A systematic approach to determine thresholds of the ocean's thermohaline circulation

Abstract

A systematic approach is proposed to determine thresholds in freshwater flux perturbations related to abrupt changes in the ocean's thermohaline circulation. The typical problem considered is the response of a thermohaline driven flow to a localized change, of specified strength and duration, in the surface freshwater flux. The initial transient response due to the freshwater anomaly is considered as a finite amplitude perturbation. An estimate of this response can be obtained by using ideas from dynamical systems theory. Central quantity to determine whether such a perturbation leads to instability (i.e. a ‘collapsed’ state) is the sign of the tendency of a specific energy functional. The approach is first illustrated with a simple box model and then shown to give good results in a global ocean general circulation model.

Predicting Climate Tipping as a Noisy Bifurcation: A Review

“…This may become particularly useful for extensive scenario studies in geo-engineering. For example, Dijkstra et al [2004] demonstrated how bifurcation diagrams can help to determine which perturbations enable thresholdcrossing in the bistable THC system, and Biggs et al [2009] studied how quickly perturbations have to be reversed to avoid jumping to coexisting attractors in a fisheries model. Furthermore, subtle microscopic nonlinearities, currently beyond the reach of climate models, may have a strong influence on the large spatial scale.…”

“…Applying a perturbation then corresponds to a temporary alteration of this potential energy landscape. Dijkstra et al [2004] observed that this [Rahmstorf, 2000]. The subcritical pitchfork bifurcation will be observed in very simple models, but will be replaced by a fold in more elaborate ones: see, for example, Fig.…”

Bounds on double-diffusive convection

“…The growth can be attributed to the presence of non-orthogonal linear modes, even when each of these modes decays exponentially (Baggett, Driscoll & Trefethen 1993;Waleffe 1995). In the thermohaline context, transient amplification has been invoked in studies of ocean circulation (Tziperman & Ioannou 2002;Dijkstra, Te Raa & Weijer 2004), and with regard to possible transitions in the paleoclimate (Bryan 1986;Stocker 1999). As far as energy stability is concerned, a sub-optimal choice of the energy norm may lead to transient growth even in situations for which there is no finite-amplitude instability.…”

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

“…One of these modes, with interdecadal period, has lead to an explanation of the physical mechanism of the Atlantic Multidecadal Oscillation [9]. Finally, implicit (Crank-Nicholson) time-stepping was used to determine thresholds for collapse of the thermohaline circulation in a fully-implicit global ocean model [8]. The implicit ocean models are, however, still far from state-of-the-art ocean models.…”