Time Step Sensitivity and Accelerated Spinup of an Ocean GCM with a Complex Mixing Scheme

Abstract

The distorted physics (DP) technique of Bryan and Lewis is applied to an ocean GCM to allow longer time steps to be taken. The model includes a hybrid vertical mixing scheme for tracers, consisting of a Kraus?Turner mixed layer model and a Richardson number?dependent diffusion term. The model also includes rotation of the diffusive tracer fluxes along the isopycnal surfaces, according to the scheme of Redi. The focus of this paper is on the interaction of DP with this mixing scheme, rather than on the physical performance of the scheme itself. With standard parameter settings as used in a recent climate change study, the equilibrium solutions produced in a long integration using DP and a time step of 1 day are not robust and drift on switching back to the standard time step of 1 h (without DP). Three regions are affected: the Antarctic Circumpolar Current, the Greenland?Iceland?Norwegian (GIN) Sea, and the base of the tropical mixed layer. The drifts are found to be due both to the DP technique itself and to the time step sensitivities in the model that are independent of DP. Modifications to the isopycnal diffusion scheme are presented, which eliminate the drifts in the Antarctic Circumpolar Current and GIN Sea. However, the drift at the base of the tropical mixed layer is found to be due to an interaction between the mixed layer model, the Richardson number?dependent diffusion, and the implicit time stepping used for the diffusion equation. This is demonstrated in an idealized one-dimensional model. In the current coarse-resolution GCM configuration, the Richardson number dependence has little effect on the model's equilibrium solution (in the small time step limit), so the time step dependence can be reduced by removing the Richardson number scheme. However, in models with finer (horizontal) resolution, such as those currently used for studies of tropical variability and the next generation of global climate models, this is unlikely to be acceptable. Integrated diffusion-only mixing schemes may be the most practical long-term solution. Meanwhile, care is needed when using hybrid mixing schemes as in the current study to ensure that time truncation errors are at an acceptable level.