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The modeling of real-valued random fields indexed by spherical coordinates arises in different disciplines of the natural sciences, especially in environmental, atmospheric and earth sciences. However, there is currently a lack of parametric models allowing a flexible representation of the spatial correlation structure of multivariate data located on a spherical surface. To bridge this gap, we provide analytical expressions of twenty-two parametric families of isotropic p-variate covariance kernels on the d-dimensional sphere, defined for any integers p > 0 and d > 1 , together with their respective spectral representations (Schoenberg matrices) and sufficient validity conditions on the covariance parameters. These families include multiquadric, sine power, exponential, Bessel and hypergeometric kernels, and provide covariances exhibiting varied shapes, short-scale and large-scale behaviors. Our construction relies on the so-called multivariate parametric adaptation approach, where a matrix-valued covariance kernel is defined on the basis of a scalar covariance to which matrix-valued parameters are applied, coupled with matrix manipulations. [ABSTRACT FROM AUTHOR]

This paper presents an algorithm for simulating Gaussian random fields with zero mean and non-stationary covariance functions. The simulated field is obtained as a weighted sum of cosine waves with random frequencies and random phases, with weights that depend on the location-specific spectral density associated with the target non-stationary covariance. The applicability and accuracy of the algorithm are illustrated through synthetic examples, in which scalar and vector random fields with non-stationary Gaussian, exponential, Matérn or compactly-supported covariance models are simulated. [ABSTRACT FROM AUTHOR]

This work pertains to the simulation of an intrinsic random field of order $$k$$ with a given generalized covariance function and multivariate Gaussian generalized increments. An iterative algorithm based on the Gibbs sampler is proposed to simulate such a random field at a finite set of locations, resulting in a sequence of random vectors that converges in distribution to a random vector with the desired distribution. The algorithm is tested on synthetic case studies to experimentally assess its rate of convergence, showing that few iterations are sufficient for convergence to take place. The sequence of random vectors also proves to be strongly mixing, allowing the generation of as many independent realizations as desired with a single run of the algorithm. Another interesting property of this algorithm is its versatility, insofar as it can be adapted to construct realizations conditioned to pre-existing data and can be used for any number and configuration of the target locations and any generalized covariance model. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the problem of simulating a Gaussian random vector with zero mean and given variance–covariance matrix, without conditioning constraints. Variants of the Gibbs sampler algorithm are presented, based on the proposal by Galli and Gao, which do not require inverting the variance–covariance matrix and therefore allow considerable time savings. Numerical experiments are performed to check the accuracy of the algorithm and to determine implementation parameters (in particular, the updating and blocking strategies) that increase the rates of convergence and mixing. [Copyright &y& Elsevier]