A Reduced-Dimensional Model for the Interhemispheric Geostrophic Meridional Overturning Circulation

TL;DR

The paper develops a reduced-dimensional model (RGGOCM) that captures the interhemispheric geostrophic meridional overturning by embedding boundary-layer temperature dynamics and a Southern Ocean–like adiabatic upwelling channel within a two-hemisphere, lat-depth framework. It extends the Callies–Marotzke approach to a double-hemisphere enclosed-basin, then adds a zonally periodic southern channel to represent adiabatic upwelling, yielding three overturning cells (NOC, SOC, AOC) with flows and isopycnal structures consistent with 3D ocean models and established scaling laws. The model reveals how Kelvin-wave–driven equatorial adjustment and boundary-layer mixing set cross-equatorial transport, stratification, and overturning strength, and it provides scalable relations for δ_T, δ_ST, δ_A and Ψ_n, Ψ_s, Ψ_e, Ψ_a as κ_b and τ_max vary. Its simplicity enables long integrations to explore extreme forcing, tipping behavior, and parameterization experiments for eddies and boundary mixing, offering a practical tool for interpreting and diagnosing the GOC under climate change. The framework thus delivers both physical insight and computational efficiency for studying the century- to millennium-scale GOC response and testing parameterizations prior to incorporation into fully three-dimensional GCMs.

Abstract

The Global Overturning Circulation (GOC) is a key component of the climate system, transporting heat, carbon, and salt throughout the global ocean. Previous reduced-dimensional models have sought to represent this three-dimensional circulation but often neglected three key observational features: (1) the meridional overturning circulation is in geostrophic balance below the Ekman layer, (2) diapycnal mixing is strongly enhanced near ocean boundaries, and (3) upwelling is partly driven by adiabatic dynamics in the Southern Ocean. Building on Callies and Marotzke (2012), we develop a reduced model that consistently incorporates all three by simulating temperature in latitude-depth space along the eastern and western boundaries of a semi-enclosed basin connected in the south to a zonally periodic re-entrant channel. The model clarifies how zonal temperature differences in the basin arise and are maintained through adiabatic and diffusive processes, giving rise to the geostrophic GOC. It also provides a transparent framework for understanding how geostrophic currents cross the equator to form the interhemispheric overturning, and how boundary-intensified mixing and Southern Ocean winds regulate polar downwelling rates. The reduced model shows good agreement with both a three-dimensional ocean model and theoretical scaling laws for stratification and overturning strength. Owing to its simplicity, it is well suited for long integrations exploring the GOC response under extreme forcing scenarios and offers a useful framework for testing eddy and mixing parameterizations.

Figures (14)

• Figure 1: Schematic of the model domain. Blue regions correspond to western and eastern boundary layer and have a zonal width of $\Delta \lambda$. The red line represents typical structure of zonal temperature profile, with zonal gradients confined to the western boundary layer. Green line represents zonal velocity, which is constant over the interior and decays to zero within the boundary layer.
• Figure 2: Temperature relaxation profile (equation (\ref{['Ts']})) for $\Delta T=25$°C, $T_{\mathrm{min}}=1$°C, $\delta_T=$ 1800 km and different values of $T_n$ (colors).
• Figure 3: Steady-state solution of the reference case: (a) Overturning streamfunction $\psi_b$ (equation (\ref{['psib']})) in Sv. (b) Eastern and western boundary temperatures, with contours at [0.6, 1, 2, 4, 6, 8, 10, 15, 23] $^\circ$C. (c) Zonal temperature difference in $^\circ$C. In all panels, red shading indicates positive values, and blue shading indicates negative values.
• Figure 4: Steady-state of the reference case performed in the MITgcm: (a) Western boundary meridional velocity, with contour intervals $1.8$ cm s$^{-1}$. (b) Interior zonal velocity, with contour intervals $0.4$ cm s$^{-1}$. (c) Western boundary vertical velocity with contour intervals $6\times 10^{-5}$ cm s$^{-1}$ for negative values and $3\times 10^{-4}$ cm s$^{-1}$ for positive values. (d) Eastern boundary vertical velocity with contour intervals $1\times 10^{-3}$ cm s$^{-1}$ for negative contours and $1\times 10^{-4}$ cm s$^{-1}$ for positive values. In all panels, red shading indicates positive values, and blue shading indicates negative values.
• Figure 5: Steady state of the reference experiment under asymmetric forcing, simulated using MITgcm: (a) overturning streamfunction computed from the zonally integrated meridional transport; (b) interior zonal velocity at 30°E; (c) western-boundary and (d) eastern-boundary vertical velocity, obtained as the longitudinal mean over a 4° band adjacent to each boundary. Contour intervals are identical to those in Figs. \ref{['F:DH_MOC']} and \ref{['F:DH_vel']}