  We introduce a physically relevant stochastic representation of the rotating
shallow water equations. The derivation relies mainly on a stochastic transport
principle and on a decomposition of the fluid flow into a large-scale component
and a noise term that models the unresolved flow components. As for the
classical (deterministic) system, this scheme, referred to as modelling under
location uncertainty (LU), conserves the global energy of any realization and
provides the possibility to generate an ensemble of physically relevant random
simulations with a good trade-off between the model error representation and
the ensemble's spread. To maintain numerically the energy conservation feature,
we combine an energy (in space) preserving discretization of the underlying
deterministic model with approximations of the stochastic terms that are based
on standard finite volume/difference operators. The LU derivation, built from
the very same conservation principles as the usual geophysical models, together
with the numerical scheme proposed can be directly used in existing dynamical
cores of global numerical weather prediction models. The capabilities of the
proposed framework is demonstrated for an inviscid test case on the f-plane and
for a barotropically unstable jet on the sphere.
