Environmental Monitoring and Assessment

, Volume 186, Issue 8, pp 4719–4742 | Cite as

Mann–Kendall trend of pollutants, temperature and humidity over an urban station of India with forecast verification using different ARIMA models

  • Sutapa ChaudhuriEmail author
  • Debashree Dutta


The purpose of the present research is to identify the trends in the concentrations of few atmospheric pollutants and meteorological parameters over an urban station Kolkata (22° 32′ N; 88° 20′ E), India, during the period from 2002 to 2011 and subsequently develop models for precise forecast of the concentration of the pollutants and the meteorological parameters over the station Kolkata. The pollutants considered in this study are sulphur dioxide (SO2), nitrogen dioxide (NO2), particulates of size 10-μm diameters (PM10), carbon monoxide (CO) and tropospheric ozone (O3). The meteorological parameters considered are the surface temperature and relative humidity. The Mann–Kendall, non-parametric statistical analysis is implemented to observe the trends in the data series of the selected parameters. A time series approach with autoregressive integrated moving average (ARIMA) modelling is used to provide daily forecast of the parameters with precision. ARIMA models of different categories; ARIMA (1, 1, 1), ARIMA (0, 2, 2) and ARIMA (2, 1, 2) are considered and the skill of each model is estimated and compared in forecasting the concentration of the atmospheric pollutants and meteorological parameters. The results of the study reveal that the ARIMA (0, 2, 2) is the best statistical model for forecasting the daily concentration of pollutants as well as the meteorological parameters over Kolkata. The result is validated with the observation of 2012.


Mann–Kendall trend ARIMA Pollutants Meteorological parameters 



The authors thank the IMD and WBPCB for providing the data for research and Department of Science and Technology (DST) for financial assistance under PURSE and INSPIRE programme. The MoES, Government of India supported Air Quality Monitoring Network (MAPAN) is acknowledged for the MOU with DAS-CU.


