The Annals of Applied Statistics

A hierarchical multivariate spatio-temporal model for clustered climate data with annual cycles

Gianluca Mastrantonio, Giovanna Jona Lasinio, Alessio Pollice, Giulia Capotorti, Lorenzo Teodonio, Giulio Genova, and Carlo Blasi

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Abstract

We introduce a Bayesian multivariate hierarchical framework to estimate a space-time model for a joint series of monthly extreme temperatures and amounts of precipitation. Data are available for 360 monitoring stations over 60 years, with missing data affecting almost all series. Model components account for spatio-temporal correlation and annual cycles, dependence on covariates and between responses. Spatio-temporal dependence is modeled by the nearest neighbor Gaussian process (GP), response multivariate dependencies are represented by the linear model of coregionalization and effects of annual cycles are included by a circular representation of time. The proposed approach allows imputation of missing values and interpolation of climate surfaces at the national level. It also provides a characterization of the so called Italian ecoregions, namely broad and discrete ecologically homogeneous areas of similar potential as regards the climate, physiography, hydrography, vegetation and wildlife. To now, Italian ecoregions are hierarchically classified into 4 tiers that go from 2 Divisions to 35 Subsections and are defined by informed expert judgments. The current climatic characterization of Italian ecoregions is based on bioclimatic indices for the period 1955–2000.

Article information

Source
Ann. Appl. Stat., Volume 13, Number 2 (2019), 797-823.

Dates
Received: March 2018
Revised: July 2018
First available in Project Euclid: 17 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1560758428

Digital Object Identifier
doi:10.1214/18-AOAS1212

Mathematical Reviews number (MathSciNet)
MR3963553

Keywords
Multivariate process cyclic effect coregionalization NNGP

Citation

Mastrantonio, Gianluca; Jona Lasinio, Giovanna; Pollice, Alessio; Capotorti, Giulia; Teodonio, Lorenzo; Genova, Giulio; Blasi, Carlo. A hierarchical multivariate spatio-temporal model for clustered climate data with annual cycles. Ann. Appl. Stat. 13 (2019), no. 2, 797--823. doi:10.1214/18-AOAS1212. https://projecteuclid.org/euclid.aoas/1560758428


