Skip to main content

Advertisement

Log in

A varying-coefficient regression approach to modeling the effects of wind speed on the dispersion of pollutants

  • Published:
Environmental and Ecological Statistics Aims and scope Submit manuscript

Abstract

The real-world monitoring system of air pollution ordinarily collects data about pollutant concentration levels at pollution sources and monitors stations in a high-frequency manner. Inspired atmospheric models, the meteorological conditions could play an important role in building up the data-driven model for dispersing atmospheric pollutants from pollution sources to monitor stations. We propose a varying-coefficient model to analyze how emissions of monitor stations are influenced by pollution sources with changing with the wind speed. To estimate the unknown coefficient curves, we use a spline basis to approximate the functions. The asymptotic properties of the proposed method are studied and show the consistency of the estimator. Inference procedures based on a resampling subject bootstrap is developed to construct the conservative confidence bands. A simulation study is carried out to demonstrate the performance of our method. Illustrated by a real-world dataset of environmental sensors collected in Shenyang, China, the proposed varying-coefficient model reveals that the wind speed changes the dispersion mechanism of atmospheric pollutants between monitor stations and pollution sources.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

Data availability

The data are provided on GitHub at https://github.com/rucwyf/VCMData.

Code Availability

Code upon request.

References

  • Boor CD (1978) A practical guide to splines. Springer, New York

    Book  Google Scholar 

  • Chiang C-T, Rice JA, Wu CO (2001) Smoothing spline estimation for varying coefficient models with repeatedly measured dependent variables. J Am Stat Assoc 96(454):605–619

    Article  Google Scholar 

  • Cimorelli AJ, Perry SG, Venkatram A, Weil JC, Paine RJ, Wilson RB, Lee RF, Peters WD, Brode RW (2005) AERMOD: a dispersion model for industrial source applications. part I: general model formulation and boundary layer characterization. J Appl Meteorol 44(5):682–693

    Article  Google Scholar 

  • Davidian M, Giltinan DM (1995) Nonlinear models for repeated measurement data. Chapman Hall, London

    Google Scholar 

  • Diggle P, Heagerty PJ, Liang K-Y, Zeger SL (1994) Analysis of longitudinal data. Oxford University Press, Oxford

    Google Scholar 

  • Efron B (1981) Nonparametric standard errors and confidence intervals. Can J Stat-revue Canadienne De Statistique 9(2):139–158

    Article  Google Scholar 

  • Efron B (1982) The jackknife, the bootstrap, and other resampling plans. Siam, Philadelphia

    Book  Google Scholar 

  • Efron B (1987) Better bootstrap confidence intervals. J Am Stat Assoc 82(397):171–185

    Article  Google Scholar 

  • Fan J, Ma Y, Dai W (2014) Nonparametric independence screening in sparse ultra-high-dimensional varying coefficient models. J Am Stat Assoc 109(507):1270–1284

    Article  CAS  Google Scholar 

  • Fan J, Zhang W (2008) Statistical methods with varying coefficient models. Stat Interface 1(1):179–195

    Article  Google Scholar 

  • Gibson MD, Kundu S, Satish M (2013) Dispersion model evaluation of PM2.5, NOx and SO2 from point and major line sources in Nova Scotia, Canada using AERMOD Gaussian plume air dispersion model. Atmos Pollut Res 4(2):157–167

    Article  CAS  Google Scholar 

  • He K, Lian H, Ma S, Huang JZ (2018) Dimensionality reduction and variable selection in multivariate varying-coefficient models with a large number of covariates. J Am Stat Assoc 113(522):746–754

    Article  CAS  Google Scholar 

  • Henry RC, Chang Y-S, Spiegelman CH (2002) Locating nearby sources of air pollution by nonparametric regression of atmospheric concentrations on wind direction. Atmos Environ 36(13):2237–2244

    Article  CAS  Google Scholar 

  • Hoover DR, Rice JA, Wu CO, Yang L-P (1998) Nonparametric smoothing estimates of time-varying coefficient models with longitudinal data. Biometrika 85(4):809–822

    Article  Google Scholar 

  • Huang J, Horowitz JL, Wei F (2010) Variable selection in nonparametric additive models. Ann Stat 38(4):2282–2313

    PubMed  PubMed Central  Google Scholar 

  • Huang JZ, Wu CO, Zhou L (2002) Varying-coefficient models and basis function approximations for the analysis of repeated measurements. Biometrika 89(1):111–128

    Article  Google Scholar 

  • Huang JZ, Wu CO, Zhou L (2004) Polynomial spline estimation and inference for varying coefficient models with longitudinal data. Stat Sin 14(3):763–788

