Abstract: Data assimilation is a process where an improved prediction is obtained from a weighted combination between experimental measurements and mathematical model data. In the present work this procedure is applied to a system for Space Climate by using a Kalman filter (KF). A simple model of the resonant three-wave coupling equations (low dimension) [1] is used to illustrate the assimilation technique. The KF is interesting aprroach, because the KF gives an output in which the balance between the data from the model and the observations is done automaticaly, through the Kalman gain. In addition, the Kalman filter computes the propagation error [2]. New formulations for data assimilation based on neural networks [3, 4] and a new approach for KF associate to the Fokker-Planck equation [5] are under investigation.

References:

1. C. Meunier, M. N. Bussac, G. Laval (1982): Intermittency at the onset of stochasticity in nonlinear resonant coupling processes, Physica D, 4(2): 236-243.

2. A.G. Nowosad, A. Rios Neto, H.F. de Campos Velho (2000): Data Assimilation Using an Adaptative Kalman Filter and Laplace Transform, Hybrid Methods in Engineering, 2(3): 291-310.

3. A.G. Nowosad, H.F. de Campos Velho, A. Rios Neto (2000): Neural Network as a New Approach for Data Assimilation, Brazilian Congress on Meteorology, 16-20 October, Rio de Janeiro (RJ), Brasil, Proceedings in CD-ROM (paper code PT00002), pp. 3078-3086.

4. A.G. Nowosad, A. Rios Neto, H.F. de Campos Velho (2000): Data Assimilation in Chaotic Dynamics Using Neural Networks, Third International Conference on Nonlinear Dynamics, Chaos, Control and Their Applications in Engineering Sciences, July 31 - August 4, Campos do Jordao (SP), Brasil, Vol. 6, Chapter 6 - Control, pp. 212-221.

5. K. Belyaev, C. A. S. Tanajura (2002): An Extension of a data assimilation method based on the application of the Fokker-Planck equation, Applied Mathematical Modelling, 26(11): 1019-1027.