Uncertainty analysis of water availability assessment through the Budyko framework

Abstract

Parametric Budyko method has been widely used to assess water availability under changing environment. Its single parameter (w) controlling the shape of the Budyko curve, is of critical importance to water availability assessment (WAA). Here, the water availability is defined as the ratio of evapotranspiration to precipitation in the context of Budyko hypothesis. As an unobserved variable, w is generally estimated through incorporating the long-term water-balance model and Budyko hypothesis, i.e. estimating w as a function of precipitation, runoff, and potential evapotranspiration over a long-term time series of these variables. Inevitably, the estimated value of w is subject to uncertainty resulting from hydro-meteorological records with limited size. Further, this uncertainty affects WAA in context of Budyko hypothesis. The uncertainty and its propagation issue is often overlooked in past research. In this paper, we develop a bootstrap-based algorithm to reveal aforementioned uncertainty. Moreover, a partial derivative-based sensitivity analysis is performed for understanding the propagation of w uncertainty on WAA. Three catchments located in the Yellow River Basin, China, are used as case study sites. Results indicate that there exists remarkable uncertainty in parameter w, which varies with the data length. The impact of such uncertainty on WAA increases quickly under the humid condition, thereafter reaches a peak under the mild condition, and decreases slowly under the arid condition. The reason behind this phenomenon is the largest sensitivity of WAA to parameter w under the mild climate condition. Moreover, a general analytical expression for determining the critical value of climate condition which maximizes the impact of parameter w uncertainty on WAA is derived in this paper. Results of this study can enhance the reliability and robustness of Budyko-based models.