Estimating correlated observation error statistics using an ensemble transform Kalman filter

Abstract

For certain observing types, such as those that are remotely sensed, the observation errors are correlated and these correlations are state- and time-dependent. In this work, we develop a method for diagnosing and incorporating spatially correlated and time-dependent observation error in an ensemble data assimilation system. The method combines an ensemble transform Kalman filter with a method that uses statistical averages of background and analysis innovations to provide an estimate of the observation error covariance matrix. To evaluate the performance of the method, we perform identical twin experiments using the Lorenz '96 and Kuramoto-Sivashinsky models. Using our approach, a good approximation to the true observation error covariance can be recovered in cases where the initial estimate of the error covariance is incorrect. Spatial observation error covariances where the length scale of the true covariance changes slowly in time can also be captured. We find that using the estimated correlated observation error in the assimilation improves the analysis.

• data assimilation
• correlated observation errors
• ensemble transform Kalman filter

6. Acknowledgements

This work was funded by the European Space Agency (ESA) and the NERC National Centre for Earth Observation (NCEO) and by the Met Office through a CASE studentship. We also thank the three anonymous reviewers whose comments were greatly appreciated. The ETKFR code is available at www.esa-da.org.