Data assimilation using a climatologically augmented local ensemble transform Kalman filter

Ensemble data assimilation methods are potentially attractive because they provide a computationally affordable (and computationally parallel) means of obtaining flow-dependent background-error statistics. However, a limitation of these methods is that the rank of their flow-dependent background-error covariance estimate, and hence the space of possible analysis increments, is limited by the number of forecast ensemble members. To overcome this deficiency ensemble methods typically use empirical localisation, which allows more degrees of freedom for the analysis increment by suppressing spatially distant background correlations. The method presented here improves the performance of an Ensemble Kalman filter by increasing the size of the ensemble at analysis time in order to boost the rank of its background-error covariance estimate. The additional ensemble members added to the forecast ensemble at analysis time are created by adding a collection of 'climatological' perturbations to the forecast ensemble mean. These perturbations are constant in time and provide state space directions, possibly missed by the dynamically forecasted background ensemble, in which the analysis increment can correct the forecast mean based on observations. As the climatological perturbations are calculated once, there is negligible computational cost in obtaining the additional ensemble members at each analysis cycle. Included here are a formulation of the method, results of numerical experiments conducted with a spatiotemporally chaotic model in one spatial dimension and discussion of possible future extensions and applications. The numerical tests indicate that the method presented here has significant potential for improving analyses and forecasts.