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