Exploring cumulative probability functions for streamflow drought magnitude: Global scale analysis and parametric vs. non-parametric comparisons

Streamflow droughts pose significant challenges to water resource management and environmental sustainability. The accurate characterization of streamflow drought magnitude is essential for effective mitigation, assessment and adaptation strategies. In this study, we explore the implications of choosing different cumulative probability distribution functions (cdfs) on the determination of streamflow drought magnitude, as assessed by the z-score values of the standardized streamflow index (SSI) and return periods. Our investigation encompasses a comprehensive global-scale analysis, with the aim of identifying the most suitable cdfs for characterizing streamflow droughts. To accomplish this objective, we incorporate global simulated streamflow values from the model WaterGAP 2.2d and observed streamflow values from 280 Global Runoff Data Centre (GRDC) stations for the period 1981 - 2010. We evaluate the performance of 118 parametric cdfs for each of the 12 calendar monthly streamflow values at each model grid cell and GRDC station to determine the best fitting parametric cdf. Moreover, we go beyond the conventional scope of such studies by further assessing the best-fitting cdfs alongside non-parametric cdfs such as the Empirical cumulative distribution function (ecdf) and the cumulative distribution function derived from the Kernel density estimation function (kcdf). Among our findings, we establish a subset of 23 parametric cdfs that exhibit the best fit for the global streamflow values concerning all 12 calendar monthly streamflow values at individual GRDC stations or grid cells within the specified period. Furthermore, we observe that the accuracy of streamflow simulation and the length of the reference period directly influence the selection of the most suitable parametric cdf. Our comparative analysis reaffirms the existing understanding that opting for the best-fitting parametric cdf, rather than a non-parametric alternative, mitigates the risk of overestimating drought magnitudes. However, we emphasize the crucial importance of considering the intended purpose, approach-specific sensitivities, and uncertainties when choosing the most suitable parametric cdf for any calendar monthly streamflow values.