Forward sensitivity based approach to Lagrangian data assimilation

Lagrangian instruments such as drifters and floats are increasingly deployed across the oceans of the world to obtain information about various physical quantities of interest related to circulation and their impact on weather and climate. A distinguishing feature of the Lagrangian data is that the position of the floats are highly nonlinear function of the state variables of the circulation model. The problem of assimilating the Lagrangian data into the models has received considerable attention. Earlier methods include applications of optimum interpolation, Kalman filters and particle filter based approach [1]

In this paper we apply a recently developed class of method known as the forward sensitivity method (FSM) which is based on the evolution of the forward sensitivity of the states of the model with respect to the control variables [2]. This method can be shown to be a dual of the classical adjoint based 4D Var method and does not need the development of the adjoint. FSM directly computes the corrections to the control as a solution to linear inverse problems that exploits the forward sensitivity information and the forecast error.

We demonstrate the power of this approach by applying it to the spectral version of the linearized shallow-water model.

[1] A. Apte, C. K. R.T. Jones and A. M. Stuart (2008) "A Bayesian approach to Lagrangian data assimilation", Tellus, 60A, 336-347

[2] S. Lakshmivarahan and John M. Lewis (2010) “Forward Sensitivity Based Approach to Dynamic Data Assimilation”, Advances in Meteorology, Volume 2010, Article ID 375615, doi 1155/2010/375615