Sains Malaysiana 44(2)(2015): 175–186

PM10 Analysis for Three Industrialized Areas using Extreme Value

(Analisis PM10 bagi Tiga Kawasan Industri menggunakan Nilai Melampau)

HASFAZILAH AHMAT^1,2*, AHMAD SHUKRI YAHAYA¹ & NOR AZAM RAMLI¹

¹Clean Air Research Group, School of Civil Engineering, Engineering Campus, Universiti Sains Malaysia, 14300 Pulau Pinang, Malaysia

²Hasfazilah Ahmat*

Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA

13500 Permatang Pauh, Pulau Pinang, Malaysia

Diserahkan: 26 Mac 2014/Diterima: 3 Ogos 2014

ABSTRACT

One of the concerns of the air pollution studies is to compute the concentrations of one or more pollutants' species in space and time in relation to the independent variables, for instance emissions into the atmosphere, meteorological factors and parameters. One of the most significant statistical disciplines developed for the applied sciences and many other disciplines for the last few decades is the extreme value theory (EVT). This study assesses the use of extreme value distributions of the two-parameter Gumbel, two and three-parameter Weibull, Generalized Extreme Value (GEV) and two and three-parameter Generalized Pareto Distribution (GPD) on the maximum concentration of daily PM10 data recorded in the year 2010 - 2012 in Pasir Gudang, Johor; Bukit Rambai, Melaka; and Nilai, Negeri Sembilan. Parameters for all distributions are estimated using the Method of Moments (MOM) and Maximum Likelihood Estimator (MLE). Six performance indicators namely; the accuracy measures which include predictive accuracy (PA), Coefficient of Determination (R2), Index of Agreement (IA) and error measures that consist of Root Mean Square Error (RMSE), Mean Absolute Error (MAE) and Normalized Absolute Error (NAE) are used to find the goodness-of-fit of the distribution. The best distribution is selected based on the highest accuracy measures and the smallest error measures. The results showed that the GEV is the best fit for daily maximum concentration for PM10 for all monitoring stations. The analysis also demonstrates that the estimated numbers of days in which the concentration of PM10 exceeded the Malaysian Ambient Air Quality Guidelines (MAAQG) of 150 mg/m³ are between ½ and 1½ days.

Keywords: Air pollution; extreme value theory (EVT); PM10; prediction

ABSTRAK

Salah satu kebimbangan di dalam kajian pencemaran udara adalah untuk menyukat kepekatan satu atau lebih zarah pencemar di dalam ruang dan masa berhubung dengan pemboleh ubah bebas, sebagai contoh untuk pelepasan ke atmosfera, faktor dan parameter cuaca. Salah satu disiplin statistik yang paling penting untuk sains gunaan dan pelbagai bidang lain untuk beberapa dekad yang lalu adalah teori nilai melampau (EVT). Kajian ini menilai penggunaan taburan nilai melampau dua parameter Gumbel, dua dan tiga parameter Weibull, Nilai Ekstrim Teritlak (GEV) dan dua dan tiga parameter Taburan Pareto Teritlak (GPD) pada kepekatan maksimum data harian PM10 yang dicatatkan dalam tahun 2010 - 2012 di Pasir Gudang, Johor; Bukit Rambai, Melaka dan Nilai, Negeri Sembilan. Parameter untuk semua taburan dianggarkan menggunakan kaedah momen (MOM) dan Penganggar Kebolehjadian Maksimum (MLE). Enam petunjuk prestasi iaitu; pengukuran kejituan termasuk Ketepatan Peramalan (PA), Pekali Penentuan (R₂), Indeks Persetujuan (IA) dan pengukuran ralat yang terdiri daripada Ralat Min Punca Kuasa Dua (RMSE), Min Ralat Mutlak (MAE) dan Ralat Mutlak Ternormal (NAE) digunakan untuk mencari kebaikan penyesuaian taburan. Taburan terbaik dipilih berdasarkan pengukuran kejituan tertinggi dan pengukuran ralat yang terkecil. Hasil kajian menunjukkan bahawa GEV adalah taburan terbaik untuk kepekatan maksimum harian bagi PM10 di kesemua stesen pemantauan. Analisis juga menunjukkan bahawa anggaran bilangan hari kepekatan PM10 melebihi Garis Panduan Kualiti Udara Ambien Malaysia (MAAQG) bagi kepekatan harian PM10 iaitu 150 μg/m³ adalah antara ½ dan 1½ hari.

