A Simple Stochastic Model for the Stability of Open Ocean Deep Convection in a Changing Climate

With a simple nonlinear analytical model we study how the variability of open ocean deep convection depends on climate parameters. For realistic parameter values the non-stochastic model is bistable: either there is a deep convection event each winter, or convection does not occur at all. The model dynamics is governed by the average buoyancy flux and its seasonal cycle. In addition, a random component of the buoyancy flux models its observed variability. The added random fluctuations induce jumps between the two states. It turns out that the probability density function of the stochastically driven model gives a qualitatively different picture of the model behavior in comparison with the non-stochastic stability diagram. In the bistable domain, the presence of the noise leads to a strong preference for one state. On the other hand, if only the non-convecting state is stable the noise will be able to trigger frequent excursions to the unstable convecting state. The convecting state can abruptly disappear when changing the parameters in the non-stochastic model. In the stochastic model however, this abruptness is replaced by a reduction of the frequency of deep convection events. We present analytical expressions that show how the frequency and length of deep convection events depend quantitatively on the buoyancy forcing parameters and the noise intensity. The occurrence of convection events hinges on a delicate balance of the noise level and the amplitude of the seasonal cycle. The results are compared with a more complex model that reproduces the variability of deep convection in the Labrador Sea. With the presented work some understanding is gained about how deep convection might change in a changing future climate.