A drought frequency formula

Abstract

The important elements of a drought phenomenon are the longest duration and the largest severity for a desired return period. These elements form a basis for designing water storage systems to cope with droughts. At times, a third element, drought intensity, is also used and is defined as the ratio of severity to duration. The commonly available statistics for the causative drought variables such as annual rainfall or runoff sequences are the mean, the coefficient of variation and the lag one serial correlation coefficient, and occasionally some indication of the probability distribution function (pdf) of the sequences. The extremal values of the duration and severity are modelled in the present paper using information on the aforesaid parameters at the truncation level equal to the mean of the drought sequence, which is generally taken as the truncation level in the analysis of droughts. The drought severity has been modelled as the product of the duration and intensity with the assumption of independence between them. An estimate of drought intensity has been realized from the concept of the truncated normal distribution of the standardized form of the drought sequences in the normalized domain. A formula in terms of the extremal severity and the T-year return period has been suggested similar to the flood frequency formulae, commonly cited in hydrological texts.