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

References

• Alegría, A., Porcu, E., Furrer, R., and Mateu, J.(2019), “Covariance Functions for Multivariate Gaussian Fields Evolving Temporally Over Planet Earth,” Stochastic Environmental Research and Risk Assessment, 33, 1593–1608. DOI: 10.1007/s00477-019-01707-w.
   Web of Science ®Google Scholar
• Apanasovich, T. V., and Genton, M. G.(2010), “Cross-Covariance Functions for Multivariate Random Fields Based on Latent Dimensions,” Biometrika, 97, 15–30. DOI: 10.1093/biomet/asp078.
   Web of Science ®Google Scholar
• Bornn, L., Shaddick, G., and Zidek, J. V.(2012), “Modeling Nonstationary Processes through Dimension Expansion,” Journal of the American Statistical Association, 107, 281–289. DOI: 10.1080/01621459.2011.646919.
   Web of Science ®Google Scholar
• Bourotte, M., Allard, D., and Porcu, E.(2016), “A Flexible Class of Non-separable Cross-covariance Functions for Multivariate Space–Time Data,” Spatial Statistics, 18, 125–146. DOI: 10.1016/j.spasta.2016.02.004.
   Web of Science ®Google Scholar
• Calder, C. A.(2008), “A Dynamic Process Convolution Approach to Modeling Ambient Particulate Matter Concentrations,” Environmetrics, 19, 39–48. DOI: 10.1002/env.852.
   Web of Science ®Google Scholar
• Cameletti, M., Lindgren, F., Simpson, D., and Rue, H.(2013), “Spatio-Temporal Modeling of Particulate Matter Concentration through the SPDE Approach,” AStA Advances in Statistical Analysis, 97, 109–131. DOI: 10.1007/s10182-012-0196-3.
   Web of Science ®Google Scholar
• Chen, W., Genton, M. G., and Sun, Y.(2021), “Space-Time Covariance Structures and Models,” Annual Review of Statistics and Its Application, 8, 191–215. DOI: 10.1146/annurev-statistics-042720-115603.
   Web of Science ®Google Scholar
• Christakos, G.(2017), Spatiotemporal Random Fields: Theory and Applications, Elsevier.
   Google Scholar
• Cox, D., and Isham, V.(1988), “A Simple Spatial-Temporal Model of Rainfall,” Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 415, 317–328.
   Google Scholar
• Cressie, N., and Lahiri, S. N.(1996), “Asymptotics for REML Estimation of Spatial Covariance Parameters,” Journal of Statistical Planning and Inference, 50, 327–341. DOI: 10.1016/0378-3758(95)00061-5.
   Web of Science ®Google Scholar
• Ezzat, A. A., Jun, M., and Ding, Y.(2018), “Spatio-Temporal Asymmetry of Local Wind Fields and its Impact on Short-Term Wind Forecasting,” IEEE Transactions on Sustainable Energy, 9, 1437–1447. DOI: 10.1109/TSTE.2018.2789685.
   PubMed Web of Science ®Google Scholar
• Gelaro, R., McCarty, W., Suárez, M. J., Todling, R., Molod, A., Takacs, L., Randles, C. A., Darmenov, A., Bosilovich, M. G., Reichle, R., Wargan, K., Coy, L., Cullather, R., Draper, C., Akella, S., Buchard, V., Conaty, A., da Silva, A. M., Gu, W., Kim, G.-K., Koster, R., Lucchesi, R., Merkova, D., Nielsen, J. E., Partyka, G., Pawson, S., Putman, W., Rienecker, M., Schubert, S. D., Sienkiewicz, M., Zhao, B.(2017), “The Modern-Era Retrospective Analysis for Research and Applications, version 2(MERRA-2),” Journal of Climate, 30, 5419–5454.
   Web of Science ®Google Scholar
• Gelfand, A. E., Schmidt, A. M., and Sirmans, C.(2002), “Multivariate Spatial Process Models: Conditional and Unconditional Bayesian Approaches Using Coregionalization,” unpublished.
   Google Scholar
• Genton, M. G., and Kleiber, W.(2015), “Cross-Covariance Functions for Multivariate Geostatistics”(with discussion), Statistical Science, 30, 147–163. DOI: 10.1214/14-STS487.
   Web of Science ®Google Scholar
• Gneiting, T.(2002), “Nonseparable, Stationary Covariance Functions for Space–Time Data,” Journal of the American Statistical Association, 97, 590–600. DOI: 10.1198/016214502760047113.
