Skip to main content
SpringerLink
Log in

B-Spline Method for Spatio-Temporal Inverse Model

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

Inverse models can be used to estimate surface fluxes in terms of the observed atmospheric concentration measurement data. This paper proposes a new nonparametric spatio-temporal inverse model and provides the global expressions for the estimates by employing the B-spline method. The authors establish the asymptotic normality of the estimators under mild conditions. The authors also conduct numerical studies to evaluate the finite sample performance of the proposed methodologies. Finally, the authors apply the method to anthropogenic carbon dioxide (CO2) emission data from different provinces of Canada to illustrate the validity of the proposed techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hoek G, Krishnan R M, Beelen R, et al., Long-term air pollution exposure and cardio-respiratory mortality: A review, Environmental Health, 2013, 12(1): 43.

    Article  Google Scholar 

  2. Ji H, Wang J, Meng B, et al, Research on adaption to air pollution in chinese cities: Evidence from social media-based health sensing, Environmental Research, 2022, 210: 112762.

    Article  Google Scholar 

  3. Phalen R F and Phalen R N, Introduction to Air Pollution Science, Bartlett Learning, Jones, 2011.

    Google Scholar 

  4. Miao Y, Porter W C, Schwabe K, et al., Evaluating health outcome metrics and their connections to air pollution and vulnerability in Southern California’s coachella valley, Science of the Total Environment, 2022, 921: 153255.

    Article  Google Scholar 

  5. Byun D and Schere K L, Review of the governing equations, computational algorithms, and other components of the models-3 community multiscale air quality (CMAQ) modeling system, Applied Mechanics Reviews, 2006, 59(2): 51.

    Article  Google Scholar 

  6. El-Harbawl M, Air quality modelling, simulation, and computational methods: A review, Environmental Reviews, 2013, 21(3): 149–179.

    Article  Google Scholar 

  7. Fast J D, Gustafson W I, Easter R C, et al., Evolution of ozone, particulates, and aerosol direct forcing in an urban area using a new fully-coupled meteorology, chemistry, and aerosol model, Journal of Geophysical Research Atmospheres, 2006, 111: D21.

    Article  Google Scholar 

  8. Zhu Y, Liang Y, and Chen S X, Assessing local emission for air pollution via data experiments, Atmospheric Environment, 2020, 252: 118323.

    Article  Google Scholar 

  9. Bergamaschi P, Krol M, Dentener F, et al., Inverse modelling of national and European CH4emissions using the atmospheric zoom model TM5, Atmospheric Chemistry and Physics, 2005, 5(1): 2431–2460.

    Article  Google Scholar 

  10. Bergamaschi P, Krol M, Meirink J F, et al., Inverse modeling of European CH4 emissions 2001–2006, Journal of Geophysical Research Atmospheres, 2010, 115: D22309.

    Article  Google Scholar 

  11. Rigby M, Manning A J, and Prinn R G, Inversion of long-lived trace gas emissions using combined Eulerian and Lagrangian chemical transport models, Atmospheric Chemistry and Physics, 2011, 11(18): 9887–9898.

    Article  Google Scholar 

  12. Zhao C, Andrews A E, Bianco L, et al., Atmospheric inverse estimates of methane emissions from Central California, Journal of Geophysical Research Atmospheres, 2009, 114: D16.

    Article  Google Scholar 

  13. Jeong S, Zhao C, Andrews A E, et al., Seasonal variation of CH4 emissions from Central California, Journal of Geophysical Research Atmospheres, 2012, 117: D11.

    Article  Google Scholar 

  14. Brioude J, Kim S W, Angevine W M, et al., Top-down estimate of anthropogenic emission inventories and their interannual variability in Houston using a mesoscale inverse modeling technique, Journal of Geophysical Research, 2011, 116(D20): D20305.

    Article  Google Scholar 

  15. Brioude J, Petron G, Frost G J, et al., A new inversion method to calculate emission inventories without a prior at mesoscale: Application to the anthropogenic CO2 emission from Houston, Texas, Journal of Geophysical Research Atmospheres, 2012, 117(D5): 214–221.

    Article  Google Scholar 

  16. Brioude J, Angevine W M, Ahmadov R, et al., Top-down estimate of surface flux in the Los Angeles Basin using a mesoscale inverse modeling technique: Assessing anthropogenic emissions of CO, NOx and CO2 and their impacts, Atmospheric Chemistry and Physics, 2013, 13(7): 3661–3677.

