Physics and dynamics of density-compensated temperature and salinity anomalies. Part I: Theory

Subducted temperature anomalies have been invoked as a possible way for midlatitudes to alter the climate variability of equatorial regions through the so-called thermocline bridge, both in the Pacific and Atlantic Oceans. To have a significant impact on the equatorial heat balance, however, temperature anomalies must reach the equatorial regions sufficiently undamped. In the oceans, the amplitude of propagating temperature (and salinity) anomalies can be altered both by diabatic (nonconservative) and adiabatic (conservative) effects. The importance of adiabatic alterations depends on whether the anomalies are controlled by wave dynamics or by passive advection associated with density compensation. Waves being relatively well understood, this paper seeks to understand the amplitude variations of density-compensated temperature and salinity anomalies caused by adiabatic effects, for which no general methodology is available. The main assumption is that these can be computed independent of amplitude variations caused by diabatic effects. Because density compensation requires the equality T'/S' = beta(S)/alpha to hold along mean trajectories, the ratio T'/S' may potentially undergo large amplitude variations if the ratio beta(S)/alpha does, where a and beta(S) are the thermal expansion and haline contraction coefficients, respectively. In the oceans, the ratio beta(S)/alpha may decrease by an order-1 factor between the extratropical and tropical latitudes, but such large variations are in general associated with diapycnal rather than isopycnal motion and hence are likely to be superimposed in practice with diabatically induced variations. To understand the individual variations of T' and S' along the mean streamlines, two distinct theories are constructed that respectively use density/salinity and density/spiciness as prognostic variables. If the coupling between the prognostic variables is neglected, as is usually done, both theories predict at leading order that temperature (salinity) anomalies should be systematically and significantly attenuated (conserved or amplified), on average, when propagating from extratropical to tropical latitudes. Along particular trajectories following isopycnals, however, both attenuation and amplification appear to be locally possible. Assuming that the density/spiciness formulation is the most accurate, which is supported by a theoretical assessment of higher-order effects, the present results provide an amplification mechanism for subducted salinity anomalies propagating equatorward, by which the latter could potentially affect decadal equatorial climate variability through their slow modulation of the equatorial mixed layer, perhaps more easily than their attenuated temperature counterparts. This could be by affecting, for instance, barrier layers by which salinity is known to strongly affect local heat fluxes and heat content.