Subscribe Now Subscribe Today
Research Article
 

Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia



Norsalwani Mohamad, Sayang Mohd Deni and Ahmad Zia Ul-Saufie Mohamad Japeri
 
Facebook Twitter Digg Reddit Linkedin StumbleUpon E-mail
ABSTRACT

Background and Objective: The analysis of the behavior of daily PM10 occurrence is becoming important nowadays and the results obtained may be useful for the prediction and decision making purposes. This study considered the behavior of PM10 concentration that related with its dependency nature. Therefore, this study is attempted to determine the sequences of polluted and non-polluted days affected by PM10 concentration based on the optimum order of a Markov chain model. Methodology: Twelve years of monitoring records which is from 2002-2013 and have been analyzed for this purpose. The PM10 concentration data that possess Markov chain properties show that the successive event is dependent on the previous event and is suited for further analysis using this model. Results: The optimum order of the Markov chain model for Shah Alam monitoring station shows that the order of two and three are optimum for threshold values less than 120 μg m–3 and a simple order is optimum for a threshold value of 150 μg m–3. The results mean that the occurrence of the polluted or non-polluted days affected by PM10 is dependent on the 2 or 3 days before the observed day for threshold value less than 120 μg m–3. For a threshold value of 150 μg m–3, the occurrence depends only on a day before the observed day. Besides that, the distribution of polluted events is well fitted based on the optimum order for each threshold value used. Conclusion: The information of polluted (non-polluted) occurrences is important in monitoring the PM10 concentrations which can be used for predicting related future events and helpful in providing the necessary precautionary measures to public and protect their health.

Services
Related Articles in ASCI
Search in Google Scholar
View Citation
Report Citation

 
  How to cite this article:

Norsalwani Mohamad, Sayang Mohd Deni and Ahmad Zia Ul-Saufie Mohamad Japeri, 2017. Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia. Journal of Environmental Science and Technology, 10: 96-106.

DOI: 10.3923/jest.2017.96.106

URL: https://scialert.net/abstract/?doi=jest.2017.96.106
 
Received: December 23, 2016; Accepted: January 16, 2017; Published: February 15, 2017


Copyright: © 2017. This is an open access article distributed under the terms of the creative commons attribution License, which permits unrestricted use, distribution and reproduction in any medium, provided the original author and source are credited.

INTRODUCTION

The PM10 particulate matter with an aerodynamic diameter of less than 10 μm, is identified as a type of air pollution that causes the greatest concern to public health and also the environment. This pollutant is also the main air pollutant exists during the haze events in Malaysia since 19801,2. Besides that, this pollutant can result in short and long term health impacts. The presence of PM10 in ambient air may cause severe health effects such as asthma, throat irritation, respiratory problems and even hospital admission3. There are five major sources of PM10 emissions: Power plants and heat, motor vehicle exhausts, industrial sources and open burning4. However, the most predominant sources of PM10 emissions in Malaysia are heavy traffic and industrial emissions5.

Statistical modelling has allowed environmental authorities to carry out daily air pollution forecasts since this model provides a good insights in short term predictions of future air pollution levels. The regression models and Artificial Neural Network (ANN) are commonly used in predicting the PM10 concentrations by previous studies6-8. Besides that, Central Fitting Distributions (CFD) and Extreme Value Distributions (EVD) can also yield good results to fit the mean concentrations of PM109. There have been many efforts made in monitoring this air pollutant. However, the sequence of polluted and non-polluted days affected by PM10 still receives less attention among researchers. A Markov chain model is dependent on its previous state and this model is highly suited to the pattern of observations. Hence, once the patterns are identified, it is possible to predict the possibility of future events based on the information of previous day event.

Markov chain models are intended to be simple models requiring only two parameters and fitting various aspects of occurrence patterns. Simple Markov chain models are widely used in describing the sequences of daily rainfall occurrences all over the world including Malaysia Chin10, Deni et al.11 and Gabriel and Neumann12. The use of this method is also beneficial in describing the sequences of daily PM10 occurrences due to this pollutant being controlled by weather conditions and showing similar persistence13. Rahimi et al.14 used Markov chain models in order to study the persistence of days affected by PM10 in Tehran and found that the first order of two states Markov chain models had a good fitting on the data of five selected stations. Furthermore, this model had been applied to other air pollution data such as those in studies by Lin13 and Lin and Huang15.

