Spatio-Temporal Cross-Covariance Functions Under the Lagrangian Framework

• Activity Number: 308 - Recent Advancements in Spatial and Spatio-Temporal Modeling
• Type: Contributed
• Date/Time: Tuesday, July 30, 2019 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistics and the Environment
• Author(s): Mary Lai Salvana* and Amanda Lenzi and Marc Genton
• Companies: KAUST and King Abdullah University of Science and Technology and King Abdullah University of Science and Technology
• Keywords: cross-covariance function; Lagrangian framework; multivariate random field; spatio-temporal; Taylor hypothesis; transport effect

Abstract

In most atmospheric data such as pollutants at different levels of the atmosphere, a special property is observed: the covariances and cross-covariances along the direction at which a prevailing weather system travels are stronger than the ones lying in other directions. This resulting dynamics prompts the use of a Lagrangian reference frame wherein we describe the development of a phenomenon in space and in time while moving or traveling with it. Such covariance models have been proposed in the past but only in the univariate setting. We propose and investigate their multivariate extension. A simulation study shows that the parameters of these covariance models can be estimated using weighted least squares and that spatio-temporal cross-covariance functions built under the Lagrangian framework outperform other spatio-temporal cross-covariance models in modeling the aforementioned phenomenon. We demonstrate the modeling approach on a bivariate pollutant dataset of particulate matter in Saudi Arabia. We observe substantial improvements in forecast accuracy.