A new approach to the spin-up problem in ocean-climate models

Abstract

The spin-up timescale in large-scale ocean models, i.e., the time it takes to reach an equilibrium state, is determined by the slow processes in the deep ocean and is usually in the order of a few thousand years. As these equilibrium states are taken as initial states for many calculations, much computer time is spent in the spin-up phase of ocean model computations. In this thesis, we propose a new approach which can lead to a reduction in spin-up time for quite a broad class of existing ocean models. Our approach is based on so-called Jacobian-Free Newton-Krylov (JFNK) methods which combine Newton's method for solving non-linear systems with Krylov subspace methods for solving large systems of linear equations. As there is no need to construct the Jacobian matrices explicitly the method can in principle be applied to existing explicit time-stepping codes. To illustrate the method we first apply it to a 3D planetary geostrophic ocean model with prognostic equations only for temperature and salinity. We compare the new method to the 'ordinary' spin-up run for several model resolutions and find a considerable reduction of spin-up time, on the order of a factor 100. The next step is to apply the JFNK methodology to the Modular Ocean Model Version 4 (MOM4), a state-of-the-art ocean model. We present the implementation of the JFNK method in MOM4 but restrict the preconditioning technique to the case for which temperature and salinity distributions are prescribed, resulting in a prescribed density field. We show that for this case the JFNK method can reduce the spin-up time to a steady equilibrium in MOM4 considerably if an accurate solution is required. A spin-off of the use of the JFNK methodology is the application of bifurcation analysis and we present bifurcation diagrams for the wind-driven ocean circulation. We also used the JFNK method (with prescribed density field) in a paleo configuration for the Oligocene and Miocene epochs. In both epochs continental geometry was completely different from present day geometry and hence the resulting ocean flows were completely different. In particular, during both epochs Panama Strait was not yet closed, providing a direct connection between the Atlantic and Pacific. During the Oligocene the net transport was westward, from the Atlantic into the Pacific, whereas in the Miocene the sign of this transport likely reversed to a net eastward transport. We use the JFNK method to investigate the robustness of this flow reversal by means of a sensitivity analysis with respect to bottom topography, continental geometry and forcing strength and find that the flow reversal is a robust feature in the MOM4 ocean model. As a final step we extend the JFNK methodology the the case of the full MOM4 equations, where temperature and salinity are part of the solution instead of prescribed fields. For an idealized test case we show that a typical speed-up of a factor 10 to 25 with respect to the original MOM4 timestepping model can be achieved.