   Web of Science ®Google Scholar
• Gneiting, T., Genton, M. G., and Guttorp, P.(2007), “Geostatistical Space-Time Models, Stationarity, Separability, and Full Symmetry,” in Statistics of Spatio-Temporal Systems. Monographs in Statistics and Applied Probability, eds. B. Finkenstaedt, L. Held, and V. Isham, pp. 151–175, Boca Raton, FL: Chapman & Hall/CRC Press.
   Google Scholar
• Gneiting, T., Kleiber, W., and Schlather, M.(2010), “Matérn Cross-Covariance Functions for Multivariate Random Fields,” Journal of the American Statistical Association, 105, 1167–1177. DOI: 10.1198/jasa.2010.tm09420.
   Web of Science ®Google Scholar
• Goyal, P., Chan, A. T., and Jaiswal, N.(2006), “Statistical Models for the Prediction of Respirable Suspended Particulate Matter in Urban Cities,” Atmospheric Environment, 40, 2068–2077. DOI: 10.1016/j.atmosenv.2005.11.041.
   Web of Science ®Google Scholar
• Greene, W. H.(2014), Econometric Analysis, Delhi: Pearson Education India.
   Google Scholar
• Huang, H., Sun, Y., and Genton, M. G.(2020), “Test and Visualization of Covariance Properties for Multivariate Spatio-Temporal Random Fields,” arXiv preprint arXiv:2008.03689.
   Google Scholar
• Inoue, T., Sasaki, T., and Washio, T.(2012), “Spatio-Temporal Kriging of Solar Radiation Incorporating Direction and Speed of Cloud Movement,” in The 26th Annual Conference of the Japanese Society for Artificial Intelligence, p. 1K2IOS1b3.
   Google Scholar
• Ip, R. H., and Li, W. K.(2015), “Time Varying Spatio-Temporal Covariance Models,” Spatial Statistics, 14, 269–285. DOI: 10.1016/j.spasta.2015.06.006.
   Web of Science ®Google Scholar
• Jun, M., and Genton, M. G.(2012), “A Test for Stationarity of Spatio-Temporal Random Fields on Planar and Spherical Domains,” Statistica Sinica, 22, 1737–1764. DOI: 10.5705/ss.2010.251.
   Web of Science ®Google Scholar
• Kallos, G., Astitha, M., Katsafados, P., and Spyrou, C.(2007), “Long-Range Transport of Anthropogenically and Naturally Produced Particulate Matter in the Mediterranean and North Atlantic: Current State of Knowledge,” Journal of Applied Meteorology and Climatology, 46, 1230–1251. DOI: 10.1175/JAM2530.1.
   Web of Science ®Google Scholar
• Katra, I., Elperin, T., Fominykh, A., Krasovitov, B., and Yizhaq, H.(2016), “Modeling of Particulate Matter Transport in Atmospheric Boundary Layer Following Dust Emission from Source Areas,” Aeolian Research, 20, 147–156. DOI: 10.1016/j.aeolia.2015.12.004.
   Web of Science ®Google Scholar
• Knox, J. B.(1974), “Numerical Modeling of the Transport Diffusion and Deposition of Pollutants for Regions and Extended Scales,” Journal of the Air Pollution Control Association, 24, 660–664. DOI: 10.1080/00022470.1974.10469953.
   Web of Science ®Google Scholar
• Li, B., and Zhang, H.(2011), “An Approach to Modeling Asymmetric Multivariate Spatial Covariance Structures,” Journal of Multivariate Analysis, 102, 1445–1453. DOI: 10.1016/j.jmva.2011.05.010.
   Web of Science ®Google Scholar
• Lonij, V. P., Brooks, A. E., Cronin, A. D., Leuthold, M., and Koch, K.(2013), “Intra-Hour Forecasts of Solar Power Production Using Measurements from a Network of Irradiance Sensors,” Solar Energy, 97, 58–66.
   Web of Science ®Google Scholar
• Mehdipour, V., Stevenson, D. S., Memarianfard, M., and Sihag, P.(2018), “Comparing Different Methods for Statistical Modeling of Particulate Matter in Tehran, Iran,” Air Quality, Atmosphere & Health, 11, 1155–1165.
   Web of Science ®Google Scholar
• Munir, S., Habeebullah, T. M., Seroji, A. R., Morsy, E. A., Mohammed, A. M., Saud, W. A., Abdou, A. E., Awad, A. H.(2013), “Modeling Particulate Matter Concentrations in Makkah, Applying a Statistical Modeling Approach,” Aerosol and Air Quality Research, 13, 901–910. DOI: 10.4209/aaqr.2012.11.0314.
