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.
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