Monday 24 Mar 2014: Stability and Predictability in the Climate
Peter Ditlevsen - Niels Bohr Institutet
It is taken for granted that the limited predictability in the initial value problem, the weather prediction, and the
predictability of the statistics are two distinct problems. Lorenz (1975)
dubbed this predictability of the first and the second kind respectively. Predictability of the first kind in a chaotic dynamical system is limited due to the well-known critical dependence on initial conditions. Predictability of the second kind is possible in an ergodic system, where either the dynamics is known and the phase space attractor can be characterized by simulation or the system can be observed for such long times that the statistics can be obtained
from temporal averaging, assuming that the attractor does not change in time. For the climate system the distinction between predictability of the first and the second kind is fuzzy. On the one hand, the predictability horizon for a weather forecast is not related to the inverse of the Lyapunov exponent of the system. These are rather associated with the much shorter times in the turbulent
boundary layer and so on. These time scales are effectively averaged on the time scales of the flow in the free atmosphere. Thus, when forecasting, say, showers in the afternoon, this is really a forecast of the second kind giving a statistical probability of convection and precipitation at a specific location at a specific time as a function
of a large scale flow pattern predicted from initial conditions. On the other hand, turning to climate change predictions, the time scales on which the system is considered quasi-stationary, such that the statistics, say mean surface temperature, can be predicted as a
function of an external parameter, say atmospheric greenhouse gas concentration, is still short in comparison to slow dynamics such as the oceanic overturning. On these time scales the state of these slow variables still depends on the initial conditions. This fuzzy distinction between predictability of the first and of the second kind is related to the lack of scale separation between fast and slow components of the climate system. The non-linear nature of the problem furthermore opens the
> possibility of multiple attractors, or multiple quasi-steady states. As the paleoclimatic record shows, the climate has been jumping between different quasi-stationary climates. Such a jump happens very fast when a critical tipping point has been reached. The question is:
Can a tipping point be predicted? This is a new kind of predictability (the third kind). If the tipping point is reached through a bifurcation, where the stability of the system is governed by some control parameter, changing in a predictable way to a
critical value, the tipping is predictable. If the sudden jump occurs because internal chaotic fluctuations, noise, push the system across a barrier, the tipping is as unpredictable as the triggering noise.
In order to hint at an answer to this question, an analysis of the Dansgaard-Oeschger climate events observed in ice core records is presented. The result of the analysis points to a fundamental limitation in predictability of the third kind.