  Near-term prediction of the structured spatio-temporal processes driving our
climate is of profound importance to the safety and well-being of millions, but
the prounced nonlinear convection of these processes make a complete
mechanistic description even of the short-term dynamics challenging. However,
convective transport provides not only a principled physical description of the
problem, but is also indicative of the transport in time of informative
features which has lead to the recent successful development of ``physics
free'' approaches to the now-casting problem. In this work we demonstrate that
their remains an important role to be played by physically informed models,
which can successfully leverage deep learning (DL) to project the process onto
a lower dimensional space on which a minimal dynamical description holds. Our
approach synthesises the feature extraction capabilities of DL with physically
motivated dynamics to outperform existing model free approaches, as well as
state of the art hybrid approaches, on complex real world datasets including
sea surface temperature and precipitation.
