Abstract/Summary

Data assimilation is a statistical technique that combines information from observations and a mathematical model in order to make the best estimate of a state at the current time, where the best estimate is known as the analysis. Basic 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, can cause significant systematic errors in the analysis. When bias is only present in the observations, VarBC (Variational Bias Correction) can correct for observation bias, and when bias is only present in the model, WC4DVar (Weak-Constraint 4D Variational Assimilation) can correct for model bias. However, when both observation and model biases are present, it is unknown 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. We highlight the importance of correctly specifying the background error statistics in VarBC to ensure that the analysis is more precise than the prior estimate. We then demonstrate the characteristics needed in anchor observations to effectively reduce the contamination of biases in the analysis, when one or both types of bias are corrected for. We find that the location and timing of anchor observations is important in their ability to reduce the contamination of bias, as well as having precise anchor observations. In this thesis we study the mathematical theory underpinning VarBC and WC4DVar, and demonstrate our results in a toy numerical system.