Balanced multivariate model errors of an intermediate coupled model for ensemble Kalman filter data assimilation

The ensemble Kalman filter (EnKF) depends on a set of ensemble forecasts to calculate the background error covariances. Without model error perturbations and the inflation of forecast ensembles, the spread of the ensemble forecasts can collapse rapidly. There are several ways to generate model perturbations, i.e., perturbations in model parameters/parameterizations, perturbations in the forcing fields of the model and adding some error terms to the right‐hand side of the model equations. In this paper, we focus on the “adding model error terms” approach, which utilizes a first‐order Markov chain model. This approach is suitable to those unforced models, such as the coupled atmosphere‐ocean models. However, for a multivariate model, the balance between different model variables could be an important issue in building its model‐error model. In this paper, we focus on building a balanced error model for an intermediate coupled model for El Niño–Southern Oscillation (ENSO) predictions. A simple approach to build such a model‐error model is proposed on the basis of the multivariate empirical orthogonal functions method. EnKF data assimilation experiments with different configurations of multivariate model error treatments (no model errors, unbalanced and balanced model errors) are performed using realistic sea surface temperature (SST) and sea level (SL) observations. Results show that it is necessary to develop balanced, multivariate model‐error models in order to successfully assimilate both SST and SL observations. The hindcasts initialized from these different assimilation experiment results also demonstrate that the balanced model errors can yield more balanced initial conditions that lead to improved predictions of ENSO events.