QUASI-FIXED POINTS AND PERIODIC-ORBITS IN THE ZEBIAK-CANE ENSO MODEL WITH APPLICATIONS IN KALMAN FILTERING .1. MONTHLY QUASI-FIXED POINTS

In an effort to apply the interactive Kalman filter to higher-dimensio nal systems, the concept of a quasi-fixed point is introduced. This is defined to be a system state where the tendency, in a suitable reduce d space, is at a minimum. It allows one to use conventional search alg orithms for the detection of quasi-fixed points. In Part I quasi-fixed points of the ENSO model of Zebiak and Cane are found when run in a p ermanent monthly mode, the reduced space being defined via a multiple EOF projection. The stability characteristics of the quasi-fixed point s are analyzed, and it is shown that they are significantly different from the (in)stabilities of the average monthly models. With these qua si-fixed points, assimilation experiments are carried out with the int eractive Kalman filter for the Zebiak-Cane model in the reduced space. It is demonstrated that the results are superior to both a seasonal K alman filter and the extended Kalman filter.