MAPPING TROPICAL PACIFIC SEA-LEVEL - DATA ASSIMILATION VIA A REDUCED-STATE SPACE KALMAN FILTER

The well-known fact that tropical sea level can be usefully simulated by linear wind driven models recommends it as a realistic test problem for data assimilation schemes. Here we report on an assimilation of m onthly data for the period 1975-1992 from 34 tropical Pacific tide gau ges into such a model using a Kalman filter. We present an approach to the Kalman filter that uses a reduced state space representation for the required error covariance matrices. This reduction makes the calcu lation highly feasible. We argue that a more complete representation w ill be of no value in typical oceanographic practice, that in principl e it is unlikely to be helpful, and that it may even be harmful if the data coverage is sparse, the usual case in oceanography. This is in p art a consequence of ignorance of the correct error statistics for the data and model, but only in part. The reduced state space is obtained from a truncated set of multivariate empirical orthogonal functions ( EOFs) derived from a long model run without assimilation. The reduced state space filter is compared with a full grid point Kalman filter us ing the same dynamical model for the period 1979-1985, assimilating ei ght tide guage stations and using an additional seven for verification [Miller et al., 1995]. Results are not inferior to the full grid poin t filter, even when the reduced filter retains only nine EOFs. Five se ts of reduced space filter assimilations are run with all tide gauge d ata for the period 1975-1992. In each set a different number of EOFs i s retained: 5, 9, 17, 32, and 93, accounting for 60, 70, 80, 90, and 9 9% of the model variance, respectively. Each set consists of 34 runs, in each of which one station is withheld for verification. Comparing e ach set to the nonassimilation run, the average rms error at the withh eld stations decreases by more than 1 cm. The improvement is generally larger for the stations at lowest latitudes. Increasing the number of EOFs increases agreement with data at locations where data are assimi lated; the added structures allow better fits locally. In contrast, re sults at withheld stations are almost insensitive to the number of EOF s retained. We also compare the Kalman filter theoretical error estima tes with the actual errors of the assimilations. Features agree on ave rage, but not in detail, a reminder of the fact that the quality of th eoretical estimates is limited by the quality of error models they ass ume. We briefly discuss the implications of our work for future studie s, including the application of the method to full ocean general circu lation models and coupled models.