Collaborative Research: Fast Spin Up of Ocean General Circulation Models Using Newton-Krylov Methods

DESCRIPTION: Numerical models of the climate system play an important role in efforts to understand past climate variability and predict future climate changes. In many studies, climate models are driven by forcing fields that are either time-independent or that vary periodically (seasonally) and it is often highly desirable to obtain equilibrium solutions of the model. Existing methods, based on the simple expedient of integrating the model until the transients have died out, are too expensive to use routinely because the deep ocean takes several thousand years to equilibrate. The principal objective of this project is to develop a practical and efficient method for computing equilibrium solutions of periodically forced ocean general circulation models (OGCMs). The general approach will be to formulate the problem as a large system of nonlinear algebraic equations to be solved with a class of methods known as matrix-free Newton-Krylov, a combination of Newton-type methods for superlinearly convergent solution of nonlinear equations, and Krylov subspace methods for solving the Newton correction equations. To render this approach practical for global models with order (107) degrees of freedom, novel matrix free preconditioning strategies will be developed. The "matrix-free" nature of the proposed approach makes it extremely flexible, allowing its use with any ocean or climate model. The method can be applied to models forced at any period, including those driven by time-independent forcing, although the main focus here is the seasonal cycle. Preliminary results suggest that this scheme can accelerate the spin up of seasonally forced OGCMs by over two orders of magnitude over current practice. The convergence properties of this technique will be analyzed, and its efficiency assessed against traditional "acceleration" methods. While the primary target is ocean climate models with a nominal resolution of one , the method will also be applied to the next generation of higher resolution models, including eddy permitting ones. The technique will be applied to obtain equilibrium solutions for various forcing estimates for both present day climate from ocean reanalysis products, and that of the Last Glacial Maximum.

OUTCOMES: The algorithm for fast spin up of ocean models has been developed and implemented. A more generic algorithm for computing steady state solutions of non-linear systems has been developed called the Newton-Krylov-Broyden. Two journal articles.