A fully-implicit model of the global ocean circulation

Abstract

With the recent developments in the solution methods for large-dimensional nonlinear algebraic systems, fullyimplicit ocean circulation models are now becoming feasible. In this paper, the formulation of such a three-dimensional global ocean model is presented. With this implicit model, the sensitivity of steady states to parameters can be investigated efficiently using continuation methods. In addition, the implicit formulation allows for much larger time steps than can be used with explicit models. To demonstrate current capabilities of the implicit global ocean model, we use a relatively low-resolution (4°horizontally and 12 levels vertically) version. For this configuration, we present: (i) an explicit calculation of the bifurcation diagram associated with hysteresis behavior of the ocean circulation and (ii) the scaling behavior of the Atlantic meridional overturning versus the magnitude of the vertical mixing coefficient of heat and salt.

Sensitivity of the Atlantic meridional overturning circulation to South Atlantic freshwater anomalies

“…The ThermoHaline Circulation Model (THCM, [19]) is a fully-implicit ocean-only model that is designed to perform numerical bifurcation analysis of the large-scale circulation.…”

“…In THCM, heat fluxes are determined by a simple two-dimensional energy balance model that is coupled to the upper ocean layer [19]. Sea-ice is not included in the model.…”

The performance of implicit ocean models on B- and C-grids

“…For example, the representation of mixing processes of heat, salt and momentum is still limited to Laplacian formulations with constant (eddy) mixing coefficients. As shown in Weijer et al [23], the magnitude of the coefficient of horizontal mixing of momentum, A H , was quite restricted. Whereas in explicit low-resolution ocean general circulation models, A H = 2.5 · 10 5 m 2 s À1 is used as a standard value on a 4°· 4°horizontal resolution, strong wiggles are found in the fully-implicit model in Weijer et al [23] for these values.…”

“…The application of continuation methods using fully-implicit ocean models [23] have helped clarify the role of multiple equilibria in rapid changes in the global ocean circulation induced by freshwater anomalies [6]. In addition, a start of a classification of oscillatory instabilities of basin wide and global ocean flows has been made [18].…”

“…Motivated by the problem of determining the sensitivity and stability of equilibrium flows, fully-implicit ocean models have been developed over the last decade [7,23]. One of the direct advantages of these methods is that relatively large time steps can be taken, since the time step is determined by accuracy instead of by numerical stability constraints.…”