Even though there are still few studies on PM10 concentration that apply this model, the advantage of using a Markov chain model as a model suitable for future prediction considering previous events, have made this model useful to be applied in this study. Subsequently, this model is also frequently used to forecasts the weather at some future time by given the current state as reported by previous studies such as Mangaraj et al.16, Deni et al.11 and Chin10.

Although, the first order of Markov chain models is simple and the calculation is easier than the higher order, but according to Chin10, a Markov chain model cannot be assumed to always be one because sometimes it is inadequate to give an appropriate model. Besides that, since the effect of being exposed to PM10 is more than 24 h as reported by World Health Organization (WHO)17, thus, there is a need to use a higher order of Markov chain models in describing the sequence of PM10 concentration (consider more than one previous events) in order to obtain a better prediction of PM10 occurrences and improving the quality of reports from the data generations. Thus, in this study, simple and higher orders are considered. The aim of this study was to determine the optimum order of Markov chain model in describing the sequence of polluted (non-polluted) days of PM10 concentration in Shah Alam, Malaysia.

MATERIALS AND METHODS

The air quality in Malaysia is monitored by the Department of Environment (DoE) through 52 continuous monitoring stations. These stations are strategically located in order to detect any significant changes of air quality in that area. This study considers the PM10 concentration data from Shah Alam, an urban area. SekolahKebangsaan Raja Muda, Shah Alam, is where the monitoring station was placed. The coordinates of this monitoring station reads 3.08° North latitude and 101.51° East longitude. The main contributor of PM10 concentration in this area is the emissions from motor vehicles, since Shah Alam is the state capital of Selangor, Malaysia and due to the increasing number of vehicles, as well as rapid urban development18.

Twelve years worth of PM10 concentration data provided by DoE from year 2002 until year 2013 were used to achieve the objective of this study. In this study, a polluted day is defined as a day when the PM10 concentration exceeds the threshold value, while a non-polluted day is defined as a day when the PM10 concentration is less than the threshold value. For example, a day with PM10 concentration of more than 50 μg m–3 is a polluted day if the threshold value is 50 μg m–3 and if the value is less than 50 μg m–3, it is considered a non-polluted day. The threshold values considered in this study are 50 μg m–3 (WHO guideline), 52 μg m–3 (Background concentration of PM10 at this station); 100, 120 and 150 μg m–3 (New Malaysia ambient air quality standard19). The purpose of using various levels of threshold values is to investigate the effect of these values with the optimum order of Markov chain model.

Table 1: Transition probabilities of the occurrence of PM10 concentration for Shah Alam station with threshold value of 50 μg m–3
Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia

The example of calculation in order to achieve the aim of this paper is illustrated at each section. For the example of calculation, all the values used were based on the 12 years data of PM10 concentration at Shah Alam monitoring station with threshold value of 50 μg m–3 and the transitions probabilities of the occurrence of PM10 concentration is shown in Table 1.

Markov chain property: The purpose of checking the Markov chain property is to statistically test whether or not the successive events are independent. Furthermore, according to Moon et al.20, the successive events can form or possess Markov chain models when the events are dependent on each other. As for the statistics, α is defined as in Eq. 1 if the successive events are independent:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(1)

where, the Pij denotes the conditional probability of the jth day event depends on the ith day event and P.j is the probability of the jth day event. Equation 1 is distributed a symptomatically as χ2 with degree of freedom of (m-1)2. The m is the total number of state (in this case: m = 2) andthe marginal probabilities for jth column of the transition probabilities (P.j):

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(2)

For example, to obtain the value of the statistics, α for threshold value of 50 μg m–3, the calculation is shown as given below and all the values used in the calculation are obtained from the transition probabilities:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia

