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.
Highlights
For a data assimilation scheme to produce an optimalData assimilation techniques combine observations with a estimate of the state, the error covariances associated with the observations and background must be well understood model prediction of the state, known as the background, to and correctly specified (Houtekamer and Mitchell, 2005).provide a best estimate of the state, known as the analysis
We find that using the estimated correlated observation error in the assimilation improves the analysis
To regularise the estimated error covariance matrix Rest are evolved using the perfect model equations but obtained from the ETKFR, we find a vector ce 2 R1ÂNp beginning from perturbed initial conditions
Summary
Data assimilation techniques combine observations with a estimate of the state, the error covariances associated with the observations and background must be well understood model prediction of the state, known as the background, to and correctly specified (Houtekamer and Mitchell, 2005). After the initial ensemble members, The DBCP diagnostic described in Desroziers et al forecast error covariance matrix and observation error (2005) makes use of the background (forecast) and analysis covariance matrix are specified, the filter is split into two innovations to provide an estimate of the observation stages: a spin-up phase where the matrix R remains static error covariance matrix. Step 3 Á Using the ensemble mean and the background estimate of the observation error covariance matrix is an innovations at time tn, calculate and store dbn 1⁄4 yn À Hxfn. The number of samples available will be limited and, the estimated observation error centring technique is required in order to preserve the covariance matrix will not be full rank In this case, it analysis ensemble mean.
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