University of North Carolina at Chapel Hill

Difficulties in the assimilation of Lagrangian data arise because the state of the prognostic model is generally described in terms of Eulerian variables computed on a fixed grid in space, as a result there is no direct connection between the model variables and Lagrangian observations that carry time-integrated information. I will present a method for assimilating Lagrangian tracer positions, observed at discrete times, directly into the model. The idea is to augment the model with tracer advection equations and to track the correlations between the flow and the tracers via the extended Kalman filter. The method is applied to point vortex flows with a Gaussian noise term that is added to simulate unresolved processes. Numerical experiments demonstrate successful tracking for systems of two and four (in regular and chaotic regime) vortices provided the observations are reasonably frequent and accurate and the system noise level is not too high. Taking into account Lagrangian nature of drifter observations allows to extract maximal information about the flow, as a result the scheme performs better than an alternative indirect approach that assimilates flow velocity estimated from consecutive tracer positions. When the noise levels are increased the scheme is prone to abrupt divergence caused by the passage of tracers through the neighborhoods of saddle-points of the velocity field. Analysis of the filter malfunction shows that it is caused by the breakdown of the tangent linear approximation (that is used to predicted the model error covariance matrix) due to the fast exponential error growth in the vicinity of a saddle.