Abstract
Predicting Earth systems is an important yet challenging problem due to
the high dimensionality, chaotic behaviour, and coupled dynamics of the
ocean, atmosphere, and other subsystems of the Earth. Numerical models
derived to predict these systems invariably contain model error due to
incomplete domain knowledge, limited capabilities of representation, and
unresolved processes due to spatial resolution. Hybrid modeling, the
pairing of a physics-driven model with a data-driven component, has
shown promise in outperforming both purely physics-driven and
data-driven approaches in predicting complex systems. Here we
demonstrate two new hybrid methods that combine temporal or
spatiotemporal models with a data-driven component that may be modally
decomposed to give insight into model error, or used to compensate a
model during prediction. These techniques are demonstrated on two Earth
system variables: coastal sea surface elevation and sea surface
temperature, which highlight that the inclusion of the data-driven
components increases the skill of predicting their evolution. Our work
demonstrates that this hybrid approach may prove valuable for: improving
models during model development, creating novel methods for data
assimilation, and enhancing predictive accuracy when available models
have significant structural error.