Nonnormal perturbation growth and optimal excitation of the thermohaline circulation using a 2D zonally averaged ocean model




Alexander, Julie

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Generalized linear stability theory is used to calculate the optimal initial conditions that result in transient amplification of the thermohaline circulation (THC) in a zonally-averaged single basin ocean model. The eigenmodes of the tangent linear model verify that the system is asymptotically stable but the nonnormality of the system permits the growth of perturbations for a finite period through the interference of nonorthogonal eigenmodes. It is found that the maximum amplification of the THC anomalies occurs after 6 years with both the thermally driven and salinity driven components playing major roles in the amplification process. The transient amplification of THC anomalies is due to the constructive and destructive interference of a large number of eigenmodes and the evolution over time is determined by how the interference pattern evolves. It is found that five of the most highly nonnormal eigenmodes are critical to the initial cancellation of the salinity and temperature contributions to the THC while 11 oscillating modes with decay timescales ranging from 2 to 6 years are the major contributors at the time of maximum amplification. This analysis demonstrates that the different dynamics of salinity and temperature anomalies allows the dramatic growth of perturbations to the THC on relatively short (interannual to decadal) timescales. In addition the ideas of generalized stability theory are used to calculate the stochastic optimals which are the spatial patterns of stochastic forcing that are most efficient at generating variance growth in the THC. It is found that the optimal stochastic forcing occurs at high latitudes and induces low-frequency THC variability by exciting the salinity-dominated modes of the THC. The first stochastic optimal is found to have its largest projection on the same five highly nonnormal eigenmodes found to be critical to the structure of the optimal initial conditions. The model’s response to stochastic forcing is not controlled by the least damped eigenmodes of the tangent linear model but rather by the linear interference of these highly nonnormal eigenmodes. The process of pseudoresonance suggests that the nonnormal eigenmodes are excited and sustained by stochastically induced perturbations which in turn lead to maximum THC variance. Finally, it was shown that the addition of wind stress did not have a large impact on the nonnormal dynamics of the linearised system. Adding wind allowed the value of the vertical diffusivity to be reduced to achieve the same maximum linearised THC amplitude as was used in the case with no wind stress.



nonnormal perturbation growth, thermohaline circulation, stochastic climate models, 2D zonally averaged ocean models