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A time–scaling property of air pollution indices: a case study of Shanghai, China
AtmosphericPollutionResearch6(2015)886Ͳ892
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spheric Pollution
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A time–scaling property of air pollution indices: a case study of Shanghai, China ZuhanLiu1,LiliWang2,HuashengZhu1 1 2
SchoolofInformationEngineering,NanchangInstituteofTechnology,NanchangJiangxi330099,China CollegeofScience,NanchangInstituteofTechnology,NanchangJiangxi330099,China
ABSTRACT
Thisstudyuseddetrendedfluctuationanalysis(DFA)andmultifractalmethodtocharacterizethetemporalfluctuationsof thethreepollutionindices(SO2,NO2andPM10)andthedailyairpollutionindices(APIs)ofShanghaiinChina.Theresults showthatthetemporalscalingbehaviorsinallthefourseriesexhibittwodifferentpowerlaws.Inshortertemporalscaling, alltheseriesindicatethesimilarpersistencecorrespondingtotheannualcycle.However,inlongertemporalscaling,the trends are different for the four series, which reflect the different inherent dynamic nature of various pollutant series. Furthermore, we investigated the frequency–size distribution of the four series. Our findings suggest that SO2, NO2 and PM10 pollution is an example of a self–organized criticality (SOC) process. The results represent that it is different SOC behaviorsthatresultinthedifferencesofpower–lawrelationsinthesefourseries.Thisworkcanbehelpfultounderstand the complex dynamic characteristics of APIs that can contribute to developing advanced techniques for air pollution forecasting. Keywords:Time–scalingproperty,detrendedfluctuationanalysis(DFA),multifractal,airpollutionindices
CorrespondingAuthor:
Zuhan Liu
:+86Ͳ0791Ͳ82086956 :+86Ͳ0791Ͳ82086956
:[email protected]
ArticleHistory: Received:11October2014 Revised:20March2015 Accepted:23March2015
doi:10.5094/APR.2015.098
1.Introduction Increasing urbanization in the past two centuries over the worldhascausedmanysocialandenvironmentalproblems,oneof whichattractsparticularattentionistheurbanairpollution(Chan and Yao, 2008; Fanget al., 2009).It has been recognizedthatthe amounts of pollutants emitted and the dispersion and transport conditionsoftheatmospherearetwomainfactorsaffectingurban airquality (Liuet al., 2013). Theirdetrimentaleffects fall notonly ontheenvironmentandhumanhealth,butalsoonthesustainable developmentofsociety. During the past decade, Shanghai, the rapid industrialization and urbanization in its history and particulate matter (PM), sulfur dioxide(SO2),andnitrogenoxides(NOX)havebecomethemajorair pollutants, which have attracted intense attention from the government and the public (Zhao et al., 2013). For example, epidemiological studies have found outdoor air pollution was associated with increased risk of total and cardiovascular hospital admissioninShanghai(Chenetal.,2010). The air pollution index (API), a referential parameter describing air pollution levels by many developed countries and regionsintheworld,providesinformationthatcouldenhancethe publicawarenessofairpollution.Itcoulddeterminethepollution indices classification and corresponding pollutant concentration limits on the basis of environmental air quality standards and the influence of various pollutants on human health and ecological environment. Meanwhile, the API reporting in China requires converting monitored daily average air quality data into integer
