Detrended cross-correlation analysis of temperature, rainfall, PM10and ambient dioxins in Hong KongKai Shi a, b, *aKey Laboratory of Ecotourism in Hunan Province, Jishou University, Jishou, Hunan 416000, ChinabCollege of Biology and Environmental Sciences, Jishou University, Jishou, Hunan 416000, Chinahi ghli ghts Uses detrended cross-correlation analysis to investigate relationships between ambient dioxins and the inuential factors. Crossover locations correspond to atmospheric circulation and regional transport hypothesis. It shows strong long-term cross-correlation between precipitation and dioxins. No signicant relationships are found between ambient dioxins and average temperature at long-term time scale.arti cle i nfoArticle history:Received 3 May 2014Accepted 7 August 2014Available online 8 August 2014Keywords:Detrended cross-correlation analysisPolychlorinated dibenzo-p-dioxinsPolychlorinated dibenzofuransLong-term cross-correlationMeteorological parameterPM10abstractUsingdetrendedcross-correlationanalysis(DCCA), weinvestigatethelong-terminuenceof somefactors, specicallyprecipitation, averagetemperatureandPM10concentrationsontheevolutionofPolychlorinateddibenzo-p-dioxins(PCDDs)anddibenzofurans(PCDFs)concentrationsinHongKong.The 15 years regular monitoring data from two general urban sites, Central/Western District and TsuenWan, are analyzed. The results show that the relationships between ambient dioxins and precipitation(orPM10)displaylong-termcross-correlationatthetimescalerangingfromonemonthtooneyear;while, no cross-correlation with each other have observed in longer temporal scaling regimes (greaterthan one year). Meantime, differentiated from the previous study, we found that precipitation has thegreatest inuence on ambient PCDD/PCDFs at the long-term time scaling (about one year) in Hong Kong.And no signicant relationships are found between ambient dioxins and average temperature at long-termtimescale. Theseresultscorrespondtoatmosphericcirculationandregionaltransporthypothe-sis and are explained in detail. The long-term cross-correlation property is discussed further, consideringthe strong inuence of the Asian monsoon system. 2014 Elsevier Ltd. All rights reserved.1. IntroductionPolychlorinated dibenzo-p-dioxins (PCDDs) and dibenzofurans(PCDFs),oftensimply termedas dioxins,are persistent andtoxicorganic pollutants that are known to be toxic to humans and ani-mals (Wu et al., 2010). A group of 17 congeners with chlorine atomsat 2,3,7 and 8 positions are most toxic and have been assigned toxicequivalentfactors(TEFs). Dioxinsintheatmospherehavemanysources, suchascombustionprocesses, metalworkingoperationsand chemical wastes (Li et al.,2007; Ng et al.,2008). Due to thepersistence of dioxins in the atmosphere, atmospheric transport isconsidered as a major pathway for the transfer of PCDD/PCDFs toterrestrial and aquatic ecosystems (Thuan et al., 2013; Wang et al.,2011a). Thusthesignicanttemporalvariationsofambientcon-centrations of PCDD/PCDFs might have correlation with the changein atmospheric conditions (Lee et al., 2007).The ambient PCDD/PCDFs concentrations can be inuenced bysome meteorological parameters, such as temperature and rainfall,in certain circumstances. For example, Li et al. (2010) reported thatatmospheric PCDD/PCDFs showsignicant inverse relationshipwithambienttemperature. RainfallhasbeenshowntoscavengePCDD/PCDFs, but their inuence is generally short within 2e3 days(Li et al., 2011). However, Lohmann et al. (1999) found that there areno correlation between PCDD/PCDFs and rainfalls. Li et al. (2011)claimed that no signicant relationships were found betweenmeteorological parameters and PCDD/PCDFs in Beijing during July2008. At thesametime, thePCDD/PCDFs concentrations were*College of Biology and Environmental Sciences, Jishou University, Jishou, Hunan416000, China.E-mail address: einboplure@163.com.Contents lists available at ScienceDirectAtmospheric Environmentj ournal homepage: www. el sevi er. com/ l ocat e/ at mosenvhttp://dx.doi.org/10.1016/j.atmosenv.2014.08.0161352-2310/ 2014 Elsevier Ltd. All rights reserved.Atmospheric Environment 97 (2014) 130e135signicantly correlated with particulate matters (Li et al., 2011; Chietal., 2008). Thesestudiesshowthattheinter-relationshipsbe-tween ambient dioxins and its inuential factors are complex anduncertaininnature. Someambiguousconclusionsmaybecomefrom the sampling periods. Depending on the study purpose