Applications of the Theory of Runs to Hydrology

Abstract

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 xn, n = 0, 1, 2,. and choosing a constant x0, one may arbitrarily classify the nth year as a surplus year if xn > x0 and call xn − x0 the surplus. Similarly if xn ≤ x0, the nth year is a deficit year with the deficit x0 − xn [Downer et al., 1967].