values,andthenthereportisreleasedtothepublic.Thatistosay, though difficult to be understood in the single conceptual numerical form, the simplified air pollutants concentration (APC) can describe air quality and air pollution levels intuitively. Since June 2000, under the requirement of the State Environmental Protection Agency of China, three major pollutants, including respirable particulate matter (PM10), sulfur dioxide (SO2) and nitrogen dioxide (NO2) have been selected for API reporting in China. Temporal evolution of air pollutants is a complex phenomenon.Itisrelatedtomanyafactors,suchasthemovement and transformation of air pollutants, pollutant emissions and climatic conditions (Penrod et al., 2014). Some previous studies indicated that some air pollutants exhibit nonlinearities, such as surface ozone (Tao et al., 2010), carbon dioxide (CO2) emissions (Tunc et al., 2009; Tang and Tan, 2015), TSP and PM10 concentͲ rations(Slinietal.,2006;Saarikoskietal.,2007),justtonameafew examples.Some studiesfocus onthe methods andmodels for air qualityassessmentandthepredictionofdailyAPItimeseries. Anumberofmethodsareavailableintheliteraturetoanalyze andforecastthetime series,suchasdeterministicmodels(Samet and Marzbani, 2014), statistical analysis (Gorji Sefidmazgi et al., 2014; Lorentzen, 2014), wavelet analysis (Liu et al., 2010; Hong, 2011; Maheswaran and Khosa, 2015), neural networks (Ibarra– Berastegietal.,2008;Kourentzesetal.,2014;Pulidoetal.,2014), R/Sandtrendanalysis(WindsorandToumi,2001;Ganetal.,2014; ScottandVarian,2014),DFA(Shietal.,2008;Shietal.,2009;Shiet al., 2010; Duhan et al., 2013), fuzzy mathematic models (Liang et al.,2010;Ruanetal.,2013;LeeandHong,2015)andSPAtechnique (Wang et al., 2013). However, both the accuracy and reliability of
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forecasting techniques could be strongly affected by our fundamentalknowledgeofthecomplexdynamiccharacteristicsof API, therefore various forecasting techniques are not often excellentinallaspects(Schlinketal.,2006) Inthestudyofcomplexphenomenasuchasseismiccrisis(de LimaandGrasman,1999;Telescaetal.,2002;Telescaetal.,2004; Kiyashchenko et al., 2004) and so forth, monofractal and multifractalanalysistechniques,developedtodrawqualitativeand quantitative information from time series, have been applied recently to the study of a large of variety of irregular, non– stationarysignals,whichcanbefoundinTelescaetal.(2002,2004) and Shi et al. (2009). And they, by now, have proved to be very usefultodetectdeepdynamicalfeatures. In China, Shanghai is the first to report APIs dating back to June 1997. API can provide overviews of air quality across the majorpartofShanghai,butthemechanismsthatdriveitstemporal evolutionsarenotveryclear,resultinginvarioustechniquesforair pollution forecasting that are often excellent in some aspects but poor in others (Schlink et al., 2006). In this paper, the authors examinethedailyAPIs,thepollutionindicesofSO2,NO2andPM10 dataofShanghaiinChinausingthethreetechniqueswhichlookfor persistence and scaling in data. These methods include PSA and multifractal analysis, which are widely used for detecting long– termmemoryandscale–invariance.Meantime,thesensitivityand reliance of these three methods will be discussed in detail. Shi et al. (2008, 2009, 2013) showed that the frequency–intensity distribution of pollution indexes were found to satisfy power–law relation that is similar to the Gutenberg–Richter law in the earthquakes study, suggesting that there was inherent dynamical connection between small and high events of air pollution. Therefore,atlast,basedontheSOCtheory,westudythenumber densityofairpollutioneventsforthepollutionindexesofSO2,NO2 andPM10.
