Hurst-Kolmogorov Dynamics and Uncertainty

The nonstatic, ever changing hydroclimatic processes are often described as nonstationary. However, revisiting the notions of stationarity and nonstationarity, defined within stochastics, suggests that claims of nonstationarity cannot stand unless the evolution in time of the statistical characteristics of the process is known in deterministic terms, particularly for the future. In reality, long-term deterministic predictions are difficult or impossible. Thus, change is not synonymous with nonstationarity, and even prominent change at a multitude of time scales, small and large, can be described satisfactorily by a stochastic approach admitting stationarity. This "novel" description does not depart from the 60- to 70-year-old pioneering works of Hurst on natural processes and of Kolmogorov on turbulence. Contrasting stationary with nonstationary has important implications in engineering and management. The stationary description with Hurst-Kolmogorov stochastic dynamics demonstrates that nonstationary and classical stationary descriptions underestimate the uncertainty. This is illustrated using examples of hydrometeorological time series, which show the consistency of the Hurst-Kolmogorov approach with reality. One example demonstrates the implementation of this framework in the planning and management of the water supply system of Athens, Greece, also in comparison with alternative nonstationary approaches, including a trend-based and a climate-model-based approach.