Spatio-temporal cross-covariance functions under the Lagrangian framework with multiple advections.

Mary Lai O. Salvaña, Amanda Lenzi, Marc G. Genton

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

When analyzing the spatio-temporal dependence in most environmental and earth sciences variablessuch as pollutant concentrations at different levels of the atmosphere, a special property is observed:the covariances and cross-covariances are stronger in certain directions. This property is attributed to thepresence of natural forces, such as wind, which cause the transport and dispersion of these variables. Thisspatio-temporal dynamics prompted the use of the Lagrangian reference frame alongside any Gaussianspatio-temporal geostatistical model. Under this modeling framework, a whole new class was birthed andwas known as the class of spatio-temporal covariance functions under the Lagrangian framework, withseveral developments already established in the univariate setting, in both stationary and nonstationaryformulations, but less so in the multivariate case. Despite the many advances in this modeling approach,efforts have yet to be directed to probing the case for the use of multiple advections, especially when severalvariables are involved. Accounting for multiple advections would make the Lagrangian framework a moreviable approach in modeling realistic multivariate transport scenarios. In this work, we establish a class ofLagrangian spatio-temporal cross-covariance functions with multiple advections, study its properties, anddemonstrate its use on a bivariate pollutant dataset of particulate matter in Saudi Arabia. Supplementarymaterials for this article are available online.
Original languageEnglish
Number of pages16
JournalJournal of the American Statistical Association
Early online date28 Jun 2022
DOIs
Publication statusE-pub ahead of print - 28 Jun 2022

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