Determination the optimum order of Markov chain models for occurrence of PM10 concentration: The sequence of polluted (non-polluted) days of daily PM10 concentration is denoted as X1, X2, X3,..., Xt,...Xn, for n-arbitrary days. A two-state Markov chain model was considered in this study where one denotes a polluted day 1 and 0 denotes a non-polluted day 0. The sequence of polluted (non-polluted) days is assumed to follow a Markov chain of a first order at time t, when X1t depends on previous events, Xt-1. Thus, the two conditional probabilities of the first order can be given by P10 = (Xt = 0∣Xt-1 = 1) and P11 = P (Xt = 1∣Xt-1 = 1). The transition probability matrix P, which describes the 2-state Markov chain model is as in Eq. 316:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(3)

where, Pij = P(X1 = j∣X0 = i) i. j = 0,1.

Note that P00+P01 = 1 and P11+P10 = 1. The definition of the conditional probabilities is as follows:

P00: The probability of a day being non-polluted given that the previous day was also a non-polluted day
P01: The probability of a day being polluted given that the previous day was a non-polluted day
P10: The probability of a day being non-polluted given that the previous day was a polluted day
P11: The probability of a day being polluted given that the previous day was also a polluted day

As for the assumption that the Markov chain is stationary, the transition probabilities of the kth order are as in Eq. 4 and the joint probability distribution for X1, X2, X3,..., Xt,...Xn is as in Eq. 510 :

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(4)

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(5)

Akaike’s Information Criteria (AIC) and Bayesian Information Criteria (BIC) are two decision criteria which commonly used by the researchers in describing the optimum order of the Markov chain models. The PM10 concentration is determined when the minimum loss function is obtained. For instance, Berchtold and Raftery21, Singh and Kripalani22, Deni et al.11 and Dastidar et al.23 applied these two loss functions in their studies. Both criteria are based on the likelihood functions for the transition probabilities of the fitted Markov chain models. The maximum likelihood function for the kth order chain can be written as:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(6)

where, Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysiais the estimated transition probabilities of each of the sequence going from state s1 to s2, from state s2 to s3 and from state sk-1 to sk (sk is the state of the most recent observation). The Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia denotes the associated transition counts. The maximum likelihood estimator used in Eq. 7 of the transition probabilities is given by:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(7)

The maximum likelihood computed is used to decide the optimum order of two different Markov chain models, say the Markov chain models of the kth and mth orders where, k<m and k = 0, 1,..., m-1. Thus the maximized likelihood ratio statistics is given by:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(8)

Where:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia

Table 2: Loss function, AIC and BIC values of Shah Alam monitoring station
Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
AIC: Akaike’s information criteria, BIC: Bayesian information criteria, *Minimum loss function

For example, the maximized likelihood ratio statistics for 0H1 is calculated where k = 0 and m = 1. The parameter estimation (P00, P11, P10 and P01) is then substituted into the equation and the value of 0H1 is given by:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia

As stated earlier, in determining the optimum order of Markov chain model, two loss functions are used, namely AIC and BIC. Tong24 proposed that the loss function (AIC) is to define risk on the basis of the AIC criteria, while the BIC criteria, introduced by Schwarz25 is to define risk on the basis of the BIC criteria. The only difference between these two criteria is the form of the penalty function. These criteria attempt to find the value of k that minimizes the loss function. The equation of AIC and BIC are as in Eq. 9 and 10, respectively:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(9)

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(10)

where, v = (sm-sk) (s-1) is the degree of freedom, s represents the number of states which in this case is 2 (polluted and non-polluted) and n is the number of the sample size. For example, for the value of AIC and BIC when k = 0 and m = 1 is given as follows:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia

All the values obtained from the loss function of AIC and BIC in determining the optimum order of Markov chain model for a threshold value of 50 μg m–3 are presented in Table 2. The comparison between the minimum values of the loss function was done in order to choose the optimum order. For example, based on Table 2, the minimum values for both functions are at order three, which means that the optimum order for this threshold is at third order of Markov chain model. Many studies had also used these two loss functions in determining the optimum order of Markov chain model11,21-23.

