Probabilistic characterization of hydrological droughts

It is proposed to use the joint distribution of probabilities of minimum water discharges and the river runoff depth to characterize the severity and danger of durable low-flow periods. The copula theory is used to construct this distribution that enables to take account of differences in the types of one-dimensional probability distributions of initial variables and of the correlation between them. The studies were carried out for the vegetation periods using the data of the runoff depth measurements in Georghiu-Dej on the Don River in 1895–1980 and in Kirov on the Vyatka River in 1878–1980. The selection of copulas was based on comparing empirical and theoretical joint distributions of low-flow characteristics. It is demonstrated that the best results for the approximation of the joint probability distribution of low-flow characteristics are obtained from the Frank copula. Plotted are the dependences of low-flow frequency on the specified values of corresponding minimum water discharges and the river runoff depth during vegetation periods. Estimated are the probability and frequency of some most severe lowflow periods observed on the Don and Vyatka rivers.