I. Fukumori and P. Malanotte-Rizzoli, "An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream Model," J. Geophys. Res., vol. 100, pp. 6777--6793, 1995.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....developed at the Naval Research Laboratory (NRL) I. INTRODUCTION Estimating the state of the ocean fields (for example, the sea surface height and ocean velocity components) is a key issue in physical oceanography. Direct application of the Kalman Bucy filter (KBf) in such data assimilation, 1] [5], problems is difficult for two reasons. First, the state equations are nonlinear and the resulting KBf is nonrigorous. Second, the KBf involves formidable computational requirements in inverting and storing the covariance matrices such that its application is limited to relatively simple ....

I. Fukumori and P. Malanotte-Rizzoli, "An approximate Kalman filter for ocean data assimilation: an example with an idealized Gulf Stream Model," J. of Geophysical Research, vol. 100, pp. 6777-6793, 1995.

....it possible to detect changes to the temperature field over time. In addition, statements about uncertainty can also be supplied from a statistical approach. Another class of models combines physical ocean dyanmics with measurements to predict the ocean flow field; see for example Miller (1986) Fukumori and Malanotte Rizzoli (1995) or Rane et al. 1996) Cummings et al. 1997) give a description of the U. S. Navy s ocean analysis systems which assimilates data from many sources. This additional information can be used to construct a first guess , which is usually incorporated in the mean field of a space or space time ....

Fukumori, I. and Malanotte-Rizzoli, P. (1995) An approximate Kalman filter for ocean data assimilation: an example with an idealized Gulf Stream model, Journal of Geophysical Research 100, 6777--6793.

....according to the standard KF equations, but at a resolution lower than that of the model that evolves the state. The resulting Kalman gain is then interpolated to the model grid and the analysis proceeds as usual. Versions of the RKF have been studied already by Le Moyne and Alvarez (1991) and by Fukumori and Malanotte Rizzoli (1994). The other two schemes are new. The first one, the singular value decomposition (SVD) Kalman filter (SVKF) utilizes a partial SVD of the tangent linear dynamics between consecutive observation times. This scheme assumes that most of the propagated error covariance is due to a small collection of ....

Fukumori, I., and P. Malanotte--Rizzoli, 1994: An approximate Kalman filter for ocean data assimilation; an example with an idealized Gulf Stream model. J. Geophys. Res. Oceans, submitted.

....to the standard KF equations, but at a resolution lower than that of the model that evolves the state. The resulting Kalman gain is then interpolated to the model grid and the analysis proceeds as usual. Other reduced resolution filters have been studied by Le Moyne and Alvarez (1991) and by Fukumori and Malanotte Rizzoli (1995). The other two schemes are new. The first one, called the partial singular value decomposition filter (PSF) utilizes a partial singular value decomposition (SVD) of the tangent linear dynamics between consecutive observation times: the tangent linear propagator is approximated by the leading ....

....a prescribed multiplicative parameter. In addition to the PSF and PEF schemes, we also evaluate the performance of a reduced resolution filter (RRF) in which the covariances are evolved at a lower resolution than that used to evolve the state vector. This covariance evolution differs from that of Fukumori and Malanotte Rizzoli (1995) in that it uses directly a coarse grid discretization of the governing differential equations. The RRF scheme produces a gain matrix at low resolution which is interpolated using cubic splines (spline interpolant with periodic boundary conditions in the east west direction and an Akima spline ....

Fukumori, I., and P. Malanotte--Rizzoli, 1995: An approximate Kalman filter for ocean data assimilation; an example with an idealized Gulf Stream model. J. Geophys. Res.

....is an estimate of the trailing error covariance matrix of this approximation, in general distinct from T kjk Gamma1 . This approach resembles the reduced rank square root filter of Verlaan and Heemink (1995) 1. d) Reduced Resolution Filter (RRF) This approximation follows the approach of Fukumori and Malanotte Rizzoli (1995; see also Cane et al. 1996, and Todling and Cohn 1996b) and involves carrying the error covariances at lower resolution than that of the state estimates. In this case, the predictability error covariance matrix is approximated for use in (1c) by S p kjk Gamma1 = B A k;k Gamma1 B) S ....

Fukumori, I, and P. Malanotte--Rizzoli, 1995: An approximate Kalman filter for ocean data assimilation: an example with an idealized Gulf Stream model. J. Geophys.

....for some years. To speed up of the (off line) steady state gain computations a Chandrasekhar type algorithm ( 17, 12, 4] or a doubling algorithm ( 1] can be applied. When there are no irregular boundaries a coarser grid combined with an interpolation scheme can be used for the gain computations ([10]) For many data assimilation problems a steady state approach is not possible and a full Kalman filter has to be used. For storm surge prediction the errors in the wind forcing are non stationary and the wind friction coefficient depends on the mean wave height which varies during a storm. As a ....

.... Gamma P (k Gamma 1jk Gamma 1) The advantage is that for a time invariant model with P 0 = 0 the rank of these matrices is m. The doubling algorithm performs steps from time k to 2k instead of to k 1. The steady state approach has been used succesfuly for large, two dimensional, models (e.g. [12, 4, 10]) Compared to a more traditional prediction by a deterministic model only, the number of additional computations is small while the reduction in errors can be large. A disadvantage is that the steady state approach can not be used for many applications because in many applications the model is ....

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I. Fukumori and P. Melanotte-Rizzoli. An approximate kalman filter for ocean data assimilation; an example with an idealized gulf stream model. Accepted for publication Journal of Geophysical Research, 1994.

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I. Fukumori and P. Malanotte-Rizzoli, "An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream Model," J. Geophys. Res., vol. 100, pp. 6777--6793, 1995.

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I. Fukumori and P. Malanotte-Rizzoli. An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model. Journal of Geophysical Research, 100(C4):6777--6793, 1995.

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I. Fukumori and P. Malanotte-Rizzoli, `An approximate Kalman filter for ocean data assimilation: an example with an idealized Gulf Stream model', J. Geophys. Res., 100, 6777 -- 6793 (1995).

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Oceanogr., 23, 1831--1855. Fukumori I. and P. Malanotte-Rizzoli, 1995: An approximate Kalman filter for ocean data assimilation: An example with an idealized Gulf Stream model. J. Geophys. Res., 100 (C12), 6777--6793.

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