An approximate Kaiman filter for ocean data assimilation: An example with an idealized Gulf Stream model

A practical method of data assimilation for use with large, nonlinear, ocean general circulation models is explored. A Kaiman filter based on approximations of the state error covariance matrix is presented, employing a reduction of the effective model dimension, the error's asymptotic steady state limit, and a time-invariant linearization of the dynamic model for the error integration. The approximations lead to dramatic computational savings in applying estimation theory to large complex systems. We examine the utility of the approximate filter in assimilating different measurement types using a twin experiment of an idealized Gulf Stream. A nonlinear primitive equation model of an unstable east-west jet is studied with a state dimension exceeding 170,000 elements. Assimilation of various pseudomeasurements are examined, including velocity, density, and volume transport at localized arrays and realistic distributions of satellite altimetry and acoustic tomography observations. Results are compared in terms of their effects on the accuracies of the estimation. The approximate filter is shown to outperform an empirical nudging scheme used in a previous study. The examples demonstrate that useful approximate estimation errors can be computed in a practical manner for general circulation models.

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

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

[3]  I. Orlanski.  A Simple Boundary Condition for Unbounded Hyperbolic Flows , 1976 .

[4]  A. Robinson,et al.  Estimation and prediction of oceanic Eddy fields , 1985 .

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

[6]  John Marshall,et al.  Determining the Ocean Circulation and Improving the Geoid from Satellite Altimetry , 1985 .

[7]  Robert N. Miller.  Toward the Application of the Kalman Filter to Regional Open Ocean Modeling , 1986 .

[8]  J. Kindle.  Sampling strategies and model assimilation of altimetric data for ocean monitoring and prediction , 1986 .

[9]  W. R. Holland,et al.  Data Constraints Applied to Models of the Ocean General Circulation. Part I: The Steady Case , 1986 .

[10]  W. Budgell,et al.  Ocean Data Assimilation and the Moan Filter: Spatial Regularity , 1987 .

[11]  William R. Holland,et al.  Data Constraints Applied to Models of the Ocean General Circulation. Part II: The Transient, Eddy-Resolving Case , 1988 .

[12]  Multidisciplinary Issues in Marine Science , 1988 .

[13]  R. E. Young,et al.  Initialization and data assimilation experiments with a primitive equation model , 1989 .

[14]  William R. Holland,et al.  Assimilation of Altimeter Data into an Ocean Circulation Model: Space versus Time Resolution Studies , 1989 .

[15]  A. Moore,et al.  The assimilation of XBT data into a layer model of the tropical pacific ocean , 1989 .

[16]  Wayne G. Leslie,et al.  Data assimilation and dynamical interpolation in GULFCAST experiments , 1989 .

[17]  Carl Wunsch.  Sampling Characteristics of Satellite Orbits , 1989 .

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

[19]  Chang-Kou Tai,et al.  Continuous assimilation of simulated Geosat altimetric sea level into an eddy‐resolving numerical ocean model: 2. Referenced sea level differences , 1990 .

[20]  Chang-Kou Tai,et al.  Continuous assimilation of Geosat altimetric sea level observations into a numerical synoptic ocean model of the California Current , 1990 .

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

[22]  Dale B. Haidvogel,et al.  A semi-spectral primitive equation ocean circulation model using vertical sigma and orthogonal curvilinear horizontal coordinates , 1991 .

[23]  George L. Mellor,et al.  A Gulf Stream model and an altimetry assimilation scheme , 1991 .

[24]  J. O'Brien,et al.  Variational data assimilation and parameter estimation in an equatorial Pacific ocean model , 1991 .

[25]  Allan R. Robinson,et al.  Shipboard Prediction with a Regional Forecast Model , 1992 .

[26]  Robert M. Chervin,et al.  Ocean general circulation from a global eddy‐resolving model , 1992 .

[27]  R. E. Young,et al.  How useful are localized clusters of traditional oceanographic measurements for data assimilation , 1992 .

[28]  C. Wunsch,et al.  The North Atlantic circulation in the early 1980s. An estimate from inversion of a finite-difference model , 1993 .

[29]  Ichiro Fukumori,et al.  Fitting Dynamic Models to the Geosat Sea Level Observations in the Tropical Pacific Ocean. Part II: A Linear, Wind-driven Model , 1993 .

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

[31]  J. Marotzke,et al.  Finding the steady state of a general circulation model through data assimilation: Application to the North Atlantic Ocean , 1993 .