   Web of Science ®Google Scholar
• Murphy, K. M., and Topel, R. H.(2002), “Estimation and Inference in Two-Step Econometric Models,” Journal of Business & Economic Statistics, 20, 88–97.
   Web of Science ®Google Scholar
• National Research Council.(2010), Global Sources of Local Pollution: An Assessment of Long-Range Transport of Key Air Pollutants to and from the United States, Washington DC: National Academies Press.
   Google Scholar
• Paciorek, C. J., Yanosky, J. D., Puett, R. C., Laden, F., Suh, H. H., et al.(2009), “Practical Large-Scale Spatio-Temporal Modeling of Particulate Matter Concentrations,” The Annals of Applied Statistics, 3, 370–397. DOI: 10.1214/08-AOAS204.
   Web of Science ®Google Scholar
• Park, M. S., and Fuentes, M.(2006), “New Classes of Asymmetric Spatial-Temporal Covariance Models,” Technical report, North Carolina State University. Dept. of Statistics.
   Google Scholar
• Porcu, E., Gregori, P., and Mateu, J.(2006), “Nonseparable Stationary Anisotropic Space–Time Covariance Functions,” Stochastic Environmental Research and Risk Assessment, 21, 113–122. DOI: 10.1007/s00477-006-0048-3.
   Web of Science ®Google Scholar
• Qadir, G. A., Euán, C., and Sun, Y.(2021), “Flexible Modeling of Variable Asymmetries in Cross-Covariance Functions for Multivariate Random Fields,” Journal of Agricultural, Biological and Environmental Statistics, 26, 1–22. DOI: 10.1007/s13253-020-00414-2.
   Web of Science ®Google Scholar
• Rabito, F. A., Yang, Q., Zhang, H., Werthmann, D., Shankar, A., and Chillrud, S.(2020), “The Association between Short-Term Residential Black Carbon Concentration on Blood Pressure in a General Population Sample,” Indoor Air, 30, 767–775. DOI: 10.1111/ina.12651.
   PubMed Web of Science ®Google Scholar
• Randles, C., Da Silva, A., Buchard, V., Colarco, P., Darmenov, A., Govindaraju, R., Smirnov, A., Holben, B., Ferrare, R., Hair, J., Shinozuka, Y., and Flynn, C. J.(2017), “The MERRA-2 Aerosol Reanalysis, 1980 Onward. Part I: System Description and Data Assimilation Evaluation,” Journal of Climate, 30, 6823–6850. DOI: 10.1175/JCLI-D-16-0609.1.
   Web of Science ®Google Scholar
• Sahu, S. K.(2012), “Hierarchical Bayesian Models for Space–Time Air Pollution Data,” in Handbook of Statistics(Vol. 30), eds. S. S. R. T. Subba Rao and C. R. Rao, pp. 477–495, Amsterdam: Elsevier.
   Google Scholar
• Sahu, S. K., Gelfand, A. E., and Holland, D. M.(2006), “Spatio-Temporal Modeling of Fine Particulate Matter,” Journal of Agricultural, Biological, and Environmental Statistics, 11, 61–86. DOI: 10.1198/108571106X95746.
   Web of Science ®Google Scholar
• Salvaña, M. L., Abdulah, S., Huang, H., Ltaief, H., Sun, Y., Genton, M. G., and Keyes, D.(2021), “High Performance Multivariate Geospatial Statistics on Manycore Systems,” IEEE Transactions on Parallel and Distributed Systems, 32, 2719–2733. DOI: 10.1109/TPDS.2021.3071423.
   Web of Science ®Google Scholar
• Salvaña, M. L., and Genton, M. G.(2020), “Nonstationary Cross-Covariance Functions for Multivariate Spatio-Temporal Random Fields,” Spatial Statistics, 36, 100411. DOI: 10.1016/j.spasta.2020.100411.
   Google Scholar
• Salvaña, M. L., and Genton, M. G.( (2021), “Lagrangian Spatio-Temporal Nonstationary Covariance Functions,” Book Chapter: Advances in Contemporary Statistics and Econometrics—Festschrift in Honor of Christine Thomas-Agnan, eds. A. Daouia, and A. Ruiz-Gazen, pp. 427–447.
   Google Scholar
• Schacht, J., Heinold, B., Quaas, J., Backman, J., Cherian, R., Ehrlich, A., Herber, A., Huang, W. T. K., Kondo, Y., Massling, A., Sinha, P. R., Weinzierl, B., Zanatta, M., and Tegen, I.(2019), “The Importance of the Representation of Air Pollution Emissions for the Modeled Distribution and Radiative Effects of Black Carbon in the Arctic,” Atmospheric Chemistry and Physics, 19, 11159–11183. DOI: 10.5194/acp-19-11159-2019.
