Investigation of wet and dry years by runs

Abstract

A technique is advanced for testing the structure of time series, with the basic statistical parameter being the mean run-length. This technique is shown to be distribution-free, as opposed to other techniques of investigation of time series like autocorrelation and variance spectrum analyses which are based on the assumption that the underlying variable is normally distributed. Application of technique to selected precipitation and river gaging stations is presented. Analytical expressions are developed by which the probabilities of sequences of wet and dry years of specified lengths can be calculated when the basic hydrologic time series are either independent or stationary dependent Gaussian processes, and the truncation level specified. Numerical values of these probabilities are obtained by means of digital computer for a first order autoregressive process. A set of tables and a set of graphs are presented in order to make the numerical values useable. The probabilities of runs of dependent variables with a common distribution do not depend on the underlying univariate distribution of the variable for a given specified truncation level. The significance of the investigation is based on the need of accurate stochastic models of hydrologic time series for the generation of samples of annual precipitation and annual river flow, for the planning design and operation of water resource systems. It is also based on the concept that runs, as statistical properties of runs, represent the best basic concept for an objective definition of drought.