    Article  Google Scholar 

  17. Miller S M, Wofsy S C, Michalak A M, et al., Anthropogenic emissions of methane in the United States, Proceedings of the National Academy of Sciences, 2013, 110(50): 20018–20022.

    Article  Google Scholar 

  18. Bruhwiler L, Dlugokencky E, Masarie K, et al., Carbon Tracker-CH4, an assimilation system for estimating emissions of atmospheric methane, Atmospheric Chemistry and Physics, 2014, 14(2): 8269–8293.

    Article  Google Scholar 

  19. Vogel F R, Ishizawa M, Chan E, et al., Regional non-CO2 greenhouse gas fluxes inferred from atmospheric measurements in Ontario, Canada, Journal of Integrative Environmental Sciences, 2012, 9(1): 41–55.

    Article  Google Scholar 

  20. Chan E, Chan D, Ishizawa M, et al., Investigation of error sources in regional inverse estimates of greenhouse gas emissions in Canada, Atmospheric Chemistry and Physics, 2015, 15: 22715–22779.

    Google Scholar 

  21. Hallin M, Lu Z, and Tran L T, Local linear spatial regression, The Annals of Statistics, 2004, 32(6): 2469–2500.

    Article  MathSciNet  MATH  Google Scholar 

  22. Wang H, Wang J, and Huang B, Prediction for spatiotemporal models with autoregression in errors, Journal of Nonparametric Statistics, 2012, 24(1): 217–244.

    Article  MathSciNet  MATH  Google Scholar 

  23. Tang Q and Chen L, B-spline estimation for varying coefficient models with spatial data, Science China Series A, 2009, 52(11): 2321–2340.

    Article  MathSciNet  MATH  Google Scholar 

  24. Stone C J, Optimal global rates of convergence for nonparametric regression, The Annals of Statistics, 1982, 10(4): 1040–1053.

    Article  MathSciNet  MATH  Google Scholar 

  25. Schumaker L, Spline Functions: Basic Theory, 3rd Edition, Cambridge University Press, Cambridge, 2007.

    Book  MATH  Google Scholar 

  26. Cressie N A C, Statistics for Spatial Data, Wiley, New Jersey, 1993.

    Book  MATH  Google Scholar 

  27. Schwarz G, Estimating the dimension of a model, The Annals of Statistics, 1978, 6(2): 461–464.

    Article  MathSciNet  MATH  Google Scholar 

  28. Pace R K, Barry R, Gilley O W, et al., A method for spatial-temporal forecasting with an application to real estate price, International Journal of Forecasting, 2000, 16(2): 229–246.

    Article  Google Scholar 

  29. Ibragimov I A and Linnik Y V, Independent and Stationary Sequences of Random Variables, Wolters-Noordhoff, Groningen, 1971.

    MATH  Google Scholar 

  30. Deo C M, A note on empirical process of strong mixing sequences, Annals of Statistics, 1973, 1(5): 870–875.

    MATH  Google Scholar 

  31. Wang H and Wang J, Estimation of the trend function for spatio-temporal models, Journal of Nonparametric Statistics, 2009, 21(5): 567–588.

    Article  MathSciNet  MATH  Google Scholar 

  32. Lu Z and Linton O, Local linear fitting under near epoch dependence, Econometric Theory, 2007, 23: 37–70.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Statistics and Data Science, Nanjing Audit University, Nanjing, 211815, China

    Hongxia Wang & Zihan Zhao

  2. Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada

    Yuehua Wu

  3. Department of Statistics and Data Science, School of Economics, Xiamen University, Xiamen, 361005, China

    Xuehong Luo

Authors
  1. Hongxia Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zihan Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuehua Wu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xuehong Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Hongxia Wang, Zihan Zhao, Yuehua Wu or Xuehong Luo.

Additional information

This research was supported by the National Social Science Fund of China under Grant No. 22BTJ021, “Qinglan project” of Colleges and Universities of Jiangsu Province and Postgraduate Research & Practice Innovation Program of Jiangsu Province under Grant No. KYCX21_1941.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, H., Zhao, Z., Wu, Y. et al. B-Spline Method for Spatio-Temporal Inverse Model. J Syst Sci Complex 35, 2336–2360 (2022). https://doi.org/10.1007/s11424-022-1206-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-022-1206-5

Keywords

Search

Navigation