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Effect analysis of air pollution control in Beijing based on an odd-and-even license plate modelXiaoyao Xie a ,*,Xiaodong Tou a ,Li Zhang ba Faculty of Law,Ningbo University,ChinabFaculty of Electrical and Computer Science,Ningbo University,Chinaa r t i c l e i n f oArticle history:Received 29November 2015Received in revised form 14September 2016Accepted 16September 2016Available online xxxKeywords:Air pollutionTraf fic control effect Davis methodOdd-and-even license plate model Environmental bene fita b s t r a c tNowadays,air pollution has become a major challenge in urban management despite rapid economic development.Meanwhile,vehicle exhaust has gradually turned into the main source of air pollution in the city.To reduce air pollution,many measures have been taken including the odd-and-even license plate rule in some cities.However,it is dif ficult to evaluate the effectiveness of those measures.In view of this,based on the Davis method,this article has taken Beijing as its subject and built an odd-and-even license plate model by a probabilistic modelling method and the analysis of means,thus to quantify the pollution caused by vehicle exhaust emissions and the actual effect of the license plate limitation rule.This paper also examines the relationship between the license plate limitation rule and urban air pollution control and to see whether,or not,the rule exerts a positive in fluence on air pollution control.The results showed that the odd-and-even license plate rule has positive impacts on air pollution control in the short-term;however,the in fluence of the limitation policy gradually diminishes and disappears as the overall number of cars increases.Therefore,it is suggested to tackle air pollution in a broader and more effective way.©2016Elsevier Ltd.All rights reserved.1.IntroductionThe general public's quality of life has been greatly improved in pace with the rapid development of China's economy,therefore,there is a higher demand for a more convenient and comfortable transportation modes.Naturally,a private car is the first choice for many.It is under this background that the number of private cars has exploded in the last two decades.As we all know,the boom in private car use does not only increase traf fic congestion but also aggravates air pollution.Taking Beijing as an example,its number of vehicles has exceeded 5.1million in August 2012and the number of drivers has exceeded 7.2million.Besides,over 40%of major air pollutants such as NO x arise from vehicles (Zhao et al.,2010a ).Beijing has adopted an odd-and-even license plate policy since 2008with the initial aim being to alleviate traf fic pressure and reduce urban environmental pollution during the preparation for the Beijing Olympics in 2008.Nevertheless,Beijing,and other municipal governments,have listed the license plate limitation rule as a key move in controlling urban air pollution and maintainingsustainable social development.Of particular note,the feasibility and effectiveness of this rule have been hotspots for academic and public discussion ever since its unveiling.Current studies of odd-and-even license plate rules are mainly concentrated around their origins,purpose,effectiveness,and so on.Most of them discuss the impacts of the policy on improving air quality.Among them,Wang et al.(2009)started from the obvious improvement in Beijing's air quality during the Beijing Olympic Games.By analysing the odd-and-even license plate rule's origin,purpose,and effect,they discussed the possibility and related is-sues,pros and cons,in institutionalising the policy;by using qualitative methods,Zhu (2012)focused on analysing the effects that traf fic congestion has on socio-economic factors such as pop-ulation,employment,GDP,energy consumption,land utilisation,environmental pollution,travel cost,and travel time.He combined a top-down system dynamics model and a bottom-up cellular automata model and started from the perspective of macro-socio-economics and a micro-traf fic model.Zhu combined the advan-tages that the system dynamics model has in scenario simulation and macro-driving factors together with the advantages of cellular automata models in microscopic traf fic flow simulation.To explore the socio-economic impacts of urban traf fic congestion,he built the*Corresponding author.E-mail address:xiexiaoyao@ (X.Xie).Contents lists available at ScienceDirectJournal of Cleaner Productionjournal ho me page:www.elsevier.co m/locate/jclepro/10.1016/j.jclepro.2016.09.1170959-6526/©2016Elsevier Ltd.All rights reserved.Journal of Cleaner Production xxx (2016)1e 10system dynamics model of the interactive relationship between urban traffic and the social economy,as well as the cellular automata model of urban traffic congestion's micro-economic costs;Chen et al.