  Traditional data assimilation uses information obtained from the propagation
of one physics-driven model and combines it with information derived from
real-world observations in order to obtain a better estimate of the truth of
some natural process. However, in many situations multiple simulation models
that describe the same physical phenomenon are available. Such models can have
different sources. On one hand there are theory-guided models are constructed
from first physical principles, while on the other there are data-driven models
that are constructed from snapshots of high fidelity information. In this work
we provide a possible way to make use of this collection of models in data
assimilation by generalizing the idea of model hierarchies into model forests
-- collections of high fidelity and low fidelity models organized in a groping
of model trees such as to capture various relationships between different
models. We generalize the multifidelity ensemble Kalman filter that previously
operated on model hierarchies into the model forest ensemble Kalman filter
through a generalized theory of linear control variates. This new filter allows
for much more freedom when treading the line between accuracy and speed.
Numerical experiments with a high fidelity quasi-geostrophic model and two of
its low fidelity reduced order models validate the accuracy of our approach.
