  In recent work, the authors have developed a generic methodology for
calibrating the noise in fluid dynamics stochastic partial differential
equations where the stochasticity was introduced to parametrize subgrid-scale
processes. The stochastic parameterization of sub-grid scale processes is
required in the estimation of uncertainty in weather and climate predictions,
to represent systematic model errors arising from subgrid-scale fluctuations.
The previous methodology used a principal component analysis (PCA) technique
based on the ansatz that the increments of the stochastic parametrization are
normally distributed.
  In this paper, the PCA technique is replaced by a generative model technique.
This enables us to avoid imposing additional constraints on the increments. The
methodology is tested on a stochastic rotating shallow water model with the
elevation variable of the model used as input data. The numerical simulations
show that the noise is indeed non-Gaussian. The generative modelling technology
gives good RMSE, CRPS score and forecast rank histogram results.
