Seminar A Parameterization of the Observation Error Covariance Matrix for Ensemble Filters

03/14/2012 - 11:00pm
Foothills Laboratory 2 - Main Auditorium

Emmanuel Cosme, Université Joseph Fourier, Grenoble, France

The standard Kalman filter observational update requires the inversion of the innovation error covariance matrix, what is prohibitive regarding its size. Most implementations of the Ensemble Kalman filter circumvent this difficulty assuming the diagonality of the observation error covariance matrix, that makes 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 specifying the matrix diagonal when observations errors are correlated, and how the new parameterization can help. The results also suggest that data thinning is not always justified in presence of correlated observation errors.

Thursday, March 15, 2012 (All day)
Location:  Foothills Laboratory 2 - Main Auditorium