andinstruments, samplesareoftentakenforday/week-longperiods.The analysis from short-term sampling can only reveal the short-termand real-time effects of various factors on PCDD/PCDFslevels. However, Dioxins have long lifetime in the air, ranging froma few days to years.In the absence of actual data,the long-terminter-relationships betweenambient dioxins andits inuentialfactorsstill remainuncertain. It seemsevident that theunder-standingof theseuncertaintiescancontributetodevelopingat-mospheric source-receptor models of PCDD/PCDFs in theatmosphere.Inordertoindicatetheinter-relationshipsbetweendifferentvariables, some time series analysis methods have been developed.The most popular is the measurement of the Pearson correlationcoefcient. However, this coefcient is not robust andcanbemisleading if outliers are present, as in real-world data character-ized by a high degree of nonstationarity (Rand, 2005). These recentwork has been shown that a lot of air pollutants concentrations (Shiet al., 2008; Lee and Lin, 2008) and meteorological factors (PetersandNeelin, 2006; VassolerandZebende, 2012) timeseriesarecharacterized by nonlinearity and nonstationarity. When time se-ries is nonstationary, the limitations of methods that assume sta-tionarity are clear. The strong cross-correlations between differentvariables may be not because cross-correlations are actually pre-sent, but simplybecausethecross-correlationfunctionisbeingused for nonstationary time series and each time series happen tohaveacharacteristicstrongsametrend, whichisinappropriate.PodobnikandStanley(2008)proposeanewmethod, detrendedcross-correlation analysis (DCCA), to investigate power-law cross-correlations between two simultaneously recorded time series inthepresenceof nonstationarity. Therefore, introducingDCCAtoresearch long-term relationships between ambient dioxins and itsinuential factors, one will have a better scientic understanding ofthetemporaltrendsofPCDD/PCDFs.However, littleresearch hasbeen found on this topic.The objective of this work is to investigate the temporal scalingof cross-correlations between the temperature, rainfall, PM10 andambient dioxins in the atmosphere of Hong Kong based on the 15years regular monitoring data, using the DCCA method.2. Materials and methods2.1. Study materialsHong Kong is situated in the southern tip of the Pearl River Deltaregion in China. Hong Kong's atmospheric conditions are under thestrong inuence of the Asian monsoon system. The surface wind inHong Kong is predominantly easterlies (E, SE, and NE winds) yeararound, with a clear seasonal pattern in the frequency distributionof northerly and southerly winds. Thus, the contributions of non-HongKongsourcestoairpollutantsoverHongKongaresigni-cant by the atmospheric transport in winter. Under the inuence ofthe northeast monsoon, winter has much less rainfall in compari-sonwithsummer andspring. Inthesummer months (MaytoAugust), thecumulativerainfallsare1408mmaveragely. Inthewintermonths(NovembertoFebruary), thecumulativerainfallsare 134 mm averagely.Since the last municipal solid waste incineration plant in HongKong was closed in 1997, a signicant reduction was expected indioxinemissionsfromthispollutionsourceafter 1997. Thus, aregulardioxin-monitoringprogramhasbeenmadebytheHongKongEnvironmental ProtectionDepartment (HKEPD) sinceJuly1997. Ambient concentrations of 17 PCDD/PCDFs have been moni-toredat twogeneral urbansites, Central/WesternDistrict andTsuenWan, sinceJuly1997. Thesamplingfrequencywasonceamonth before July 1999 and roughly once every 12 days afterwards.The reported data are 24-h average concentrations on the day ofsampling in pg I-TEQ/m3. In this paper, we have used these dioxin-monitoring data from July 1997 to June 2012. At the correspondingtime, daily precipitation, daily average temperature and dailyaverage PM10 concentrations of Central/Western District and TsuenWan sites, fromJuly 1997 to June 2012, are collected. These data areshown in Fig. 1.2.2. Methodsdetrendedcross-correlationanalysis (DCCA) canbeusedtoinvestigate the long-term cross-correlations between two nonsta-tionary time series (Podobnik and Stanley, 2008). It has successfullybeen applied to economics (Sequeira Junior et al., 2010; Wang et al.,2011b), meteorologic (Vassoler and Zebende, 2012) time series.The DCCA procedure consists of four steps.For two time series, {xi,i 1,2,,N} and {yi,i 1,2,,N},rst wedetermine the proles as two new series.xk Xki1xi x andyk Xki1yi y; k 1; 