Qualitative Behavior and Nonoscillation of Stommel's Thermohaline Box Model

Ruddick, Barry; Zhang, Lingqi

doi:10.1175/1520-0442(1996)009<2768:qbanos>2.0.co;2

“…However, in the absence of horizontal mixing, any stable positive equilibrium is a spiral point, indicating that internal oscillations are possible. Such oscillations do not exist in Stommel's model (Cessi, 1994; Ruddick and Zhang, 1996), due in part to its symmetry, which prohibits a phase lag in the response. By introducing a vertical dimension, this symmetry is removed here; further consequences of this are explored in .…”

Section: Equilibrium Solutionmentioning

confidence: 99%

Can limited ocean mixing buffer rapid climate change?

Oliver

¹

,

Watson

²

,

Stevens

³

2005

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A B S T R A C T It has been argued that diapycnal mixing has a strongly stabilizing role in the global thermohaline circulation (THC). Negative feedback between THC transport and low-latitude buoyancy distribution is present in theory based on thermocline scaling, but is absent from Stommel's classical model. Here, it is demonstrated that these two models can be viewed as opposite limits of a single theory. Stommel's model represents unlimited diapycnal mixing, whereas the thermocline scaling represents weak mixing. The latter limit is more applicable to the modern ocean, and previous studies suggest that it is associated with a more stable THC. A new box model, which can operate near either limit, is developed to enable explicit analysis of the transient behaviour. The model is perturbed from equilibrium with an increase in surface freshwater forcing, and initially behaves as if the only feedbacks are those present in Stommel's model. The response is buffered by any upper ocean horizontal mixing, then by propagation of salinity anomalies, each of which are stabilizing mechanisms. However, negative feedback associated with limited diapycnal mixing only prevents thermohaline catastrophe in a modest parameter domain. This is because the time-scale associated with vertical advective-diffusive balance is much longer than the time required for the THC to change mode. The model is then tuned to allow equilibrium THC transport to be independent of the rate of mixing. The equilibrium surface salinity difference controls the classical THC-transport/salinity positive feedback, whereas the equilibrium interior density difference controls the mean-flow negative feedback. When mixing is strong, unrealistic vertical homogenization occurs, causing a convergence in surface and interior meridional gradients. This reduces positive feedback, and increases stability, in the tuned model. Therefore, Stommel's model appears to overestimate, rather than underestimate, THC stability to high-frequency changes in forcing.

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“…The dynamical properties of the ocean model by itself is similar to those of Stommel's box model in that it exhibits stable haline equilibrium modes and a spirally stable thermal mode. Ruddick and Zhang [] prove that Stommel‐like models cannot exhibit oscillations under steady forcing.…”

Section: Model Dynamicsmentioning

confidence: 99%

Millennial‐scale oscillations between sea ice and convective deep water formation

Saha

¹

2015

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During the last ice age there were several quasiperiodic abrupt warming events. The climatic effects of the so-called Dansgaard-Oeschger (D-O) events were felt globally, although the North Atlantic experienced the largest and most abrupt temperature anomalies. Similar but weaker oscillations also took place during the interglacial period. This paper proposes an auto-oscillatory mechanism between sea ice and convective deep water formation in the North Atlantic as the source of the persistent cycles. A simple dynamical model is constructed by coupling and slightly modifying two existing models of ocean circulation and sea ice. The model exhibits mixed mode oscillations, consisting of decadal-scale small-amplitude oscillations and a large-amplitude relaxation fluctuation. The decadal oscillations occur due to the insulating effect of sea ice and leads to periodic ventilation of heat from the polar ocean. Gradually, an instability builds up in the polar column and results in an abrupt initiation of convection and polar warming. The unstable convective state relaxes back to the small-amplitude oscillations from where the process repeats in a self-sustained manner. Freshwater pulses mimicking Heinrich events cause the oscillations to be grouped into packets of progressively weaker fluctuations, as observed in proxy records. Modulation of this stable oscillation mechanism by freshwater and insolation variations could account for the distribution and pacing of D-O and Bond events. Physical aspects of the system such as sea ice extent and oceanic advective flow rates could determine the characteristic 1500 year time scale of D-O events. The model results with respect to the structure of the water column in the Nordic seas during stadial and interstadial phases are in agreement with paleoproxy observations.

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“…However, in the absence of horizontal mixing, any stable positive equilibrium is a spiral point, indicating that internal oscillations are possible. Such oscillations do not exist in Stommel's model (Cessi, 1994;Ruddick and Zhang, 1996), due in part to its symmetry, which prohibits a phase lag in the response. By introducing a vertical dimension, this symmetry is removed here; further consequences of this are explored in Section 4.2.…”

Section: Equilibria and Stability Dependent On Surface Buoyancy Forcingmentioning

confidence: 99%

Can limited ocean mixing buffer rapid climate change?

Oliver

¹

,

Watson

²

,

Stevens

³

2005

Tellus A: Dynamic Meteorology and Oceanography

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A B S T R A C T It has been argued that diapycnal mixing has a strongly stabilizing role in the global thermohaline circulation (THC). Negative feedback between THC transport and low-latitude buoyancy distribution is present in theory based on thermocline scaling, but is absent from Stommel's classical model. Here, it is demonstrated that these two models can be viewed as opposite limits of a single theory. Stommel's model represents unlimited diapycnal mixing, whereas the thermocline scaling represents weak mixing. The latter limit is more applicable to the modern ocean, and previous studies suggest that it is associated with a more stable THC. A new box model, which can operate near either limit, is developed to enable explicit analysis of the transient behaviour. The model is perturbed from equilibrium with an increase in surface freshwater forcing, and initially behaves as if the only feedbacks are those present in Stommel's model. The response is buffered by any upper ocean horizontal mixing, then by propagation of salinity anomalies, each of which are stabilizing mechanisms. However, negative feedback associated with limited diapycnal mixing only prevents thermohaline catastrophe in a modest parameter domain. This is because the time-scale associated with vertical advective-diffusive balance is much longer than the time required for the THC to change mode. The model is then tuned to allow equilibrium THC transport to be independent of the rate of mixing. The equilibrium surface salinity difference controls the classical THC-transport/salinity positive feedback, whereas the equilibrium interior density difference controls the mean-flow negative feedback. When mixing is strong, unrealistic vertical homogenization occurs, causing a convergence in surface and interior meridional gradients. This reduces positive feedback, and increases stability, in the tuned model. Therefore, Stommel's model appears to overestimate, rather than underestimate, THC stability to high-frequency changes in forcing.

show abstract

Qualitative Behavior and Nonoscillation of Stommel's Thermohaline Box Model

Cited by 19 publications

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Can limited ocean mixing buffer rapid climate change?

Can limited ocean mixing buffer rapid climate change?

Millennial‐scale oscillations between sea ice and convective deep water formation

Can limited ocean mixing buffer rapid climate change?

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