2.DataandMethods 2.1.DataDescription The study is based on the data of the API reporting in Shanghai, which is published on the website of Shanghai Environment Monitoring Center(http://www.semc.com.cn/). Due totheinstrumentcalibrationandmaintenance,APIdatawerelost for3daysin1998.Forthemissingdatamayaffectthequantitative results of time–scaling analysis, so they were estimated by the arithmetic mean API value of the previous day and next day. We haveuseddaily pollution indices datafromJuly1st (1998)toJune 30th(2012).SetthedataofJuly1st,1998ascaseNo.1,thensetthe dataofJuly2nd,1998asNo.2,andaccordinglysetthedataofJune 30th, 2012 as No. 5 113 in API time series. So, the length of time serieswasN=5113. Moreover,otherfactorsliketimeserieslength,edgeeffectand noise may also impact time–scaling property. To eliminate the boundaryeffect,thedatawereextendedbycyclemethod(Faiman and Horovitz, 1996; Chavanne and Gallup, 1998). The method worksonthehypothesisthatanaturaltimeseriesisacombination of both a low–dimensional dynamical system and a high– dimensional (random) noise. Unlike linear filters, nonlinear ones only remove those noisy data points. Those points can be then replaced by estimates computed from a nonlinear interpolation process (Jazwinski, 1970; Harvey, 1989). The Matlab 7.8 and R softwareswereadoptedtoaccomplishthecalculations. Figure1representsthedailyAPIsandthepollutionindicesof PM10, NO2 and SO2 from July 1st (1998) to June 30th (2012). The normalizationinFigure1,accordingtosomeconcernedresearches showthatPM10istheprimarypollutantcomparedwithothersfor the air pollution in Shanghai (Wang and Zhang, 2007; Shi, 2008; Yangetal.,2008).Therefore,APIsareverysimilartoPM10.Dueto
the needs of the development of economy and traffic, NO2 emissions are still increasing with a record high. Since March 1, 2003, Chinese Government implemented stricter vehicle emission standards [(Limits and measurement methods for emissions from light–duty vehicles (II) and Limits and measurement methods for exhaust pollutants from compression ignition and gas fuelled positive ignition engines of vehicles (China I)] to strengthen the motor vehicle pollution management, which made the index of NO2wasdecreased.
Figure1.ThedailyAPIsandpollutionindicesofPM10,NO2andSO2in Shanghai,fromJuly1998toJune2012.Thedatalengthsallare5113 days.
2.2.Methods Detrendedfluctuationanalysis.Thedetrendedfluctuationanalysis (DFA) was proposed by Peng et al. (1994), which is an advanced method for determining the scaling behavior of data in the presence of possible trends without knowing their origin. The methodologyoperatesonthepollutionindices,{x(t),t=1,2,…,N}, whereNisthelengthoftheseries. x istheaveragevalueofthe originaltimeseries. Theseriesisfirstintegratedasfollows:
ݕሺ݇ሻ ൌ ቀݔሺݐሻ െ
xቁ
ሺ݇ ൌ ͳǡ ʹǡ ǥ ǡ ܰሻ
(1)
௧ୀଵ
Next, one measures the vertical characteristic scale of the accumulatedtimeseriesbydividingthelatterintoboxesofequal length, n. In each box, a least–squares line is fit to the data, representing the trend in that box. The ordinate of the straight– line segments is denoted by yn(k). Next, the accumulated series, y(k)forobservationk,isdetrendedbysubtractingthelocaltrend, yn(k), in each box. The root–mean–square fluctuation of this integratedanddetrendedtimeseriesiscalculatedusing: ே
ͳ ܨሺ݊ሻ ൌ ඩ ሾݕሺ݇ሻ െ ݕ ሺ݇ሻሿଶ ݊
(2)
ୀଵ
Thesamecalculationisrepeatedoverdifferentboxsizes,n.If F(n) behaves as a power–law function of n then the data present scaling: F(n)ĝnd. The DFA exponent (d) is defined as the slope of theregressionlineforallpoints[lg(n),lg[F(n)]]. Forwhitenoise,wherethevalueatoneinstantiscompletely uncorrelated with any previous values, the integrated value y(k)
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corresponds to a random walk and d=0.5; 0.5чdч1, indicates persistent long–range power–law correlations; 0
SO2indices,forn
Figure 2. DFAofthedailyAPIs.
