References
- Apanasovich, T. V., Genton, M. G., and Sun, Y. (2012), “A Valid Matérn Class of Cross-Covariance Functions for Multivariate Random Fields With Any Number of Components,” Journal of the American Statistical Association, 107, 180–193.
- Atlas, R., Hoffman, R. N., Leidner, S. M., Sienkiewicz, J., Yu, T.-W., Bloom, S. C., Brin, E., Ardizzone, J., Terry, J., Bungato, D., and Jusem, J. C. (2001), “The Effects of Marine Winds from Scatterometer Data on Weather Analysis and Forecasting,” Bulletin of the American Meteorological Society, 82, 1965–1990.
- Bevilacqua, M., Fassò, A., Gaetan, C., Porcu, E., and Velandia, D. (2016), “Covariance Tapering for Multivariate Gaussian Random Fields Estimation,” Statistical Methods & Applications, 25, 21–37.
- Bijlsma, S., Hafkenscheid, L., and Lynch, P. (1986), “Computation of the Streamfunction and Velocity Potential and Reconstruction of the Wind Field,” Monthly Weather Review, 114, 1547–1551.
- Bolin, D., and Lindgren, F. (2011), “Spatial Models Generated by Nested Stochastic Partial Differential Equations, with an Application to Global Ozone Mapping,” The Annals of Applied Statistics, 5, 523–550.
- Bourgault, G., and Marcotte, D. (1991), “Multivariable Variogram and its Application to the Linear Model of Coregionalization,” Mathematical Geology, 23, 899–928.
- Brennan, M. J., Hennon, C. C., and Knabb, R. D. (2009), “The Operational use of QuikSCAT Ocean Surface Vector Winds at the National Hurricane Center,” Weather and Forecasting, 24, 621–645.
- Constantinescu, E. M., and Anitescu, M. (2013), “Physics-based Covariance Models for Gaussian Processes with Multiple Outputs,” International Journal for Uncertainty Quantification, 3, 47–71.
- Cornford, D. (1998), “Flexible Gaussian Process Wind Field Models,” Tech. Rep. NCRG/98/017, Neural Computing Research Group, Aston University, Birmingham.
- Cornford, D., Csató, L., Evans, D. J., and Opper, M. (2004), “Bayesian Analysis of the Scatterometer Wind Retrieval Inverse Problem: Some New Approaches,” Journal of the Royal Statistical Society, Series B, 66, 609–626.
- Cressie, N., and Huang, H.-C. (1999), “Classes of Nonseparable, Spatio-temporal Stationary Covariance Functions,” Journal of the American Statistical Association, 94, 1330–1339.
- Cressie, N., and Wikle, C. K. (2011), Statistics for Spatio-Temporal Data, New York: Wiley.
- Daley, R. (1991), Atmospheric Data Analysis, Cambridge: Cambridge University Press.
- Foley, K., and Fuentes, M. (2008), “A Statistical Framework to Combine Multivariate Spatial Data and Physical Models for Hurricane Surface Wind Prediction,” Journal of Agricultural, Biological, and Environmental Statistics, 13, 37–59.
- Freeden, W., and Schreiner, M. (2009), Spherical Functions of Mathematical Geosciences: A Scalar, Vectorial, and Tensorial Setup, Advances in Geophysical and Environmental Mechanics and Mathematics, Berlin: Springer-Verlag.
- Furrer, R., Genton, M. G., and Nychka, D. (2006), “Covariance Tapering for Interpolation of Large Spatial Datasets,” Journal of Computational and Graphical Statistics, 15, 502–523.
- Fuselier, E. J., and Wright, G. B. (2009), “Stability and Error Estimates for Vector Field Interpolation and Decomposition on the Sphere with RBFs,” SIAM Journal on Numerical Analysis, 47, 3213–3239.
