Spatio-Temporal Cross-Covariance Functions under the Lagrangian Framework with Multiple Advections

@article{Salvaa2022SpatioTemporalCF,
  title={Spatio-Temporal Cross-Covariance Functions under the Lagrangian Framework with Multiple Advections},
  author={Mary Lai O. Salva{\~n}a and Amanda Lenzi and Marc G. Genton},
  journal={Journal of the American Statistical Association},
  year={2022}
}
When analyzing the spatio-temporal dependence in most environmental and earth sciences variables such 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 the presence of natural forces, such as wind, which cause the transport and dispersion of these variables. This spatio-temporal dynamics prompted the use of the Lagrangian reference frame… 

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References

SHOWING 1-10 OF 64 REFERENCES
Nonstationary cross-covariance functions for multivariate spatio-temporal random fields
Spatio-temporal modeling of particulate matter concentration through the SPDE approach
TLDR
This work considers a hierarchical spatio-temporal model for particulate matter (PM) concentration in the North-Italian region Piemonte and proposes a strategy to represent a GF with Matérn covariance function as a Gaussian Markov Random Field (GMRF) through the SPDE approach.
Cross-Covariance Functions for Multivariate Geostatistics
TLDR
The main approaches to building cross-covariance models are reviewed, including the linear model of coregionalization, convolution methods, the multivariate Mat\'{e}rn and nonstationary and space-time extensions of these among others, and specialized constructions, including those designed for asymmetry, compact support and spherical domains, are covered.
Test and Visualization of Covariance Properties for Multivariate Spatio-Temporal Random Fields
TLDR
This work formally defines these properties for multivariate spatio-temporal random fields and uses functional data analysis techniques to visualize them, hence providing intuitive interpretations and proposing a rigorous rank-based testing procedure to conclude whether the simplified properties of covariance are suitable for the underlying multivariate spacetime data.
Covariance functions for multivariate Gaussian fields evolving temporally over planet earth
TLDR
This work proposes a flexible parametric family of matrix-valued covariance functions, with both marginal and cross structure being of the Gneiting type, and introduces a different multivariateGneiting model based on the adaptation of the latent dimension approach to the spherical context.
Spatio-Temporal Asymmetry of Local Wind Fields and Its Impact on Short-Term Wind Forecasting
TLDR
It is concluded that local wind fields exhibit strong signs of nonseparability and asymmetry, and an enhanced procedure for short-term wind speed forecast is proposed, making use of the spatio-temporal lens.
A test for stationarity of spatio-temporal random fields on planar and spherical domains
A formal test for weak stationarity of spatial and spatio-temporal ran- dom fields is proposed. We consider the cases where the spatial domain is planar or spherical, and we do not require
Time varying spatio-temporal covariance models
Statistical methods for regular monitoring data
Summary.  Meteorological and environmental data that are collected at regular time intervals on a fixed monitoring network can be usefully studied combining ideas from multiple time series and
Nonseparable, Stationary Covariance Functions for Space–Time Data
Geostatistical approaches to spatiotemporal prediction in environmental science, climatology, meteorology, and related fields rely on appropriate covariance models. This article proposes general
...
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