Resilience of hybrid ensemble/3DVAR analysis schemes to model error and ensemble covariance error

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.