Stochastic Analysis of the Marginal and Dependence Structure of Streamflows: From Fine-Scale Records to Multi-Centennial Paleoclimatic Reconstructions

The identification of the second-order dependence structure of streamflow has been one of the oldest challenges in hydrological sciences, dating back to the pioneering work of H.E Hurst on the Nile River. Since then, several large-scale studies have investigated the temporal structure of streamflow spanning from the hourly to the climatic scale, covering multiple orders of magnitude. In this study, we expanded this range to almost eight orders of magnitude by analysing small-scale streamflow time series (in the order of minutes) from ground stations and large-scale streamflow time series (in the order of hundreds of years) acquired from paleoclimatic reconstructions. We aimed to determine the fractal behaviour and the long-range dependence behaviour of the stream- flow. Additionally, we assessed the behaviour of the first four marginal moments of each time series to test whether they follow similar behaviours as suggested in other studies in the literature. The results provide evidence in identifying a common stochastic structure for the streamflow process, based on the Pareto–Burr–Feller marginal distribution and a generalized Hurst–Kolmogorov (HK) dependence structure.