(2011)studied the Beijing Olympic Games2008 when the odd-and-even license plate rule was one of the policies that the government implemented to improve air quality.They found that this policy brought benefits to air quality by reducing 24.9%of air pollution indices compared with the same period in 2007.Nevertheless,there are more studies pointing out the limi-tations of the policy,per se,and its explicit,hidden risks.Cao et al. (2014)and several other researchers studied the effects of the li-cense plate limitation rule after Beijing's Olympics in2008.They tracked the change of air pollution index,inhalable particles,ni-trogen dioxide,and sulphur dioxide and adopted a breakpoint regression method to solve its endogenous problem.They concluded that,although the air quality in Beijing was improved during the Olympic Games,it was not as an outcome of the license plate limitation rule.Enderle et al.analysed the factors affecting traffic congestion.From an economic perspective,they pointed out that,using the odd-and-even license plate rule would only bring short-term benefits and it would not do any good to the long-term and stable development of urban economy through the analysis of urban residential demand for cars,parking lots,and the impact on the automobile industry(Enderle et al.,2012;Zhang et al.,2013). Shen et al.(2014)introduced Harbin's car ownership situation in recent years.They analysed car ownership and its exhaust com-ponents by statistical methods.It turned out that the vehicle exhaust emissions have little effect on air pollution in Harbin;but, as car ownership rises,it would also have negative impacts on air quality.Besides Beijing,the odd-and-even license plate rule has been implemented in many cities in China.Yet as it turns out,the policy does not live up to popular expectations.Taking the Guangzhou Asian Games for example,the policy has been adopted but its effectiveness is limited(Huang et al.,2012).Another case in point is Chengdu,on the whole,the limitation policy did not work as expected since its inception in2012(Xu and Hou,2015).The study of this policy has led to some achievements,which will inspire our follow-up studies,however,there are still some de-ficiencies.First of all,a lot of studies are only conducted in a qual-itative way,failing to quantify the extent of the impact of the policy. Secondly,as the air quality will be affected by the type of regional climate,studies of other cities,except Beijing,cannot be a good explanation of the merits of Beijing's odd-and-even license plate stly,many studies use mathematical tools to analyse the policy,but most of them just compare the before,and after,effects of carrying out the odd-and-even license plate rule,or simply analyse the effects of various factors on air quality,and there is lack of predictions of air quality in the future although it is a predictable condition.In view of this,this paper attempts to use a probabilistic modelling method and analysis of means to build up an odd-and-even license plate rule simulation and analyse the change of means in this model.This paper explores the effects degree of ve-hicles on urban air pollution and thereby discusses the degree of improvement of the rule quantitatively.2.ModelsThere are a large number of qualitative studies,both domestic and overseas,of the odd-and-even license plate rule:many suc-cessful cases that have offered detailed analyses of the effects of the rule.Among them,the most exemplary is the Air Pollution Index (API)explanatory model proposed by Lucas and Davis(2008).This model took the Hoy No Circula(HNC,literally“Don't drive today”,a vehicle limitation rule)initiated by the Mexican Government in 1989as its object of study.Davis utilised high-frequency metrical data from the monitoring station and explored the relevance be-tween the limitation rule and air pollution by mathematical model. To be specific,Davis used the HNC's influence1(HNC)and a timeline covariant x t to explain the change of log(API).In the meantime, Davis employed a large