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## A Singular Evolutive Extended Kalman Filter For Data Assimilation In Oceanography (1996)

Venue: | Journal of Marine Systems |

Citations: | 107 - 9 self |

### Citations

3855 | A new approach to linear filtering and prediction problems - Kalman - 1960 |

879 | Geophysical Fluid Dynamics - Pedlosky - 1979 |

798 | Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics
- Evensen
- 1994
(Show Context)
Citation Context ...umoris[1995], for example, undersamples the computational grid used for the filter description. Several studies are based on some ways of projecting the filter evolution on a reduced dimension basis [=-=Evensen, 1994-=-; Cane et al., 1995, Hoang et al., 1995]. Another approach consists in relying on physical considerations which will naturally decrease the degree of freedom of the system: long wave approximation in ... |

438 | Multivariate Observations, - Seber - 1984 |

198 | Data assimilation in meteorology and oceanography, in: - Ghil, Malanotte-Rizzoli - 1991 |

162 | Unified notation for data assimilation: operational, sequential and variational. - Ide, Courtier, et al. - 1997 |

144 |
Advanced data assimilation in strongly nonlinear dynamical system,
- Miller, Ghil, et al.
- 1994
(Show Context)
Citation Context ...currently available state estimate, yielding the so-called extended Kalman filter (EKF) [Ghil et al., 1982]. The application of EKF to nonlinear models has been the subject of various investigations [=-=Miller et al., 1994-=-; Evensen, 1993, 1994]. It may however result in instability in the covariance evolution equation [Evensen, 1992; Gauthier at al., 1993]. An attractive feature of the EKF is that it is recursive. Comp... |

86 | Using the Extended Kalman Filter With a Multilayer Quasi-Geostrophic Ocean Model,”
- Evensen
- 1992
(Show Context)
Citation Context ...cation of EKF to nonlinear models has been the subject of various investigations [Miller et al., 1994; Evensen, 1993, 1994]. It may however result in instability in the covariance evolution equation [=-=Evensen, 1992; Gauthier-=- at al., 1993]. An attractive feature of the EKF is that it is recursive. Computation is done "on line" as soon as new observations are available. Assuming that at a time t i , one already h... |

76 | Mapping tropical Pacific sea level: Data assimilation via a reduced state space Kalman filter,
- Cane, Kaplan, et al.
- 1996
(Show Context)
Citation Context ...ements which, for N = 10 5 , comes out to about five billion. It is questionable whether one can have even a crude knowledge on such a huge number of parameters. This point is discussed at length in [=-=Cane et al., 1995-=-]. Here we note, only briefly, that a statistical estimate based on a sample of length T has a convergence rate of 1= p T and in practice T would be only a tiny fraction of N . Therefore if one tries ... |

75 | An approximate Kalman filter for ocean data assimilation; an example with an idealized Gulf Stream model. - Fukumori, Malanotte-Rizzoli - 1995 |

65 | The role of mesoscale eddies in the general circulation of the ocean—Numerical experiments using a wind-driven quasi-geostrophic model - Holland - 1978 |

41 | Approximate data assimilation schemes for stable and unstable dynamics - Cohn, Todling - 1996 |

39 | Simplification of the Kalman filter for meteorological data assimilation
- Dee
- 1991
(Show Context)
Citation Context ...proach consists in relying on physical considerations which will naturally decrease the degree of freedom of the system: long wave approximation in the tropics [Cane and Patton, 1984] and geostrophy [=-=Dee, 1991-=-], being examples, amongst others. Here we adopt a somewhat different approach while retaining the idea of reducing the KF working space. Indeed, on physical grounds, it would seems legitimate to assu... |

31 | Assimilation of simulated wind lidar data with a Kalman filter. - Gauthier, Courtier, et al. - 1993 |

27 |
Assimilation of sea surface topography into an ocean circulation model using a steady-state smoother
- Fukumori, Benveniste, et al.
- 1993
(Show Context)
Citation Context ... Firstly, one can simply reduce the dimension of the model state vector to make it compatible with the computational constraint [Miller and Cane, 1989; Gaspar and Wunsch, 1989; Gourdeau et al., 1992; =-=Fukumori et al., 1993-=-; Benveniste et al., 1994]. Quite often, one also assumes a certain asymptotic property of constancy for the error covariance matrix [Gourdeau et al., 1992; Fu et al., 1993; Benveniste et al., 1994; F... |

25 |
Fitting dynamic models to the Geosat sea-level observations in the tropical Pacific Ocean. Part 1: A free wave model.
- Fu, Vazquez, et al.
- 1991
(Show Context)
Citation Context ...ourdeau et al., 1992; Fukumori et al., 1993; Benveniste et al., 1994]. Quite often, one also assumes a certain asymptotic property of constancy for the error covariance matrix [Gourdeau et al., 1992; =-=Fu et al., 1993-=-; Benveniste et al., 1994; Fukumori et Malanotte-Rizzoli, 1995, Fukumori, 1995). Secondly, one might consider reducing the KF working space until the computation becomes feasible (without necessarily ... |

24 |
A Kalman filter analysis of sea level heights in the tropical Pacific,
- Miller, Cane
- 1989
(Show Context)
Citation Context ... the system in some way. Schematically several strategies are possible. Firstly, one can simply reduce the dimension of the model state vector to make it compatible with the computational constraint [=-=Miller and Cane, 1989-=-; Gaspar and Wunsch, 1989; Gourdeau et al., 1992; Fukumori et al., 1993; Benveniste et al., 1994]. Quite often, one also assumes a certain asymptotic property of constancy for the error covariance mat... |