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References

  • Andrieu, C. and Thoms, J. (2008). A tutorial on adaptive MCMC. Stat. Comput. 18 343–373.
  • Bai, Y., Song, P. X.-K. and Raghunathan, T. E. (2012). Joint composite estimating functions in spatiotemporal models. J. R. Stat. Soc. Ser. B. Stat. Methodol. 74 799–824.
  • Bailey, R. G. (1983). Delineation of ecosystem regions. Environ. Manag. 7 365–373.
  • Bailey, R. G. (2004). Identifying ecoregion boundaries. Environ. Manag. 34 S14–S26.
  • Balint, P. J., Stewart, R. E., Desai, A. and Walters, L. C. (2011). Wicked Environmental Problems. Island Press, Washington, DC.
  • Banerjee, S., Carlin, B. P. and Gelfand, A. E. (2015). Hierarchical Modeling and Analysis for Spatial Data, 2nd ed. Monographs on Statistics and Applied Probability 135. CRC Press, Boca Raton, FL.
  • Banerjee, S., Gelfand, A. E., Finley, A. O. and Sang, H. (2008). Gaussian predictive process models for large spatial data sets. J. R. Stat. Soc. Ser. B. Stat. Methodol. 70 825–848.
  • Bevilacqua, M., Gaetan, C., Mateu, J. and Porcu, E. (2012). Estimating space and space-time covariance functions for large data sets: A weighted composite likelihood approach. J. Amer. Statist. Assoc. 107 268–280.
  • Bevilacqua, M., Fassò, A., Gaetan, C., Porcu, E. and Velandia, D. (2016a). Covariance tapering for multivariate Gaussian random fields estimation. Stat. Methods Appl. 25 21–37.
  • Bevilacqua, M., Alegria, A., Velandia, D. and Porcu, E. (2016b). Composite likelihood inference for multivariate Gaussian random fields. J. Agric. Biol. Environ. Stat. 21 448–469.
  • Blangiardo, M. and Cameletti, M. (2015). Spatial and Spatio-Temporal Bayesian Models with R-INLA. Wiley, Chichester.
  • Blasi, C., Capotorti, G., Copiz, R., Guida, D., Mollo, B., Smiraglia, D. and Zavattero, L. (2014). Classification and mapping of the ecoregions of Italy. Plant Biosyst. 148 1255–1345.
  • Chung, M., Binois, M., Gramacy, R. B., Moquin, D. J., Smith, A. P. and Smith, A. M. (2018). Parameter and uncertainty estimation for dynamical systems using surrogate stochastic processes. Preprint. Available at arXiv:1802.00852.
  • Daniels, M. J. and Kass, R. E. (1999). Nonconjugate Bayesian estimation of covariance matrices and its use in hierarchical models. J. Amer. Statist. Assoc. 94 1254–1263.
  • Daniels, M. J. and Pourahmadi, M. (2009). Modeling covariance matrices via partial autocorrelations. J. Multivariate Anal. 100 2352–2363.
  • Datta, A., Banerjee, S., Finley, A. O. and Gelfand, A. E. (2016a). Hierarchical nearest-neighbor Gaussian process models for large geostatistical datasets. J. Amer. Statist. Assoc. 111 800–812.
  • Datta, A., Banerjee, S., Finley, A. O., Hamm, N. A. S. and Schaap, M. (2016b). Nonseparable dynamic nearest neighbor Gaussian process models for large spatio-temporal data with an application to particulate matter analysis. Ann. Appl. Stat. 10 1286–1316.
  • Diggle, P. J. and Ribeiro, P. J. Jr. (2002). Bayesian inference in Gaussian model-based geostatistics. Geogr. Environ. Model. 6 129–146.
  • Eidsvik, J., Shaby, B. A., Reich, B. J., Wheeler, M. and Niemi, J. (2014). Estimation and prediction in spatial models with block composite likelihoods. J. Comput. Graph. Statist. 23 295–315.
  • Faye, E., Herrera, M., Bellomo, L., Silvain, J.-F. and Dangles, O. (2014). Strong discrepancies between local temperature mapping and interpolated climatic grids in tropical mountainous agricultural landscapes. PLoS ONE 9 e105541.
  • Ferraro Petrillo, U. and Raimato, G. (2014). TeraStat Computer cluster for high performance computing, Dept. Statistical Science, Sapienza Univ. Rome. Available at http://www.dss.uniroma1.it/en/node/6554.
  • Fick, S. E. and Hijmans, R. J. (2017). WorldClim 2: New 1-km spatial resolution climate surfaces for global land areas. Int. J. Climatol.. 37 4302–4315.
  • Finley, A. O., Banerjee, S. and Gelfand, A. E. (2012). Bayesian dynamic modeling for large space-time datasets using Gaussian predictive processes. J. Geogr. Syst. 14 29–47.
  • Finley, A. O., Datta, A., Cook, B. C., Morton, D. C., Andersen, H. E. and Banerjee, S. (2017). Efficient algorithms for Bayesian nearest neighbor Gaussian processes. Preprint. Available at arXiv:1702.00434.
  • 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.
