A System of Data Assimilation Based on Parallel Second Order Adjoint and Reduced Rank Kalman-Filter Methods

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Four-dimensional variational analysis (4-D Var) is the most advanced data assimilation system currently employed in operational numerical weather prediction centers. While the scheme has many strengths and advantages, one shortcoming is that the error covariance matrix is fixed. The Kalman filter (KF) approach alleviates this shortcoming by explicitly propagating the error covariance matrix for model variables so that it is flow dependent. However, the computer memory requirement for the KF approach is very large, rendering it unfeasible in operational applications. To address this problem, this project will study the feasibility of developing a reduced rank Kalman filter to be coupled with the 4-D Var system. Namely, the 4-D Var scheme will be used to perform the analysis but the background cost function will use a flow-dependent error covariance matrix for the subspace defined by the leading Hessian singular vectors. The research will be built on an advanced numerical weather prediction model for which the second order adjoint system will be developed. A comparison of the reduced rank Kalman filter with the ensemble Kalman filter (EnKF) will be made using the ECMWF analysis data and satellite observations. 4-D Var remains the leading-edge technology for data assimilation of NWP systems. This research has the potential to improve 4-D Var applications in the operational environment.