Probabilities and return periods of multisite droughts

Because droughts cover extensive areas, it is important to consider multisite droughts in a region. Probability distribution of joint droughts at a number of sites is derived assuming that flows are cross-correlated first-order Markov processes. A geometric distribution is found with a parameter that depends on the threshold probability, lag-one autocorrelation coefficients, and the multivariate probability of remaining below the threshold. Computation of the parameter of the geometric distribution is discussed. An expression is obtained for the return period of multisite droughts. Application of the derived expression is shown in an example.