Quasi-Fixed Points and Periodic Orbits in the Zebiak—Cane ENSO Model with Applications in Kalman Filtering. Part I: Monthly Quasi-Fixed Points

Abstract

In an effort to apply the interactive Kalman filter to higher-dimensional systems, the concept of a quasi-fixed point is introduced. This is defined to be a system state where the tendency, in a suitable reduced space, is at a minimum. It allows one to use conventional search algorithms 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 permanent monthly mode, the reduced space being defined via a multiple EOP projection. The stability characteristics of the quasi-fixed points are analyzed, and it is shown that they are significantly different from the (in)stabilities of the average monthly models. With these quasi-fixed points, assimilation experiments are carried out with the interactive Kalman filter for the Zebiak?Cane model in the reduced space. It is demonstrated that the results are superior to both a seasonal Kalman filter and the extended Kalman filter.