Non-equilibrium dynamics of climate variability: insight from dynamic bifurcations

Understanding the internally induced natural (unforced) variability of climate systems remains an outstanding scientific challenge especially for climate systems, which are far from equilibrium. Such systems are driven by internal non-linear processes, which make the evolution of this system transient. Transient behavior of the non-linear system is very sensitive to fluctuations and initial conditions. Therefore it is extremely difficult to predict future changes in such systems from observational data alone, since there is only one realization (of many possible transients) available. Our aim is to bring the methodology of non-equilibrium dynamics to bear on understanding the internally induced climate variability by modeling transient scenarios of climate change.

In this study, we consider the dynamics of the thermohaline circulation and the variations in the Earth’s temperature as examples of the transient scenarios. We study the evolution of the system whose parameters are near critical values - bifurcation points. The control parameter is a function of a time, and it evolves slowly through the critical value undergoing a dynamic bifurcation, that makes the system non-autonomous, its evolution is completely transient, and its dynamics is non-equilibrium. We assume the rate at which the control parameter crosses its critical value to be small compared to the response time of the system. We study the non-equilibrium dynamics of the system at different control parameter profiles (monotonic or periodic function, rate of change, initial values).

Our results show that depending on the control parameters and its vicinity to the bifurcation points, the system may be closer or further away from equilibrium, may exhibit multiple equilibria, different kind of instabilities and oscillations around equilibria. In contrast to the scenarios with the time-independent parameters, non-equilibrium dynamics framework allows us to explicitly examine the transients and provide us with a diagnostic tool to reproduce the dynamics of observational data.