Fitting the higher order of Markov chain model: The information obtained from the transition probabilities was also used to calculate the frequency distribution of the order of Markov chain model, which was used to assess the performance of the higher order. The first order of Markov chain model was considered only for one preceding day and, similarly for the second order, the observed day depends on two preceding days and as does the other order. The joint probabilities of the kth order of the Markov chain model is the following11:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(11)


n>k+1; k = 0, 1.....

The conditional probabilities of events of n polluted days with the kth order of the Markov chain can be written as Eq. 1211. From this equation, [n] represents n times. For example, the conditional probability of two consecutive polluted days can be written as P(011∣0). The expected number of polluted days is computed by multiplying the conditional probabilities obtained from Eq. 12 with the total number of non-polluted days. For instance, the number of non-polluted days of this station for a threshold value of 50 μg m–3 is 1981 days (Table 1). The chi-square test with a degree of freedom of d = v-1 was employed in this study to compare the observed and expected distributions of polluted events:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
(12)

In assessing the best fitted higher order Markov chain model, the expected distribution which was closer to the observed distribution of polluted events was considered. The information from the transition probabilities was used to calculate the frequency. For example, the conditional probabilities of the first order of Markov chain model for polluted events in Shah Alam with a threshold value of 50 μg m–3 are given by:

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia

The calculation of the conditional probabilities was continued until the maximum duration of polluted days for a sequence of polluted days was met. For example, the maximum number of polluted days for the Shah Alam station was 25 days for the 12 years worth of data used. Then, to get the expected frequencies of the first and higher orders, the conditional probabilities obtained from Eq. 12 were multiplied with the number of non-polluted days as mentioned earlier.

RESULTS AND DISCUSSION

Characteristics of PM10 concentration: The descriptive statistics of PM10 concentration data in Shah Alam monitoring station are shown in Table 3. Based on the Table 3, the maximum PM10 concentration value of 587 μg m–3 had occurred at Shah Alam monitoring station in August (11/8/2005) which may due to the haze event caused by trans-boundary pollution from Kalimantan and Sumatera in Indonesia26. The background concentration of PM10 is based on the median value, thus, the value of 52 μg m–3 was used for threshold value based on background concentration. The average daily of PM10 concentration from year 2002 until 2013 as illustrated in Fig. 1. Figure 1 shows that, higher values recorded were between 161st-231st days due to the occurrence of the dry season (Southwest monsoon) in Malaysia that occurred in the months of June until August9.

Table 3: Descriptive statistics of PM10 concentration data in Shah Alam monitoring station
Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia


Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
Fig. 1: Average daily of PM10 concentration from year 2002 until 2013

Table 4: Conditional probabilities of the sequence of polluted and non-polluted days of PM10 concentration and the values of α for all threshold values
Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia

The conditional probabilities of the sequence of polluted and non-polluted days of PM10 concentration and the values of α for all threshold values which obtained from Eq. 1 is shown in Table 4, respectively. These values were used to check whether the successive events (polluted or non-polluted) are independent of each other or not. The events could form Markov chain models or possess Markov chain properties if the events were dependent on each other. Table 4 shows that, the values of α for all threshold values used show that the successive events are dependent on each other and possess the Markov chain property where the value of α is larger than χ2 with a value of 3.84 at a 5% level with 1° of freedom. Therefore, future analysis could be done since the events of PM10 concentration occurrence are dependent on each other. The values of the conditional probabilities that were used to analyse the persistency of the events in the area of study are shown in Table 4. Based on the Table 4, the conditional probabilities for both events show an increasing values where these values indicate the strong relationship between the observed and the previous event, which also means that the probabilities of getting polluted or non-polluted day influencing by previous events is higher regardless of threshold value used. For example, the probability of getting a polluted day based on the previous day that was also a polluted day (P11), is greater than the unconditional probability (P1). Indirectly, it also means that the higher persistency of polluted days indicates the occurrence of two or more consecutive polluted days for a given threshold value. Besides, the probability of two consecutive polluted days (P11) is found higher than the probability of polluted day (P1), which may be due to the behavior of PM10 concentration dependency since the effect of PM10 according to WHO is more than 24 h.

