Abstract
We reconsider the problem of the stability of the thermohaline circulation as described by a two-dimensional Boussinesq model with mixed boundary conditions. We determine how the stability properties of the system depend on the intensity of the hydrological cycle. We define a two-dimensional parameters’ space descriptive of the hydrology of the system and determine, by considering suitable quasi-static perturbations, a bounded region where multiple equilibria of the system are realized. We then focus on how the response of the system to finite-amplitude changes in the surface freshwater forcings depends on their rate of increase. We show that it is possible to define a robust separation between slow and fast regimes of forcing. Such separation between slow and fast regimes is obtained by singling out an estimate of the critical rate of increase for the anomalous forcing. The critical rate of increase is of the same order of magnitude of the ratio between the typical intensity of the hydrological cycle and the advective time scale of the system. Basically, if the change of the forcing is faster than the estimated critical rate, the system responds similarly to the case of instantaneous changes of the same amplitude. Specularly, if the change of the forcing is slower than the critical rate, the behavior of the system resembles the response to quasi-static changes of the same amplitude. Furthermore, since the advective time scale is proportional to the square root of the vertical diffusivity, our analysis supports the conjecture that the efficiency of the vertical mixing might also be one of the key factors determining the response of the THC system to transient changes in the surface forcings. These results should be taken into account when engineering global warming scenario and paleoclimatic experiments with GCMs.
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Acknowledgements
We wish to thank Fabio Dalan, Antonello Provenzale, Antonio Speranza, Peter H. Stone, and Ronald J. Stouffer for useful discussions. We also acknowledge the suggestions of two anonymous reviewers.
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Appendix
Appendix
1.1 Relevance of the vertical diffusivity ψψψ
The vertical diffusivity KV, or, equivalently, the diapycnal diffusivity Kd, is the critical parameter controlling the maximum THC strength Ψmax in ocean models (Bryan 1987; Wright and Stocker 1992). On the other hand, an estimate of its value in the real ocean is a subject of current research (Gregg et al. 2003). Scaling theories proposing a balance between vertical diffusion and advection processes suggest, in the case of three-dimensional hemispheric model of the Atlantic ocean, a power law dependence \(\Psi _{{\max }} \sim K^{{2/3}}_{v}\) (Zhang et al. 1999; Dalan et al. 2004). In the case of two-dimensional models, the expected dependence is \(\Psi _{{\max }} \sim K^{{1/2}}_{v}\) (Knutti et al. 2000). This relation is verified in our model in the range 0.6 cm2 s−1 < KV < 4.0 cm2 s−1 (Fig. 9). In this study, the value of KV has been selected so that the corresponding northern sinking equilibrium state characterized by an hydrological cycle determined by ΦN=ΦS=Φav has an overturning circulation ~37 Sv (KV=1.0 cm2 s−1). With this choice of K V we can define an advective time scale τ for the system as τ=V/Ψmax~350 year. Similarly, if we change K V over the range shown in Fig. 8, the advective time scale would range over the interval 150 year<τ<400 year. Notice that by choosing a value for K V , we also define a diffusive time scale τd=D2/K V ~8,000 year, which is very long compared to the advective time scale. Given the parameters chosen for our simulations, our model integrations estimate Φinf~0.04 Sv and Φsup~0.73 Sv, so that Φav~0.39 Sv.
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Lucarini, V., Calmanti, S. & Artale, V. Destabilization of the thermohaline circulation by transient changes in the hydrological cycle. Clim Dyn 24, 253–262 (2005). https://doi.org/10.1007/s00382-004-0484-z
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DOI: https://doi.org/10.1007/s00382-004-0484-z