Constrained adaptive bias correction for satellite radiance assimilation in the ECMWF 4D-Var system

This memorandum investigates the use of a modified version of Variational Bias Correction in which a constraint is imposed on the size of the bias correction by adding a new term to the variational cost function (Constrained Variational Bias Correction, CVarBC). This novel approach is aimed at situations where significant model bias has previously led to problems with variational bias corrections drifting over time, prompting ad-hoc decisions to provide anchoring information through assimilating certain observations without bias corrections. Two such situations are investigated: upper stratospheric temperature observations from AMSU-A which are presently anchored through assimilating channel 14 without a bias correction; and ozone observations from hyperspectral infrared instruments which are presently anchored by assimilating one channel per instrument without bias correction.

In both situations, CVarBC is able to successfully constrain drift in the bias corrections, while at the same time being able to correct observational bias pattern that were previously ignored when these observations were assimilated without bias correction (e.g., inter-satellite biases or scan-dependent biases in the case of AMSU-A). This leads to a better consistency of the analysis with other observations. In the case of the ozone channels, CVarBC can be used to avoid assuming that single selected channels are unbiased, by instead weakly constraining the bias correction for all ozone-sensitive channels from hyperspectral infrared observations. The new approach leads to a more robust system with benefits for maintenance, particularly for reanalysis applications.