number of data relating to number of cars and air pollution to analyse the change in pollutants such as sulphur dioxide,nitrous oxide,and ozone on a daily or annual basis. Furthermore,he also observed petrol use,automobile growth,and public traffic mode choice:based thereon,Davis concluded that the limitation rule did not generate a significant improvement in air quality.Besides,he added that this rule will engender a growth in automobile numbers to a certain extent.Davis's explanatory model for Mexican air pollution is as shown by the following formula(1): logðAPIÞMexico¼h0þh1lðHNCÞþh2x tþm t(1) In(1),1(HNC)is the observable variable after the implementa-tion of odd-and-even license plate rule,coefficient h1is the influ-ential factor that HNC has on air pollution.X t is a timeline coefficient which includes the indicator variable of every month, day,and hour.So to speak,Davis'analysis and argument are quiet creative and foresighted in their partial explanation for the limitation rule's failure.Nevertheless,the model's general applicability remains open to question.For example,Davis's model cannot be applied directly to explain and judge whether,or not,Beijing's vehicle limitation rule is effective in improving air quality for several rea-sons.Firstly,China's air pollution is closely related to seasonal and environmental factors such as temperature,humidity,rainfall,and wind speed.Beijing has a typical temperate and monsoonal climate with four clearly distinct seasons(Li et al.,2012;Zhou et al.,2014). Therefore,seasonal factors should be critical in describing Beijing's air pollution.Secondly,Davis's study emphasis on the comparison between air qualities before and after the limitation rule,thus does not give full play to its explanatory function.Besides,Davis'model does not simulate the petrol use,vehicle growth,and public traffic before the implementation of the limitation rule.(Viard and Fu, 2015).Thirdly,Davis worked out that the license plate limitation rule has greatly boosted automobile purchases in Mexico.Yet obviously,this conclusion does notfit Beijing.Though the number of automobiles in Beijing is soaring,the limitation rule cannot strongly promote automobile purchases given citizens'income levels in Beijing.2.1.The establishment of an air pollution modelAs a matter of fact,those doubts over Davis'model have not denied the model totally,but only to point out that this model is restricted.In other words,if we take full consideration of a certain area's specific conditions and transform Davis'model properly,the adapted model would still have strong explanatory power.It is under this construct that this paper has designed a model.To elaborate thereon,this paper has constructed a suitable mathe-matical model to explain Beijing's air pollution by taking full consideration of Beijing's conditions and introducing environ-mental variables such as automobile numbers,rainfall,tempera-ture,wind speed,and so on.API,as an index measuring air quality,cannot be predicted for a specific future value since its numerical value is a random number. We get the API data for Beijing from the Ministry of Environmental Protection of the People's Republic of China(MEP).For example,the API's logarithms from1June2006to31May2007are distributed as shown in Fig.1.It is worth noting that,the variation of air quality and the variety of factors affecting the air quality have the feature of a long timeX.Xie et al./Journal of Cleaner Production xxx(2016)1e10 2span and a large amount of data,so in a broad sense,the data be-longs to the category of big data.The concept of big data is generally used to analyse vast amounts of data in the computer communi-cation field,its utilisation,and treatment,but for the hundreds of thousands of data items on air quality collected in this paper,mathematical statistical tools can be used for processing these big data.Here we assume this stochastic process to be stable in the short-term,and meet ergodicity requirements.In that case,we can use horal mean value to describe a certain day's random distribution of log(API)approximately.The study found that this stochastic pro-cess almost complies with the Gaussian distribution.f ðx Þ¼1ffiffiffiffiffiffi2p p e Àðx Àm Þ22(2)In (2),f (x )means that the daily log(API)is the probability den-sity of x .m and s are the mean value and variance of the Gaussian distribution respectively.By the methods of moments estimation,we can