A simple method for reducing seasonal bias and drift in eddy resolving ocean models

An effective and computationally efficient method is described for reducing bias and drift in eddy resolving ocean models. The basic idea is to nudge the model towards gridded climatologies of observed temperature and salinity in prescribed frequency-wavenumber bands; outside of these bands the model’s dynamics are not directly affected by the nudging and the model state can evolve prognostically. Given the restriction of the nudging to certain frequency-wavenumber bands, the method is termed spectral nudging. The frequency-wavenumber bands are chosen to capture the information in the climatology and thus are centered on the climatological frequencies of 0, 1 cycle per year and its harmonics, and also low wavenumbers (consistent with the smooth nature of gridded climatologies). The method is first tested using a linear, barotropic ocean model forced by a time-varying wind stress curl. For this example it is possible to give explicit expressions for the effect of spectral nudging on the model’s response to wind forcing. The method is then applied to an eddy permitting model of the North Atlantic driven by realistic surface fluxes. It is shown that the model maintains a statistical steady state over the several decades of integration with no evidence of bias or drift. Further the seasonal cycle of coastal sea level, and the spatial distribution of sea level variance, are shown to agree well with independent sea level measurements made by tide gauges and altimeters, respectively. The application of spectral nudging to shelf and coupled atmosphere–ocean modelling is discussed.