**Uncertainty Quantification Working Group**

May 2, 11:30 AM, CNLS Conf. Room, TA-3, Bldg. 1690

## Data assimilation with extended Kalman filter

Jim Kao, X-4

### Abstract

Data assimilation attempts to optimally determine the state of a physical system from a
limited number of observations. The extended Kalman filter (EKF) is characterized by
solving the full nonlinear state evolution, and by using successive linearizations about
the currently estimated state to advance the error-covariance matrix in time. It thus
provides a consistent first-order approximation to the optimal estimate of the nonlinear
state at the observation time. The EKF method combines the observations and modeled
state variables to obtain the "assimilated" field variables with an optimal gain matrix
coefficient, which is a function of the forecast error-covariance and the observational
errors. The assimilated fields can be used as initial conditions for further model
prediction. They can also be used inside of a model as a forcing function through a form
of Newtonian nudging. In this talk, examples of applying EKF to atmospheric and oceanic
systems will be given. An ongoing experiment of using EKF in shock related physical
systems will be introduced.