A Method for Assimilating Lagrangian Data into a Shallow-Water Equation Ocean Model

Hayder Salman

University of North Carolina at Chapel Hill

Lagrangian measurements provide a significant portion of the data collected in the ocean. Difficulties arise in their assimilation, however, since Lagrangian data are described in a moving frame of reference that do not correspond to the fixed grid locations used to forecast the prognostic flow variables. We present a new method for assimilating Lagrangian data into models of the ocean that removes the need for any commonly used approximations. We accomplish this by augmenting the state vector of the prognostic variables with the Lagrangian drifter coordinates at assimilation. We show that our method is best formulated using the Ensemble Kalman Filter resulting in an algorithm that is essentially transparent for assimilating Lagrangian data. We test the method using a set of twin experiments on the shallow-water system of equations for an unsteady double gyre flow configuration. Our numerical simulations show that our method is capable of correcting the flow even if the assimilation time interval is of the order of the Lagrangian auto-correlation time-scale (T_L) of the flow. These results clearly demonstrate the benefits of our method over other techniques which require assimilation times of 20% to 50% of (T_L), a direct consequence of the approximations introduced in assimilating
their Lagrangian data. Detailed parametric studies show that our method is particularly effective if the classical ideas of localization
developed for the Ensemble Kalman Filter are extended to our Lagrangian formulation. The method that we have developed, therefore, provides an approach that allows us to fully realize the potential of Lagrangian data for assimilation in more realistic ocean models.

This work is in collaboration with Christopher K.R.T. Jones, Leonid Kuznetsov, and Kayo Ide.

Last Update: March 25, 2005