Drought analysis of monthly hydrological sequences: a case study of Canadian rivers

Two parameters of importance in hydrological droughts viz. the longest duration, L-T and the largest severity, S-T (in standardized form) over a desired return period, T years, have been analysed for monthly flow sequences of Canadian rivers. An important point in the analysis is that monthly sequences are non-stationary (periodic-stochastic) as against annual flows, which fulfil the conditions of stochastic stationarity. The parameters mean, mu, standard deviation, sigma (or coefficient of variation), lagl serial correlation, rho, and skewness, gamma (which is helpful in identifying the probability distribution function) of annual flow sequences, when used in the analytical relationships, are able to predict expected values of the longest duration, E(L-T) in years and the largest standardized severity, E(S-T). For monthly flow sequences, there are 12 sets of these parameters and thus the issue is how to involve these parameters to derive the estimates of E(L-T) and E(S-T). Moreover, the truncation level (i.e. the monthly mean value) varies from month to month. The analysis in this paper demonstrates that the drought analysis on an annual basis can be extended to monthly droughts simply by standardizing the flows for each month. Thus, the variable truncation levels corresponding to the mean monthly flows were transformed into one unified truncation level equal to zero. The runs of deficits in the standardized sequences are treated as drought episodes and thus the theory of runs forms an essential tool for analysis. Estimates of the above parameters (denoted as mu(av), sigma(av), rho(av), and gamma(av)) for use in the analytical relationships were obtained by averaging 12 monthly values for each parameter. The product- and L-moment ratio analyses indicated that the monthly flows in the Canadian rivers fit the gamma probability distribution reasonably well, which resulted in the satisfactory prediction of E(L-T). However, the prediction of E(S-T) tended to be more satisfactory with the assumption of a Markovian normal model and the relationship E(S-T) approximate to E(L-T) was observed to perform better.