HR: 14:40h
AN: H13I-05    [Abstracts]
TI: A Reduced Extended Kalman Filter Method For Data Assimilation And Parameter Optimization
AU: * Kao, C J
EM: kao@lanl.gov
AF: Los Alamos National Lab, MS T087, Los Alamos National Lab, Los Alamos, NM 87545, United States
AB: This work is an extension of our two recent papers [Kao et al., Data assimilation with an extended Kalman filter for an impact-produced shock-wave study, J. Comp. Phys., 196 (2004), 705-723, and Kao et al., Estimating model parameters for an impact-produced shock-wave simulation: Optimal use of partial data with the extended Kalman filter, J. Comp. Phys., 214 (2006), 725-737 ] about the applications of the extended Kalman filter (EKF) to data assimilation in predictive codes. We have shown through the above two studies that the EKF method successfully estimates the evolving model state variables as well as model parameters of a shock-wave system by merging single-point pressure data into an Euler-equations computer code. We here intend to introduce a reduced EKF for the same purposes in terms of data assimilation and parameter optimization, but with a much smaller computational cost so that the applications of EKF to multi-dimensional realistic problems can be made possible. One of the distinctive features of EKF is that, as the system evolves forward in time, the EKF algorithm tracks the time-dependent error-covariance matrix of the model's state variables and parameters based on a consistent tangent-linear approximation of the model dynamics. When data becomes available at one instant in time, the update of the model state variables and parameters is achieved through a functional form of the linear merger of the model prediction and the data, subjective to the minimization of the trace of the error-covariance matrix of the model state variables and parameters. It, however, has been a concern that the calculation for the time evolution of the error-covariance matrix in applying EKF is computationally demanding and prohibitively expensive for real multi-dimensional problems. Several simplified approaches of EKF have been proposed to reduce the computational burden. This current study was actually motivated by Dee's work [Dee, P. D., 1991: Simplification of the Kalman filter for meteorological data assimilation. Q. J. Meteorol. Soc., 117, 365-384] and the results revealed in Evensen's study [Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods for forecast error statistics. J. Geophys. Res., 99, C5, 10143-10162]. In Kao et al. (2006), we were aware of that the errors associated with the model parameters are the main source of the total variances of the model state variables. Our simplification presented here somewhat resembles to the approach by Dee but takes it to an extreme by not considering the sensitivity due to the internal dynamics in the error propagation at all. Our method operates on the formalism in Kao et al. (2006) which is based upon an augmentation that the model parameters are treated as a part of the state variable vector, where the model parameters receive no influence from model dynamics and are only subject to a system error. The two groups within this augmented state vector would create four blocks in the error-covariance matrix among which a well-defined inter-relationship associated with error propagation can be derived. The test of the reduced EKF against the full EKF using the shock-wave model and cloud microphysics model will be presented. With cost effectiveness up to orders of magnitudes, the results are also satisfactory in terms of the assimilated field variables and optimized model parameters.
DE: 3275 Uncertainty quantification (1873)
SC: Hydrology [H]
MN: 2007 Fall Meeting