So far we have examined the stability of the global climate system, which includes the ice sheets and carbon cycle. We now focus on the ocean-atmosphere system and anything external to this component of the climate system will be considered as a boundary condition or a forcing.
The time-scale of ocean advective processes is of the order of a few thousand years. This provides a rough upper limit to the period of quasi-periodic oscillations that the ocean-atmosphere system may exhibit in the absence of external forcing. Most known oscillatory modes resulting from the coupling between ocean and atmosphere dynamics have periods ranging from a few weeks (e.g. the Maiden Julian oscillation) to a few years (e.g. ENSO). The nonlinear nature of the ocean-atmosphere system and its number of degrees of freedom can bring about aperiodic changes in regime manifested by abrupt transitions.
These elementary considerations demonstrate that the ocean-atmosphere system may exhibit a vast range of nontrivial variations without even the presence of external forcing. An external forcing, however, may modulate the amplitude of the frequency of the quasi-periodic oscillations, influence the statistical distribution of the time spent in different regimes (e.g. positive versus negative North Atlantic
Oscillation index), and increase or decrease the transition probability between the different regimes. For example, at least two ocean-atmosphere models show a reduction in the amplitude of eastern tropical Pacific temperature inter-annual variability when mid-Holocene insolation is prescribed (Otto-Bliesner 1999; Liu et al. 2000). Clement et al. (2000) show that reduced El Niño during the mid-Holocene is consistent with our understanding of the Bjerknes feedback and this also appears to be in agreement with the interpretation of an alluvial record in Ecuador (Rodbell et al. 1999). By contrast, analysis of the influence of orbital forcing on the North Atlantic Oscillation is, so far, inconclusive (Gladstone et al. 2005).
Accurate modeling of sub-decadal modes of variability requires relatively highresolution models run over several thousands of years, which is unachievable with current technology. There is therefore a need to separate the modeling of the longer and shorter modes of variability despite the possible interactions linking them. The shortest modes may be parameterized by means of diagnostic equations or stochastic noise in lower-resolution climate models.
Concentrating on long-period modes, two nonlinear terms in the constitutive equations of ocean motion may cause instability or sustained oscillations. These are advection and convection.
Advection designates the transport of heat and salt by the main ocean currents. Given that ocean currents are determined by the distribution of density, it is conceivable that advective processes cause oscillations or instabilities. An important contribution to this theory is Stommel's (1961) "box-model" of the thermohaline circulation made up of four differential equations. This model presents an instability featuring a sharp decrease in advective transport, balanced by an increase in diffusive transport. This transition is more commonly known as the shut-down of the thermohaline circulation. We know that such a shut-down is very unlikely to have occurred during the Holocene.
A refined version of Stommel's model incorporating realistic propagation times suggests that advective processes may also cause sustained oscillations (Welander 1986), which are absent in Stommel's original model. This proposition was further investigated by analyzing the eigenvectors of a three-dimensional ocean model (Weijer and Dijkstra 2003). Three modes of free-damped oscillations were identified that are associated with the propagation of temperature and salinity anomalies through the conveyor belt and their periods range between two and four millennia.
Weijer and Dijkstra suggested that advective oscillations may explain the mil-lenia cycle observed in the North Atlantic record of lithic fraction (Bond et al. 1997). Advective oscillations do tend to occur in EMICs (which account for the interactions with the atmosphere and sea-ice), but only for certain parameter ranges. A well-documented example is the 200-year oscillation featured by the ECBILT atmosphere model coupled to a low-resolution three-dimensional ocean with a flat bottom (Weber et al. 2004). The 200-year oscillation mode may be efficiently excited and phase-locked by solar forcing, giving rise to a resonant response of the ocean-atmosphere system at the corresponding frequency. The response is manifested by variations in the North Atlantic meridional overturning cell as well as in temperature in the North Atlantic region.
Convection is the vigorous vertical mixing of water that occurs when denser water lies on lighter water. Its role is to restore gravitational stability. It is a self-maintained process: convection acts as a heat pump and prevents formation of sea-ice. The resulting heat exchange between the ocean surface and the atmosphere contributes to the increase in density of the surface water, and this promotes further convection. Deep ocean convection occurs today in the Norwegian Sea, the Labrador Sea, and in the Ross and the Weddell Seas. There is geochemical evidence that convection did not take place in the Labrador Sea before 6000 years ago (Solignac et al. 2004).
What may be the effect of deep-ocean convection on climate variability? A conceptual model with two degrees of freedom (Welander 1982) shows that con-vective instability may induce spontaneous and repeated shut-off and restarts of convection, termed flip-flops. Convective feedback may therefore constitute a plausible explanation for abrupt cooling and warming observed in the Norwegian Sea during the Holocene (Andersen et al. 2004).
