Identification of the best architecture of a multilayer perceptron in modeling daily total ozone concentration over Kolkata, India

Abstract

Autoregressive neural network (AR-NN) models of various orders have been generated in this work for the daily total ozone (TO) time series over Kolkata (22.56°N, 88.5°E). Artificial neural network in the form of multilayer perceptron (MLP) is implemented in order to generate the AR-NN models of orders varying from 1 to 13. An extensive variable selection method through multiple linear regression (MLR) is implemented while developing the AR-NNs. The MLPs are characterized by sigmoid non-linearity. The optimum size of the hidden layer is identified in each model and prediction are produced by validating it over the test cases using the coefficient of determination (R 2) and Willmott’s index (WI). It is observed that AR-NN model of order 7 having 6 nodes in the hidden layer has maximum prediction capacity. It is further observed that any increase in the orders of AR-NN leads to less accurate prediction.

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Refrences

  1. Abdollahian, M., R. Foroughi, and N. Debnath (2006), Optimal statistical model for forecasting ozone, J. Comput. Meth. Sci. Eng. 6,Suppl. 2, 321–336.

    Google Scholar 

  2. Aksoy, B., S. Incecik, S. Topcu, D. Demirhan Bari, C. Kahya, Y. Acar, M. Ozunlu, and M. Ekici (2009), Total ozone over Ankara and its forecasting using regression models, Int. J. Remote Sens. 30, 4387–4400, DOI: 10.1080/01431160802562297.

    Article  Google Scholar 

  3. Allen, D.R., and R.A. Reck (1997), Daily variation in TOMS total ozone data, J. Geophys. Res. 102,D12, 13603–13608, DOI: 10.1029/97JD00632.

    Article  Google Scholar 

  4. Badescu, V. (1994), Verification of a simple relationship of cloud shade to point cloudiness, Renew. Energ. 5, 1503–1505, DOI: 10.1016/0960-1481 (94)90196-1.

    Article  Google Scholar 

  5. Bandyopadhyay, G., and S. Chattopadhyay (2007), Single hidden layer artificial neural network models versus multiple linear regression model in forecasting the time series of total ozone, Int. J. Environ. Sci. Tech. 4, 141–149.

    Google Scholar 

  6. Bandyopadhyay, G., and S. Chattopadhyay (2008), A probe into the chaotic nature of total ozone time series by correlation dimension method, Soft Comput. 12, 1007–1012, DOI: 10.1007/s00500-007-0267-7.

    Article  Google Scholar 

  7. Benvenuto, F., and A. Marani (2000), Neural networks for environmental problems: Data quality control and air pollution nowcasting, Global Nest: Int. J. 2,3, 281–292.

    Google Scholar 

  8. Cannon, A.J., and P.H. Whitfield (2002), Downscaling recent streamflow conditions in British Columbia, Canada using ensemble neural network models, J. Hydrol. 259, 136–151, DOI: 10.1016/S0022-1694(01)00581-9.

    Article  Google Scholar 

  9. Cartalis, C., and C. Varotsos (1994), Surface ozone in Athens, Greece, at the beginning and at the end of the 20th century, Atmos. Environ. 28, 3–8, DOI: 10.1016/1352-2310(94)90018-3.

    Article  Google Scholar 

  10. Chattopadhyay, G., and S. Chattopadhyay (2009a), Autoregressive forecast of monthly total ozone concentration: A neurocomputing approach, Comput. Geosci. 35, 1925–1932, DOI: 10.1016/j.cageo.2008.11.007.

    Article  Google Scholar 

  11. Chattopadhyay, G., and S. Chattopadhyay (2009b), Predicting daily total ozone over Kolkata, India: Skill assessment of different neural network models, Meteorol. Appl. 16, 179–190, DOI: 10.1002/met.97.

    Article  Google Scholar 

  12. Chen, J.L., S. Islam, and P. Biswas (1998), Nonlinear dynamics of hourly ozone concentrations: nonparametric short term prediction, Atmos. Environ. 32, 1839–1848, DOI: 10.1016/S1352-2310(97)00399-3.

    Article  Google Scholar 

  13. Claude, H., U. Kohler, and W. Steinbrecht (2004), Evolution of ozone and temperature trends at Hohenpeissenberg (Germany). In: C.S. Zerefos (ed.), Proc. XX Quadrennial Ozone Symposium, 1–8 June 2004, Kos, Greece, 314–315.

  14. Comrie, A.C. (1997), Comparing neural networks and regression models for ozone forecasting, J. Air Waste Manage. 47, 360–363.

    Google Scholar 

  15. Corani, G. (2005), Air quality prediction in Milan: Feed-forward neural networks, pruned 16 neural networks and lazy learning, Ecol. Model. 185, 513–529, DOI: 10.1016/j.ecolmodel.2005.01.008.

