Data assimilation is the process of finding the best estimate of the current state of a system. In numerical weather prediction (NWP) this system is the atmosphere and oceans. In most operational weather forecasting centres variational data assimilation is performed using a different set of variables from the actual model variables. The transformation of variables simplifies the problem by assuming that the errors in the transformed variables are uncorrelated The validity of this hypothesis is key to the accuracy of the data assimilation. Recently a potential vorticity (PV) based set of variables has been proposed. These new variables are thought to exploit more accurately important dynamical properties of the atmosphere. Here we present new results, obtained with a simplified 1-D shallow water model, comparing the PV-based variables to the vorticity-based variables currently used at operational weather forecasting centres, including the Met Office.