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A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the"proportionality of scales" property (Tsyroulnikov, 2001) is presented. Thegenerator is based on a third-order in time stochastic differential equationwith a pseudo-differential spatial operator defined on a limited area 2D or 3Ddomain in the Cartesian coordinate system. The generated pseudo-random fieldsare homogeneous and isotropic in spacetime (with the scaled vertical andtemporal coordinates). The correlation functions in any spatio-temporaldirection belong to the Mat\'ern class. The spatio-temporal correlations arenon-separable. A spectral-space numerical solver is implemented and acceleratedexploiting properties of real-world geophysical fields, in particular,smoothness of their spatial spectra. The generator is designed to createadditive or multiplicative, or other spatio-temporal perturbations thatrepresent uncertainties in numerical prediction models in geophysics. Theprogram code of the generator is publicly available.

A spatio-temporal stochastic pattern generator for simulation of uncertainties in geophysical ensemble prediction and ensemble data assimilation