Using the Extended Kalman Filter with a

The formulation of the extended Kalman lter for a multilayer nonlinear quasi-geostrophic ocean circulation model is discussed. The nonlinearity in the ocean model leads to an approxima-tive equation for error covariance propagation, where the transition matrix is dependent on the state trajectory. This nonlinearity complicates the dynamics of the error covariance propagation, and eeects which are nonexistent in linear systems contribute signiicantly. The transition matrix can be split into two parts, where one part results in pure evolution of error covariances in the model velocity eld, and the other part contains a statistical correction term caused by the nonlinearity in the model. This correction term leads to a linear unbounded instability, which is caused by the statistical linearization of the nonlinear error propagation equation. Diierent ways of handling this instability are discussed. Further, nonlinear small-scale instabilities also develop, since energy is accumulated at wavelengths 22x, owing to the numerical discretization. These small-scale oscillations are removed with a Shapiro lter, and the eeect they have on the error covariance propagation is discussed. Some data assimilation experiments are performed using the full extended Kalman lter, to examine the properties of the lter. An experiment where only the rst part of the transition matrix is used to propagate the error covariances is also performed. This simpliied experiment actually performs better than the full extended Kalman lter because the unbounded instability associated with the statistical correction term is avoided.