The effective use of anchor observations in variational bias correction in the presence of model bias

Abstract

In numerical weather prediction, satellite radiance observations have a significant impact on forecast skill. However, radiance observations must usually be bias‐corrected for the satellite data to have a positive impact. Many operational centres use variational bias correction (VarBC) to correct the observation biases, but VarBC assumes that there is no model bias within the system. As model biases are often non‐negligible, unbiased observations (anchor observations) are known to play an important role in VarBC to reduce the contamination of model bias. However, more work is needed to understand what properties the network of anchor observations needs to have to reduce most contamination of model bias. We derive analytical expressions to show the sensitivity of the bias correction to the anchor observations and the expected value of the error in the analysed bias‐correction coefficients. We find that the precision and location of the anchor observations are important in reducing the contamination of model bias in the estimate of observation bias. Anchor observations work best at reducing the effect of model bias when they observe the same state variables as the bias‐corrected observations. When this is not the case, strong background‐error correlations become more important, as they allow more information about the model bias to be passed from the anchor observations to the bias‐corrected observations. The model bias observed by both the biased and anchor observations must be similar, otherwise the anchor observations cannot reduce the contamination of model bias in the observation‐bias correction. These results show that, in operational systems, regions with sparse anchor observations could be more susceptible to model biases within the radiance observation‐bias corrections. We demonstrate these results in a series of idealised numerical experiments that use the Lorenz 96 model as a simplified model of the atmosphere.