Reconciling the Stommel Box Model with the Stommel–Arons Model: A Possible Role for Southern Hemisphere Wind Forcing?

Abstract In the Stommel box model, the strength of the overturning circulation is parameterized in terms of the density (and hence the pressure) difference between the two boxes. Straub has pointed out that this parameterization is not consistent with the Stommel–Arons model for the abyssal circulation. In particular, the zonally averaged density field implied by the Stommel–Arons model is unrelated to the strength or the direction of the meridional overturning circulation. Here, the inconsistency is examined using the abyssal circulation model of Kawase and a variant to include the effect of Southern Hemisphere wind forcing. The important parameter is R, the ratio of two timescales: the timescale for a perturbation to the density field to propagate, by either wave or advective processes, from a high-latitude source to the equator and the timescale for the dissipation of a perturbation to the density field by diapycnal mixing. If the model is forced only by a deep water source in the northern basin, it is found that the model behaves like the Stommel–Arons model when R ≪ 1 (the “weak” damping regime) and like the Stommel box model when R ≫ 1 (the “strong” damping regine). Estimates of R suggest that coarse-resolution models generally reside in or near the Stommel box model regime (R ≫ 1), which is probably why these models generally support the Stommel box model hypothesis and corroborate the momentum-based closure used in zonally averaged models. On the other hand, it is not clear that the real world is also in the strong damping regime. Indeed, it is easy to obtain estimates for R, using realistic parameter values, that sit in the weak damping regime. It is shown that, even in the weak damping regime (R ≪ 1), adding forcing by the Southern Hemisphere circumpolar westerlies generally moves the model into the Stommel box model regime. It therefore is concluded that, at least in the context of the Kawase model, the inconsistency noted by Straub can be removed by including the effect of Southern Hemisphere wind forcing and that the Stommel box model approach probably has wider applicability than is suggested by estimates of R alone.

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