  We introduce and test methods for the calibration of the diffusion term in
Stochastic Partial Differential Equations (SPDEs) describing fluids. We take
two approaches, one uses ideas from the singular value decomposition and the
Biot-Savart law. The other backpropagates through an ensemble forecast, with
respect to diffusion parameters, to minimise a probabilistic ensemble
forecasting metric. We describe the approaches in the specific context of
solutions to SPDEs describing the evolution of fluid particles, sometimes
called inviscid vortex methods. The methods are tested in an idealised setting
in which the reference data is a known realisation of the parameterised SPDE,
and also using a forecast verification metric known as the Continuous Rank
Probability Score (CRPS).
