Sigma-Point Kalman Filter Data Assimilation Methods for Strongly Nonlinear Systems

Performance of an advanced, derivativeless, 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 ensemble Kalman filter (EnKF) schemes. Three particular cases—namely, the state, parameter, and joint estimation of states and parameters from a set of discontinuous noisy observations—are studied. The problems associated with the use of tangent linear model (TLM) or 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 model is proposed and investigated for higher-dimensional systems. A low-dimensional Lorenz 1963 model and a higher-dimensional Lorenz 1995 model are used as the test beds for data assimilation experiments. The results of SPKF data assimilation schemes are compared with those of standard EKF and EnKF, in which 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 showed 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.