Abstract
ABSTRACTIn recent years, hybrid data-assimilation methods which avoid computation of tangent linear and adjoint models by using ensemble 4-dimensional cross-time covariances have become a popular topic in Numerical Weather Prediction. 4DEnsembleVar is one such method. In spite of its capabilities, its application can sometimes become problematic due to the not-trivial task of localising cross-time covariances. In this work we propose a formulation that helps to alleviate such issues by exploiting the presence of model error, i.e. a weak-constraint 4DEnsembleVar. We compare the weak-constraint 4DEnsembleVar to that of other data-assimilation methods. This is part II of a two-part paper. In part I, we describe the 4DEnsembleVar framework and problems with localised temporal cross-covariances associated with this method are discussed and illustrated on the Korteweg de Vries model. We also introduce our weak-constraint 4DEnsemble-Var formulation and show how it can alleviate—at least partially—the problem of having low-quality time cross-covariances. The second part of this paper deals with experiments on larger and more complicated models, namely the Lorenz 1996 model and a modified shallow-water model with simulated convection, both of them under the presence of model error. We investigate the performance of weak-constraint 4DEnsembleVar against strong-constraint 4DEnsembleVar (both with and without localisation) and other traditional methods (4DVar and the Local Ensemble Transform Kalman Smoother). Using the analysis root mean square error (RMSE) as a metric, these methods have been compared considering observation density (in time and space), observation period, ensemble sizes and assimilation window length. In this part we also explain how to perform outer loops in the EnVar methods. We show that their use can be counter-productive if the presence of model error is ignored by the assimilation method. We show that the addition of a weak-constraint generally improves the RMSE of 4DEnVar in cases where model error has time to develop, especially in cases with long assimilation windows and infrequent observations. We have assumed good knowledge of the statistics of this model error.
Highlights
This is the second part of a study to introduce a new hybrid ensemble-variational (EnVar) data assimilation (DA) method, which takes into consideration the presence of model error
Using the analysis root mean square error (RMSE) as a metric, these methods have been compared considering observation density, observation period, ensemble sizes and assimilation window length. In this part we explain how to perform outer loops in the EnVar methods. We show that their use can be counter-productive if the presence of model error is ignored by the assimilation method
Our experiments on the Korteweg de Vries (KdV) (Part I) and the Lorenz 1996 (L96) models showed how incorporating the WC can help alleviate problems which occur in SC4DEnVar, and we investigate whether these results still stand on the larger, more realistic and non-linear shallow-water equation (SWE) system
Summary
This is the second part of a study to introduce a new hybrid ensemble-variational (EnVar) data assimilation (DA) method, which takes into consideration the presence of model error We have denominated this method a weak-constrained 4DEnsembleVar (WC4DEnVar). We showed that our method distributes the analysis increments over more time instants in the assimilation window (other than the initial time), and it alleviates—at least partially—the problems generated by wrongly localised time cross-covariances. For this purpose we used the Korteweg de Vries (KdV) model for the perfect evolution of a coherent structure (a soliton)
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