get parameters m and s from the sample.8>>>>><>>>>>:b m ¼X ¼1n X n i ¼1X i b s ¼1n X n i ¼1ÀX i ÀX Á2(3)However,in the long-term,the distribution of log(API)'s mean value is changing gradually while the change in the corresponding variance is smaller.The mean value in formula (2)stands for the average change of API,the variance stands for the degree of divergence of API and the average thereof.Though the mean value and variance show rheological properties over time,the change of API mean value is a factor that cannot be ignored.We suppose that the distribution of mean value is a function of time m ¼m (t )while variance s is a constant.An existing study of Beijing's air quality shows that temperature,humidity,and wind speed are three critical factors in fluencing theconcentration of Beijing's air pollution [5].Meanwhile,humidity is closely related to rainfall.Rainfall has a more obvious impact on air quality.Here we assume that the mean value m would meet the following correlativity:m ¼a V þb T þg H þl W þJ(4)In (4),V stands for number of automobiles,T stands for tem-perature,H for precipitation,W for wind speed,while J stands for other factors,for instance,in recent years electric cars have been used more widely (Shi et al.,2016),and it has improved the areas surrounding Beijing in terms of ef ficiency in utilising natural re-sources (Zhu et al.,2016);a ,b ,g ,l denote in fluence coef ficients for corresponding factors.2.2.Calculation of model parametersIn (4),we introduced the number of automobiles,temperature,precipitation,wind speed,and other factors as in fluential over API change.To estimate the in fluential coef ficient between different factors,we must first have a detailed understanding of how each factor changes with time.Here,for convenience when quoting data from the model,we assume 1January 2006as the first day.The mode functions from 1January 2006to 1January 2010.2.2.1.Change of number of automobilesFor the number of automobiles,we analysed data drawn from Beijing Statistical Information Net (BSIN)(BSIN,2007,2009,2011,2013,2015).Here we take the annual number of automobiles as the number at the end of a year,namely,the number at the beginning of the next year.We match the annual change of auto-mobile numbers by rational polynomial.It turns out the cubic function fits this best:V ¼À1:432Â10À8t 3þ5:828t 2þ0:0567t þ224:7(5)During the rule's trial period in 2007and the 2008Olympic Games,the government has launched a very strict odd-and-even license plate rule.As a result,the number of automobiles ontheFig.1.Log(API)of Beijing air from 1June 2006to 31May 2007.X.Xie et al./Journal of Cleaner Production xxx (2016)1e 103road was only0.5%of the total amount.Afterwards,the limitation rule is implemented onfive days per week,excepting weekends.If we ignore the change in automobile numbers for weekdays and weekends,then the limitation effect can be represented as:0.8Â5/ 7þ1Â2/7¼6/7,namely,the number of automobiles is6/7of its previous number.2.2.2.Changes in temperature,precipitation,and wind speedBeijing has a temperate monsoon climate:it is cold and arid in winter,and hot and rainy in summer with an obvious monsoon season.Therefore,factors such as precipitation,temperature,and wind speed vary seasonally.The weather data came from the Sta-tistical Yearbook of Beijing(Yearbook,2011,2008,2009,2010.The change of the three factors from2006to2010are shown in Fig.2.2.2.3.Other factors JBy taking the mean value30days before,and after,log(API)as a statistical average analysis,wefind that the average log(API)had no obvious change,and it underwent a linear variation.Thus it was assumed that the influence of other factors was linear influence: J¼ktþb(6)2.2.4.Model parameter regressionfittingA regression model from formula(4)was adopted:m¼b a Vþb b Tþb g Hþb l WþJþε¼b a Vþb b Tþb g Hþb l Wþb ktþb bþε(7) This is a multiple linear regression model,with which we can find out every influential coefficient by multiple regression least squares method(Feng,2003).8>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>:x i¼1nX nj¼1x ijy¼1nX ni¼1y iS kj¼X ni¼1Àx ijÀx iÁx kj¼X ni¼1x kjÀx kÀx ijÀx iÁs ky¼X ni¼1x kj y jÀyX ni¼1x kj(8)Here x ij,(i¼1,2,3,4,5,6)represent V j,T j,H j,W j,t j,b j;y i stands for m i. Then,the standard set of variance is:8>><>>:b0¼yÀb1x1À/Àb5x5S11b1þS12b2þ/þS15b5¼s1y/S51b1þS52b2þ/þS55b5¼s5y(9)In(9),b5,b4,/b0stand for a^,b^,g^,l^,k^,b^respectively,we can use this formula