Stabilization of Climate Regimes by Noise in a Simple Model of the Thermohaline Circulation

Adam Hugh Monahan Institut für Mathematik, Humboldt-Universität zu Berlin, Berlin, Germany

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Abstract

Salinity dynamics in a simple two-box model of the thermohaline circulation (THC) is considered. The model parameterizes fluctuating eddy transport and buoyancy forcing by two independent stochastic processes. The associated stationary probability density function is calculated analytically, and its structure is analyzed in the space of the three parameters of the model. It is found that over a broad range of model parameters in which the stationary density is technically bimodal, the population of one regime is very much larger than that of the other, so the system behaves effectively unimodally. This preferential population of one regime is denoted stabilization. This phenomenon is only relevant if the timescale of THC variability is less than the mean residence times of the destabilized regime, so that the system may be described by its stationary probability density. These average residence times are calculated, and it is found that stabilization occurs over a broad range of parameter values. The stabilization phenomenon has important consequences for the stability of the THC. It is shown that the inclusion of stochastic processes in the model results in random hysteresis responses to steady changes in freshwater forcing, such that the transitions between regimes generally occur some distance away from the bifurcation points at which transitions occur in the deterministic model.

Corresponding author address: Adam Hugh Monahan, School of Earth and Ocean Sciences, University of Victoria, P.O. Box 3055 STN CSC, Victoria, BC V8P 5C2, Canada. Email: monahana@uvic.ca

Abstract

Salinity dynamics in a simple two-box model of the thermohaline circulation (THC) is considered. The model parameterizes fluctuating eddy transport and buoyancy forcing by two independent stochastic processes. The associated stationary probability density function is calculated analytically, and its structure is analyzed in the space of the three parameters of the model. It is found that over a broad range of model parameters in which the stationary density is technically bimodal, the population of one regime is very much larger than that of the other, so the system behaves effectively unimodally. This preferential population of one regime is denoted stabilization. This phenomenon is only relevant if the timescale of THC variability is less than the mean residence times of the destabilized regime, so that the system may be described by its stationary probability density. These average residence times are calculated, and it is found that stabilization occurs over a broad range of parameter values. The stabilization phenomenon has important consequences for the stability of the THC. It is shown that the inclusion of stochastic processes in the model results in random hysteresis responses to steady changes in freshwater forcing, such that the transitions between regimes generally occur some distance away from the bifurcation points at which transitions occur in the deterministic model.

Corresponding author address: Adam Hugh Monahan, School of Earth and Ocean Sciences, University of Victoria, P.O. Box 3055 STN CSC, Victoria, BC V8P 5C2, Canada. Email: monahana@uvic.ca

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