  In numerical modeling of the Earth System, many processes remain unknown or
ill represented (let us quote sub-grid processes, the dependence to unknown
latent variables or the non-inclusion of complex dynamics in numerical models)
but sometimes can be observed. This paper proposes a methodology to produce a
hybrid model combining a physical-based model (forecasting the well-known
processes) with a neural-net model trained from observations (forecasting the
remaining processes). The approach is applied to a shallow-water model in which
the forcing, dissipative and diffusive terms are assumed to be unknown. We show
that the hybrid model is able to reproduce with great accuracy the unknown
terms (correlation close to 1). For long term simulations it reproduces with no
significant difference the mean state, the kinetic energy, the potential energy
and the potential vorticity of the system. Lastly it is able to function with
new forcings that were not encountered during the training phase of the neural
network.
