Documents, videos, animations etc. relating to our work.




Schematics and animations

  • Predictability on the Lorenz attractor

    In a nonlinear system, here the Lorenz (1963) model, but the principle applies to the real atmosphere too, the growth of initial uncertainties during a given forecast period is flow dependent. The set of initial conditions indicated by the black circle is located in three different regions of the attractor: from some initial states the forecast evolution can be highly predictable (top left), from other initial states it can be highly unpredictable (bottom).
  • Predictability on the Lorenz attractor (animation)
    This link brings you to an animation of the Lorenz system showing bundles of evolving time series (ensembles) of the X component of the Lorenz (1963) model starting from three different regions on the attractor. The top line demonstrates a highly predictable situation with the bundle of trajectories hardly diverging over time and where the exact initial conditions are not of crucial importance. The bottom line shows an example of a highly unpredictable situation where the ensemble diverges rapidly.
  • The chaotic climate system
    The following two animations show an analogue toy model of the climate system and demonstrate how a nonlinear system can respond to an external forcing, such as associated with climate change.

    The analogue model is in the form of a magnetic pendulum that, if operated in a free unforced mode (see the first animation), exhibits quasi-chaotic behaviour. Similar to the real atmosphere, the dynamics of the pendulum can be characterised by a few quasi-stationary states, which in the real atmosphere are called weather regimes. For example, think of the yellow magnet as representing a spell of anomalously warm weather and the opposite white magnet as representing a period of cold weather. Similarly, perhaps the pink and blue magnets can be thought of representing wet and dry weather regimes respectively. The pendulum swings between these four preferred states in a seemingly random way; none of the four regimes is preferred. If observed over a long time, then in the "unforced" configuration, each of the regimes is equally likely.

    Suppose a relatively weak external forcing is now being applied to our analogue toy model (see the second animation). Perhaps think of the forcing as representing changes in the concentration of greenhouse gases in the atmosphere due to increased anthropogenic emissions. In the animation the forcing is realised by moving a wedge under one side of the base of the pendulum. What happens to the statistics of the pendulum under such a forcing? While the system is still essentially chaotic, we see that the probability that the pendulum lies near any of the four regimes, is no longer the same for each regime. For example, the yellow magnet attracts the pendulum more often than the cold magnet. Using the analogy with weather regimes, one would say that the anomalous warm state occurs more often than the anomalous cold state. Note that the forcing does not imply that the cold state will never occur - it is merely less likely. In this model, it would be wrong to think of the response as comprising a forced response linearly superposed on the system's natural variability. Rather the time-averaged forced response is determined by the changes in the frequency of occurrence of the regimes.

    In the paper by Dawson et al. (2012) we show that the real atmosphere does exhibit such regime behaviour, but that coarse resolution climate models can have difficulty simulating them. We also show that it is possible to simulate such regimes in a sufficiently high resolution climate model. However, climate institutes struggle to find the computer resources to integrate their models at the required resolutions. It is urgent that appropriate resources are found. This may require more active international collaboration between climate institutes.