2; ; N: (1)Second, wedividetheproles{xk}and{yk}intoNsint(N/n)nonoverlapping segments of equal length n. Since the length N ofthe series is usually not a multiple of the considered timescale n, ashortpartattheendoftheprolemayremain. Inordernottodisregardthispartoftheseries, thesameprocedureisrepeatedstarting fromthe opposite end. Thereby, 2Nssegments are obtainedaltogether.Next, we calculate the local trend ~xk;i and ~ yk;i for each of the 2Nssegments bytting (least squarest) a polynominal of order 1 todata and deteremine the covariance of residuals in each box.f2DCCAn; i1nXinkixk ~xk;iyk ~ yk;i: (2)Finally, calculate the detrended covariance by summing over alloverlapping all segments of length n,Fn12NsX2NSi1f2DCCAn; ivuut: (3)If F(n) behaves as a power-law function of n, the data presentscaling.Fnfnl: (4)The cross-correlation exponentl can be obtained by observingthe slope of logelog plot of F(n) versus n by ordinary least squares. lquantitatively measures the cross-correlation of two series in termsof long-term cross-correlation exists. If l > 0.5, there are long-termcross-correlations between two series, namely the cross-correlations between two series are persistent. An increase of oneseries is likely to be followed by an increase of the other series inthe future. If l < 0.5, the cross-correlations between two series areanti-persistent. An increase of one series is likely to be followed by adecrease of the other series in the future. Ifl 0.5, the series arenot cross-correlated with each other, and the change of one seriescannot affect the behavior of the other series.K. Shi / Atmospheric Environment 97 (2014) 130e135 131In this study, some variables, such as average temperature andprecipitation, have a periodic trend due to seasonal changes. It wasfound that when many noisy signals in real systems display peri-odic trends, so that the scaling results obtained from the detrenductuation analysis become difcult to analyze (Hu et al., 2001). Inthis case, a possible approach is to rst lter out the periodic trendsbefore we attempt to quantify correlations in the data.So before the standard DCCA procedure, one should eliminatethe periodic seasonal trends as followed.Consider two record Ciand Ti, i 1,2,,N, where Cirepresent thedailytotal dioxinconcentrationinunitsof pgI-TEQ/m3, andTirepresent the daily average temperature, daily precipitation or dailyaverage PM10 concentrations series. N is the number of days in theconsidered record.For eliminatingtheperiodicseasonaltrends, we calculatethedepartures of Ci and Ti,xi Ci Ciandyi Ti Ti; (5)from the mean Ci or Ti. Ciand Tiare calculated for each calendardate i, e.g., 1st of January,which has been obtained by averagingover all years in the record. Thus, {xi,i 1,2,,N} and {yi,i 1,2,,N}have no the periodic seasonal trends.3. Results and discussionFig. 2showsDCCAcalculationfortotaldioxinconcentrationsandprecipitationof Central/WesternDistrict. Basedonlogelogplots of F(n) versus n, one crossover point can be detected for thecurveof F(n) versusn. Thecrossoverhasbeenfoundtoreectsuddenchanges in cross-correlationbehavior of the signal atdifferent time scales. The sampling frequency was once a month. Sothe smallest time interval in the data is one month. In Fig. 2, thenatural logarithm of the timescale n at the crossover point is 2.485.So the timing for the crossover point is about 12 months, which isdue to annual periodicity. To determine the statistical properties ofcross-correlation between total dioxin concentrations and precip-itation, we compute the scaling exponents for different timescaling. For shorter time scaling, the plot can betted to a straightline with a cross-correlation exponent l1 0.937 0.042 in the 95%condence interval, which exhibits high long-term cross-correla-tions. Over longer time scaling, a line witha decreased slopFig. 