Spatial analysis and visualization of global data on multi-resolution hexagonal grids

Abstract

In this article, computation for the purpose of spatial visualization is presented in the context of understanding the variability in global environmental processes. Here, we generate synthetic but realistic global data sets and input them into computational algorithms that have a visualization capability; we call this a simulation–visualization system. Visualization is key here, because the algorithms which we are evaluating must respect the spatial structure of the input. We modify, augment, and integrate four existing component technologies: statistical conditional simulation, Discrete Global Grids (DGGs), Array Set Addressing, and a visualization platform for displaying our results on a globe. The internal representation of the data to be visualized is built around the need for efficient storage and computation as well as the need to move up and downresolutions in a mutually consistent way. In effect, we have constructed a Geographic Information System that is based on a DGG and has desirable data storage, computation, and visualization capabilities. We provide an example of how our simulation–visualization system may be used, by evaluating a computational algorithm called Spatial Statistical Data Fusion that was developed for use on big, remote-sensing data sets.

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References

  1. Alder, J., Hostetler, S., & Williams, D. (2013). An interactive web application for visualizing climate data. Eos, Transactions American Geophysical Union, 94(22), 2324–9250.

    Article  Google Scholar 

  2. Aumann, H. H., Chahine, M. T., Gautier, C., Goldberg, M. D., Kalnay, E., McMillin, L. M., et al. (2003). AIRS/AMSU/HSB on the Aqua mission: Design, science objectives, data products, and processing systems. IEEE Transactions on Geoscience and Remote Sensing, 41(2), 253–264.

    Article  Google Scholar 

  3. Carr, D., Kahn, R., Sahr, K., & Olsen, T. (1997). ISEA discrete global grids. Statistical Computing and Statistical Graphics Newsletter, 8(2/3), 31–39.

    Google Scholar 

  4. Cressie, N., & Johannesson, G. (2006). Spatial prediction for massive datasets. Mastering the Data Explosion in the Earth and Environmental Sciences: Proceedings of the Australian Academy of Science Elizabeth and Frederick White Conference. Australian Academy of Science, pp. 1–11.

  5. Cressie, N., & Johannesson, G. (2008). Fixed rank kriging for very large spatial data sets. Journal of the Royal Statistical Society, Series B, 70(1), 209–226.

    MathSciNet  Article  Google Scholar 

  6. Cressie, N. A. C. (1993). Statistics for Spatial Data (rev ed.). New York: Wiley.

    Google Scholar 

  7. Crowell, S., Baker, D., Schuh, A., Basu, S., Jacobson, A. R., Chevallier, F., et al. (2019). The 2015–2016 carbon cycle as seen from OCO-2 and the global in situ network. Atmospheric Chemistry and Physics, 19(15), 9797–9831. https://doi.org/10.5194/acp-19-979-2019.

    Article  Google Scholar 

  8. Eldering, A., Solish, B., Kahn, P., Boland, S., Crisp, D., & Gunson, M. (2012). High precision atmospheric \(\text{CO}_{2}\) measurements from space: The design and implementation of OCO-2. Proceedings of the 2012 IEEE Aerospace Conference, Big Sky, Montana, USA, March 3–10.

  9. Erickson, D. J., Mills, R. T., Gregg, J., Blasing, T. J., Hoffman, F. M., Andres, R. J., Devries, M., Zhu, Z., & Kawa, S. R. (2008). An estimate of monthly global emissions of anthropogenic \(\text{ CO }_{2}\): Impact on the seasonal cycle of atmospheric \(\text{ CO }_{2}\). Journal of Geophysical Research—Biogeosciences, 113(G1), Article G01023.

  10. Górski, K. M., Hivon, E., Banday, A. J., Wandelt, B. D., Hansen, F. K., Reinecke, M., et al. (2007). HEALPix: A framework for high-resolution discretization and fast analysis of data distributed on the sphere. The Astrophysical Journal, 622(2), 759–771.

    Article  Google Scholar 

  11. Kawa, S. R., Erickson III, D. J., Pawson, S., & Zhu, Z. (2004). Global \(\text{ CO }_{2}\) transport simulations using meteorological data from the NASA data assimilation system. Journal of Geophysical Research, 109, Article D18312.

  12. Ladstdter, F., et al. (2010). Exploration of climate data using interactive visualization. Journal of Atmospheric and Oceanic Technology, 27, 667–679.

