Hydrological statistics for engineering design in a varying climate

The intensive research of recent years has shown that climate has always, throughout the Earth's history, changed irregularly on all time scales. However, hydrological statistics, the branch of hydrology that deals with uncertainty and risk and is a primary tool for hydrologic design, in its current state is not consistent with the varying character of climate. More specifically, hydrological statistics is based on classical statistics and on the implicit assumption of a stable climate. Climatic variation, anthropogenic or natural, increases the variability and uncertainty of hydrological processes. A better alternative to base hydrological statistical estimation and hypothesis testing is offered by the study of the Hurst phenomenon, which has been detected in many long hydroclimatic time series and is stochastically equivalent to a multiple time scale climatic fluctuation following a simple scaling law over time scale. Under the hypothesis of this simple scaling behaviour, typical statistics used in hydrology such as sample means, variances, autocorrelations and Hurst coefficients, and the variability thereof, are found theoretically to differ, in some cases dramatically, from the classical ones. The more consistent, based on the simple scaling hypothesis, representation of typical statistical tasks such as estimation, prediction and hypothesis testing is demonstrated by means of case studies.