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• Comparison of Budyko-based methods to separate catchment and climate effects on flow. • Probabilistic nature of catchment parameter and its uncertainty considered. • New, improved Two-Stage Decomposition method proposed for separation. • Proposed method considers uncertainty in evaporative index using bootstrap method. • Proposed method more robust than using any single earlier-practiced method. Streamflow variability is affected by both climate change and direct human impacts within the catchment. Quantification of the role of these two factors have significant implications for water resources. In recent years, Budyko-based analytical methods have been widely used for such quantification due to their simplicity and efficacy. This paper presents a comparison of such methods to attribute changes in streamflow in four Model Parameter Estimation Experiment (MOPEX) catchments in the contiguous United States. Further, a new, improved Two-stage Decomposition method to separate the role of climate and catchment changes on streamflow is proposed, considering the uncertainty in the catchment parameter that further leads to a range of evaporative index values within a catchment. We find that climate and catchment effects are sensitive to the choice of Budyko equation, disaggregation algorithm and approximation technique. Further, the catchment parameter can be expressed probabilistically, to account for the uncertainty because of limited hydro-meteorological records. The proposed approach employs a bootstrap analysis to obtain the stochastic range of the catchment parameter, considering different choices of Budyko equations. We argue that rather than relying on a single Budyko-based approach for separation of climate and catchment effects on streamflow, the proposed method offers a more robust way by considering the entire range of uncertainty of the catchment parameter. [ABSTRACT FROM AUTHOR]