Hydrological model performance and parameter estimation in the wavelet-domain

This paper proposes a method for rainfall-runoff model calibration and performance analysis in the wavelet-domain by fitting the estimated wavelet-power spectrum (a representation of the time-varying frequency content of a time series) of a simulated discharge series to the one of the corresponding observed time series. As discussed in this paper, calibrating hydrological models so as to reproduce the time-varying frequency content of the observed signal can lead to different results than parameter estimation in the time-domain. Therefore, wavelet-domain parameter estimation has the potential to give new insights into model performance and to reveal model structural deficiencies. We apply the proposed method to synthetic case studies and a real-world discharge modeling case study and discuss how model diagnosis can benefit from an analysis in the wavelet-domain. The results show that for the real-world case study of precipitation - runoff modeling for a high alpine catchment, the calibrated discharge simulation captures the dynamics of the observed time series better than the results obtained through calibration in the time-domain. In addition, the wavelet-domain performance assessment of this case study highlights the frequencies that are not well reproduced by the model, which gives specific indications about how to improve the model structure.