New resaults on realistic applications! Researchers: (alphabetic order) - Chin, Mike Toshio1,4 - Griffa, Annalisa1,2 - Mariano, Arthur1 - Molcard, Anne1,2 - Özgökmen, Tamay1 - Piterbarg, Leonid3 - Taillandier, Vincent - 1RSMAS, Miami - 2CNR, Italy - 3USC, Los Angeles - 4JPL, Los Angeles Sponsors: - ONR - EEC (MFSTEP) Publications: - Molcard, A., A.C. Poje, and T.M. Özgökmen, 2006: Directed drifter launch strategies for Lagrangian data assimilation using hyperbolic trajectories. Ocean Modelling, 12, 268-289. (PDF) - Taillandier, V., A Griffa and A. Molcard, 2006: A variational approach for the reconstruction of regional scale Eulerian velocity fields from Lagrangian data. Ocean Modelling, 13 (1), 1-24. (PDF) - Taillandier V., A. Griffa, P.M. Poulain, K. Beranger, 2006: Assimilation of ARGO float positions in the North Western Mediterranean Sea and impact on ocean circulation simulations. Geophys. Res. Lett., 33, L11604, doi:10.1029/2005GL025552. (PDF) - Taillandier V., A. Griffa, 2006: Implementation of position assimilation for ARGO floats in a realistic Mediterranean ocean model and twin experiment testing. Submitted to Ocean Sciences. - 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, In Press. - 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, in press. - Molcard A., A. Griffa and T.M. Özgökmen, 2005: Lagrangian data assimilation in a multi-layer model. J. Atmos. Ocean. Tech., 22, No. 1., 70-83. (PDF) - 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. (PDF) - 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. (PDF) - 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. (PDF)

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. 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. Improvements of the method, applications to a realistic regional model and assimilation of Argo float positions in the Mediterranean Sea The metod has been improved in several ways. The velocity correction is performed along the estimated trajectory minimizing a cost function which measures the distance between the observed float position at the end of a sequence and the position of a prior trajectory advected in the model (background) velocity field. Shear drifts, such as the ones  occurring during vertical motion for Argo floats, can be taken into account in the computation of the prior trajectory. The methodology is general and can be expanded to consider other types of integrated velocity information, such as for instance information from gliders. Also the mass correction is improved using an inverse technique, where the corrected velocity profile is assumed geostrophically maintained with respect to mass variations in temperature T and salinity S, by enforcing the thermal wind and the equation of state. The method has been implemented in a realistic OPA regional model of the North-Western Mediterranean and it has been tested using the twin experiment approach (Taillandier et al., 2006a, Taillandier and Griffa, 2006). The region is characterized by a vigorous mesoscale field (with time scales longer than a few days), and by a superimposed strong inertial signal (with time scale of 19h). The assimilation is targeted to correct the mesoscale field, so that the correction applies to velocity averaged over a few days. A further improvement of the method has been introduced to take into account the presence of the higher frequency inertial fluctuations, considering them as a superimposed signal characterized by a simple feature model (Fig. 5). Figure 5: Error in the velocity field reconstruction versus sampling time. The various blue lines indicate different coverage (i.e. number of floats used), increasing toward the bottom. The red lines indicate results from the improved method, taking into account inertial oscillations. The improvement is very effective for sampling time< 1 day, (from Taillandier et al., 2006a). The method has then been applied to in-situ Argo float data (Taillandier et al., 2006b). This is the first time that position data from Argo floats are assimilated in a realistic model, and it is expected to have a significant impact for operational systems. Four Argo floats, released in the North Western Mediterranean in the context of the operational MFSTEP project, have been used during winter 2005. The results are very encouraging, showing significant and consistent changes in the ocean circulation, The velocity and mass fields are locally corrected consistently with the float drift, as shown in the example in Fig. 6 for a float in the Balearic Sea. Also, comparison with independent data of transport through the Channel of Corsica (which is not directly sampled by the floats) indicates that results are more realistic with assimilation (Fig. 7), showing a non negligible impact of the assimilation process on the large scale circulation of the basin.   Figure 6: Video showing a comparison of results from OPA model in the Balearic Sea without (left panel) and with (right panel) assimilation. Salinity (shades) and currents (arrows) at 350 m are shown, with superimposed Argo float trajectories with tails corresponding to 10 days (2 cycles). The assimilation tends to modify the fields consistently with the float drift (from Taillandier et al., 2006b).  Figure 7: Net transport trough the Corsica Channel: blue (red) line indicates the model transport without (with) assimilation, while the black line indicates the transport from current meter data (courtesy of G.P. Gasparini). The assimilation tends to bring the model transport closer to the data (from Taillandier et al., 2006b).