1. The regular monitoring ambient total dioxins concentrations, precipitation, average temperature and average PM10 concentrations of Central/Western District and Tsuen Wansites, from July 1997 to June 2012.Fig. 2. DCCA plot of total dioxins and precipitation in Central/Western District site.Fig. 3. DCCA plot of total dioxins and precipitation in Tsuen Wan site.K. Shi / Atmospheric Environment 97 (2014) 130e135 132(l2 0.477 0.063 in the 95% condence interval), which is close to0.5, indicates that total dioxin concentrations and precipitation arenot cross-correlated with each other.Fig. 3showsDCCAcalculationfortotaldioxinconcentrationsandprecipitationofTsuenWan. Theresultissimilartologelogplots of F(n) versus n in Fig. 2. It indicates that high long-termcross-correlationsproperty(l1 0.9200.039inthe95%condenceinterval) betweentotal dioxinconcentrations andprecipitationcomes up to about 12 months. For time spans greater than one year,the two series are characterized by not cross-correlated with eachother (l2 0.522 0.057 in the 95% condence interval).Figs. 4 and 5 display DCCA calculation for total dioxin concen-trations and average temperature of Central/Western District andTsuen Wan respectively. In these logelog plots of F(n) versusn, theresultsexhibitclearpower-law scalingrelationshipatthewholescale of 15 years. In the original series, as to Central/Western Dis-trict, l 0.512 0.078; while as to Tsuen Wan, l 0.474 0.073 inthe 95% condence interval. They exhibit that there are no cross-correlationspropertiesbetweentotal dioxinconcentrationsandaverage temperature at theconsideredtime scaling.The trendiscontrary to that of precipitation obviously.Figs. 6 and 7 exhibit DCCA calculation for total dioxin concen-trations and PM10 concentrations of Central/Western District andTsuen Wan respectively. These observed Fnfnlrelationships allexhibit two scaling regimes withcrossover point of about 12months. Inthe 95%condenceinterval, as toCentral/WesternDistrict, l1 0.733 0.024 at shorter time scaling andl2 0.502 0.059 at time scaling greater than one year. As toTsuenWan, l1 0.798 0.025 and l2 0.467 0.041. The trend is similarto that of precipitation obviously. However, obvious difference be-tween Figs. 2 and 3 and Figs. 6 and 7 still exit, which can be seen theexponentl1 values in Figs. 6 and 7 are smaller than that in Figs. 2and 3.In order to verify that the exponentl indeed reects some in-formationofcross-correlationspropertiesoftwoseries, weper-formedthesameanalysisonrandomlyshufedversionsof theoriginaltwoseries. Randomly shufedseriescanbeobtainedbyshufing the original time series. It destroys any temporal corre-lations in the data, while the shufed data still remain exactly thesame uctuation distributions. If the shufed time series followtherandom (white) noise, then the persistence found above does notcome from the data themselves, but from their time evolution re-lations. The calculated l value for shufedseries is shownin Figs. 2e7. Wefoundlvaluesareall closeto0.5. Therandomlyshufed series indicates the obvious randomness and non-correlation, which differs signicantly from the calculated for theoriginal series.Thelong-termevolutionof ambient PCDD/PCDFsconcentra-tions arethecomplexcombinedresults of somebasinfactors(Zhengetal., 2008). Differentfactorshaddifferenteffect aboveambientPCDD/PCDFsatdifferenttimescaling. Intheirrelation-ships with precipitationand PM10 concentrations, the high long-termcross-correlations signies that the ambient PCDD/PCDFsconcentrations uctuations, fromsmall time intervals (down to onemonth) to larger ones (upto one year), are positivelycross-correlation with precipitation and PM10concentrations in apower-law fashion. This scaling comes from the time evolution andnotfromthevaluesof thedata. Forexample, thereisavariedtendency in precipitation or PM10 concentrations to be followed byanother varied tendency in ambient PCDD/PCDFs concentrations atadifferenttimeinapower-lawfashion. Usually, theshort-termcorrelations are described by the cross-correlation function,whichobeys theclassical Markov-typestochasticbehavior anddeclines exponentially with a certain decay time. In opposite, thelong-term cross-correlation imply that the cross-correlation rela-tion between ambient dioxins and precipitation or PM10declines asFig. 4. DCCA plot of total dioxins and average temperature in Central/Western Districtsite.Fig. 5. DCCA plot of total dioxins and average temperature in Tsuen Wan site.Fig. 6. DCCA plot of total dioxins and average PM10 concentrations in Central/WesternDistrict site.K. Shi / Atmospheric Environment 97 (2014) 130e135 133a more slowly decaying relation (power-law) in time rather thanexponentially. The power-law cross-correlations relationshipsderived from the real measurements could also serve as a tool toimprove the atmospheric source-receptor models of PCDD/PCDFs.More specically, the scaling property detected in the real obser-vationsofPCDD/PCDFsconcentrationscouldbeusedtotestthescalingperformanceof theleadingatmosphericsource-receptormodelsofPCDD/PCDFsunderdifferentscenariosofmeteorolog-ical condition and to improve the performance of the atmosphericchemistry-transport models.Lohmannetal. (1999)claimedthatambientdioxinshavenosignicant correlation against precipitation.Li et al.