   Web of Science ®Google Scholar
• Schlather, M.(2010), “Some Covariance Models Based on Normal Scale Mixtures,” Bernoulli, 16, 780–797. DOI: 10.3150/09-BEJ226.
   Web of Science ®Google Scholar
• Schmidt, D., Chen, W.-C., Ostrouchov, G., and Patel, P.(2020), “Guide to the pbdBASE Package,” https://rdrr.io/cran/pbdBASE/f/inst/doc/pbdBASE-guide.pdf.
   Google Scholar
• Shao, Y., Wyrwoll, K.-H., Chappell, A., Huang, J., Lin, Z., McTainsh, G. H., Mikami, M., Tanaka, T. Y., Wang, X., and Yoon, S.(2011), “Dust Cycle: An Emerging Core Theme in Earth System Science,” Aeolian Research, 2, 181–204. DOI: 10.1016/j.aeolia.2011.02.001.
   Web of Science ®Google Scholar
• Shinozaki, K., Yamakawa, N., Sasaki, T., and Inoue, T.(2016), “Areal Solar Irradiance Estimated by Sparsely Distributed Observations of Solar Radiation,” IEEE Transactions on Power Systems, 31, 35–42. DOI: 10.1109/TPWRS.2015.2393636.
   Web of Science ®Google Scholar
• Shor, T., Kalka, I., Geiger, D., Erlich, Y., and Weissbrod, O.(2019), “Estimating Variance Components in Population Scale Family Trees,” PLoS Genetics, 15, e1008124. DOI: 10.1371/journal.pgen.1008124.
   PubMed Web of Science ®Google Scholar
• Stein, M. L.(2005a), “Space–Time Covariance Functions,” Journal of the American Statistical Association, 100, 310–321. DOI: 10.1198/016214504000000854.
   Web of Science ®Google Scholar
• Stein, M. L.(2005b), “Statistical Methods for Regular Monitoring Data,” Journal of the Royal Statistical Society, Series B, 67, 667–687.
   Google Scholar
• Takemura, T., and Suzuki, K.(2019), “Weak Global Warming Mitigation by Reducing Black Carbon Emissions,” Scientific Reports, 9, 1–6. DOI: 10.1038/s41598-019-41181-6.
   PubMed Web of Science ®Google Scholar
• Tanrikulu, S., Soong, S., Tran, C., and Beaver, S.(2009), “Fine Particulate Matter Data Analysis and Modeling in the Bay Area,” Bay Area Air Quality Mangements Dristrict, Research and Modeling Section Publication, p. 106.
   Google Scholar
• Ukhov, A., Mostamandi, S., da Silva, A., Flemming, J., Alshehri, Y., Shevchenko, I., and Stenchikov, G.(2020), “Assessment of Natural and Anthropogenic Aerosol Air Pollution in the Middle East using MERRA-2, CAMS Data Assimilation Products, and High-Resolution WRF-Chem Model Simulations,” Atmospheric Chemistry and Physics, 20, 9281–9310. DOI: 10.5194/acp-20-9281-2020.
   Web of Science ®Google Scholar
• Van Donkelaar, A., Martin, R. V., Brauer, M., Hsu, N. C., Kahn, R. A., Levy, R. C., Lyapustin, A., Sayer, A. M., and Winker, D. M.(2016), “Global Estimates of Fine Particulate Matter Using a Combined Geophysical-Statistical Method with Information from Satellites, Models, and Monitors,” Environmental Science & Technology, 50, 3762–3772.
   PubMed Web of Science ®Google Scholar
• Wackernagel, H.(2003), Multivariate Geostatistics: An Introduction with Applications(3rd ed.), Berlin: Springer.
   Google Scholar
• Zhang, H., and Cai, W.(2015), “When Doesn’t Cokriging Outperform Kriging?” Statistical Science, 30, 176–180. DOI: 10.1214/15-STS518.
   Web of Science ®Google Scholar
• Zhang, Z., and Chen, Q.(2007), “Comparison of the Eulerian and Lagrangian Methods for Predicting Particle Transport in Enclosed Spaces,” Atmospheric Environment, 41, 5236–5248. DOI: 10.1016/j.atmosenv.2006.05.086.
   Web of Science ®Google Scholar
• Zhelonkin, M., Genton, M. G., and Ronchetti, E.(2012), “On the Robustness of Two-Stage Estimators,” Statistics & Probability Letters, 82, 726–732.
   Web of Science ®Google Scholar