An analysis of non-normal Markovian extremal droughts

Abstract

Abstract:In many arid and semi-arid environments of the world, years of extended droughts are not uncommon. The occurrence of a drought can be re¯ected by the de®ciency of the rainfall or stream¯ow sequences below the long-term mean value, which is generally taken as the truncation level for the identi®cation of the droughts. The commonly available statistics for the above processes are mean, coecient of variation and the lag-one serial correlation coecient, and at times some indication of the probability distribution function (pdf) of the sequences. The important elements of a drought phenomenon are the longest duration and the largest severity for a desired return period, which form a basis for designing facilities to meet exigencies arising as a result of droughts. The sequences of drought variable, such as annual rainfall or stream¯ow, may follow normal, lognormal or gamma distributions, and may evolve in a Markovian fashion and are bound to in¯uence extremal values of the duration and severity. The eect of the aforesaid statistical parameters on the extremal drought durations and severity have been analysed in the present paper. A formula in terms of the extremal severity and the return period`T' in years has been suggested in parallel to the¯ood frequency formula, commonly cited in the hydrological texts. #

Global analysis of runs of annual precipitation and runoff equal to or below the median: run magnitude and severity

“…The conclusion that run magnitude is strongly related to the coefficient of variation is consistent with the equations ofŞen (1977) and Sharma (1997bSharma ( , 1998. The importance of the coefficient of skewness to run magnitude, noted by Sharma (1997bSharma ( , 1998, was observed to be secondary to the coefficient of variation in the present analysis.…”

“…The conclusion that run magnitude is strongly related to the coefficient of variation is consistent with the equations ofŞen (1977) and Sharma (1997bSharma ( , 1998. The importance of the coefficient of skewness to run magnitude, noted by Sharma (1997bSharma ( , 1998, was observed to be secondary to the coefficient of variation in the present analysis. The importance of skewness to run magnitude would increase when the threshold is the mean, as used by Sharma (1997bSharma ( , 1998, rather than the median, because as the sample skewness increases so the percentage of sample values below the threshold increases, resulting in increases in run length, magnitude and severity.…”

“…The importance of the coefficient of skewness to run magnitude, noted by Sharma (1997bSharma ( , 1998, was observed to be secondary to the coefficient of variation in the present analysis. The importance of skewness to run magnitude would increase when the threshold is the mean, as used by Sharma (1997bSharma ( , 1998, rather than the median, because as the sample skewness increases so the percentage of sample values below the threshold increases, resulting in increases in run length, magnitude and severity. The conclusion that run magnitude is strongly related to annual variability and to a lesser extent skewness highlights the importance of using a percentile-based threshold for drought analysis.…”

Analysis of annual hydrological droughts: the case of northwest Ontario, Canada

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Analytical procedures for weekly hydrological droughts: a case of Canadian rivers

“…*The station identifiers are the same as defined in Table 1. (Todorovic & Woolhiser, 1975) and has been successfully used for the analysis and prediction of hydrological droughts on an annual basis (Sen, 1980a;Guven, 1983;Sharma, 1998Sharma, , 2000. The theorem also provides satisfactory estimates of E(L T ) and E(M T ) on a monthly (Sharma & Panu, 2008) and an annual (Panu & Sharma, 2009) basis in Canadian environments.…”