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Covariance functions for multivariate Gaussian fields evolving temporally over planet earth


Alegria, Alfredo; Porcu, Emilio; Furrer, Reinhard; Mateu, Jorge (2019). Covariance functions for multivariate Gaussian fields evolving temporally over planet earth. Stochastic Environmental Research and Risk Assessment, 33(8-9):1593-1608.

Abstract

The construction of valid and flexible cross-covariance functions is a fundamental task for modeling multivariate space–time data arising from, e.g., climatological and oceanographical phenomena. Indeed, a suitable specification of the covariance structure allows to capture both the space–time dependencies between the observations and the development of accurate predictions. For data observed over large portions of planet earth it is necessary to take into account the curvature of the planet. Hence the need for random field models defined over spheres across time. In particular, the associated covariance function should depend on the geodesic distance, which is the most natural metric over the spherical surface. In this work, we propose a flexible parametric family of matrix-valued covariance functions, with both marginal and cross structure being of the Gneiting type. We also introduce a different multivariate Gneiting model based on the adaptation of the latent dimension approach to the spherical context. Finally, we assess the performance of our models through the study of a bivariate space–time data set of surface air temperatures and precipitable water content.

Abstract

The construction of valid and flexible cross-covariance functions is a fundamental task for modeling multivariate space–time data arising from, e.g., climatological and oceanographical phenomena. Indeed, a suitable specification of the covariance structure allows to capture both the space–time dependencies between the observations and the development of accurate predictions. For data observed over large portions of planet earth it is necessary to take into account the curvature of the planet. Hence the need for random field models defined over spheres across time. In particular, the associated covariance function should depend on the geodesic distance, which is the most natural metric over the spherical surface. In this work, we propose a flexible parametric family of matrix-valued covariance functions, with both marginal and cross structure being of the Gneiting type. We also introduce a different multivariate Gneiting model based on the adaptation of the latent dimension approach to the spherical context. Finally, we assess the performance of our models through the study of a bivariate space–time data set of surface air temperatures and precipitable water content.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
07 Faculty of Science > Institute for Computational Science
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Environmental Engineering
Physical Sciences > Environmental Chemistry
Physical Sciences > Safety, Risk, Reliability and Quality
Physical Sciences > Water Science and Technology
Physical Sciences > General Environmental Science
Uncontrolled Keywords:Environmental Engineering, General Environmental Science, Safety, Risk, Reliability and Quality, Water Science and Technology, Environmental Chemistry
Language:English
Date:1 September 2019
Deposited On:16 Dec 2019 09:07
Last Modified:21 Jun 2024 02:16
Publisher:Springer
ISSN:1436-3240
OA Status:Green
Publisher DOI:https://doi.org/10.1007/s00477-019-01707-w