    Article  Google Scholar 

  16. Demir, G., G. Altay, C.O. Sakar, S. Albayrak, H. Ozdemir, and S. Yalcin (2008), Prediction and evaluation of tropospheric ozone concentration in Istanbul using artificial neural network modeling according to time parameter, J. Sci. Ind. Res. India 67, 674–679.

    Google Scholar 

  17. Dorffner, G. (1996), Neural network for time series processing, Neural Netw. World 6, 447–468.

    Google Scholar 

  18. Errera, Q., and D. Fonteyn (2001), Four-dimensional variational chemical assimilation of CRISTA stratospheric measurements, J. Geophys. Res. 106,D11, 12253–12266, DOI: 10.1029/2001JD900010.

    Article  Google Scholar 

  19. Eskes, H., A. Segers, and P. van Velthoven (2005), Ozone forecasts of the stratospheric polar vortex-splitting event in September 2002, J. Atmos. Sci. 62, 812–821, DOI: 10.1175/JAS-3337.1.

    Article  Google Scholar 

  20. Gardner, M.W., and S.R. Dorling (1998), Artificial neural networks — the multilayer perceptron: A review of applications in atmospheric sciences, Atmos. Environ. 32, 2627–2636, DOI: 10.1016/S1352-2310(97)00447-0.

    Article  Google Scholar 

  21. Gilleland, E., and D. Nychka (2005), Statistical models for monitoring and regulating ground-level ozone, Environmetrics 16, 535–546, DOI: 10.1002/env.720.

    Article  Google Scholar 

  22. Graf-Jacottet, M., and M.H. Jaunin (1998), Predictive models for ozone and nitrogen dioxide time series, Environmetrics 9, 393–406, DOI: 10.1002/(SICI)1099-095X(199807/08)9:4〈393::AID-ENV310〉3.0.CO;2-W.

    Article  Google Scholar 

  23. Hansen, G., and T. Svenøe (2005), Multilinear regression analysis of the 65-year Tromsø total ozone series, J. Geophys. Res. 110, D10103, DOI: 10.1029/2004JD005387.

    Article  Google Scholar 

  24. Hauglustaine, D., L. Emmons, M. Newchurch, G. Brasseur, T. Takao, K. Matsubara, J. Johnson, B. Ridley, J. Stith, and J. Dye (2001), On the role of lightning NOx in the formation of tropospheric ozone plumes: A global model perspective, J. Atmos. Chem. 38, 277–294, DOI: 10.1023/A:1006452309388.

    Article  Google Scholar 

  25. Hrust, L., Z.B. Klaić, V. Križan, O. Antonić, and P. Hercog (2009), Neural network forecasting of air pollutants hourly concentrations using optimised temporal averages of meteorological variables and pollutant concentrations, Atmos. Environ. 43,35, 5588–5596, DOI: 10.1016/j.atmosenv.2009.07.048.

    Article  Google Scholar 

  26. Jacob, D.J. (2000), Heterogeneous chemistry and tropospheric ozone, Atmos. Environ. 34, 2131–2159, DOI: 10.1016/S1352-2310(99)00462-8.

    Article  Google Scholar 

  27. Kamarthi, S.V., and S. Pittner (1999), Accelerating neural network training using weight extrapolation, Neural Networks 12,9, 1285–1299, DOI: 10.1016/S0893-6080(99)00072-6.

    Article  Google Scholar 

  28. Koçak, K., L. Saylan, and O. Sen (2000), Nonlinear time series prediction of O3 concentration in Istanbul, Atmos. Environ. 34,8, 1267–1271, DOI: 10.1016/S1352-2310(99)00323-4.

    Article  Google Scholar 

  29. Kondratyev, K.Y., and C. Varotsos (2000), Atmospheric Ozone Variability: Implications for Climate Change, Human Health and Ecosystems, Springer, Chichester.

    Google Scholar 

  30. Kondratyev, K.Y., and C.A. Varotsos (2001a), Global tropospheric ozone dynamics—part I: Tropospheric ozone precursors, Environ. Sci. Pollut. Res. 8, 57–62, DOI: 10.1007/BF02987295.

    Article  Google Scholar 

  31. Kondratyev, K.Y., and C.A. Varotsos (2001b), Global tropospheric ozone dynamics—part II: Numerical modeling of tropospheric ozone variability, Environ. Sci. Pollut. Res. 8, 113–119, DOI: 10.1007/BF02987304.

    Article  Google Scholar 

  32. Lahoz, W.A., Q. Errera, R. Swinbank, and D. Fonteyn (2007), Data assimilation of stratospheric constituents: a review, Atmos. Chem. Phys. 7, 5745–5773, DOI: 10.5194/acp-7-5745-2007.

