  Stochastic partial differential equations have been used in a variety of
contexts to model the evolution of uncertain dynamical systems. In recent
years, their applications to geophysical fluid dynamics has increased
massively. For a judicious usage in modelling fluid evolution, one needs to
calibrate the amplitude of the noise to data. In this paper we address this
requirement for the stochastic rotating shallow water (SRSW) model. This work
is a continuation of [LvLCP23], where a data assimilation methodology has been
introduced for the SRSW model. The noise used in [LvLCP23] was introduced as an
arbitrary random phase shift in the Fourier space. This is not necessarily
consistent with the uncertainty induced by a model reduction procedure. In this
paper, we introduce a new method of noise calibration of the SRSW model which
is compatible with the model reduction technique. The method is generic and can
be applied to arbitrary stochastic parametrizations. It is also agnostic as to
the source of data (real or synthetic). It is based on a principal component
analysis technique to generate the eigenvectors and the eigenvalues of the
covariance matrix of the stochastic parametrization. For SRSW model covered in
this paper, we calibrate the noise by using the elevation variable of the
model, as this is an observable easily obtainable in practical application, and
use synthetic data as input for the calibration procedure.
