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

TL;DR

This paper introduces a stochastic pattern generator for simulating realistic spatio-temporal uncertainties in geophysical models, based on a third-order stochastic differential equation with Matérn class correlations.

Contribution

It presents a novel spatio-temporal Gaussian field generator satisfying the proportionality of scales, with a spectral solver optimized for geophysical applications.

Findings

Generates homogeneous, isotropic pseudo-random fields in space and time.

Correlations belong to the Matérn class and are non-separable.

Code implementation is publicly available.

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 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.