TheresultsofDFAalsodisplaythatthesefourtimeseriesare characterized by scale free and self–affine–type fractal behaviors (Liuetal.,2014a).Thereisnoobviousdifferenceinthevaluesofɲ1 seen in the four series, implying that ɲ1 is independent of the pollutantspecies.ɲ1indicatessomesimilardynamiccharacteristics ofvariouspollutants’temporalevolutioninannualcycle.However, some obvious differences among various pollutants in temporal evolutionstillexist,whichcanbedescribedbyɲ2.ɲ2ofAPIsindices exhibit similar values which show some expectable stochastic characteristics.However,forɲ2ofthepollutionindicesofSO2and PM10, they show higher persistence or long–term memory at a large temporal scale; for the pollution indices of NO2, it shows anti–persistenceatalargetemporalscale.Thismayrelatetolong– termclimatologicalprocesses,somemeteorologicalvariables,such astemperatureandwindspeed,andthelengthofthedataandthe internaldynamicsofairpollutants(Cogliani,2001;Shietal.,2008). Furthermore,thespectrumwithɲ>0.5representlongmemoryup tothetimescaleconsidered.Thisisthetemporalanalogytospatial fractalscalingobservedin,forexample,thebranchingpatternsof a tree, the pulmonary bronchioles, or the arterial system. Thus, fluctuationsatallscaleswithintherangearerelatedtoeachother andafractalandlongmemorybehaviormaybeassumed. Table1.DFAofthedailyAPIs,SO2,,NO2andPM10
APIs
SO2
NO2
PM10
ɲ1
0.795
0.815
0.856
0.775
nc
2.648
2.579
2.532
2.562
ɲ2
0.547
1.482
0.347
0.902
3.2.Resultsofmultifractalanalysis WefoundthatthedailyAPIs,thepollutionindicesofSO2,NO2 and PM10, from July 1998 to June 2012, exhibit the high persistence or long term memory in about one year. We investigate the temporal evolution of the local persistence in the four series, which may reflect some information about the temporal evolution dynamics of air pollution and these four time series generated by certain environmental systems may be members of a special class of complex processes, termed multifractals, which require a large number of exponents to characterizetheirscalingproperties.
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Figure4ashowsthemultifractalparametersforSO2indicesin eachyear.Wecanobviouslyseethatȴɲvariationisstableat0.23– 0.40,whichshowsthatthesingularityoffluctuationdistributionfor SO2 indices in each year is similar and its difference between the highest and lowest points is relatively stable. However, ȴf values change greatly, and this is because complex fractal structural change to be resulted in by was different intrinsic dynamic mechanism in each year. But the right endpoint lower or shorter thantheleftendpointforalmostallmultifractalspectrum(ȴf>0), which illustrates the probability for the index felling the lowest is alwaysshorterthanthatofthehighest.AstoB,theirvaluesineach yearareallpositivewhichindicatestheshapeoff(ɲ)curveinclines toleftandrelativelylowfractalindicesaredominant.
Figure3.Multifractalspectraf(ɲ)forthedailyAPIs,thepollutionindices ofSO2,NO2 andPM10.
Multifractal analysis results exhibit the clear difference of multifractalitybetweenthedailyAPIs,thepollutionindicesofSO2, NO2 and PM10 in Figure 3. We can clearly recognize that they are differentintheshapeoff(ɲ)~ɲcurvesdifferentfromtheMarche It is obvious that the shape of f(ɲ) curves for APIs indices is like hooks and PM10 is like a little bell to the right, however, SO2 and NO2arelikehookstotheleft.Thesedifferentshapesreflectinner dynamical characteristics of four pollution indices. Meanwhile, it also shows that multifractal analysis as an effective and new tool which completely reveals the differences from fractal structure of complicateddynamicbehavioramongvariouspollutants. Moreover, we calculated the multifractalparameters (ȴɲ, ȴf, B)offourpollutionindices. ȴɲvaluesofAPIs, PM10,NO2 andSO2 indices are 0.368, 0.393, 0.461 and 0.312, respectively; ȴf are– 0.322,–0.264, 0.112 and 0.261, respectively; the B values are– 0.520,–0.397,0.638,and1.149,respectively.ComparedwithPM10 and NO2, the minimum ȴɲ of SO2 shows that its multifractal spectraf(ɲ)arerelativelydenseandthedegreeofmultifractalityis relativelyweak,soastofurtherexplainthatthesingularityofSO2 pollutionindex fluctuation is smaller, and there is insignificant variation for highest and