to work out all influential factors.Taking the change in number of automobiles triggered by the odd-and-even license plate rule,we can get following results by using software(MATLAB™2012a):8>>>>>><>>>>>>:b a¼0:0002b b¼À0:0008b g¼À0:0002b l¼0:0727b k¼À0:0001b b¼1:8035(10)Thefigure of log(API)'s actual value,statistical mean value in a short period,and mean value of log(API)stimulated by model is shown as follows:from Fig.3,the change in each simulatedfigure can simulate the change in log(API).From(2),(3),(7),and(10),we see that this model is a distri-bution function of log(API)as a distributed variable x and time tin Fig.2.Change in precipitation,temperature,and wind speed from1January2006to1January2010.X.Xie et al./Journal of Cleaner Production xxx(2016)1e104the form of their two-dimensional probability density function.f ðx ;t Þ¼1ffiffiffiffiffiffi2p p se Àðx Àm ðt ÞÞ22(11)Among which:8>>>>>>>>>>>>>>>>>>>>><>>>>>>>>>>>>>>>>>>>>>:b s ¼1n X n i ¼1ÀX i ÀX Á2m ðt Þ¼b a V þb b T þb g H þb l W þb kt þb b b a ¼0:0002b b ¼À0:0008b g ¼À0:0002b l ¼0:0727b k ¼À0:0001bb ¼1:8035(12)3.Veri fication and application of modelThe second part of this paper has successfully established an air pollution model,and based on the existing data about relevant factors,we have estimated the in fluence coef ficients of each factor;however,we have to test the effectiveness of the model in practice.Thus,in this part,the argument mainly covers two aspects:firstly,we will verify the model through speci fic data,and test its validity,as well as its applicability in the future;secondly,based on the model,we analyse the number of vehicles because it changes year-by-year,and investigate the speci fic effects of the odd-and-even license plate rule.Meanwhile,we will use this model to simulate the degree of air pollution without this limitation rule,which will be compared with the actual situation.All of these steps can pro-vide data support for further discussion of the effect of the odd-and-even license plate rule.3.1.Veri fication of the air pollution modelAccording to the modelling process in the second part,the present model is based on probability and statistics to investigate the variation of the mean value.Therefore,to verify the model,we have to:on the one hand,test the distribution of the API,to see whether,or not,it is a random distribution and whether,or not,the established distribution rule is correct.On the other hand,we verify the mean value in the probability distribution,to see whether,or not,we can successfully predict the real changes in API when there are changes in the number of vehicles,precipitation,temperature,and wind speed.3.1.1.Veri fication of the correctness of the stochastic process used in the modelIn Section 2.2,we used API data from 1January 2006to 2010;but,in the first half of 2012,the government announced a new regulation which will replace the existing API with and Air Quality Index (AQI).In Beijing,the AQI standards were applied in the air monitoring report after 2014,but due to the calculation differences between AQI and API (in calculating the AQI,main pollutants include fine particulate matter,inhalable particles,sulphur dioxide,nitrogen dioxide,ozone,and carbon monoxide,while in calculating the API,the main pollutants only include inhalable particles,sulphur dioxide,and nitrogen dioxide).Thus,when analysing the model,we have to select pre-2014time periods:in this paper,the time period selected ran from 1January 2012to 1January 2013,and we still adopted the timing methods in this model.Suppose that 1January 2006is the first day,so from 1January 2012to 1January 2013,there are 2192e 2558days.During the period from 1January 2012to 1January 2013,from the scatter diagram of the API,we can see that the distribution of log(API)is strongly random,which means that in one year,it is a random distribution.So the assumption of stochasticity in the model can still be met.Therefore,Fig.4shows the frequency his-togram for this period and the probability distribution curve which is based on formulae (2)and(3).Fig.3.A comparison between actual,and simulated log(API)values.X.Xie et al./Journal of Cleaner Production xxx (2016)1e 105Above all,during that period,and based on the analysis of a stochastic process,the probability distribution models can explain the distribution change of log(API).3.1.2.Model veri fication:mean change in APIIn 2012,the precipitation,temperature,and wind speed data