This hypothesis seems verified in the view of a few long experiments with low-resolution ocean-atmosphere models. A long steady-state experiment with the climate model of the Geophysical Fluid Dynamics Laboratory (GFDL; ocean resolution of about 400 km) exhibits a spontaneous abrupt cooling in the Denmark Strait after about 2000 years of integration. The anomaly, which has no apparent cause, persists for around 30 years (Hall and Stouffer 2001). Similar events were then observed with other models, in particular the ECBILT-CLIO model (ocean resolution of about 300 km but the atmosphere is coarser; Goosse et al. 2002). A way to describe these events is to say that climate is trapped for some time in an infrequently visited region of the climatic attractor. Let us call it the "cold state". The trapping process is, in ECBILT-CLIO, the persistence of a cyclonic pressure anomaly around Scandinavia causing southward advection of sea-ice in response to the convection shut-down. This is a trap because the southward advection maintains the convection shut-down and the cyclonic anomaly.
The probability of visiting the cold state may be increased in the presence of external forcing, such as a decrease in solar irradiance (enhances sea-ice formation), a volcanic eruption (Goosse and Renssen 2004), or a freshwater discharge (Renssen et al. 2002). This probability also increases during the Holocene because of the gradual cooling of the Norwegian Sea induced by orbital forcing (Figure 4.6).
It is important to realize that the time spent by climate in the "cold state" is stochastic. In other words, the system's response may be analyzed statistically but may not be predicted precisely. If this is correct, the cold events found in diatom-based temperature reconstructions in the sub-Polar Atlantic (Rekjanes Ridge, Andersen et al. 2004) cannot be ascribed to a precise forcing event, but they are expected to occur more frequently at the end of the Holocene, after a volcanic eruption or during periods of reduced solar irradiance.
Convective instability is also a potential player in the outstanding negative temperature recorded in Greenland, North Atlantic, and Europe around 8200 years
Sea-surface temperature (°C)
Figure 4.6 Sea-surface temperature and surface water density predicted by the atmosphere-ocean-vegetation climate model of intermediate complexity ECBILT-CLIO-VECODE. Only the orbital forcing is taken into account. Other boundary conditions (including ice sheets and land-sea mask) are as today. The model features a cooling in these two regions but convective regimes exhibit contrasting trends. Convection shut-downs occur increasingly frequently in the Norwegian Sea with, in
Sea-surface temperature (°C)
Surface density (kg m-3 - 1000)
particular, two sharp cold events around 2400 years BP and 1800 years BP. These events are triggered by stochastic sea-ice advances maintained by cyclonic anomalies in the atmospheric circulation caused by the cooling itself. By contrast, convection is very stable in the Labrador Sea. Surface density increases during the Holocene in response to enhanced heat exchanges between the surface and increasingly cold winds blowing from Canada. (Data are from Renssen etal. 2005.)
ago (von Grafenstein et al. 1998). It is intriguing that the cooling persisted more than a century (Thomas et al. 2007) but its hypothetical cause, an outburst of a proglacial lake complex shortly termed Lake Agassiz, occurred in a few years at most (Teller et al. 2002). In fact, such "cold-state trapping" explains that a given amount of freshwater discharged in the Labrador Sea generally induces a more persistent cooling (up to 500 years) in ECBILT-CLIO when it is released in 10 years (this triggers convective instability) than in 50 years (Renssen et al. 2002).
Experiments with the CLIMBER-2 EMIC (Bauer et al. 2004) also show that a freshwater pulse of a size compatible with geologic evidence may lead the ocean circulation to a "cold state", with convection persisting south of 60°N only. As in Renssen et al. (2002), the cold state is metastable, which means that it is resilient to small perturbations but unstable to larger ones. As a consequence, the ocean may remain in this cold state for one or two centuries depending on the natural atmospheric variability. Note that this variability is parameterized under the form of white noise in CLIMBER-2.3 because it is not resolved explicitly .
LeGrande et al. (2006) provides a further argument to the Lake Agassiz hypothesis. "Model E" of the Goddard Institute for Space Studies (GISS) explicitly simulates a range of variables (dust, calcite, ocean and atmospheric water oxygen isotopic ratio, 10Be ratios, methane emissions) and experiments that simulate the outburst are in broad agreement with the relevant climate records.
At last, a cautionary tale. So far, spontaneous transitions and persistent cooling due to the convective feedback were simulated in models that do not resolve the details of the convective process. A model resolving spatial scales of a few tens of kilometers would be more suitable to study the properties of convective instability in the presence of long-term atmospheric variability, but this presently would be very technologically demanding.
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