- Gelfand, A. E., Schmidt, A. M., Banerjee, S., and Sirmans, C. F. (2004), “Nonstationary Multivariate Process Modeling Through Spatially Varying Coregionalization,” Test, 13, 263–312.
- 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.
- Gneiting, T., and Raftery, A. E. (2007), “Strictly Proper Scoring Rules, Prediction, and Estimation,” Journal of the American Statistical Association, 102, 359–378.
- Górski, K. M., Hivon, E., Banday, A. J., Wandelt, B. D., Hansen, F. K., Reinecke, M., and Bartelmann, M. (2005), “HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere,” The Astrophysical Journal, 622, 759.
- Goulard, M., and Voltz, M. (1992), “Linear Coregionalization Model: Tools for Estimation and Choice of Cross-Variogram Matrix,” Mathematical Geology, 24, 269–286.
- Guinness, J., and Fuentes, M. (2016), “Isotropic Covariance Functions on Spheres: Some Properties and Modeling Considerations,” Journal of Multivariate Analysis, 143, 143–152.
- Hitczenko, M., and Stein, M. L. (2012), “Some Theory for Anisotropic Processes on the Sphere,” Statistical Methodology, 9, 211–227.
- Holton, J. R. (2004), An Introduction to Dynamic Meteorology, International Geophysics Series, Amsterdam, Boston, Heidelberg: Elsevier.
- Hsu, N.-J., Chang, Y.-M., and Huang, H.-C. (2012), “A Group Lasso Approach for Non-Stationary Spatial–Temporal Covariance Estimation,” Environmetrics, 23, 12–23.
- Jones, R. H. (1963), “Stochastic Processes on a Sphere,” Annals of Mathematical Statistics, 34, 213–218.
- Jun, M. (2011), “Non-Stationary Cross-Covariance Models for Multivariate Processes on a Globe,” Scandinavian Journal of Statistics, 38, 726–747.
- ——— (2014), “Matérn-Based Nonstationary Cross-Covariance Models for Global Processes,” Journal of Multivariate Analysis, 128, 134–146.
- Jun, M., and Stein, M. L. (2007), “An Approach to Producing Space-Time Covariance Functions on Spheres,” Technometrics, 49, 468–479.
- ——— (2008), “Nonstationary Covariance Models for Global Data,” The Annals of Applied Statistics, 2, 1271–1289.
- Kadri-Harouna, S., and Perrier, V. (2012), “Helmholtz–Hodge Decomposition on [0, 1]d by Divergence-Free and Curl-Free Wavelets,” in Curves and Surfaces, eds. Boissonnat, J.-D., Chenin, P., Cohen, A., Gout, C., Lyche, T., Mazure, M.-L., and Schumaker, L., Berlin: Springer vol. 6920 of Lecture Notes in Computer Science, pp. 311–329.
- Kaufman, C. G., Schervish, M. J., and Nychka, D. W. (2008), “Covariance Tapering for Likelihood-Based Estimation in Large Spatial Datasets,” Journal of the American Statistical Association, 103, 1545–1555.
- Kleiber, W., and Nychka, D. (2012), “Nonstationary Modeling for Multivariate Spatial Processes,” Journal of Multivariate Analysis, 112, 76–91.
- Marinucci, D., and Peccati, G. (2011), Random Fields on the Sphere: Representation, Limit Theorems and Cosmological Applications, vol. 389 of London Mathematical Society Lecture Note Series, Cambridge University Press.
- Matsuo, T., Nychka, D. W., and Paul, D. (2011), “Nonstationary Covariance Modeling for Incomplete Data: Monte Carlo EM Approach,” Computational Statistics & Data Analysis, 55, 2059–2073.
- Narcowich, F. J., Ward, J. D., and Wright, G. B. (2007), “Divergence-Free RBFs on Surfaces,” Journal of Fourier Analysis and Applications, 13, 643–663.