    Google Scholar 

  • Lai M-J, Schumaker LL (2007) Spline functions on triangulations. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Lee K, Lee YK, Park BU, Yang SJ (2018) Time-dynamic varying coefficient models for longitudinal data. Comput Stat Data Anal 123:50–65

    Article  Google Scholar 

  • Lin H, Zhang R, Shi J (2017) Local estimation for varying-coefficient models with longitudinal data. Commun Stat-theory Methods 46(15):7511–7528

    Article  Google Scholar 

  • Liu S (2017) Efficient estimation of longitudinal data additive varying coefficient regression models. Acta Math Appl Sin 33(2):529–550

    Article  Google Scholar 

  • Liu S, Lian H (2018) Robust estimation and model identification for longitudinal data varying-coefficient model. Commun Stat-Theory Methods 47(11):2701–2719

    Article  Google Scholar 

  • Lushi E, Stockie JM (2010) An inverse Gaussian plume approach for estimating atmospheric pollutant emissions from multiple point sources. Atmos Environ 44(8):1097–1107

    Article  CAS  Google Scholar 

  • Pancras JP, Ondov JM, Poor N, Landis MS, Stevens RK (2006) Identification of sources and estimation of emission profiles from highly time-resolved pollutant measurements in Tampa, FL. Atmos Environ 40:467–481

    Article  Google Scholar 

  • Park BU, Mammen E, Lee YK, Lee ER (2015) Varying coefficient regression models: a review and new developments. Int Stat Rev 83(1):36–64

    Article  Google Scholar 

  • Ramsay JO, Silverman BW (2005) Functional data analysis, 2nd edn. Springer Science & Business Media, New York

    Book  Google Scholar 

  • Schumaker L (2007) Spline functions: basic theory, 3rd edn. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Tang Q, Cheng L (2008) M-estimation and B-spline approximation for varying coefficient models with longitudinal data. J Nonparametric Stat 20(7):611–625

    Article  Google Scholar 

  • Venkatram A, Fitz D, Bumiller K, Du S, Boeck M, Ganguly C (1999) Using a dispersion model to estimate emission rates of particulate matter from paved roads. Atmos Environ 33(7):1093–1102

    Article  CAS  Google Scholar 

  • Verbeke G, Molenberghs G (2000) Linear mixed models for longitudinal data. Springer, New York

    Google Scholar 

  • Vonesh EF, Chinchilli VM (1996) Linear and nonlinear models for the analysis of repeated measurements. Marcel Dekker, New York

    Book  Google Scholar 

  • Weitkamp EA, Lipsky EM, Pancras PJ, Ondov JM, Polidori A, Turpin BJ, Robinson AL (2005) Fine particle emission profile for a large coke production facility based on highly time-resolved fence line measurements. Atmos Environ 39(36):6719–6733

    Article  CAS  Google Scholar 

  • Williams B, Christensen WF, Reese CS (2011) Pollution source direction identification: embedding dispersion models to solve an inverse problem. Environmetrics 22(8):962–974

    Article  CAS  Google Scholar 

  • Wu CO, Yu KF (2002) Nonparametric varying-coefficient models for the analysis of longitudinal data. Int Stat Rev 70(3):373–393

    Article  Google Scholar 

  • Xue L, Zhu L (2007) Empirical likelihood for a varying coefficient model with longitudinal data. J Am Stat Assoc 102(478):642–654

    Article  CAS  Google Scholar 

  • Zhang X, Wang J-L (2015) Varying-coefficient additive models for functional data. Biometrika 102(1):15–32

    Article  CAS  Google Scholar 

  • Zhao P, Xue L (2009) Empirical likelihood inferences for semiparametric varying-coefficient partially linear errors-in-variables models with longitudinal data. J Nonparametric Stat 21(7):907–923

    Article  Google Scholar 

Download references

Acknowledgements

The authors thank the editor, the associate editor, and the reviewers for their comments that helped significantly improve this work. This research was supported by the National Key R &D Program of China (Grant No. 2018YFC2000302), by Public Computing Cloud, Renmin University of China, and partially by the National Natural Science Foundation of China (Grant No. 11801560).

Author information

Authors and Affiliations

Authors

Contributions

Conceptualization and data preparation: HY; Methodology: KH;Simulation and real data analysis:YW and WS;Writing—original draft preparation: KH and WS; Writing—review and editing: KH, YW and HY.

Corresponding author

Correspondence to Hanfang Yang.

Additional information

Handling Editor Pierre Dutilleul.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary file 1 (pdf 304 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

He, K., Wang, Y., Su, W. et al. A varying-coefficient regression approach to modeling the effects of wind speed on the dispersion of pollutants. Environ Ecol Stat 29, 433–452 (2022). https://doi.org/10.1007/s10651-022-00535-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10651-022-00535-6

Keywords

Navigation