The Spectral Diagram as a new tool for model assessment in the frequency domain: Application to a global ocean general circulation model with tides

Abstract Here we introduce a new tool, the Spectral Diagram (SD), for the comparison of time series in the frequency domain. The SD provides a novel way to display the coherence function, power, amplitude, phase, and skill score of discrete frequencies of two time series. Each SD summarises these quantities in a single plot for multiple targeted frequencies. The versatility of SDs is demonstrated through a series of sea-level comparisons between observations from tide gauges and the model results from a global eddy-permitting ocean general circulation model (MOM5) with explicit tidal forcing. Phase information for the eight principal lunisolar constituents (M2, S2, N2, K2, K1, O1, P1, Q1) is added to the default configuration of MOM5. Inaccurate estimation of phase information is an important source of barotropic errors in ocean modelling, thereby compromising the skill scores in regions where amplitudes are close to the tidal gauge datasets. The greatest contribution of SD analysis is the indication that some diurnal estimates can be improved by adjusting the phase lag in the model as severe underestimation of semidiurnal amplitudes is the main reason for lower skill scores despite higher coherence. Although the SD has been designed for tidal analysis, it is a powerful tool for detecting co-oscillating patterns in multi-scale analyses, and this approach might provide guidance in devising skill scores for inter-comparing model results.