The stochastic variational approach for geophysical fluid dynamics was
introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving
stochastic parameterisations for unresolved scales. This paper applies the
variational stochastic parameterisation in a two-layer quasi-geostrophic model
for a beta-plane channel flow configuration. We present a new method for
estimating the stochastic forcing (used in the parameterisation) to approximate
unresolved components using data from the high resolution deterministic
simulation, and describe a procedure for computing physically-consistent
initial conditions for the stochastic model. We also quantify uncertainty of
coarse grid simulations relative to the fine grid ones in homogeneous (teamed
with small-scale vortices) and heterogeneous (featuring horizontally elongated
large-scale jets) flows, and analyse how the spread of stochastic solutions
depends on different parameters of the model. The parameterisation is tested by
comparing it with the true eddy-resolving solution that has reached some
statistical equilibrium and the deterministic solution modelled on a
low-resolution grid. The results show that the proposed parameterisation
significantly depends on the resolution of the stochastic model and gives good
ensemble performance for both homogeneous and heterogeneous flows, and the
parameterisation lays solid foundations for data assimilation.