An iterative approach for handling satellite radiance bias correction and non-gaussian observation errors in the Ensemble Kalman Filter

Variational radiance bias correction (VarBC) algorithms update the bias correction coefficients in the variational minimization process by treating them as part of the control vector with a simple, static background-error specification, assuming that errors in the bias coefficients are not correlated with other variables. Variational quality control algorithms (VarQC) incorporate the effect of 'heavy-tailed', non-Gaussian observation error distributions through the addition of an extra term in the cost function. Both VarBC and VarQC are not straightforward to mimic in an Ensemble Kalman Filter (EnKF) assimilation system, because the Kalman Gain computation in the EnKF requires Gaussian observation errors and flow-adaptive, ensemble-estimated background error covariances for all variables. In the case of VarBC, ensemble-based estimates of radiance bias coefficient background errors is problematic, since there is no a-priori reason to expect cross-covariances between bias coefficent errors and errors in other variables should be non-zero. This, together with the fact that there is usually no dynamical model for the evolution of the bias coefficients, means that ensemble-based estimates of bias coefficient background errors are likely to be dominated by sampling noise.

Here we present an iterative method mimicing VarBC and VarQC in the EnKF, which we refer to as EnKF-QC and EnKF-BC. Both methods require updates of ensemble mean observation priors (O - B) values during the iteration. In the case of EnKF-QC, these updated values are used to iteratively estimate the probablity of a "gross" observation error. In the case of EnKF-BC, the updated values are used to update the radiance bias correction coefficients. If the process is iterated until convergence, it is algorithmically identical to VarBC and VarQC.

We demonstrate the use of EnKF-BC and EnKF-QC in an EnKF assimilation system based upon the NCEP Global Forecast System (GFS). The EnKF-BC is shown to perform just as well for satellite radiances as the VarBC component of the NCEP Global Statistical Interpolation (GSI) variational system. The EnKF-QC system is demonstrated by assimilating only surface pressure observations for the month of December, 1999. For the two severe storms that battered Europe on Dec 26 and 27th, the EnKF-rQC was able to "redeem" several important observations that were rejected by a simple ensemble-based background check that uses assumes Gaussian observation errors.