A multi-model ensemble Kalman filter for data assimilation and forecasting

Abstract

Data assimilation (DA) aims to optimally combine model forecasts and noisy observations. Multimodel DA generalizes the variational or Bayesian formulation of the Kalman filter, and we prove here that it is also the minimum variance linear unbiased estimator. However, previous implementations of this approach have not estimated the model error, and have therewith not been able to correctly weight the separate models and the observations. Here, we show how multiple models can be combined for both forecasting and DA by using an ensemble Kalman filter with adaptive model error estimation. This methodology is applied to the Lorenz96 model, and it results in significant error reductions compared to the best model and to an unweighted multi-model ensemble.

Deep Learning-Enhanced Ensemble-Based Data Assimilation for High-Dimensional Nonlinear Dynamical Systems

“…As a test case, the proposed hybrid framework has been applied to EnKF, a specific ensemble-based DA algorithm that is used with Gaussian observation noise. However, one can readily extend this hybrid framework to other types of novel extensions of regular EnKF, e.g., multi-model EnKF [51] or other ensemble-based DA algorithms, e.g., particle filters. Particle filters are especially useful for systems with strong non-Gaussian observation noise.…”

Asymptotic behavior of the forecast-assimilation process with unstable dynamics

“…The models can differ by their spatial resolution, by the physical processes taken into consideration and by the numerical discretization of the PDEs governing them. Multi-model DA is discussed in some detail by Bach and Ghil, 100 including the issue of model error growth in this situation. It would be of considerable interest to extend the rigorous results herein to such a broader setting.…”