Quasi-Fixed Points and Periodic-Orbits in the Zebiak-Cane Enso Model with Applications in Kalman Filtering .2. Periodic-Orbits

In part II of this study on the application of the interactive Kalman filter to higher-dimensional systems, a modification suited to periodically forced systems is introduced. As in Part I, the object of study here is the ENSO model of Zebiak and Cane, but here the technique of quasi-fixed points is applied to certain Poincare maps of that system that are related to the forcing period of 1 year. As a result, it is possible to search the model systematically for possible periodic orbits, no matter whether they are stable or unstable. An unstable 4-year cycle is found in the model, and it is argued that this cycle can be traced back to a 4-year limit cycle, which is known to exist under weak atmosphere-ocean coupling. All other quasi-fixed points are related to orbits that do not appear to be periodic. The findings are applied to the modified version of the interactive Kalman filter, which deals with cycles as regimes. Comparing these results with the findings in Part I, it is found that the filter performances improve using, in the following order, the extended filter, the interactive filter with cycles, a seasonal average filter, and the original interactive Kalman filter from Part I.