On the robustness of methods to account for background bias in data assimilation to uncertainties in the bias estimates

Fundamental to the theory of data assimilation is that the data (i.e., the observations and the background) provide an unbiased estimate of the true state. There are many situations when this assumption is known to be far from valid; and without bias correction (BC), significant biases will be present in the resulting analysis. Here, we compare two methods to account for biases in the background that do not require a change to the data assimilation algorithm: explicit BC and covariance inflation (CI). When the background bias is known perfectly it is clear that the BC method outperforms the CI method, in that it can completely remove the effect of the background bias whereas the CI method can only reduce it. However, the background bias can only be estimated when unbiased observations are available. A lack of unbiased observations means that the estimate of the background bias will always be subject to sample errors and structural errors due to poor assumptions about how the bias varies in space and time. Given these difficulties in estimating the background bias, the robustness of the two methods in producing an unbiased analysis is studied within an idealised linear system. It is found that the CI method is much less sensitive to errors in the background bias estimate and that a smooth estimate of the bias is crucial to the success of the BC method. However, the CI method is more sensitive to uncorrected biases in the observations.