    Article  Google Scholar 

  13. Nguyen, H., Cressie, N., & Braverman, A. (2012). Spatial statistical data fusion for remote-sensing applications. Journal of the American Statistical Association, 107, 1004–1018.

    MathSciNet  Article  Google Scholar 

  14. Olea, R. A. (1984). Sampling design optimization for spatial functions. Mathematical Geology, 16(4), 369–392.

    Article  Google Scholar 

  15. Petersen, D. P., & Middleton, D. (1962). Sampling and reconstruction of wave-number-limited functions in n-dimensional euclidean spaces. Information Control, 5, 279–323.

    MathSciNet  Article  Google Scholar 

  16. Peterson, P. (2007). Python for scientific computing. Computing in Science and Engineering, 9(90), 10–20.

    Google Scholar 

  17. Randerson, J. T., Thomps, M. V., Conw, T. J., Fun, I. Y., & Field, C. B. (1997). The contribution of terrestrial sources and sinks to trends in the seasonal cycle of atmospheric carbon dioxide. Global Biogeochemistry Cycles, 11(4), 535–560. https://doi.org/10.1029/97GB02268.

    Article  Google Scholar 

  18. Rodriges Zalipynis R. A., Zapletin E. A., & Averin G. V. (2011). The Wikience: Community data science. Concept and implementation. Proceedings of the 7th International Scientific-Technical Conference “Informatics and Computer Technologies (ICT-2011)”, November 22–23, 2011, Donetsk, Ukraine, Vol. 1, pp. 113–117.

  19. Rummelt, N. I., & Wilson, J. N. (2011). Array set addressing: Enabling technology for the efficient processing of hexagonally sampled imagery. Journal of Electronic Imaging, 20(2), Article 023012.

    Google Scholar 

  20. Sahr, K. (2011). Hexagonal discrete global grid systems for geospatial computing. Archives of Photogrammetry, Cartography and Remote Sensing, 22, 363–376.

    Google Scholar 

  21. Sahr, K., White, D., & Kimerling, A. J. (2003). Geodesic discrete global grid systems. Cartography and Geographic Information Science, 30(2), 121–134.

    Article  Google Scholar 

  22. Shi, T., & Cressie, N. (2007). Global statistical analysis of MISR aerosol data: A massive data product from NASA’s Terra satellite. Environmetrics, 18, 665–680.

    MathSciNet  Article  Google Scholar 

  23. Snyder, J. P. (1992). An equal-area map projection for polyhedral globes. Cartographica, 29(1), 10–21.

    Article  Google Scholar 

  24. Takahashi, T., Sutherland, S. C., Sweeney, C., Poisson, A., Metzl, N., Tilbrook, B., et al. (2002). Global sea-air \(\text{ CO }_{2}\) flux based on climatological surface ocean p\(\text{ CO }_{2}\), and seasonal biological and temperature effects. Deep-Sea Research Part II—Topical Studies In Oceanography, 49(9–10), 1601–1622.

    Article  Google Scholar 

  25. van der Werf, G. R., Randerson, J. T., Giglio, L., Collatz, G. J., Kasibhatla, P. S., & Arellano, A. F. (2006). Interannual variability in global biomass burning emissions from 1997 to 2004. Atmospheric Chemistry and Physics, 6, 3423–3441.

    Article  Google Scholar 

  26. Wikle, C. K., & Berliner, L. M. (2005). Combining information across spatial scales. Technometrics, 47, 80–91.

    MathSciNet  Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank Abhishek Chatterjee for processing and providing inputs on the use of PCTM/GEOS-4 global model data. They would also like to thank Jonathan Bradley, Jonathan Hobbs, Vineet Yadav, Chun-Houh Chen, Wolfgang Härdle, Antony Unwin, and Han-Ming (Hank) Wu for their contributions and comments. The work described in this article was carried out in part by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA. It was supported by NASA’s Earth Science Technology Office through its Advanced Information Systems Technology program. Cressie’s research was partially supported by an Australian Research Council Discovery Project DP190100180. Kang’s research was partially supported by the Simons Foundation’s Collaboration Award (#317298) and the Taft Research Center at the University of Cincinnati.

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Correspondence to T. Stough.

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Stough, T., Cressie, N., Kang, E.L. et al. Spatial analysis and visualization of global data on multi-resolution hexagonal grids. Jpn J Stat Data Sci 3, 107–128 (2020). https://doi.org/10.1007/s42081-020-00077-w

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Keywords

  • Geographic Information Science
  • Discrete global grids
  • Raster data modelling
  • Spatial analysis
  • Remote sensing