Fractal domain refinement of models simulating hydrological time series

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.