Applications of the Theory of Runs to Hydrology

The problem of runs is one of long history among hydrologists. Classically a run is defined as a sequence of observations of the same kind preceded and succeeded by one or more observations of a different kind. Considering a sequence of random variables x n , n = 0, 1, 2,. and choosing a constant x 0 , one may arbitrarily classify the n th year as a surplus year if x n > x 0 and call x n − x 0 the surplus. Similarly if x n ≤ x 0 , the n th year is a deficit year with the deficit x 0 − x n [ Downer et al ., 1967].