A new fractal-theory-based criterion for hydrological model calibration

Abstract

Fractality has been found in many areas and has been used to describe the internal features of time series. But is it possible to use fractal theory to improve the performance of hydrological models? This study aims at investigating the potential benefits of applying fractal theory in model calibration. A new criterion named the ratio of fractal dimensions (RD) is defined as the ratio of the fractal dimensions of simulated and observed streamflow series. To combine the advantages of fractal theory with classical criteria based on squared residuals, a multi-objective calibration strategy is designed. The selected classical criterion is the Nash–Sutcliffe efficiency (E). The E–RD strategy is tested in three study cases with different climates and geographies. The results reveal that, in most aspects, introducing RD into model calibration makes the simulation of streamflow components more reasonable. Also, pursuing a better RD during calibration leads to only a small decrease in E. We therefore recommend choosing the parameter set with the best E among the parameter sets with RD values of around 1.