lowest point of the index. However, the maximum ȴɲ of NO2 then shows its strongest multifractal characteristics. There exist great differences between multifractal spectrumf(ɲ)~ɲofPM10andSO2(NO2)indices,whicharemainly embodiesinnegativeȴfandBvalues.Thisshowsthatspectraf(ɲ) ~ɲofPM10indices(APIs)istotherightandthesingularvaluesfor range of ɲ left are larger, which also shows the event o larger pollution indices occupies the leading position with some local pollutionindexfelling. The PSA results show that the daily APIs and SO2, NO2 and PM10 indices exhibit the high persistence or long term memory in aboutoneyear.Asaresultofthetimeevolutionofairpollutantin city and its air pollution control measures, every year time series hasadifferentdynamiccharacteristics,thus,theyexhibitdifferent complicated characteristics. The difference may be quantitatively demonstrated using multifractal spectrum. The research of multifractalcharacteristicschangesofeveryyeartimeseries(from July1998toJune2012)cancontributetodiscussingtimeevolution dynamic behavior of each air pollutant and developing advanced techniques for air pollution forecasting. Therefore, in the present study, the changes of multifractal characteristics for three atmospheric pollutants were analyzed in the span of one year. So 1998 July to 2012 June is divided into 14 years, and their multifractalswerecalculated,respectively.Theresultsareshownin Figure4.
Figure4.MultifractalparameterforthedailyAPIs,thepollutionindicesof SO2,NO2andPM10ineachyear.Lineswith“”,“”ۻand“Ÿ”denote, respectively,ȴɲ,ȴfandB.
Figure4bshowsthemultifractalparametersforNO2indicesin eachyear.Forȴɲ,itsvaluesofthefirstsixyears(from1998Julyto 2004June)andrecentfouryears(from2009Julyto2012June)are steadily rising from 0.382 (0.354) to 0.591 (0.572), indicating that thesingularityoffluctuationdistributionandthedifferenceofthe highest and lowest points are increasing year by year. These fluctuating ȴf values mainly results from rise or fall of f(ɲmin), suggesting that the probability of event for largest index is also fluctuating, butthat of the smallest index is more stable. For Bin each year, they fluctuated between positive and negative values, and overall it is negative in the first four years and B value of the second year is much smaller than that of the first year, showing thatNO2indicespresentarisingtrendduringthisperiod,butrising slightly significantly after 2002 June. And yet the index show a downwardtrendafter2003June,sorepeatedly,thetrendbecome slight until 2006 June. This shows that although sometimes larger index events is still dominant, but the index smaller event has shownitsdominantrole,namely,duetovariousreasonsresulting in NO2 sometimes up, sometimes down, was extremely unstable, butitslastshowingasmalldeclinetrend.Thesedemonstratethat, althoughsometimesthelargerpollutioneventsstilldominate,the smaller event has gradually shown its dominant role. In other words, due to various reasons NO2 sometimes gets up and sometimes down, it gets extremely unstable, but it last shows a smalldrop. Figure4c shows the multifractal parameters for PM10 indices in each year. It is obvious that ȴɲ values are generally on a downward trend indicating that the singularity of fluctuation distributionandthedifferenceofthehighestandlowestpointsare decreasing year by year, and the distribution of PM10 indices presents more and more uniformity. For ȴf, its changes are most pronouncedafterJuly2004,mainlyresultingfromf(ɲmin)increasing
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while f(ɲmax) decreasing. Thatmeans the number of event for the largestindexhasincreased,butthatofthesmallesthasdecreased. Generally,TheBvalueshowsgrowthtrend,theɲ~f(ɲ)curveshow developingtendencyfromrighttoleft.In14years,exceptforJuly 2004toJune2005,theBareallnegative,indicatingthattheevents oflargerNO2indicesarealmostdominated. Figure4d shows that the multifractal parameters for APIs in eachyeararesimilartothatofPM10. Now,itisdemonstratedthatsomemethods,suchasiterated functionsystems,areusefulintimeseriespredictingbasedonthe fractalscalingfeatureofthedata.Thus,anaturalstepforwardin this line of research would be the use of the different fractal