The Model Forest Ensemble Kalman Filter

Traditional data assimilation fuses information obtained from the propagation of a single physics-based model with information obtained from real-world observations, in order to better estimate the true state or parameters of some natural process. However, in many situations, multiple simulation models that describe the same physical phenomenon are available. Such models can come from different sources. On one hand there are theory-guided models constructed from first physical principles, while on the other there are data-driven models are constructed from snapshots of high-fidelity information. While sequences of physics-based models of different fidelity levels can be organized in linear hierarchies, collections of models built using different approaches do not fit this simple structure. This work develops a coherent methodology to employ this collection of models in data assimilation by generalizing the idea of model hierarchies to model forests. Here model forests represent collections of models organized in a manner that captures various relationships between them. We generalize the multifidelity ensemble Kalman filter—which operates with linear model hierarchies—to the model forest ensemble Kalman filter through a generalized theory of linear control variates. This new filter can coherently employ different types of models, and allows for much more freedom when balancing analysis accuracy and computational speed. Numerical experiments with a high-fidelity quasi-geostrophic model and two of its low-fidelity reduced-order models illustrate the benefits of the model forest approach.