    Article  Google Scholar 

  33. Massart, B.G.J., and O.M. Kvalheim (1998), Ozone forecasting from meteorological variables — Part I: Predictive models by moving window and partial least squares regression, Chemometr. Intell. Lab. 42, 179–190, DOI: 10.1016/S0169-7439(98)00063-X.

    Article  Google Scholar 

  34. Monge Sanz, B.M., and N.J. Medrano Marqués (2004), Total ozone time series analysis: A neural network model approach, Nonlinear Proc. Geophys. 11, 683–689, DOI: 10.5194/npg-11-683-2004.

    Article  Google Scholar 

  35. Monge Sanz, B., and N. Medrano Marques (2003), Artificial neural networks applications for total ozone time series. In: M.J. A’lvarez Jr. (ed.), Proc. 7th Inter. Work-Conference on Artificial and Natural Neural Networks, IWANN, Menorca, Spain, June 2003, Springer, Berlin, 806–813.

    Google Scholar 

  36. Muller, M.D., A.K. Kaifel, M. Weber, S. Tellmann, J.P. Burrows, and D. Loyola (2003), Ozone profile retrieval from Global Ozone Monitoring Experiment (GOME) data using a neural network approach (Neural Network Ozone Retrieval System (NNORSY)), J. Geophys. Res. 108,D16, 4497, DOI: 10.1029/2002JD002784.

    Article  Google Scholar 

  37. NASA (1998), Earth Probe Total Ozone Mapping Spectrometer (TOMS) Data Products User’s Guide, NASA Technical Publication 20771, Goddard Space Flight Center Greenbelt, Maryland.

  38. Nunnari, G., A.F.M. Nucifiora, and C. Radineri (1998), The application of neural techniques to the modelling of time series of atmospheric pollution data, Ecol. Model. 111, 187–205, DOI: 10.1016/S0304-3800(98)00118-5.

    Article  Google Scholar 

  39. Oliveira, K.A. de, Á. Vannucci, and E.C. da Silva (2000), Using artificial neural networks to forecast chaotic time series, Physica A 284, 393–404, DOI: 10.1016/S0378-4371(00)00215-6.

    Article  Google Scholar 

  40. Pastor-Bárcenas, O., E. Soria-Olivas, J.D. Martín-Guerrero, G. Camps-Valls, J.L. Carrasco-Rodríguez, and S. del Valle-Tascón (2005), Unbiased sensitivity analysis and pruning techniques in neural networks for surface ozone modelling, Ecol. Model. 182, 149–158, DOI: 10.1016/j.ecolmodel.2004.07.015.

    Article  Google Scholar 

  41. Peréz, P., A. Trier, and J. Reyes (2000), Prediction of PM2.5 concentrations several hours in advance using neural networks in Santiago, Chile, Atmos. Environ. 34, 1189–1196, DOI: 10.1016/S1352-2310(99)00316-7.

    Article  Google Scholar 

  42. Principe, J.C., A. Rathie, and J.M. Kuo (1992), Prediction of chaotic time series with neural networks and the issue of dynamic modeling, Int. J. Bifurcat. Chaos 2, 989–996, DOI: 10.1142/S0218127492000598.

    Article  Google Scholar 

  43. Prybutok, R., Y. Junsub, and D. Mitchell (2000), Comparison of neural network models with ARIMA and regression models for prediction of Houston’s daily maximum ozone concentrations, Euro. J. Operat. Res. 122, 31–40, DOI: 10.1016/S0377-2217(99)00069-7.

    Article  Google Scholar 

  44. Rojas, R. (1996), Neural Networks: A Systematic Introduction, Springer, New York.

    Google Scholar 

  45. Rubin, M.B. (2001), The history of ozone. The Schönbein period, 1839–1868, Bull. Hist. Chem. 26, 40–56.

    Google Scholar 

  46. Seinfeld, J.H., and S.N. Pandis (1998), Atmospheric Chemistry and Physics — From Air Pollution to Climate Change, John Wiley & Sons, New York.

    Google Scholar 

  47. Silverman, D., and J.A. Dracup (2000), Artificial neural networks and longrange precipitation prediction in California, J. Appl. Meteorol. 39, 57–66, DOI: 10.1175/1520-0450(2000)039〈0057:ANNALR〉2.0.CO;2.

    Article  Google Scholar 

  48. Sivakumar, B., R. Berndtsson, and U. Lall (2004), Preface: Nonlinear deterministic dynamics in hydrologic systems: Present activities and future challenges, Nonlinear Proc. Geoph. 11, 1–2, http://www.nonlin-processes-geophys.net/prefaces/preface49.pdf.