Kata kunci: Nilai melampau (EVT); pencemaran udara; peramalan teori; PM10

RUJUKAN

Abd-el-hakim, Nagi, S. & Khalaf S Sultan. 2004. Maximum likelihood estimation from record-breaking data for the generalized pareto distribution. International Journal of Statistics LXII 3: 377-389.

Afroz, R., Mohd Nasir Hassan & Noor Akma Ibrahim. 2003. Review of air pollution and health impacts in Malaysia. Environmental Research 92(6): 71-77.

Bermudez, P. de Zea & Kotz, S. 2010. Parameter estimation of the generalized pareto distribution-Part II. Journal of Statistical Planning and Inference 140(6): 1374-1388.

Bury, K. 1999. Statistical Distributions in Engineering. London: Cambridge University Press.

Chapman, S. 2004. MATLAB Programming for Engineers. 3rd ed. Australia: Thomson.

Coles, S. 2001. An Introduction to Statistical Modeling of Extreme Values. Bristol: Springer series in statistics.

Dasgupta, R. & Bhaumik, D.K. 1995. Upper and lower tolerance limits of atmospheric ozone level and extreme value distribution. Sankhya: The Indian Journal of Statistics 57(B2): 182-199.

Horowitz, J. & Barakat, S. 1979. Statistical analysis of the maximum concentration of an air pollutant: Effects of autocorrelation and non-stationarity. Atmospheric Environment (1967) 13(6): 811-818.

Jamal, H.H., Pillay, M.S., Zailina, H., Shamsul, B.S., Sinha, K., Zaman Huri, Z., Khew, S.L., Mazrura, S., Ambu, S., Rahimah, A. & Ruzita, M.S. 2004. A Study of Health Impact & Risk Assessment of Urban Air Pollution in Klang Valley, Malaysia. Kuala Lumpur: UKM Pakarunding Sdn Bhd.

Junninen, H., Niska, H., Tuppurainen, K., Ruuskanen, J. & Kolehmainen, M. 2004. Methods for imputation of missing values in air quality data sets. Atmospheric Environment 38(6): 2895-2907.

Kao, T.C. & Lin, C.H. 2010. Setting margin levels in futures markets: An extreme value method. Nonlinear Analysis: Real World Applications 11(6): 1704-1713.

Kotz, S. & Nadarajah, S. 2000. Extreme-Value Distributions: Theory and Applications. London: Imperial College Press.

Kuchenhoff, H. & Thamerus, M. 1996. Extreme value analysis of Munich air pollution data. Environmental and Ecological Statistics 3: 127-141.

Lee, Muhammad Hisyam, Nur Haizum Abd. Rahman, Suhartono, Mohd Talib Latif, Maria Elena Nor & Nur Arina Bazilah Kamisan. 2012. Seasonal ARIMA for forecasting air pollution index: A case study. American Journal of Applied Sciences 9(4): 570-578.

Lu, H.C. 2002. The statistical characters of PM10 concentration in Taiwan area. Atmospheric Environment 36(3): 491-502.

Lu, H.C. & Fang, G.C. 2003. Predicting the exceedances of a critical PM10 concentration - A case study in Taiwan. Atmospheric Environment 37(8): 3491-3499.

Malaysia Environmental Quality Report 2012. Putrajaya: Department of Environment Malaysia.

Malaysia Environmental Quality Report 2011. Putrajaya: Department of Environment Malaysia.

Malaysia Environmental Quality Report 2010. Putrajaya: Department of Environment Malaysia.

Malaysia Environmental Quality Report 2009. Putrajaya: Department of Environment Malaysia.

Malaysia Environmental Quality Report 2008. Putrajaya: Department of Environment Malaysia.

Malaysia Environmental Quality Report 2007. Putrajaya: Department of Environment Malaysia.

Malaysia Environmental Quality Report 2006. Putrajaya: Department of Environment Malaysia.

Malaysia Environmental Quality Report 2005. Putrajaya: Department of Environment Malaysia.

Malaysia Environmental Quality Report 2004. Putrajaya: Department of Environment Malaysia.

