Climate change: Detection and its impact on hydrologic design

Abstract

Controversy regarding origins of the so‐called Hurst phenomenon has continued since the first appearance of Hurst's work. There appear to be at least two general mechanisms which might generate geophysical time series displaying the Hurst phenomenon. The first is nonstationarity of process mean level, perhaps owing to dynamic characteristics of the entire earth geophysical system. The second generating mechanism is a stationary model structure such as the Box‐Jenkins models with parameters such that substantial low‐frequency effects are present. A series of Monte Carlo tests have been performed which show that it will generally be very difficult to distinguish between the two generating mechanisms on the basis of geophysical records of lengths usually available. The Monte Carlo experiments are augmented by analysis of several series of tree ring growth indices ranging in length from 506 to 1164 years. Analysis of these sequences for nonstationarity in mean level showed that the sequences were entirely compatible with stationary Box‐Jenkins models earlier fit to the data by Hipel (1975). However, a similar analysis of the variance of the time series showed that there was evidence of nonstationarity in the variances of the records such that the time series were not compatible with the constant variance assumption of the stationary Box‐Jenkins models. Finally, several reservoir simulations were made by using the sequent peak algorithm for type A (nonstationary mean) and type B (constant mean) models which had been found to be statistically indistinguishable in the Monte Carlo experiments. The results showed that so long as nonstationarity in mean level was modest and demand levels were not too high the models give very similar results; however, at high demand levels or large nonstationarity in process mean, substantial differences in storage requirements may result.