Calibration of Concentration Parameters Based on Frequency Decomposition of Fourier Series

Abstract

The unstable and unreasonable parameter identification results are achieved because of the nonlinear effect (e.g., the cross-autocorrelation parameters). The XAJ (Xin’anjiang) model shows a certain correlation among confluence parameters, which primarily causes calibration results to be instable and unreasonable. To address the mentioned problem, the correlation between parameters should be overcome, and more estimation information should be presented. Accordingly, a novel objective function based on the Fourier expansion (FOF) was introduced to calibrate confluence parameters in the XAJ model. The flow processes were separately expanded with the Fourier series, and the independent and frequency-dependent objective functions were yielded with different frequency structures of the surface flow, interflow, and groundwater. To prove that the method is feasible, theoretic derivation and application analysis in a case of the Changzao basin were conducted. As revealed from the results, the method is capable of effectively increasing the information in parameter calibration and fully exploiting the physical mechanism of confluence parameters to calibrate the decomposition dimensionality reduction of confluence parameters.