachabe, 2002). The estimated GWET from the WTF method is at the point or local scale, requiring a high density of observation wells to capture the spatial variability of GWET (Lautz, 2008).The estimated GWET from the WTF method provides insights into the controlling factors of GWET. These factors include meteorological variables (Kray et al., 2012), vegetation type (Butler et al., 2007

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\frac{\mathrm{E}\mathrm{T}}{\mathrm{A}\mathrm{W}\mathrm{E}\mathrm{T}}=\frac{1}{{\Gamma }(k)}\left[{k}^{-1}\gamma \left(k+1,k\frac{{\mathrm{E}\mathrm{T}}_{P}}{\mathrm{A}\mathrm{W}\mathrm{E}\mathrm{T}}\right)+\frac{{\mathrm{E}\mathrm{T}}_{P}}{\mathrm{A}\mathrm{W}\mathrm{E}\mathrm{T}}{\Gamma }\left(k,k\frac{{\mathrm{E}\mathrm{T}}_{P}}{\mathrm{A}\mathrm{W}\mathrm{E}\mathrm{T}}\right)\right]

where

{\Gamma }(k)

is the gamma function;

\gamma \left(k+1,\frac{k}{P}{E}_{p}\right)

is the lower incomplete gamma function, and

{\Gamma }\left(k,\frac{k}{P}{E}_{p}\right)

is the upper incomplete gamma function; and

k

Section: Methodsmentioning

confidence: 99%

Climatic Control on Mean Annual Groundwater Evapotranspiration in a Three‐Stage Precipitation Partitioning Framework

Zhang

Yao

Geurink³

et al. 2023

Water Resources Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…The shape parameter value for a specific basin will vary based on its climatological (ET P , P) and hydrological (ET, baseflow, streamflow) characteristics (Equation 1). The shape parameter ω has been used extensively as an indicator to reflect the characteristics of a basin such as climate (Feng et al, 2012(Feng et al, , 2015Xu et al, 2013), vegetation (Li et al, 2013), topography (Yang et al, 2014;Bai et al, 2020), and combinations of the above mentioned parameters (Milly, 1993(Milly, , 1994Zhang et al, 2001Zhang et al, , 2004Porporato et al, 2004;Donohue et al, 2007;Yang et al, 2007Yang et al, , 2009Abatzoglou and Ficklin, 2017;Yao and Wang, 2022). For example, Li et al (2013) found a strong correlation between ω and annual vegetation coverage in 26 major global river basins.…”

Section: The Budyko Shape Parameter ωmentioning

confidence: 99%

The Budyko shape parameter as a descriptive index for streamflow loss

Tran,

Yang,

Condon

et al. 2023

Front. Water

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Increases in evapotranspiration (ET) from global warming are decreasing streamflow in headwater basins worldwide. However, these streamflow losses do not occur uniformly due to complex topography. To better understand the heterogeneity of streamflow loss, we use the Budyko shape parameter (ω) as a diagnostic tool. We fit ω to 37-year of hydrologic simulation output in the Upper Colorado River Basin (UCRB), an important headwater basin in the US. We split the UCRB into two categories: peak watersheds with high elevation and steep slopes, and valley watersheds with lower elevation and gradual slopes. Our results demonstrate a relationship between streamflow loss and ω. The valley watersheds with greater streamflow loss have ω higher than 3.1, while the peak watersheds with less streamflow loss have an average ω of 1.3. This work highlights the use of ω as an indicator of streamflow loss and could be generalized to other headwater basin systems.

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“…The model has been widely used in land surface hydro-thermal coupling simulation and evolution mechanism analysis (Yang et al, 2021;Li and Quiring, 2022). Several methods have been proposed for studying the Budyko hypothesis, among which the p-fu (Xing et al, 2018;Ning et al, 2019), Choudhury-yang (Zhang et al, 2018;Meng et al, 2019;Hou et al, 2022), and Wang and Tang (Yao and Wang, 2022) formulas are commonly used. In the Budyko formula, the underlying surface parameter n reflects the influence of catchment characteristics and determines the shape of the Budyko curve.…”

Section: Introductionmentioning

confidence: 99%

Attribution analysis of runoff evolution in Kuye River Basin based on the time-varying budyko framework

Huang

Wang

et al. 2023

Front. Earth Sci.

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The underlying surface parameters in the Budyko framework (such as parameter n in the Choudhury–Yang equation) are crucial for studying the relationship between precipitation, evapotranspiration, and runoff. It is important to accurately quantify the influence of climate and human activities on the evolution of underlying surface characteristic parameters. However, due to the spatiotemporal heterogeneity of underlying surface parameters, it is often difficult to accurately quantify these relationships. In this study, taking the Kuye River Basin located in the northern Loess Plateau as the research object, we first used trend analysis and non-linear regression methods to estimate the evolution characteristics of runoff and underlying surface parameter n. We then determined the contribution of runoff changes by using the elasticity coefficient method under the 9-year moving average window. The results showed that: 1) the Kuye River Basin runoff underwent a sudden change in 1997, and the complex human activities are the main reasons for the sharp runoff decrease. 2) In addition to precipitation and potential evapotranspiration, temperature changes will alter the basin’s underlying surface parameters, ultimately changing the runoff. Moreover, climate change first inhibited and then promoted the runoff reduction trend. 3) Human activities, represented by changes in vegetation coverage and coal mining, considerably influenced runoff evolution in Kuye River Basin. More importantly, the change of runoff in the Kuye River Basin caused by coal mining is approximately four times that of the normalized vegetation index. This study can improve the applicability of the Budyko framework in the Loess Plateau sub-basin and provide scientific guidance for water resource management.

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Hydrological Basis of Different Budyko Equations: The Spatial Variability of Available Water for Evaporation

Cited by 11 publications

References 84 publications

Climatic Control on Mean Annual Groundwater Evapotranspiration in a Three‐Stage Precipitation Partitioning Framework

Climatic Control on Mean Annual Groundwater Evapotranspiration in a Three‐Stage Precipitation Partitioning Framework

The Budyko shape parameter as a descriptive index for streamflow loss

Attribution analysis of runoff evolution in Kuye River Basin based on the time-varying budyko framework

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