Climate change, the Hurst phenomenon, and hydrological statistics

The intensive research of recent years on climate change has led to the strong conclusion that climate has always, throughout the Earth's history, changed irregularly on all time scales. Climate changes are closely related to the Hurst phenomenon, which has been detected in many long hydroclimatic time series and is stochastically equivalent to a simple scaling behaviour of climate variability over time scale. The climate variability, anthropogenic or natural, increases the uncertainty of the hydrological processes. It is shown that hydrological statistics, the branch of hydrology that deals with uncertainty, in its current state is not consistent with the varying character of climate. Typical statistics used in hydrology such as means, variances, cross- and auto-correlations and Hurst coefficients, and the variability thereof, are revisited under the hypothesis of a varying climate following a simple scaling law, and new estimators are studied which, in many cases, differ dramatically from the classical ones. The new statistical framework is applied to real-world examples for typical tasks such as estimation and hypothesis testing where, again, the results depart significantly from those of the classical statistics.