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

2016/05/06 by Michael Tsyrulnikov, Dmitry Gayfulin, Tsyrulnikov, Michael +1
Environmental Science · Earth and Planetary Sciences · Computer Science · #Soil Geostatistics and Mapping #Meteorological Phenomena and Simulations #Geochemistry and Geologic Mapping

paper · pdf · doi:10.48550/arxiv.1605.02018

Abstract

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 Matérn 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.

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