Optimum order of Markov chain model in describing the sequence of PM10 concentration at Shah Alam monitoring station: The AIC and BIC values for Shah Alam monitoring Station with different threshold values of PM10 concentration is shown in Table 5. Table 5 shows the threshold value less than 120 μg m–3, the higher order or an order of more than one is optimum for both AIC and BIC, which means that the occurrence of polluted (non-polluted) events for this station is dependent on the events of two or three days before the observed day. However, according to Katz27, the AIC has the tendency to overestimate the optimum order. It was also found that the BIC estimate for rainfall data of the Tel Aviv data is unity. Besides that, Dastidar et al.23 stated the use of the BIC also gives a mathematical formulation with a principle of parsimony in model building. Thus, this study considers the optimum order obtained from the minimum loss function of the BIC. The table also shows an order of three is optimal for threshold values of less than 100 μg m–3, which best describes the sequence. While for a threshold value of 120 μg m–3, the optimum order is two. As for a threshold value of 150 μg m–3, a simple order is the optimum order that best describes the sequence of polluted (non-polluted) days of PM10 concentration at this station. Thus, it can be concluded that the higher order is more appropriate in describing the sequence of polluted (non-polluted) days of PM10 concentration at this station for threshold value less than 120 μg m–3.

Besides that, the results obtained also show that there are less dependency on previous events when the threshold value is increasing, which indicates that it is not accurately predict occurrences of PM10 concentration when the threshold value used is more than 120 μg m–3 for this station. Indirectly, this study also suggests the reason why the limit or threshold value of PM10 should be revised to suit with Malaysia now-a-days so that better prediction based on previous events can be made for early precaution to the public and the environment, as suggested by DoE28.

Table 5: AIC and BIC values for Shah Alam monitoring station with different threshold values of PM10 concentration
Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
*Minimum loss function

Appropriate order for polluted events: Since the third order is found to be the optimum order in the sequence of PM10 concentrations, therefore, the investigation on the fitting will be carry out further by considering the distribution of polluted events at this monitoring station. The observed and expected frequency distribution is computed as shown in Table 6. The chi-square goodness of fit test is considered as to select the most successful and the best fitted model for each threshold used. All the expected frequencies are more than 5 days and met the assumption of chi-square test. Table 6 shows that, at α = 0.05 level of significant, there is enough evidence to conclude that the observed and expected days of polluted events at threshold value of 50 and 52 μg m–3 for first and second order of Markov chain model is seems not satisfy in representing the distributions of polluted event at this station since the null hypothesis is rejected. However, the threshold value of 50 and 52 μg m–3 for third order produce better fit since the chi-square statistics value is lower than other order and the observed and expected days of polluted events also well describe the distribution. This study also can conclude that higher order (order three) produce better fit than other order since the value of chi-square produced is lower than other order at all threshold value used.

Figure 2 provides the observed and expected frequencies for the threshold value used in this study based on the appropriate order of the first three orders of the Markov chain models, known as order of one (MCM1), order of two (MCM2) and order of three (MCM3) for the distribution of the polluted events at this station. However, the results obtained show that the order more than one (MCM2 and MCM3) are the most appropriate order that best describe the distribution of the polluted events at Shah Alam monitoring station. The observed and expected frequencies of polluted events based on the best fitted order of Markov chain model at threshold values of 50, 52, 100 and 120 μg m–3 is shown in Fig. 2, respectively. Obviously, the expected frequencies of polluted events obtained from the order really describe the observed distributions, since among χ2, χ2 for order three (MCM3) is the best fitted order for threshold values of 50, 52 and 100 μg m–3, while for a threshold value of 120 μg m–3, the distribution of polluted events does fit at the order of two (MCM2). Besides that, Fig. 2 also shows the number of polluted events decreasing when the threshold value of PM10 increases. In conclusion, threshold value used is also important in determining the optimum order and also describing the distribution of polluted events at this monitoring station.

