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

Abstract

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.

A hydrological model skill score and revised R-squared

“…It is intuitive that the acceptability of model predictability is synonymous with the model's performance or quality. In this line, there is a large number of recent studies which has focused on metrics for assessing model performance and examples of the relevant papers include Bai et al (2021), Clark et al (2021), Stoffel et al (2021), Ye et al (2021), Lamontagne et al (2020), Liu (2020), Barber et al (2019), Jackson et al (2019), Mizukami et al (2019), Rose & McGuire (2019), Towner et al (2019, Pool et al (2018), Lin et al (2017) and Jie et al (2016). Due to efforts in improving how to judge model performance, several 'goodness-of-fit' metrics exist in the literature.…”

Review: Fractal Geometry in Precipitation

“…The box-counting method considers variable fields such as rainfall, which involves multiple scales and dimensions that characterize intense regions [67]. The box-counting method is based on the idea of separating data into boxes and counting the resulting number of boxes [68,69]. When applied for the analysis of time series, the box-counting method aggregates neighboring data points by placing adjacent individuals into boxes.…”