The global thermohaline circulation in box and spectral low-order models. Part 1: single basin models

Abstract

Much of the knowledge about ocean circulation stems from rather simple analytical models. The behavior of the meridional overturning and, more specifically, the thermohaline-induced part of the global ocean circulation, under changing surface conditions, is often judged by the bifurcation structure of box models with very low (low-order) resolution. The present study proposes a new low-order model of the thermohaline-driven circulation, which is constructed by severe truncation of a spectral decomposition of the two-dimensional equations of motion (vorticity and heat/salt balances). The physical ingredients of the new model are superior to box models because it has a continuous lateral and vertical representation of the fields and finite diffusion coefficients for heat and salt. The building of the spectral model involves much mathematical labor because the structure functions must be constructed in accordance with the boundary conditions for conservation of momentum, mass, heat, and salt. Furthermore, a number of complicated coupling coefficients must be evaluated. Like the box models, the spectral model is a dynamical system with mathematical complexity, but in most of the versions that we analyze, it still can be handled by standard analytical procedures. These versions are the spectral counterparts of the classical box models of Stommel, Rooth, and Welander, adjusted to the Atlantic overturning. A detailed comparison of the model types reveals a similar bifurcation pattern of box and spectral low-order configurations under symmetric and asymmetric forcing conditions and slight perturbations thereof (we use mixed boundary conditions for heat and salt and the surface freshwater flux as a continuation parameter). Comparison of the spectral low-order models with models towards a higher resolved range, namely, the two-dimensional overturning models for the meridional plane, reveals a close resemblance as well. A major difference of box and spectral models is the appearance of parameter windows in the latter, where only unstable steady states exist. The spectral models then show limit cycles, as well as chaotic trajectories with time scales of thousands of years.