Researchers: (alphabetic order) - Chin, Mike Toshio1,4 - Griffa, Annalisa1,2 - Mariano, Arthur1 - Molcard, Anne1,2 - Özgökmen, Tamay1 - Piterbarg, Leonid3 - 1RSMAS, Miami - 2CNR, Italy - 3USC, Los Angeles - 4JPL, Los Angeles Sponsors: - ONR - EEC (MFS) Publications: - Chin, T.M., K. Ide, C.K.R.T. Jones, L. Kuznetsov, and A.J. Mariano, 2004: Dynamic consistency and Lagrangian data in oceanography: mapping, assimilation, and optimization schemes. LAPCOD book chapter, accepted. - Molcard, A., T.M. Özgökmen, A. Griffa, L.I. Piterbarg, and T.M. Chin, 2004: Lagrangian data assimilation in ocean general circulation models. LAPCOD book chapter, accepted. - Molcard A., A. Griffa and T.M. Özgökmen, 2004: Lagrangian data assimilation in a multi-layer model, J. Atmos. Ocean. Tech., 22, No. 1., 70-83. - Chin, T.M, T.M. Özgökmen, and A.J. Mariano, 2004: Multi-variate spline and scale-specific solution for variational analyses. J. Atmos. Ocean. Tech., 21(2), 379-386. - Molcard A., L.I. Piterbarg, A. Griffa, T.M. Özgökmen, A.J. Mariano, 2003: Assimilation of drifter positions for the reconstruction of the Eulerian circulation field. J. Geophys. Res., 108, (C3), 1-21. - Özgökmen T.M., A. Molcard, T.M. Chin, L.I. Piterbarg, A. Griffa, 2003: Assimilation of drifter positions in primitive equation models of midlatitude ocean circulation. J. Geophys. Res., 108, (C7), 3238, doi:10.1029/2002jc001719.

Because of the increases in the realism of Ocean General Circulation Models (OGCMs) and in the coverage of Lagrangian data sets in most of the world's oceans, assimilation of Lagrangian data in OGCMs emerges as a natural avenue to improve ocean state forecast with many potential practical applications such as environmental pollutant transport, biological and defense-related problems. A Lagrangian data assimilation method has been developed and applied to oceanographic models of increasing complexity and realism, including a quasi-geostropic model and two versions of the primitive equation Miami Isopycnic Ocean Model (MICOM) with 1.5 and multiple layers, respectively. The main goal is to develop a simple and portable method that can be applied to realistic models and configurations. Methodological tests have been performed using the "twin experiment" approach and considering the double-gyre configuration. The main assimilation module consists of correcting the Eulerian velocity of the model considering directly the Lagrangian information, i.e. the successive positions recorded by drifting buoys. A schematic view of the method, based on the Optimal Interpolation approach, is provided in (Fig. 1) Trajectories are forecasted in the model and compared with observed trajectories, and the Eulerian velocity is modified in order to minimize the trajectory difference. Once the velocity is corrected, the other mass variables (density or layer thickness depending on the model characteristics) are modified assuming geostrophic balance and mass conservation. Examples of results for the double gyre twin experiments in the 1.5 layer are given in (Fig. 2, Fig. 3), while the error function for the 3 layer case is shown in (Fig. 4). In all cases, approximately 20-30 drifting buoys released in the most energetic western area are considered. The results show that the method is highly effective, even for this relatively small number of data. Comparison with different methods where the exact Lagrangian nature of the data is not considered, show the advantage of the present methodology (Fig. 5). Figures: Figure 1 Schematic illustration of the Lagrangian data assimilation scheme (model grid layout is shown in the background). Observed drifter positions are shown at time t0 (point A1) and after an interval Δt (point A2). Using the model forecast, a simulated particle trajectory is computed starting from A1 at time t and ending at C1 at time t0+Δt. The Eulerian velocity field within a circle of influence is then corrected using the assimilation algorithm, which acts to minimize the distance between the observed (A2) and forecasted (C1) particle position. The corrected position is shown at C2. Figure 2 Example of Lagrangian data assimilation results for a 1.5 Miami Isopycnic Model (MICOM) in a double-gyre configuration, using the twin-experiment approach. The CONTROL run is regarded as the "true" ocean, where numerical drifters are deployed. They are then assimilated in ASSIM run, which starts from rest, Drifter trajectories (first column) and layer thickness h (contour interval 30 m) for the CONTROL run (second column) and for ASSIM (third column) are shown at selected times (t=10, 30, 90 days). The main features of CONTROL are already present in ASSIM at t=10 days, showing the effectiveness of assimilation. Figure 3 Video showing an example of Lagrangian data assimilation results for a quasi-geostrophic 1.5 model, in a setting similar to the one in Fig. 2. Figure 4 Relative error for Lagrangian assimilation as function of time for three experiments using a three-layer MICOM model. Each column refers to one experiment, characterized by the layer where the floats are launched. Each row refers to the results in a single layer. The three lines in each panel show results for the three different assimilation samplings: 12 s, 3 days, 6 days. The assimilation appears effective in all cases, and especially so for launchings in layer 1 and 3, which are more strongly correlated. Figure 5 Comparison between performance of 3 assimilation schemes: OI-PsLag (Pseudo-Lagrangian OI), KF-PsLag (Pseudo-Lagrangian Kalman filter) and OI-Lag (Lagrangian OI). The comparison is made as function of the number of drifters, using 2 basic parameters which characterize the time evolution of the error metric: the e-folding time scale (upper panel) and the residual error (lower panel). The Lagrangian assimilation performs consistently better than the pseudo-Lagrangian schemes, even the more refined Kalman filter one.