A new strategy for optimal drifter deployment using Lagrangian data assimilation method

We present a new approach to an observing system design for Lagrangian data as the optimal drifter deployment strategy. Because Lagrangian data contain time-integrated information of the velocity field, if assimilated correctly, they can significantly help improve ocean data assimilation systems which may rely on observations of temperature, salinity, and sea surface height.

Our strategy for optimal drifter deployment is built on the Lagrangian data assimilation (LaDA) method that uses the augmented state representation. In other words, the model forecasts the drifter positions corresponding to the future observations in addition to the ocean state. Thus our LaDA method assimilates the Lagrangian data directly into the ocean state variables through their error correlations while eliminating the need for any conventionally used approximation in assimilating the Lagrangian data.

As a first step towards realistic applications of the LaDA method, we formulate it as an ensemble Kalman filter (EnKF) and test on the basin-scale shallow-water ocean circulation model as the observing system simulation experiments (OSSEs). We show that the LaDA method is capable of estimating the ocean flow correctly using a small number of drifters. The assimilation time interval can be of the order of the Lagrangian correlation time scale of the flow. This clearly demonstrates the benefits of our LaDA method over other methods which require shorter assimilation periods. Our LaDA method is particularly effective if the localization idea developed for EnKF is extended for the Lagrangian augmentation.

The Lagrangian augmentation also allows us to use dynamical systems theory for design of the comprehensive observing system. Our strategy is to first construct a flow template through analysis of Lagrangian dynamics. This template cannot be obtained correctly by analysis of the instantaneous Eulerian velocity or streamfunction field. Detection of the hyperbolic trajectories in the flow field is particularly of essence because they are associated with the special material lines called “invariant manifolds.” The invariant manifolds provide a global map of the fate and past for the Lagrangian particles. Our strategy is then to deploy the drifters according to the flow template. This strategy is tested using the basin-scale shallow-water ocean model. The results show that, by judicious choice of deployment location and timing based on the flow template, the LaDA method can efficiently estimate both the basin-scale circulation and local coherent structures.