are known (Yearbook,2013),as shown in Fig.5.In 2012,formula (5)can be applied to all estimations of the number of vehicles and thence we can predict the value of log(API)(MEP,2016).From Fig.6,after analysing the value of log(API),the statisticalaverage,and the simulated value in the model,the model was able to simulate the mean value of the air quality distribution in 2012.After 2014,the model still worked,but as is known,the quality control system is replaced by AQI,so the model cannot directly verify the air quality,but by finding some related factors and calculating the API,it can verify this indirectly.3.2.The effect of the odd-and-even license plate rule on the number of vehiclesIn Section 3.1,the reasonableness of the model can beproven,Fig.4.Frequency histogram and probability density function curve of log(API)from 1January 2012to 1January2013.Fig.5.Change in precipitation,temperature,and wind speed in 2012.X.Xie et al./Journal of Cleaner Production xxx (2016)1e 106whether it is the distribution of the API,or its predictive effect for the API.Thus,this mathematical model has measured the degree of in fluence of each factor on air quality,and based on the model,we can quantify and simulate the effects of a regime without a license plate limitation rule,for comparison with current effects.Further-more,we investigated the actual number of vehicles and the vari-ations in the API,and by predicting the value of log(API)without the odd-and-even license plate rule,we undertook a comparative analysis.parison between the observable variables before,and after,implementation of the odd-and-even license plate ruleAround July 2007,from formula (5),the number of vehicles was approximately 2.93million,during the Lucky Beijing test events (17August 2007to 20August 2007)was the first time in which the odd-and-even license plate rule came into effect.The vehicles whose license plate is odd can be driven on odd-numbered days,while others can be driven on even-numbered days.During the Olympic Games,from 20July 2008to 27July 2008,the odd-and-even license plate rule remained unchanged.This rule can cut the number of vehicles on the road by one half,which thus restricts approximately 1.465million vehicles.Under this rule,the number of vehicles being restricted is large:if we use the number of un-restricted vehicles,as shown in Fig.7,the number of vehicles soared,under these circumstances,by limiting the number of the vehicles on the roads,the rule can only delay the time taken for the growth in traf fic.In time,the high growth rate of the number of vehicles became transitory and a decreasing trend in the number of the vehicles was predicted:the number of the unrestricted vehicles will gradually reach its highest point on urban roads.That is to say,the function of the license plate limitation rule can only delay the time for the number of unrestricted vehicles to reach a maximum.From 2006to 2010,the average growth rate has exceeded 14%,after August 2008,the effectiveness of the license plate rule will be one seventh of its original level (around 14.29%),which is the same as the annual growth rate.Thereby,we can deduce that the effec-tiveness of the vehicle limitation rule can only last for a year:i.e.,vehicle emissions can rise to the level of a year ago.Over time,thepositive effects brought by the rule will diminish.3.2.2.The effect of the license plate limitation rule on the API in BeijingTo analyse the in fluence of the license plate limitation rule on air quality in Beijing,we examined both long-,and short-term effects:in the short term,the rule can restrict a seventh of all vehicles and indeed,it can decrease the value of log(API).From the model,before 7July 2007,the value of log(API)was 1.8977,and after the impo-sition of the limitation rule,its value was 1.8681,a decrease of 0.0296.That is to say,the actual value of API fell from 79to 74.The air quality improved by about 7.1%(that is 100.0296À1¼7.1%).During the Olympic Games,the license plate limitation rule was signi ficant;the concentrations of sulphur dioxide and carbon monoxide were reduced by 13%and 12%,respectively.Furthermore,the concentration of nitrogen dioxide is reduced by 43%(Witte et al.,2009).Albeit that the effort required to implementtheparison between the actual distribution and simulated values oflog(API).Fig.7.Changes in the number of unrestricted vehicles.X.Xie et al./Journal of Cleaner Production xxx (2016)1e 107。