Table 6: Chi-square test, degree of freedom and p-value of observed and expected length of polluted days for Shah Alam monitoring station
Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
*p-value <α = 0.05, **Smallest value of χ2 for each threshold value

Image for - Modeling of Daily PM10 Concentration Occurrence Using Markov Chain Model in Shah Alam, Malaysia
Fig. 2(a-d):
Observed and expected frequencies of polluted events based on the best fitted order of Markov chain model at threshold values of (a) 50 μg m–3, (b) 52 μg m–3, (c) 100 μg m–3 and (d) 120 μg m–3

CONCLUSION

This study has successfully discussed a complete description of the occurrence of PM10 concentration at the Shah Alam monitoring station by using Markov chain model. For threshold value of less than 120 μg m–3, the optimum order for this station is order of 2 and 3. This results indicate that the occurrence of polluted (non-polluted) days depends on the two or three days before the observed day and early prediction can be made by responsible authorities as they can predict the event of two or three days prior. As for a threshold value of 150 μg m–3, an order of one is the optimum order, which indicates that prediction can be made by referring to the day before the observed day. As a conclusion, the higher order Markov chain model is appropriate in making the prediction of PM10 concentrations based on the minimum loss function at this monitoring station.

SIGNIFICANCE STATEMENTS

This study discover the future prediction of PM10 concentration events by considering the previous day events which beneficial in monitoring the effect of PM10 concentrations at the area of study. This study will help the researcher or authorities to provide the necessary information and early prediction of PM10 occurrences at particular area. Therefore, the effect of PM10 concentrations may be reduce by taking early precaution especially to high risk people such as children and elderly people.

ACKNOWLEDGMENT

The authors are greatly thankful to Universiti Teknologi Mara (UiTM), under Grant 600-RMI/IRAGS 5/3 (36/2015). Special recognition goes to the Department of Environment (DoE) and Alam Sekitar Malaysia Sdn. Bhd (ASMA) for providing the air quality data for this study.

REFERENCES

1:  Awang, M.B., A.B. Jaafar, A.M. Abdullah, M.B. Ismail and M.N. Hassan et al., 2000. Air quality in Malaysia: Impacts, management issues and future challenges. Respirology, 5: 183-196.
CrossRef  |  Direct Link  |  

2:  Field, R.D., G.R. van der Werf and S.S. Shen, 2009. Human amplification of drought-induced biomass burning in Indonesia since 1960. Nat. Geosci., 2: 185-188.
CrossRef  |  Direct Link  |  

3:  Fellenberg, G., 2000. The Chemistry of Pollution. John Wiley and Sons Ltd., England

4:  DoS., 2013. Compendium of environment statistics. Department of Statistics, Malaysia, pp: 1-278.

5:  Ul-Saufie, A.Z., A.S. Yahaya, N.A. Ramli and H. Abdul Hamid, 2012. Robust regression models for predicting PM10 concentration in an industrial area. Int. J. Eng. Technol., 2: 364-370.
Direct Link  |  

6:  Chaloulakou, A., G. Grivas and N. Spyrellis, 2003. Neural network and multiple regression models for PM10 prediction in Athens: A comparative assessment. J. Air Waste Manage. Assoc., 53: 1183-1190.
CrossRef  |  Direct Link  |  

7:  Ul-Saufie, A.Z., A.S. Yahaya, N.A. Ramli and H.A. Hamid, 2012. Future PM10 concentration prediction using quantile regression models. Proceedings of the 2nd International Conference on Environmental and Agriculture Engineering, Volume 37, May 27-June 1, 2012, Singapore, pp: 15-19-

8:  Huebnerova, Z. and J. Michalek, 2014. Analysis of daily average PM10 predictions by generalized linear models in Brno, Czech Republic. Atmos. Pollut. Res., 5: 471-476.
CrossRef  |  Direct Link  |  

9:  Yusof, N.F.F.M., N.A.R. Ramli and A.S. Yahaya, 2011. Extreme value distribution for prediction of future PM10 exceedences. Int. J. Environ. Prot., 1: 28-36.
Direct Link  |  