23 |
Assimilation of TOPEX sea level measurements with a reducedgravity, shallow water model of the tropical Pacific
- Fukumori
- 1995
(Show Context)
Citation Context ...ten, one also assumes a certain asymptotic property of constancy for the error covariance matrix [Gourdeau et al., 1992; Fu et al., 1993; Benveniste et al., 1994; Fukumori et Malanotte-Rizzoli, 1995, =-=Fukumori, 1995-=-). Secondly, one might consider reducing the KF working space until the computation becomes feasible (without necessarily reducing the size of the model !). Fukumoris[1995], for example, undersamples ... |

20 | A singular evolutive Kalman filter for data assimilation in oceanography - Pham, Verron, et al. - 1998 |

18 |
A numerical model for low-frequency equatorial dynamics,
- Cane, Patton
- 1984
(Show Context)
Citation Context ..., 1995, Hoang et al., 1995]. Another approach consists in relying on physical considerations which will naturally decrease the degree of freedom of the system: long wave approximation in the tropics [=-=Cane and Patton, 1984-=-] and geostrophy [Dee, 1991], being examples, amongst others. Here we adopt a somewhat different approach while retaining the idea of reducing the KF working space. Indeed, on physical grounds, it wou... |

14 |
Estimates from altimeter data of barotropic Rossby waves in the northwestern Atlantic Ocean.
- Gaspar, Wunsch
- 1989
(Show Context)
Citation Context .... Schematically several strategies are possible. Firstly, one can simply reduce the dimension of the model state vector to make it compatible with the computational constraint [Miller and Cane, 1989; =-=Gaspar and Wunsch, 1989-=-; Gourdeau et al., 1992; Fukumori et al., 1993; Benveniste et al., 1994]. Quite often, one also assumes a certain asymptotic property of constancy for the error covariance matrix [Gourdeau et al., 199... |

14 | Convergence and stability properties of the discrete Riccati operator equation and the associated optimal control and filtering problems. - HAGER, HoROWITZ - 1976 |

13 | Open Boundary Conditions for the Extended Kalman Filter with a Quasigeostrophic
- Evensen
- 1993
(Show Context)
Citation Context ...tate estimate, yielding the so-called extended Kalman filter (EKF) [Ghil et al., 1982]. The application of EKF to nonlinear models has been the subject of various investigations [Miller et al., 1994; =-=Evensen, 1993-=-, 1994]. It may however result in instability in the covariance evolution equation [Evensen, 1992; Gauthier at al., 1993]. An attractive feature of the EKF is that it is recursive. Computation is done... |

8 |
Geosat sea-level assimilation in a tropical Atlantic model using Kalman filter
- Gourdeau, Arnault, et al.
- 1992
(Show Context)
Citation Context ...trategies are possible. Firstly, one can simply reduce the dimension of the model state vector to make it compatible with the computational constraint [Miller and Cane, 1989; Gaspar and Wunsch, 1989; =-=Gourdeau et al., 1992-=-; Fukumori et al., 1993; Benveniste et al., 1994]. Quite often, one also assumes a certain asymptotic property of constancy for the error covariance matrix [Gourdeau et al., 1992; Fu et al., 1993; Ben... |

7 | Approximate Kalman filters for unstable dynamics - Cohn, Todling - 1995 |

5 | Sequential estimation, data assimilation and initialization - Ghil, Cohn, et al. - 1982 |

4 | Assimilation of altimeter data in a multilayer quasi{geostrophic ocean model by simple nonlinear adaptive lter - Hoang, DeMey, et al. - 1995 |

2 |
Sequential estimation and satellite data assimilation in meteorology and oceanography
- Ghil
- 1986
(Show Context)
Citation Context ... the observations up to this time. Since Kalman [1960], this problem has been the source for numerous developments in various fields of science and in particular that of atmospheric and oceanic flow [=-=Ghil, 1986-=-; Ghil and Malanotte-Rizzoli, 1991]. However, the Kalman filter was designed for a linear system only. For a nonlinear system, one often resorts to linearization of the operators M and H around the cu... |

2 |
Stochastic and Filtering Theory
- Jazwinski
- 1970
(Show Context)
Citation Context ...process. As a beneficial side effect, it also attenuates the unaccounted errors in the past, thus reducing their propagation and possible accumulation. This is a type of error compensation technique [=-=Jazwinski, 1970-=-]. It actually enhances the stability of the filter. Although the arguments in section 3.2.2 are no longer valid here (Q i being not constant), those in section 3.1.1 may be adapted to show this stabi... |

2 | Assimilation of Oceanic altimeter data using a quasi-geostrophic model and the extended Kalman filter. Rapport technique du projet - Pham, Roubaud - 1995 |

1 |
Sequential estimation; data assimilation and initilization
- Ghil, Cohn, et al.
- 1982
(Show Context)
Citation Context ...ar system only. For a nonlinear system, one often resorts to linearization of the operators M and H around the currently available state estimate, yielding the so-called extended Kalman filter (EKF) [=-=Ghil et al., 1982-=-]. The application of EKF to nonlinear models has been the subject of various investigations [Miller et al., 1994; Evensen, 1993, 1994]. It may however result in instability in the covariance evolutio... |

1 |
The role of mesosccale eddies in the general circulation of the ocean. Numerical experiments using a wind-driven quasi-geostrophic model
- Holland
- 1978
(Show Context)
Citation Context ...lation, commonly used to describe the dynamical evolution of geophysical fluids such as the atmosphere or the ocean [Pedlosky, 1987]. In the present case, it is considered in its layered formulation [=-=Holland, 1978-=-]. The ocean is thus subdivided into N layers of constant density. Vertical momentum is transferred vertically by the pressure coupling between layers. Horizontal circulation in each layer is represen... |