Examining uncertainty of parameter w for the Budyko curve

Parametric Budyko method has been extensively used to assess water availability. Its single parameter w, controlling the shape of the Budyko curve, is of vital importance to water availability assessment (WAA). As for the w estimation, general way is incorporating the long-term water-balance equation and Budyko hypothesis using the runoff, precipitation, and potential evapotranspiration data. However, the size of hydrometeorological records is generally limited, which contains less information and fails to perfectly depict the transformation relation among hydrometeorological factors, thus leading to large uncertainty on w estimation and subsequently resulting in WAA uncertainty when using the Budyko hypothesis. With the above background, we proposed one bootstrapping-based method to disclose the uncertainty of parameter w for the Budyko curve, and then derived specific function describing the impact of w uncertainty on WAA as a function of climatic conditions. The proposed bootstrapping-based method and derived function are exemplarily applied to the Yellow River Basin, China. Corresponding results reveal that there exists remarkable uncertainty in parameter w due to the limited hydrological records through use of bootstrapping-based method. Furthermore, the derived function indicates that the impact of parameter w uncertainty on WAA is conditional on the climatic conditions, which reaches the maximum in transitional climate regions compared to the humid and arid regions. These findings can enhance the reliability and robustness of hydrological applications of the Budyko-based model.