The standard Kalman filter observational update requires the inversion of the observation error covariance matrix, which is computationally prohibitive regarding its size. Most implementations of the Ensemble Kalman filter circumvent this difficulty by assuming the diagonality of the observation error covariance matrix, making the analysis calculation numerically tractable. However, when observation errors are actually correlated spatially, such hypothesis yields too much weight to the observations, and may lead to the collapse of the ensemble. Correlations between observation errors is one motivation for data thinning, that is, a reduction of the observation data set to remove those error-correlated observations.

I will present a parameterization of the observation error covariance matrix that preserves its diagonal shape, but represents a simple first order autoregressive correlation structure of the observation errors. This parameterization is based upon an augmentation of the observation vector with gradients of observations. Numerical applications to ocean altimetry show the detrimental effects of making the matrix diagonal when observation errors are correlated, and how the new parameterization can help. The results also suggest that data thinning is not always justified in the presence of correlated observation errors.