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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 magni-tude. 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 paleocli-matic reconstructions. We aimed to determine the fractal behaviour and the long-range de-pendence behaviour of the streamflow. Additionally, we assessed the behaviour of the first four marginal moments of each time series to test whether they follow similar behaviours as sug-gested 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 dis-tribution and a generalized Hurst–Kolmogorov (HK) dependence structure. [ABSTRACT FROM AUTHOR]

The geophysical and hydrological processes governing river flow formation exhibit persistence at several timescales, which may manifest itself with the presence of positive seasonal correlation of streamflow at several different time lags. We investigate here how persistence propagates along subsequent seasons and affects low and high flows. We define the high-flow season (HFS) and the low-flow season (LFS) as the 3-month and the 1-month periods which usually exhibit the higher and lower river flows, respectively. A dataset of 224 rivers from six European countries spanning more than 50 years of daily flow data is exploited. We compute the lagged seasonal correlation between selected river flow signatures, in HFS and LFS, and the average river flow in the antecedent months. Signatures are peak and average river flow for HFS and LFS, respectively. We investigate the links between seasonal streamflow correlation and various physiographic catchment characteristics and hydro-climatic properties. We find persistence to be more intense for LFS signatures than HFS. To exploit the seasonal correlation in the frequency estimation of high and low flows, we fit a bi-variate meta-Gaussian probability distribution to the selected flow signatures and average flow in the antecedent months in order to condition the distribution of high and low flows in the HFS and LFS, respectively, upon river flow observations in the previous months. The benefit of the suggested methodology is demonstrated by updating the frequency distribution of high and low flows one season in advance in a real-world case. Our findings suggest that there is a traceable physical basis for river memory which, in turn, can be statistically assimilated into high- and low-flow frequency estimation to reduce uncertainty and improve predictions for technical purposes. [ABSTRACT FROM AUTHOR]

We investigate the recently published CAMELS dataset, which is one of the most comprehensive large-scale datasets in terms of river flow timeseries and attributes of catchments minimally impacted by human activities. We examine the stochastic properties of daily river flow and rainfall series and investigate the links between the two at various lags, through climacogram-based stochastics tools (i.e. the climacogram and cross-climacogram) examining the variance versus spatio-temporal scale. We also explore the impact of various climatic and geophysical catchment attributes such as seasonality and timing of precipitation, aridity, mean catchment slope and soil conductivity, on the identified rainfall-runoff stochastic relationships. [ABSTRACT FROM AUTHOR]