  • Gelfand, A. E., Diggle, P. J., Fuentes, M. and Guttorp, P., eds. (2010). Handbook of Spatial Statistics. Chapman & Hall/CRC Handbooks of Modern Statistical Methods. CRC Press, Boca Raton, FL.
  • Gneiting, T. (2002). Nonseparable, stationary covariance functions for space-time data. J. Amer. Statist. Assoc. 97 590–600.
  • Gneiting, T. (2013). Strictly and non-strictly positive definite functions on spheres. Bernoulli 19 1327–1349.
  • Gneiting, T. and Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. J. Amer. Statist. Assoc. 102 359–378.
  • Gräler, B., Pebesma, E. and Heuvelink, G. (2016). Spatio-temporal interpolation using gstat. RFID J. 8 204–218.
  • Gramacy, R. B. and Apley, D. W. (2015). Local Gaussian process approximation for large computer experiments. J. Comput. Graph. Statist. 24 561–578.
  • Grimit, E. P., Gneiting, T., Berrocal, V. J. and Johnson, N. A. (2006). The continuous ranked probability score for circular variables and its application to mesoscale forecast ensemble verification. Q. J. R. Meteorol. Soc. 132 2925–2942.
  • Guinness, J. (2018). Permutation and grouping methods for sharpening Gaussian process approximations. Technometrics. To appear.
  • Hannah, L., Roehrdanz, P. R., Ikegami, M., Shepard, A. V., Shaw, M. R., Tabor, G., Zhi, L., Marquet, P. A. and Hijmans, R. J. (2013). Climate change, wine, and conservation. Proc. Natl. Acad. Sci. USA 110 6907–6912.
  • Heaton, M. J., Datta, A., Finley, A., Furrer, R., Guhaniyogi, R., Gerber, F., Gramacy, R. B., Hammerling, D., Katzfuss, M., Lindgren, F., Nychka, D. W., Sun, F. and Zammit-Mangion, A. (2017). A case study competition among methods for analyzing large spatial data. Preprint. Available at arXiv:1710.05013.
  • Hijmans, R. J., Cameron, S. E., Parra, J. L., Jones, P. G. and Jarvis, A. (2005). Very high resolution interpolated climate surfaces for global land areas. Int. J. Climatol. 25 1965–1978.
  • Jona Lasinio, G., Mastrantonio, G. and Pollice, A. (2013). Discussing the “big $n$ problem.” Stat. Methods Appl. 22 97–112.
  • Katzfuss, M. and Guinness, J. (2017). A general framework for Vecchia approximations of Gaussian processes. Preprint. Available at arXiv:1708.06302.
  • Li, S., Dragicevic, S., Castro, F. A., Sester, M., Winter, S., Coltekin, A., Pettit, C., Jiang, B., Haworth, J., Stein, A. and Cheng, T. (2016). Geospatial big data handling theory and methods: A review and research challenges. ISPRS J. Photogramm. Remote Sens. 115 119–133.
  • Loveland, T. R. and Merchant, J. M. (2004). Ecoregions and ecoregionalization: Geographical and ecological perspectives. Environ. Manag. 34 S1.
  • Metzger, M. J., Bunce, R. G. H., Jongman, R. H. G., Sayre, R., Trabucco, A. and Zomer, R. (2013). A high-resolution bioclimate map of the world: A unifying framework for global biodiversity research and monitoring. Glob. Ecol. Biogeogr. 22 630–638.
  • Mücher, C. A., Klijn, J. A., Wascher, D. M. and Schaminée, J. H. J. (2010). A new European landscape classification (LANMAP): A transparent, flexible and user-oriented methodology to distinguish landscapes. Ecol. Indicators 10 87–103.
  • Nychka, D., Furrer, R., Paige, J. and Sain, S. (2017). fields: Tools for spatial data. R package version 9.6, Univ. Corporation for Atmospheric Research, Boulder, CO.
  • Pebesma, E. J. (2004). Multivariable geostatistics in S: The gstat package. Comput. Geosci. 30 683–691.
  • Pesaresi, S., Galdenzi, D., Biondi, E. and Casavecchia, S. (2014). Bioclimate of Italy: Application of the worldwide bioclimatic classification system. J. Maps 10 538–553.
  • R Core Team (2017). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.
  • Shirota, S. and Gelfand, A. E. (2017). Space and circular time log Gaussian Cox processes with application to crime event data. Ann. Appl. Stat. 11 481–503.
  • Spiegelhalter, D. J., Best, N. G., Carlin, B. P. and van der Linde, A. (2002). Bayesian measures of model complexity and fit. J. R. Stat. Soc. Ser. B. Stat. Methodol. 64 583–639.
  • WMO (2016). Guidelines on Best Practices for Climate Data Rescue. WMO—Guidelines 1182. World Meteorological Organization, Geneva.
  • Wood, S. N. (2017). Generalized Additive Models: An Introduction with R, 2nd ed. Texts in Statistical Science Series. CRC Press/CRC, Boca Raton, FL.
  • Xu, G., Liang, F. and Genton, M. G. (2015). A Bayesian spatio-temporal geostatistical model with an auxiliary lattice for large datasets. Statist. Sinica 25 61–79.