characteristicsofAPItodevelopnewpredictingmethods. Thedifferencesamongthesefourmultifractalspectraindicate that heterogeneity (disordered state) characterizes NO2 and PM10 indices dynamics owing to airflow, pollutant emissions and other related factors; while the atmospheric buffer capability results in SO2 indices being characterized by a dynamical change from heterogeneity (disordered state) toward homogeneity (ordered state). As to APIs, they are determined by air quality indices, variouspollutantsandtheireffectsonhumanhealth,sothereare more complex temporal evolution dynamics and physical mechanism,therefore,APIsdisplaythe“richest”signalinstructure inthesefourseries. 3.3.Cumulativefrequency–sizedistribution Previous studies indicate that the atmosphere share all characteristic features of SOC systems, which is an excellent example of an SOC process (Vattay and Harnos, 1994; Peters and Christensen, 2006). The movements and transformation of air pollutantsoccurintheatmosphere.Thus,theairpollutantsshould also share these generic dynamical properties. From the complex point of view, the power–law scaling and long–term memory can be recognized as the footprint of SOC behaviors. Cumulative frequency–sizedistributionsassociatedwithmanynaturalsystems exhibit power law scaling. This is the typical “critical” dynamical behaviorfoundintheSOCsystems(Matsoukasetal.,2000;Liuet al., 2014b). A power law applied to a cumulative distribution has the relation N=cr–ʄ, where N is the cumulative number of events perunittimewithsizegreaterthanorequaltothemagnitude(r), Oisthescalingexponent,cisaconstant. Figure5showsthenumberdensity(N)ofairpollutionevents (of SO2, NO2 and PM10), with size greater than or equal to some pollution index value (r), respectively. Note the similarity to the Gutenberg–Richter law in the earthquakes study (Turcotte and Malamud, 2004). We found that these pollution indexes in Shanghai exhibit different power law behavior. For NO2 and PM10 indexes, the plots exhibit curvature, showing obviously two differentscalingregionswiththescalingexponentof0.024(0.031) and 0.025 (0.008), respectively, while for SO2 indexes, only one scaling region appears with the scaling exponent of 0.085. Therefore, the results show that the SOC of SO2 series is fully developed (continuous high persistence at all the scales that we have analyzed), while the PM10 and NO2 series seem to be only partially developed (reduced organization for NO2 series and increasedorganizationforPM10atlargerscales).Wenotethatthe power law breaks down in smaller pollution index magnitude regions. We think that low monitoring frequency of pollution indexes series result in the low–size tail of the frequency distribution. Shi et al. (2010, 2013) and Peters and Christensen (2006) have found a similar phenomenon in water pH, PM10 and rainfall,respectively.
Figure5.Thenumberdensity(N)ofSO2,NO2andPM10pollutionevents, withsize greaterthanorequaltosomepollutionindexvalue(r).
Wethinkthatthefluctuationofpollutionindexvaluesdonot lookverydifferentfromavalanchesfromthepointofviewofSOC. Inordertofurtherexplainit,weshowananalogybetweentheair pollutants and the sand–pile. In the complex atmospheric environment, air pollution is affected by several variables driving thechangeofAPC,suchasthemovementsandtransformationof air pollutants, precipitation and climate condition, interact and correlate with each other and so on. All the variables driving the changeofairpollutantsinteractwitheachotherandtheseinter– relationshipsarecomplex,nonlinear.Wedefinethemeasurement valueofairpollutionasanavalancheevent,andthemagnitudesof variouspollutionindexvaluesasavalanchesizesinagranularpile. AndthesuperpositionoflocalAPCrepresentsthechainofforcesin the sand–pile. When the amounts of microscopic condensed air pollutants reach some threshold magnitude, the air pollutant masses can be transported on microscopic scales by diffusion or convection. They reach a new location, where the local APC is lower,andcanbediluted. IfthelocalAPCinthe neighborhood is also high, the amount of condensed air pollutants masses will increase. Once the system reaches some critical point by its own internal tuning, any small fluctuation, in principle, can trigger a chainreactionliketheavalanchesinthesand–pile.Itisimportant