Fractal domain refinement of models simulating hydrological time series

ABSTRACT

Fractal analysis of a time series provides information on how the series varies across all (possible) temporal scales with respect to a given statistical measure. Dynamic hydrological models are typically optimized/calibrated using performance criteria defined in the time domain; however, the performance of models in simulating the fluctuation structure of a time series is seldom investigated. We use a multi-objective pattern search algorithm to calibrate a combined 15-minute resolution recharge–groundwater flow model. The non-dominated simulations of the model are then analysed in the fractal domain using robust detrended fluctuation analysis. The results show that some non-dominated simulations can be eliminated based on poor performance in the fractal domain, hence ensuring that the fluctuation structure of the optimized simulations is captured; this was named fractal-domain-refinement. Furthermore, some recharge parameters are sensitive to fractal-domain-refinement. This gives insights into which parameters are sensitive to the fractal behaviour of the simulated variable.

KEYWORDS:

• hydrological models
• long-term memory
• fractal domain refinement

Editor A. FioriAssociate Editor G. Chiogna

Editor A. FioriAssociate Editor G. Chiogna

Acknowledgements

JPRS and JPB publish with the permission of the Executive Director of the British Geological Survey (NERC). We extend our gratitude to Ms Katie Muchan from the Centre for Ecology and Hydrology, Wallingford, United Kingdom, for facilitating the use of the meteorological data at the Wallingford site, and Mr Ian Longhurst from the British Geological Survey, Wallingford, United Kingdom, for producing the illustration of the conceptual model (Fig. 4). The meteorological data can be requested from UK Centre for Ecology and Hydrology (UKCEH) from the following link: https://www.ceh.ac.uk/our-science/projects/wallingford-met-site; and the river stage and groundwater level data, which are managed by the British Geological Survey (BGS), can be downloaded from 10.5285/637eeed6-7175-4346-9321-0c14332456c6 (Sorensen, 2022).

Disclosure statement

No potential conflict of interest was reported by the authors.