Modeling of Hydrological Droughts

Abstract

Hydrological droughts may be referred to as sustained and regionally extensive occurrences of below average water availability mainly in the  e form of streamflows. Two parameters of importance in modeling hydrological droughts are the longest duration (LT) and the largest magnitude (in standardized form (Sr» over a desired return period of T-year. For the estimation of expected values of duration and magnitude denoted as E(LT) and E(ST), two modeling approaches are in vogue: time series simulation approach (experimental) and probability theory based approach (analytical). Hydrological droughts are largely identified using the truncation level approach, and the chosen truncation level represents the average flow condition such as the median or mean of an annual or monthly flow sequence. Unlike the meteorological droughts, there is paucity of indices for hydrological droughts. In tandem with standardized precipitation index (SPI) commonly used in meteorological droughts, an index dubb~d as standardized hydrological index (SHI) has recently been proposed, The runs of deficits in the SHI sequence are treated as drought episodes and thus the theory of runs forms an essential tool for analysis. The statistics such as the mean, standard deviation (or coefficient of variation,' cv), lag-i serial correlation, skewness and conditional probabilities of annual or monthly SHI sequences, when invoked in the probability based analytical relationships are capable of reasonably predicting E(LT) and E(ST). The results presented . in this paper demonstrate that E(LT) on annual or monthly basis can be predicted using the theorem of extremes of random numbers of random variables applied to runs in SHI sequences of Canadian rivers. The drought magnitude E(ST) was found to be predicted satisfactorily via the model E(ST)'" E(LT). The estimates of E(LT) and E(ST) can equally be predicted using regression equations derived from the applicatiDnof time series simulation based approach .. Key words: Conditional probability, Markovian gamma model, Markovian normal model, standardized magnitude, standardized hydrological index, theory of runs.