A Comparison of Adaptive Kalman Filters for a Tropical Pacific Ocean Model

The Kalman filter is the optimal linear assimilation scheme only if the first- and second-order statistics of the observational and system noise are correctly specified. If not, optimality can be reached in principle by using an adaptive filter that estimates both the state vector and the system error statistics. In this study, the authors compare the ability of three adaptive assimilation schemes at estimating an unbiased, stationary system noise. The adaptive algorithms are implemented in a reduced space linear model for the tropical Pacific. Using a twin experiment approach, the algorithms are compared by assimilating sea level data at fixed locations mimicking the tropical Pacific tide gauges network. It is shown that the description of the system error covariance matrix requires too many parameters for the adaptive problem to be well posed. However, the adaptive procedures are efficient if the number of noise parameters is dramatically reduced and their performance is shown to be closed to optimal, that is, based on the true system noise covariance. The link between those procedures is elucidated, and the question of their applicability and respective computational cost is discussed.

[1]  Sadashiva S. Godbole Kalman filtering with no A-priori information about noise-White noise case: Part I: Identification o , 1973, CDC 1973.

[2]  Mark A. Cane,et al.  A Numerical Model for Low-Frequency Equatorial Dynamics , 1984 .

[3]  G. Wittum,et al.  Adaptive filtering , 1997 .

[4]  Yves Menard,et al.  Geosat sea-level assimilation in a tropical Atlantic model using Kalman filter , 1992 .

[5]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series , 1964 .

[6]  Mark A. Cane,et al.  Modeling Sea Level During El Niño , 1984 .

[7]  S. Godbole,et al.  Kalman filtering with no A-priori information about noise-White noise case: Part I: Identification of covariances , 1973, CDC 1973.

[8]  R. Daley The Lagged Innovation Covariance: A Performance Diagnostic for Atmospheric Data Assimilation , 1992 .

[9]  Alexey Kaplan,et al.  Mapping tropical Pacific sea level : Data assimilation via a reduced state space Kalman filter , 1996 .

[10]  Antonio J. Busalacchi,et al.  Hindcasts of Sea Level Variations during the 1982-83 El Nino , 1985 .

[11]  Norbert Wiener,et al.  Extrapolation, Interpolation, and Smoothing of Stationary Time Series, with Engineering Applications , 1949 .

[12]  M. Ghil,et al.  Data assimilation in meteorology and oceanography , 1991 .

[13]  Stephen E. Cohn,et al.  A Kalman filter for a two-dimensional shallow-water model, formulation and preliminary experiments , 1985 .

[14]  T. Kailath,et al.  An innovations approach to least-squares estimation--Part II: Linear smoothing in additive white noise , 1968 .

[15]  M.L.J. Hautus,et al.  Controllability and observability conditions of linear autonomous systems , 1969 .

[16]  D. Dee On-line Estimation of Error Covariance Parameters for Atmospheric Data Assimilation , 1995 .

[17]  Andrew H. Jazwinski,et al.  Adaptive filtering , 1969, Autom..

[18]  R. Mehra On the identification of variances and adaptive Kalman filtering , 1970 .

[19]  Nori,et al.  “ An Approximate Kalman Filter for Ocean Data Assimilation ; An Example with an Idealized Gulf Stream Modelt , 1995 .

[20]  D. Dee Simplification of the Kalman filter for meteorological data assimilation , 1991 .

[21]  B. Tapley,et al.  Adaptive sequential estimation with unknown noise statistics , 1976 .

[22]  P. Bélanger Estimation of noise covariance matrices for a linear time-varying stochastic process , 1972, at - Automatisierungstechnik.

[23]  Robert N. Miller,et al.  A Kalman Filter Analysis of Sea Level Height in the Tropical Pacific , 1989 .

[24]  Stanley B. Goldenberg,et al.  Time and Space Variability of Tropical Pacific Wind Stress , 1981 .

[25]  Carl Wunsch,et al.  Assimilation of Sea Surface Topography into an Ocean Circulation Model Using a Steady-State Smoother , 1993 .

[26]  Mark A. Cane,et al.  Experimental forecasts of El Niño , 1986, Nature.

[27]  Michael Ghil,et al.  An efficient algorithm for estimating noise covariances in distributed systems , 1985 .

[28]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[29]  R. G. Jacquot,et al.  Techniques for Adaptive State Estimation through the Utilization of Robust Smoothing , 1987 .

[30]  R. E. Livezey,et al.  Statistical Field Significance and its Determination by Monte Carlo Techniques , 1983 .

[31]  Antonio J. Busalacchi,et al.  Sea surface topography fields of the tropical Pacific , 1995 .