TIME-STEP SENSITIVITY AND ACCELERATED SPINUP OF AN OCEAN GCM WITH A COMPLEX MIXING SCHEME

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 include s a hybrid vertical mixing scheme for tracers, consisting of a Kraus-T urner mixed laver model and a Richardson number-dependent diffusion te rm. The model also includes rotation of the diffusive tracer fluxes al ong the isopycnal surfaces, according to the scheme of Redi. The focus of this paper is on the interaction of DP with this mixing scheme, ra ther than on the physical performance of the scheme itself. With stand ard parameter settings as used in a recent climate change study the eq uilibrium 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 stand ard time step of 1 h (without DP). Three regions are affected: the Ant arctic 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 isopycn al diffusion scheme are presented, which eliminate the drifts in the A ntarctic Circumpolar Current and GIN Sea. However the drift at the bas e of the tropical mixed layer is found to be due to an interaction bet ween 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 ti me step limit), so the time step dependence can be reduced by removing the Richardson number scheme. However, in models with finer (horizont al) resolution, such as those currently used for studies of tropical v ariability and the next generation of global climate models, this is u nlikely to be acceptable. Integrated diffusion-only mixing schemes may be the most practical long-term solution. Meanwhile, care is needed w hen using hybrid mixing schemes as in the current study to ensure that time truncation errors are at an acceptable level.