The importance of the timing of anchor observations in 4D variational bias correction: Theory and idealised experiments

Abstract Variational bias correction (VarBC), by correcting for significant biases in satellite radiances, is a key component of many modern numerical weather prediction (NWP) systems. However, there is a risk that VarBC may be contaminated by biases present in the assimilating model, inducing a bias in the analysis and in turn reducing forecast skill. Due to the limited reliability of metrics for assessing the value of anchor observations in NWP, this article instead takes the approach of developing and exemplifying new theory to understand how to optimise the impact of anchor observations (assimilated observations with negligible bias) to minimise the contamination of model bias in VarBC. This is important because the number and variety of satellite radiances assimilated is expected to increase in the future. Therefore, the new theory presented can guide how the anchor observation network should also be developed. The new insight may also be crucial in optimising the anchoring effect of historically sparse observations in the context of reanalyses. We present this new theory and theory‐driven examples to show that the timing of the anchor observations can impact the accuracy of VarBC substantially. Anchor observations towards the end of the assimilation window provide more information about the accumulated model bias and offer a stronger constraint on VarBC, as such VarBC is more successful at quantifying and correcting the radiance biases only. However, precise anchor observations at the end of the window can increase the contamination of the initial state analysis by model bias. The interaction between the model bias contamination of VarBC and the initial state analysis is studied in idealised cycled data assimilation experiments using the Lorenz 96 model, highlighting the importance of VarBC for an accurate analysis of the state.