10:  Chin, E.H., 1977. Modeling daily precipitation occurrence process with Markov Chain. Water Resourc. Res., 13: 949-956.
CrossRef  |  Direct Link  |  

11:  Deni, S.M., A.A. Jemain and K. Ibrahim, 2009. Fitting optimum order of Markov chain models for daily rainfall occurrences in Peninsular Malaysia. Theor. Applied Climatol., 97: 109-121.
CrossRef  |  Direct Link  |  

12:  Gabriel, K.R. and J. Neumann, 1962. A markov chain model for daily rainfall occurrence at Tel Aviv. Q. J. Royal Meteorol. Soc., 88: 90-95.
CrossRef  |  Direct Link  |  

13:  Lin, G.Y., 1981. Simple Markov chain model of smog probability in the South coast air basin of California. Prof. Geogr., 33: 228-236.
CrossRef  |  Direct Link  |  

14:  Rahimi, J., J. Bazfarshan and A. Rahimi, 2014. Study of persistence of days infected pollutant particulate matter (PM10) in city of Tehran using Markov chain model. J. Environ. Sci. Technol., 15: 79-90.
Direct Link  |  

15:  Lin, G.Y. and L.C. Huang, 1985. Statistical models for predicting air pollution in taipei. Proc. Nat. Sci. Counc. ROC(A), 9: 47-59.
Direct Link  |  

16:  Mangaraj, A.K., L.N. Sahoo and M.K. Sukla, 2013. A markov chain analysis of daily rainfall occurrence at Western Orissa of India. J. Reliab. Stat. Stud., 6: 77-86.
Direct Link  |  

17:  WHO., 2000. Particulate Matter. In: Air Quality Guidelines, WHO (Ed.). 2nd Edn., WHO Regional Office for Europe, Denmark, pp: 1-40

18:  Shuhaili, A., A. Fadzil, S.I. Ihsan and W.F. Faris, 2013. Air pollution study of vehicles emission in high volume traffic: Selangor, Malaysia as a case study. WSEAS Trans. Syst., 12: 67-84.
Direct Link  |  

19:  DoE., 2013. New Malaysia ambient air quality standard. http://www.doe.gov.my/portalv1/wp-content/uploads/2013/01/Air-Quality-Standard-BI.pdf.

20:  Moon, S.E., S.B. Ryoo and J.G. Kwon, 1994. A Markov chain model for daily precipitation occurrence in South Korea. Int. J. Climatol., 14: 1009-1016.
CrossRef  |  Direct Link  |  

21:  Berchtold, A. and A.E. Raftery, 2002. The mixture transition distribution model for high-order Markov chains and non-Gaussian time series. Stat. Sci., 17: 328-356.
Direct Link  |  

22:  Singh, S.V. and R.H. Kripalani, 1986. Analysis of persistence in daily monsoon rainfall over India. J. Climatol., 6: 625-639.
CrossRef  |  Direct Link  |  

23:  Dastidar, A.G., D. Ghosh, S. Dasgupta and U.K. De, 2010. Higher order Markov chain models for monsoon rainfall over West Bengal, India. Indian J. Radio Space Phys., 39: 39-44.
Direct Link  |  

24:  Tong, H., 1975. Determination of the order of a Markov chain by Akaike's information criterion. J. Applied Probab., 12: 488-497.
CrossRef  |  Direct Link  |  

25:  Schwarz, G., 1978. Estimating the dimension of a model. Ann. Stat., 6: 461-464.
Direct Link  |  

26:  Mahmud, M. and N.H. Abu Hanifiah, 2009. Air pollution during the haze event of 2005: The case of perai, pulau pinang, Malaysia. Malays. J. Soc. Space, 2: 1-15.
Direct Link  |  

27:  Katz, R.W., 1981. On some criteria for estimating the order of a markov chain. Technometrics, 23: 243-249.
CrossRef  |  Direct Link  |  

28:  DoE., 2013. Annual report 2013. Department of Environment (DoE), Ministry of Natural Resources and Environment, Kuala Lumpur, Malaysia.

©  2021 Science Alert. All Rights Reserved