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Lagrangian data assimilation and overcoming the saddle effect
Christopher K.R.T. Jones, Kayo Ide, Liyan Liu, Amit Apte, Juan Restrepo
University of North Carolina at Chapel Hill
ckrtj@email.unc.edu(Abstract received 05/01/2005 for session D)
ABSTRACT
We present and discuss issues essential to the assimilation of Lagrangian data in general. By removing the necessity for a commonly used approximation, in terms of velocity, in assimilating Lagrangian data, a recently developed Lagrangian data assimilation (LaDA) method has been shown to offer a variety of advantages (Ide et al 2002, Kuznetsov et al 2003, Salman et al, 2005). Success of LaDA depends on properly estimating the error correlation between the ocean model variables and drifter positions within the augmented state space. We examine the information propagation process for the error variance and correlations using variants of the Kalman filter, e.g., Extended Kalman filter (EKF), Ensemble Kalman filter (EnKF), Sequential Evolutive Extended Kalman (SEEK). The estimation process may, however, fail when the Lagrangian instrument passes near to a (Lagrangian) saddle point of the ocean flow. This leads to a sudden divergence of the filter, termed the "saddle effect" (see LAPCOD, 2002). We present a series of strategies to attack this problem using tracer control, ensemble filter, and a path integral method. On the basis of these approaches, we develop an efficient and robust LaDA method that overcomes the saddle effect. Finally, an application of LaDA for estimation of the sub-surface flow using surface drifter observations will be presented.
Ide, K., L. Kuznetsov and C.K.R.T. Jones, 2002: Lagrangian data assimilation for point-vortex system. J. Turbulence, 3, 053.
Kuznetsov, L., K. Ide and C.K.R.T. Jones, 2003: A method for assimilation of Lagrangian data. Mon. Wea. Rev., 131(10), 2247-2260.
Salman, H., L. Kuznetsov, C.K.R.T. Jones and K. Ide, 2005: A method for assimilating Lagrangian data into a shallow-water equation ocean model, Mon. Wea. Rev., Sub judice.
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2005 LAPCOD Meeting, Lerici, Italy, June 13-17, 2005