Martins, E.S. & Stedinger, J.R. 2000. Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data. Water Resources Research 36(3): 737-744.

Mohamed Noor, Norazian, Cheng Yau Tan, Mohd Mustafa Al- Bakri Abdullah, Nor Azam Ramli & Ahmad Shukri Yahaya. 2011. Modelling of PM10 concentration in industrialized area in Malaysia : A case study in Nilai. In 2011 International Conference on Environment and Industrial Innovation, 13: 18-22. Singapore: IACSIT Press.

Oztekin, T. 2005. Comparison of parameter estimation methods for the three-parameter generalized pareto distribution. Turk. J. Agric. For. 29: 419-428.

Petrov, V., Guedes Soares, C. & Gotovac, H. 2013. Prediction of extreme significant wave heights using maximum entropy. Coastal Engineering 74(4): 1-10.

Quintela-del-Río, A. & Francisco-Fernández, M. 2011. Analysis of high level ozone concentrations using nonparametric methods. The Science of the Total Environment 409(2): 1123-1133.

Reeve, D.T., Randell, D., Ewans, K.C. & Jonathan, P. 2012. Uncertainty due to choice of measurement scale in extreme value modelling of North Sea storm severity. Ocean Engineering 53(10): 164–176.

Reyes, H.J., Vaquera, H. & Villasenor, J.A. 2010. Estimation of trends in high urban ozone levels using the quantiles of (GEV). Environmetrics 21: 470-481.

Reynolds, A.M. 2012. Gusts within plant canopies are extreme value processes. Physica A: Statistical Mechanics and Its Applications 391(11): 5059-5063.

Rinne, H. 2008. The Weibull Distribution: A Handbook. Florida: CRC Press.

Roberts, E.M. 1979. Review of statistics of extreme values with applications to air quality data Part I . Review. Journal of the Air Pollution Control Association 29(6): 632-637.

Singh, V.P. & Guo, H. 1995. Parameter estimation for 3-parameter generalized pareto distribution by the principle of maximum entropy (POME). Hydrological Sciences 40(2): 165-181.

Smith, R.L. 1989. Extreme value analysis of environmental time series: An application to trend detection in ground-level ozone. Statistical Sciences 4(4): 367-393.

Su, F.C., Jia, C. & Batterman, S. 2012. Extreme value analyses of VOC exposures and risks: A comparison of RIOPA and NHANES datasets. Atmospheric Environment 62(12): 97- 106.

Surman, P.G., Bodero, J. & Simpson, R.W. 1987. The prediction of the numbers of violations of standards and the frequency of air pollution episodes using extreme value theory. Atmospheric Environment 21(8): 1843-1848.

Talib, M.L., Rozali, M.O., Norela, S., Ahmad Daud, M.N. & Permata, N.J. 2002. Air quality in several industrial areas in Malaysia. In Proceedings of the Regional Symposium on Environment and Natural Resources, edited by Omar, R., Ali Rahman, Z., Latif, M.T., Lihan, T. & Adam, J.H. April 10-11. Renaissance Hotel, Kuala Lumpur. pp. 703-710.

Torrielli, A., Repetto, M.P. & Solari, G. 2013. Extreme wind speeds from long-term synthetic records. Journal of Wind Engineering and Industrial Aerodynamics 115(4): 22-38.

Tsai, M.S. & Chen, L.C. 2011. The calculation of capital requirement using extreme value theory. Economic Modelling 28(1): 390-395.

Yahaya, Ahmad Shukri & Nor Azam Ramli. 2008. Modelling of carbon monoxide concentration in major towns in Malaysia: A case study in Penang, Kuching and Kuala Lumpur. USM Short Term Grant. Penang: Universiti Sains Malaysia.

Yao, F., Wen, H. & Luan, J. 2013. CVaR measurement and operational risk management in commercial banks according to the peak value method of extreme value theory. Mathematical and Computer Modelling 58(1-2): 15-27.

Yap, X.Q. & Hashim, M. 2013. A robust calibration approach for PM10 prediction from MODIS aerosol optical depth. Atmospheric Chemistry and Physics 13(3): 3517-3526.

*Pengarang untuk surat-menyurat; email: hasfazilah.ahmat@gmail.com