Sigma-point Kalman filter data assimilation methods for strongly nonlinear dynamical models.

Performance of an advanced derivative-less, sigma-point Kalman filter (SPKF) data assimilation scheme in a strongly nonlinear dynamical model is investigated. The SPKF data assimilation scheme is compared against standard Kalman filters such as the extended Kalman filter (EKF) and the ensemble Kalman filter (EnKF) schemes. Three particular cases, namely the state estimation, parameter estimation, and joint estimation of states and parameters from a set of discontinuous noisy observations are studied. The problems associated with the use of the tangent linear model (TLM) or the Jacobian when using standard Kalman filters are eliminated when using SPKF data assimilation algorithms. Further, the constraints and issues of SPKF data assimilation in real ocean or atmospheric models are emphasized. A reduced sigma-point subspace approach is proposed and investigated for higher dimensional systems. A low dimensional Lorenz '63 model and a higher dimensional Lorenz '95 model are used as the test-bed for data assimilation experiments. The results of the SPKF data assimilation schemes are compared with those of the standard EKF and EnKF where a highly nonlinear chaotic case is studied. It is shown that the SPKF is capable of estimating the model state and parameters with better accuracy than EKF and EnKF. Numerical experiments show that in all cases, the SPKF can give consistent results with better assimilation skills than EnKF and EKF, and can overcome the drawbacks associated with the use of EKF and EnKF. --P.iii-iv.