  A resolution-independent data-driven stochastic parametrization method for
subgrid-scale processes in coarsened fluid descriptions is proposed. The method
enables the inclusion of high-fidelity data into the coarsened flow model,
thereby enabling accurate simulations also with the coarser representation. The
small-scale parametrization is introduced at the level of the Fourier
coefficients of the coarsened numerical solution. It is designed to reproduce
the kinetic energy spectra observed in high-fidelity data of the same system.
The approach is based on a control feedback term reminiscent of continuous data
assimilation. The method relies solely on the availability of high-fidelity
data from a statistically steady state. No assumptions are made regarding the
adopted discretization method or the selected coarser resolution. The
performance of the method is assessed for the two-dimensional Euler equations
on the sphere. Applying the method at two significantly coarser resolutions
yields good results for the mean and variance of the Fourier coefficients.
Stable and accurate large-scale dynamics can be simulated over long integration
times.
