A limited-area spatio-temporal stochastic pattern generator for simulation of uncertainties in ensemble applications

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 space-time (with the scaled vertical and temporal coordinates). The correlation functions in any spatio-temporal direction belong to the Matérn class. The spatio-temporal correlations are non-separable. A spectral in space and finite-difference in time numerical solver is implemented and accelerated by exploiting properties of real-world geophysical fields, in particular, the 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 generator is tested with the meteorological COSMO model as a source of additive spatio-temporal perturbations to the forecast-model fields. The program code of the generator is publicly available