Temporal scaling phenomena in groundwater-floodplain systems using robust detrended fluctuation analysis

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.