to note that the system is “tuned” to a critical state solely by its own internal dynamics rather than external dynamics. The high correspondenceofthesimulated results toobservationssupports thatthethree kindsof pollutantsevolutionactsasaSOCprocess on calm weather. And SOC is a useful framework to explain the nonlinearevolutionofthethreekindsofpollutantconcentrations. Therefore,wemayinterprettheairpollution,whichgoesthrough verylargefluctuations,asconsequencesofSOCprocesses.Sothe power–lawscalinginthesepollutionindexesseriesisequivalentto thatofavalanchesizeevolution. InFigure5,wefoundtwodifferentscalingregionsforNO2and PM10series,andonlyonescalingregionforSO2series.ForNO2and PM10 pollution, atmospheric motion and pollution discharge changegreatly.SoweinferthattheSOCofairpollutants(NO2and PM10) and SOC of airflow may independently affect the temporal variationofNO2andPM10indifferentregimesrespectively,andit is these compound mechanisms that result in the appearance of two different power–law regions for NO2 and PM10 pollution. However, for SO2 pollution, owing to the effect of atmospheric buffercapability,atmosphericmotionandpollutiondischargehave small fluctuation and the independent effect of airflow SOC becomes small. Thus the SOC of NO2 and PM10 pollution play a majorroleinthetemporalvariationofairpollution.Atthecritical state, high persistence, and scale–invariant of the three kinds of
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pollutant concentrations will emerge from the dissipative system. This insight will inspire new research into the macro–effect of air pollutionprocessesandimprovementofmodelingofairpollution (Shietal.,2013). 4.Conclusions Based on the DFA and multifractal methods, we have identified that daily APIs, the pollution indexes of SO2, NO2 and PM10 exhibit the persistence or long–term memory and multifractal characteristics, which are well characterized by scale freeandself–affinetypefractalbehaviors.Thepower–lawscaling and long–term memory in these pollution indexes can be recognized as the footprint of SOC behaviors. All the four series obey two different power laws in shorter and longer temporal scaling regimes in the three technologies. In annual cycle, the scale–freepower–lawbehaviorofthesefourpollutionindexesare verysimilartoeachotherwithveryclosevaluesforɲ1,indicating some similar dynamic characteristics of various pollution indexes’ temporalevolution,whichisthesameSOCoftheatmospherethat drives the evolution of various pollution indexes in one year. Meantime, in longer temporal scaling regimes ɲ2 may reveal the inherentlydifferentdynamicnatureofvariouspollutantseries. To be specific, for one–year periods, the three pollution indexes (SO2, NO2 and PM10) and the daily air pollution indexes (APIs)ofShanghaiinChinaindicateshighpersistence;overlonger time periods, SO2 and PM10 indices still indicate high persistence, but APIs better like the stochastic process and NO2 index shows anti–persistence.Itisconcludedthatthevaluesofɲindicatesthat the DFA is a reliable and sensitive method. The multifractal parameters (ȴɲ, ȴf, B) control the data distribution and help understanding the dynamical characters of the four pollution indexes.Furthermore,multifractalcharacteristicschangesofevery year time series for three air pollutants (from 1998 July to 2012 June)arestudied. Finally, our findings indeed suggest that SO2, NO2 and PM10 pollutionisanexampleofaSOCprocess.Theanalysisshowsthat for NO2 and PM10 pollution, their SOC and SOC of airflow may affectthetemporalvariationofNO2andPM10pollutionindifferent regimes respectively; while for SO2 pollution, owing to the atmosphere buffered capability, the SOC of SO2 pollution plays a major role in its temporal variation. The comparison among the threepollutionindexes(SO2,NO2andPM10) seriescanbehelpful for further understanding of atmospheric buffer function and improvementofmodelingofairquality. Acknowledgments ThisworkwassupportedbytheNationalNaturalScienceFund of the People’s Republic of China (61461032 and 61401189). The authorsaregratefultotheeditorandrefereesfortheircomments givenfortheimprovementofthemanuscript.
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