- Nychka, D., Bandyopadhyay, S., Hammerling, D., Lindgren, F., and Sain, S. (2015), “A Multiresolution Gaussian Process Model for the Analysis of Large Spatial Datasets,” Journal of Computational and Graphical Statistics, 24, 579–599.
- Nychka, D., Wikle, C., and Royle, J. A. (2002), “Multiresolution Models for Nonstationary Spatial Covariance Functions,” Statistical Modelling, 2, 315–331.
- Pan, J., Yan, X.-H., Zheng, Q., and Liu, W. T. (2001), “Vector Empirical Orthogonal Function Modes of the ocean Surface Wind Variability Derived from Satellite Scatterometer Data,” Geophysical Research Letters, 28, 3951–3954.
- Pan, J., Yan, X.-H., Zheng, Q., Liu, W. T., and Klemas, V. V. (2003), “Interpretation of Scatterometer Ocean Surface Wind Vector EOFs over the Northwestern Pacific,” Remote Sensing of Environment, 84, 53–68.
- Park, C. C. (2001), The Environment: Principles and Applications, London and New York: Routledge.
- Piolle, J.-F., and Bentamy, A. (2002), “QuikSCAT Scatterometer Mean Wind Field Products User Manual,” Ifremer, Department of Oceanography from Space, Ref.: C2-MUT-W-04-IF, Version 1.0, May 2002.
- Potthoff, J. (2010), “Sample Properties of Random Fields III: Differentiability,” Communications on Stochastic Analysis, 4, 335–353.
- Reich, B. J., and Fuentes, M. (2007), “A Multivariate Semiparametric Bayesian Spatial Modeling Framework for Hurricane Surface Wind Fields,” The Annals of Applied Statistics, 1, 249–264.
- Richmond, A. D., and Kamide, Y. (1988), “Mapping Electrodynamic Features of the High-Latitude Ionosphere from Localized Observations: Technique,” Journal of Geophysical Research: Space Physics, 93, 5741–5759.
- Risser, M. D., and Calder, C. A. (2015), “Regression-Based Covariance Functions for Nonstationary Spatial Modeling,” Environmetrics, 26, 284–297.
- Sabaka, T. J., Hulot, G., and Olsen, N. (2010), “Mathematical Properties Relevant to Geomagnetic Field Modeling,” in Handbook of Geomathematics, eds. Freeden, W., Nashed, M. Z., and Sonar, T., Berlin: Springer, pp. 503–538.
- Scheuerer, M., and Schlather, M. (2012), “Covariance Models for Divergence-Free and Curl-Free Random Vector Fields,” Stochastic Models, 28, 433–451.
- Schlather, M., Malinowski, A., Menck, P. J., Oesting, M., and Strokorb, K. (2015), “Analysis, Simulation and Prediction of Multivariate Random Fields with Package Random Fields,” Journal of Statistical Software, 63, 1–25.
- Shukla, J., and Saha, K. (1974), “Computation of Non-Divergent Streamfunction and Irrotational Velocity Potential from the Observed Winds,” Monthly Weather Review, 102, 419–425.
- Stein, M. L. (2007), “Spatial Variation of Total Column Ozone on a Global Scale,” The Annals of Applied Statistics, 1, 191–210.
- Wikle, C. K., and Cressie, N. (1999), “A Dimension-Reduced Approach to Space-Time Kalman Filtering,” Biometrika, 86, 815–829.
- Wikle, C. K., Milliff, R. F., Nychka, D., and Berliner, L. M. (2001), “Spatiotemporal Hierarchical Bayesian Modeling Tropical Ocean Surface Winds,” Journal of the American Statistical Association, 96, 382–397.
- Zhang, H. (2004), “Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics,” Journal of the American Statistical Association, 99, 250–261.
- Zhang, Z., Beletsky, D., Schwab, D. J., and Stein, M. L. (2007), “Assimilation of Current Measurements into a Circulation Model of Lake Michigan,” Water Resources Research, 43, W11407.