Abstract
An index method of evaluating non-stationary behaviour is proposed. ARMA models are initially fitted to annual hydrologic time series. Evolutionary spectra are estimated from overlapping sub-samples formed from a sequence of observations. Chi-squared variables are obtained over a high-frequency band of the spectrum and standardized by means of the theoretical median value of chi-squared to form a K index. Empirical distributions of K are calculated from stationary series simulated using the same model structures and sequence lengths as in the historical sets. The time series of K formed from overlapping sections, in relation to its median value and extreme percentiles provides a measure of non-stationarity. Eleven annual flow, precipitation and a tree ring series from northern Utah, U.S.A., and the Nile flows at Aswan dam, Egypt, are investigated. The proposed method should help in estimating the time horizons over which stationarity is a reasonable assumption and the resilience which needs to be provided in planning future schemes.
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