<p>Understanding how climate change influences actual evapotranspiration (AET) is essential for guiding water resource adaptation strategies. If AET variations are mainly driven by climate variability, adaptation efforts should prioritize climatic interventions; otherwise, adjustments in land cover and vegetation may be more effective. The Budyko framework is widely used to estimate long-term water balance and assess the relative contributions of climate and watershed characteristics in shaping hydrological responses. However, its application to complex heterogeneous watersheds introduces significant uncertainties. This study develops a Hierarchical Bayesian modeling approach to explicitly quantify uncertainties within the Budyko framework and assess their implications for both AET estimation and attribution analysis. The propagation of uncertainties associated with the watershed characteristic parameter (ω) to AET estimation and the attribution analysis of AET changes is thoroughly examined for 28 watersheds in Ontario, Canada. The results reveal significant variations in model uncertainty across both modeling stages and spatial domains. By incorporating the Markov Chain Monte Carlo (MCMC) sampling method into the Budyko modeling framework, posterior distributions for both ω and AET were derived. The findings demonstrate that the Hierarchical Bayesian approach can effectively quantify uncertainties arising from variations in watershed characteristics. Posterior distributions of AET in urbanized watersheds are more likely to display multimodal characteristics compared to those in predominantly forested watersheds. Moreover, probabilistic attribution analysis results were also obtained by further examining the relationships among precipitation (P), potential evapotranspiration (PET), vegetation index (M), and seasonal factor (S) under uncertainty. The analysis reveals that most of the 28 watersheds exhibit a climate-dominated pattern in AET changes. This framework distinguishes climate and anthropogenic impacts on AET changes, thereby supporting more targeted and resilient water resource management under climate change. It provides critical insights for improving water resources management by identifying the dominant drivers of AET variability and guiding region-specific adaptation strategies.</p> Graphical Abstract <p></p> <p>Based on the graphical snapshot, this study was conducted to quantify the uncertainties in actual evapotranspiration (AET) estimation and attribution analysis within the Budyko Framework across 28 watersheds in Ontario, Canada. A hierarchical Bayesian approach was introduced to propagate multi-layer, multi-source uncertainties. Prior distributions were defined for three uncertainty layers that reflect spatial dependence and watershed-specific characteristics, and posterior distributions were subsequently derived for the watershed parameter (ω) and AET estimates. To assess drivers of AET change, a temporal change-point was identified within the study period, and the attribution analysis of AET variation between two time period was conducted by generating the posterior distributions of the relative contributions of climatic and anthropogenic factors. All posterior outputs, including those for watershed parameters (α, β₀, β₁, and ω), AET, and attribution components, showed substantial spatial variability across the 28 watersheds. The results provided robust decision support for AET-related watershed management and policy development. The findings also underscore the importance of uncertainty quantification in future Budyko-based modeling studies.</p>

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Uncertainty Quantification in the Budyko Framework for Understanding Evapotranspiration Changes in Canadian Watersheds: A Hierarchical Bayesian Approach

  • Zehao Yan,
  • Zhong Li,
  • Brian Baetz

摘要

Understanding how climate change influences actual evapotranspiration (AET) is essential for guiding water resource adaptation strategies. If AET variations are mainly driven by climate variability, adaptation efforts should prioritize climatic interventions; otherwise, adjustments in land cover and vegetation may be more effective. The Budyko framework is widely used to estimate long-term water balance and assess the relative contributions of climate and watershed characteristics in shaping hydrological responses. However, its application to complex heterogeneous watersheds introduces significant uncertainties. This study develops a Hierarchical Bayesian modeling approach to explicitly quantify uncertainties within the Budyko framework and assess their implications for both AET estimation and attribution analysis. The propagation of uncertainties associated with the watershed characteristic parameter (ω) to AET estimation and the attribution analysis of AET changes is thoroughly examined for 28 watersheds in Ontario, Canada. The results reveal significant variations in model uncertainty across both modeling stages and spatial domains. By incorporating the Markov Chain Monte Carlo (MCMC) sampling method into the Budyko modeling framework, posterior distributions for both ω and AET were derived. The findings demonstrate that the Hierarchical Bayesian approach can effectively quantify uncertainties arising from variations in watershed characteristics. Posterior distributions of AET in urbanized watersheds are more likely to display multimodal characteristics compared to those in predominantly forested watersheds. Moreover, probabilistic attribution analysis results were also obtained by further examining the relationships among precipitation (P), potential evapotranspiration (PET), vegetation index (M), and seasonal factor (S) under uncertainty. The analysis reveals that most of the 28 watersheds exhibit a climate-dominated pattern in AET changes. This framework distinguishes climate and anthropogenic impacts on AET changes, thereby supporting more targeted and resilient water resource management under climate change. It provides critical insights for improving water resources management by identifying the dominant drivers of AET variability and guiding region-specific adaptation strategies.

Graphical Abstract

Based on the graphical snapshot, this study was conducted to quantify the uncertainties in actual evapotranspiration (AET) estimation and attribution analysis within the Budyko Framework across 28 watersheds in Ontario, Canada. A hierarchical Bayesian approach was introduced to propagate multi-layer, multi-source uncertainties. Prior distributions were defined for three uncertainty layers that reflect spatial dependence and watershed-specific characteristics, and posterior distributions were subsequently derived for the watershed parameter (ω) and AET estimates. To assess drivers of AET change, a temporal change-point was identified within the study period, and the attribution analysis of AET variation between two time period was conducted by generating the posterior distributions of the relative contributions of climatic and anthropogenic factors. All posterior outputs, including those for watershed parameters (α, β₀, β₁, and ω), AET, and attribution components, showed substantial spatial variability across the 28 watersheds. The results provided robust decision support for AET-related watershed management and policy development. The findings also underscore the importance of uncertainty quantification in future Budyko-based modeling studies.