  1. Akaike, H. (1969). Fitting autoregressive models for prediction. Annals of the Institute of Statistical Mathematics, 21, 243–247.CrossRefGoogle Scholar
  2. Akaike, H. (1970). Statistical predictor identification. Annals of the Institute of Statistical Mathematics, 22, 203–217.CrossRefGoogle Scholar
  3. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle, in Perron, B. N. and Csaki, F. (eds), 2nd International Symposium in Information Theory, Budapest: Akademial Kiodo, 207 – 261.Google Scholar
  4. Akaike, H. (1979). A Bayesian extension of the minimum AIC procedure of autoregressive model fitting. Biometrika, 66(2), 237–242.CrossRefGoogle Scholar
  5. Beveridge, S., & Oickle, C. (1994). Comparison of Box-Jenkins and objective methods for determining the order of a non-seasonal ARMA Model. Journal of Forecasting, 13, 419–434.CrossRefGoogle Scholar
  6. Brockwell, P. J., & Davis, R. A. (1996). Introduction to time series and forecasting. New York: Springer.CrossRefGoogle Scholar
  7. Chaudhuri, S., & Middey, A. (2013). Effect of meteorological parameters and environmental pollution on thunderstorm and lightning activity over an urban metropolis of India. Urban Climate, 3, 67–75.CrossRefGoogle Scholar
  8. DeCaria, A. J., Pickering, K. E., Stenchikov, G. L., & Ott, L. E. (2005). Lightning generated NOX and its impact on tropospheric ozone production: a three-dimensional modeling study of a stratosphere-troposphere experiment: radiation, aerosols and ozone (STERAO-A) thunderstorm. Journal of Geophysical Research, 110, D14303. doi: 10.1029/2004JD005556.CrossRefGoogle Scholar
  9. De Gooijer, J. G., Abraham, B., Gould, A., & Robinson, L. (1985). Methods for determining the order of an autoregressive moving average process: a survey. International Statistical Review, 53, 301–329.CrossRefGoogle Scholar
  10. Domonkos, P., Kysel, J. Y., Piotrowicz, K., Petrovic, P., & Likso, T. (2003). Variability of extreme temperature events in south–central Europe during the 20th century and its relationship with large-scale circulation. International Journal of Climatology, 23, 978–1010.CrossRefGoogle Scholar
  11. Hannan, E. J. (1980). The estimation of the order of an ARMA process. Annals of Statistics, 8, 1071–1081.CrossRefGoogle Scholar
  12. Hargreaves, P. R., Leidi, A., Grubb, H. J., Howe, M. T., & Mugglestone, M. A. (2000). Local and seasonal variations in atmospheric nitrogen dioxide levels at Rothamsted, UK, and relationships with meteorological conditions. Atmospheric Environment, 34, 843–853.CrossRefGoogle Scholar
  13. Hirsch, R. M., Slack, J. R., & Smith, R. A. (1982). Techniques for trend assessment for monthly water quality data. Water Resources Research, 18, 107–121.CrossRefGoogle Scholar
  14. Hurvich, C. M., & Tsai, C. L. (1989). Regression and time series model selection in small samples. Biometrika, 76, 297–307.CrossRefGoogle Scholar
  15. Gilbert, R. O. (1987). Statistical methods for environmental pollution monitoring. New York: Van Nostrand Reinhold Co.. 320 pp.Google Scholar
  16. Jones, R. H. (1975). Fitting autoregressions. Journal of American Statistics Association, 70, 90–592.Google Scholar
  17. Luo, Y., Liu, S., Fu, S. F., Liu, J., Wang, G., & Zhou, G. (2008). Trends of precipitation in Beijiang River Basin, Guangdong Province. China. Hydrological Processes, 22, 2377–2386.CrossRefGoogle Scholar
  18. Libiseller, C., Grimvall, A., Waldén, J., & Saari, H. (2005). Meteorological normalisation and non-parametric smoothing for quality assessment and trend analysis of tropospheric ozone data. Environmental Monitoring and Assessment, 100(1–3), 33–52.CrossRefGoogle Scholar
  19. Middey, A., & Chaudhuri, S. (2013). The reciprocal relation between lightning and pollution and their impact over Kolkata, India. Environmental Science and Pollution Research, 20(5), 3133–3139.CrossRefGoogle Scholar
  20. Montgomery, D. C., & Johnson, L. A. (1976). Forecasting and time series analysis. New York: McGraw-Hill.Google Scholar
  21. Reeves, C. E., Penkett, A., Bauguitte, S., Law, K. S., Evans, M. J., Bandy, B. J., Monks, P. S., Edwards, G. D., Phillips, G., Barjat, H., Kent, J., Dewey, K., Schmitgen, S., & Kley, D. (2002). Potential for photochemical ozone formation in the troposphere over the North Atlantic as derived from aircraft observations during ACSOE. Journal of Geophysical Research, 107(D23), 4707. doi: 10.1029/2002JD002415.CrossRefGoogle Scholar
  22. Salmi, T., Maata, A., Antilla, P., Ruoho-Airola, T., & Amnell, T. (2002). Detecting trends of annual values of atmospheric pollutants by the Mann–Kendall test and Sen’s slope estimates—the Excel template application Makesens (p. 35). Helsinki, Finland: Finnish Meteorological Institute.Google Scholar
  23. Shahid, S. (2011). Trends in extreme rainfall events of Bangladesh. Theoretical and Applied Climatology, 104, 489–499.CrossRefGoogle Scholar
  24. Shrestha, A. B., Wake, C. P., Mayewski, P. A., & Dibb, J. E. (1999). Maximum temperature trends in the Himalaya and its vicinity: an analysis based on temperature records from Nepal for the period 1971–94. Journal of Climate, 12, 2775–2786.CrossRefGoogle Scholar
  25. Shibata, R. (1976). Selection of the order of an autoregressive model by Akaike’s information criterion. Biometrika, 63(1), 117–126.CrossRefGoogle Scholar
  26. Söderström T. (1977) On model structure testing in system identification. International Journal of Control, 26, 1–18.Google Scholar
  27. Stedman, J. R., Goodwin, J. W. L., King, K., Murrells, T. P., & Bush, T. J. (2001). An empirical model for predicting urban roadside nitrogen dioxide concentrations in the UK. Atmospheric Environment, 35, 1451–1463.CrossRefGoogle Scholar
  28. Stoica, P., Eykhoff, P., Jansen, P., & Söderström, T. (1986). Model selection by cross-validation. International Journal of Control, 43, 1841–1878.CrossRefGoogle Scholar
  29. Yue, S., Pilon, P., Phinney, B., & Cavadias, G. (2002). The influence of autocorrelation on the ability to detect trend in hydrological series. Hydrological Processes, 16, 1807–1829.CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Atmospheric SciencesUniversity of CalcuttaKolkataIndia

Personalised recommendations