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With the help of a physically based recharge-groundwater flow model and robust detrended fluctuation analysis (r-DFAn), the effect of local (catchment-scale) forcing on groundwater levels’ scaling behavior in a riparian aquifer in Wallingford, UK, is investigated. The local forcings investigated in this study include the rainfall’s temporal scaling behavior (which is simulated by changing rainfall’s intermittency parameter in a β-lognormal multiplicative random cascade model), the aquifer’s physical parameters (saturated hydraulic conductivity, specific yield, the empirical coefficients of the water retention curve, and the river stage’s scaling behavior). Groundwater level’s scaling behaviour was found to be most sensitive to rainfall’s fractal behaviour. Additionally, there is preliminary evidence suggesting that changes to the rainfall’s local scaling behaviour (i.e., change to the series’ scaling that induces crossovers) affects the groundwater’s and the recharge’s local scaling behaviour.

Long-term memory has been studied for decades and it has long been acknowledged that hydrological and hydro-meteorological time series exhibit this property. Physically, long-term memory is explained by saying that the stronger the long-term memory the more likely a series will ‘remember’ its previous value, in other words, the longer a time series is likely to persist in the proximity of a certain value. To increase the benefit of the study of long-term memory, we investigate the extent to which this explanation is accurate and descriptive of long-term memory by developing a ‘persistence measure’ that quantifies the intuitive description of long-term memory. The ‘persistence measure’ is compared to the scaling exponent (α) which quantifies long-term memory using detrended fluctuation analysis. A total of 17,359 series, including hydrological and hydro-meteorological series, downloaded from online sources and 130 synthetic series are analyzed. The main outcome is that two regimes are found. The first is for series with α ≲ 1.05 where the persistence measure is not sensitive to the scaling exponent. Hence, changes in α does not lead to an increase in the memory strength (i.e. the persistence measure). The second regime is for series with α ≳ 1.05 where a statistically significant positive correlation was found. Hence, for a certain range of values of α the physical explanation of long-term memory holds. Nevertheless, it is proposed that adding additional factors may create a more robust ‘persistence measure’ that can be easily understood and incorporated in hydrologists’ work.

Fine tuning of metal ion reduction kinetics is crucial to the successful synthesis of designer bimetallic nanomaterials with well-defined morphologies and tailored localization of the constituent e...

In order to determine objectively the fractal behaviour of a time series, and to facilitate potential future attempts to assess model performance by incorporating fractal behaviour, a multi-order robust detrended fluctuation analysis (r-DFAn) procedure is developed herein. The r-DFAn procedure allows for robust and automated quantification of mono-fractal behaviour. The fractal behaviour is quantified with three parts: a global scaling exponent, crossovers, and local scaling exponents. The robustness of the r-DFAn procedure is established by the systematic use of robust regression, piecewise linear regression, Analysis of Covariance (ANCOVA) and Multiple Comparison Procedure to determine statistically significant scaling exponents and optimum crossover locations. The MATLAB code implementing the r-DFAn procedure has also been open sourced to enable reproducible results. r-DFAn will be illustrated on a synthetic signal after which is used to analyse high-resolution hydrologic data; although the r-DFAn procedure is not limited to hydrological or geophysical time series. The hydrological data are 4 year-long datasets (January 2012 to January 2016) of 1-min groundwater level, river stage, groundwater and river temperature, and 15-min precipitation and air temperature, at Wallingford, UK. The datasets are analysed in both time and fractal domains. The study area is a shallow riparian aquifer in hydraulic connection to River Thames, which traverses the site. The unusually high resolution datasets, along with the responsive nature of the aquifer, enable detailed examination of the various data and their interconnections in both time- and fractal-domains.