    Article  Google Scholar 

  49. Soukharev, B.E., and L.L. Hood (2006), Solar cycle variation of stratospheric ozone: Multiple regression analysis of long-term satellite data sets and comparisons with models, J. Geophys. Res. 111, D20314, DOI: 10.1029/2006JD007107.

    Article  Google Scholar 

  50. Sousa, S.I.V., F.G. Martins, M.C. Pereira, and M.C.M. Alvim-Ferraz (2006), Prediction of ozone concentrations in Oporto city with statistical approaches, Chemosphere 64,7, 1141–1149, DOI: 10.1016/j.chemosphere.2005.11.051.

    Article  Google Scholar 

  51. Struthers, H., R. Brugge, W.A. Lahoz, A. O’Neill, and R. Swinbank (2002), Assimilation of ozone profiles and total column measurements into a global general circulation model, J. Geophys. Res. 107,D20, 4438, DOI: 10.1029/2001JD000957.

    Article  Google Scholar 

  52. Thompson, A.M., J.C. Witte, R.D. Hudson, H. Guo, J.R. Herman, and M. Fujiwara (2001), Tropical tropospheric ozone and biomass burning, Science 291, 2128–2132, DOI: 10.1126/science.291.5511.2128.

    Article  Google Scholar 

  53. Varotsos, C. (2005), Power-law correlations in column ozone over Antarctica, Int. J. Remote Sens. 26, 3333–3342, DOI: 10.1080/01431160500076111.

    Article  Google Scholar 

  54. Varotsos, C., and D. Krik-Davidoff (2006), Long-memory processes in ozone and temperature variations at the region 60 degrees S — 60 degrees N, Atmos. Chem. Phys. 6, 4093–4100, DOI: 10.5194/acp-6-4093-2006.

    Article  Google Scholar 

  55. Varotsos, C., D. Alexandris, G. Chronopoulos, and C. Tzanis (2001), Aircraft observations of the solar ultraviolet irradiance throughout the troposphere, J. Geophys. Res. 106,D14, 14843–14854, DOI: 10.1029/2001JD900045.

    Article  Google Scholar 

  56. Viotti, P., G. Liuti, and P. Di Genova (2002), Atmospheric urban pollution: Application of an artificial neural network to the city of Perugia, Ecol. Model. 148, 27–46, DOI: 10.1016/S0304-3800(01)00434-3.

    Article  Google Scholar 

  57. Wang, W., W. Lu, X. Wang, and A. Leung (2003), Prediction of maximum daily ozone level using combined neural network and statistical characteristics, Environ. Int. 29, 555–562, DOI: 10.1016/S0160-4120(03)00013-8.

    Article  Google Scholar 

  58. Widrow, B., and M.A. Lehr (1990), 30 years of adaptive neural networks: perceptron, Madaline and backpropagation, Proc. IEEE 78,9, 1415–1442, DOI: 10.1109/5.58323.

    Article  Google Scholar 

  59. Wilks, D.S. (2006), Statistical Methods in Atmospheric Sciences, 2nd ed., Elsevier, Amsterdam.

    Google Scholar 

  60. Willmott, C.J. (1982), Some comments on the evaluation of model performance, Bull. Amer. Meteor. Soc. 63, 1309–1313, DOI: 10.1175/1520-0477(1982) 063〈1309:SCOTEO〉2.0.CO;2.

    Article  Google Scholar 

  61. Willmott, C.J., R.E. Davis, J.J. Feddema, K.M. Klink, D.R. Legates, C.M.A. Rowe, G. Steven, and J. O’Donnell (1985), Statistics for the evaluation and comparison of models, J. Geophys. Res. 90,C5, 8995–9005, DOI: 10.1029/JC090iC05p08995.

    Article  Google Scholar 

  62. Wolff, G. (1998), Air pollution. In: R.A. Meyer (ed.), Encyclopedia on Environmental Analysis and Remediation, John Wiley, New York, 129–150.

    Google Scholar 

  63. Yegnanarayana, B. (2004), Artificial Neural Networks, Prentice Hall, India.

    Google Scholar 

  64. Yi, J., and V.R. Pybutok (1996), A neural network model forecasting for prediction of daily maximum ozone concentration in an industrialized urban area, Environ. Pollut. 92,3, 349–357, DOI: 10.1016/0269-7491(95)00078-X.

    Article  Google Scholar 

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De, S.S., De, B.K., Chattopadhyay, G. et al. Identification of the best architecture of a multilayer perceptron in modeling daily total ozone concentration over Kolkata, India. Acta Geophys. 59, 361–376 (2011). https://doi.org/10.2478/s11600-010-0047-0

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Key words

  • autoregressive neural network
  • daily total ozone
  • multilayer perceptron
  • coefficient of determination
  • Willmott’s index