The role of anchor observations in disentangling observation and model bias corrections in 4DVar

Data assimilation theory relies on the assumption that the background, model, and observations are unbiased. However, this is often not the case and, if biases are left uncorrected, this can cause significant systematic errors in the analysis. When bias is only present in the observations, Variational Bias Correction (VarBC) can correct for observation bias, and when bias is only present in the model, Weak-Constraint 4D Variational Assimilation (WC4DVar) can correct for model bias. However, when both observation and model biases are present, it can be very difficult to understand how the different bias correction methods interact, and the role of anchor (unbiased) observations becomes crucial for providing a frame of reference from which the biases may be estimated. This work presents a systematic study of the properties of the network of anchor observations needed to disentangle between model and observation biases when correcting for one or both types of bias in 4DVar.

We extend the theory of VarBC and WC4DVar to include both biased and anchor observations, to find that the precision and timing of the anchor observations are important in reducing the contamination of model/observation bias in the correction of observation/model bias. We show that anchor observations have the biggest impact in reducing the contamination of bias when they are later in the assimilation window than the biased observations, as such, operational systems that rely on anchor observations that are earlier in the window will be more susceptible to the contamination of model and/or observation biases. We also compare the role of anchor observations when VarBC/WC4DVar/both are used in the presence of both observation and model biases. We find that the ability of VarBC to effectively correct for observation bias when model bias is present, is very dependent on precise anchor observations, whereas correcting model bias with WC4DVar or correcting for both biases performs reasonably well regardless of the precision of anchor observations (although more precise anchor observations reduces the bias in the state analysis compared with less precise anchor observations for all three cases). This demonstrates that, when it is not possible to use anchor observations, it may be better to correct for both observation and model biases, rather than relying on only one bias correction technique.

We demonstrate these results in a series of idealised numerical experiments that use the Lorenz 96 model as a simplified model of the atmosphere.