Resilience of Hybrid Ensemble/3DVAR Analysis Schemes to Model Error and Ensemble Covariance Error

Abstract

Previous idealized numerical experiments have shown that a straightforward augmentation of an isotropic error correlation matrix with an ensemble-based error correlation matrix yields an improved data assimilation scheme under certain conditions. Those conditions are (a) the forecast model is perfect and (b) the ensemble accurately samples the probability distribution function of forecast errors. Such schemes blend characteristics of ensemble Kalman filter analysis schemes with three-dimensional variational data assimilation (3DVAR) analysis schemes and are called hybrid schemes. Here, we test the robustness of hybrid schemes to model error and ensemble inaccuracy in the context of a numerically simulated two-dimensional turbulent flow. The turbulence is produced by a doubly periodic barotropic vorticity equation model that is constantly relaxing to a barotropically unstable state. The types of forecast models considered include a perfect model, a model with a resolution error, and a model with a parameterization error. The ensemble generation schemes considered include the breeding scheme, the singular vector scheme, the perturbed observations system simulation scheme, a gridpoint noise scheme, and a scheme based on the ensemble transform Kalman filter (ETKF). For all combinations examined, it is found that the hybrid schemes outperform the 3DVAR scheme. In the presence of model error a perturbed observations hybrid and a singular vector hybrid perform best, though the ETKF ensemble is competitive.