On Rigorous Drought Assessment Using Daily Time Scale: Non-Stationary Frequency Analyses, Revisited Concepts, and a New Method to Yield Non-Parametric Indices

Abstract

Some of the problems in drought assessments are that: analyses tend to focus on coarse temporal scales, many of the methods yield skewed indices, a few terminologies are ambiguously used, and analyses comprise an implicit assumption that the observations come from a stationary process. To solve these problems, this paper introduces non-stationary frequency analyses of quantiles. How to use non-parametric rescaling to obtain robust indices that are not (or minimally) skewed is also introduced. To avoid ambiguity, some concepts on, e.g., incidence, extremity, etc., were revisited through shift from monthly to daily time scale. Demonstrations on the introduced methods were made using daily flow and precipitation insufficiency (precipitation minus potential evapotranspiration) from the Blue Nile basin in Africa. Results show that, when a significant trend exists in extreme events, stationarity-based quantiles can be far different from those when non-stationarity is considered. The introduced non-parametric indices were found to closely agree with the well-known standardized precipitation evapotranspiration indices in many aspects but skewness. Apart from revisiting some concepts, the advantages of the use of fine instead of coarse time scales in drought assessment were given. The links for obtaining freely downloadable tools on how to implement the introduced methods were provided.