(2011) foundthatrainfall hasbeenshowntoscavengePCDD/PCDFs, buttheirinuenceisgenerallyshort within2e3days. Differentiatefromthese ambiguous conclusions, in this study, at the longer term timescaling (about one years), the greatest impact comes from precip-itationintheevolutionof ambient PCDD/PCDFs inHongKongbased on the 15 years regular monitoring data. So the wet depo-sition is the major removal mechanism for ambient PCDD/PCDFs inHongKong. Higherrainfall mayresultsinlowerambientPCDD/PCDFsconcentrationsinsummer, whiletheoppositeistrueinwinter.The atmosphere plays a major role in transport and depositionof natural and anthropogenic PCDD/PCDFs, thus acting as the mainpathwayfortransportingPCDD/PCDFsfromemissionsourcestovarious environmental compartmentsin South ChinaSea(Thuanetal., 2013). ForHongKong, in summer, precipitation phenome-nonis dominatedbytheprevailingsoutherlyor southeasterlymonsoon wind from to the South China Sea or the Northwest Pa-cic Ocean. In winter, air masses and pollutants typically originatefrom northern China owning to the northeast monsoon. It is wellknownthat precipitationphenomenonandparticulatematterstime series (Shi et al., 2008, 2009) exhibited obvious annual peri-odicity due to the systematic variations in response to seasonal andother factors. Thus, the high long-term cross-correlations betweenambientdioxinsandprecipitationorPM10, withcrossoverpointwith about 12 months, can be well understood.Several prior studies (Louie and Sin, 2003; Sin et al., 2002; Ngetal., 2008)showedthatPCDD/PCDFsconcentrationsintheat-mospherearemuchhigher inthewinterthaninthesummer,which is the observed winter effect In Hong Kong. In this study, theaverage ambient air PCDD/PCDFs concentrations during the sum-mer (July and August) and winter (December and January) seasonsranged from 0.074 to 0.148 pg I-TEQ/m3at Central/Western Districtsiteandfrom0.041to0.126pgI-TEQ/m3at TsuenWansite.AlthoughPCDD/PCDFsconcentrationsduringwinteraresigni-cantly highly than those during the other seasons, DCCA calcula-tionsinectthatnosignicantrelationshipsarefoundbetweenambient dioxins and average temperature in long-term time scale.This result canbeexplainedindetail. Generally, theobservedwinter effects are often explained via seasonally-controlled com-bustionprocessesof fossil fuels, degradationratesandseasonalchangeinairmassmovement. HongKongislocatedinthesub-tropical region, and home heating is not needed at all during thewinter. This eliminates a very important emission source of PCDD/PCDFs, whichis assumedmajor responsibilityfor theelevatedwinter concentration in other studies areas. Some evidences indi-catedthatincompletecombustionofthemotorenginesismoreseriousinwinter, whichcanelevatePCDD/PCDFslevelsemittedfrom vehicles. Atthesametime, thedegradationratesofPCDD/PCDFs in summer are faster than that in winter. However, the smalltemperature difference (only 8 C) in summer and winter in HongKong may not be the main cause for winter effect. This long-termrelationbetweenambientdioxinsandaveragetemperaturealsosuggests that the high ambient temperature may be not the mainremoval mechanismof PCDD/PCDFsinHongKongatlong-termtime scale.The synoptic meteorology in Hong Kong, which is inuenced bythe Asiatic monsoon, results in large winter-summer contrasts inairpollutionmass. Stronglong-termcross-correlationsbetweenPM10and dioxins substantiate the hypothesis of the regionaltransportof PCDD/PCDFstoHongKongfromnorthernChina. Anumber of known dioxin sources such as waste incineration powerplants, small wasteincinerationfactories andopenburningofelectronic wastes in the Pearl River Delta are situated the north ofHong Kong. Through prevailing northeasterly wind in winter, thedioxin emissions may be transported to Hong Kong.4. ConclusionsBased on 15 monitoring data, the scaling and cross-correlationspropertiesbetweenambientdioxinsandprecipitation(tempera-ture, PM10) in the atmosphere of Hong Kong have been analyzed byusingDCCAtechnique. Wehaveidentiedthattherelationshipsbetweenambient dioxins andprecipitation(andPM10) exhibitlong-term cross-correlated at the time scale of about 12 months.However, in longer temporal scaling regimes, no cross-correlatedwitheachotherhasobserved. BytheDCCAexponent, wefoundthat the greatest impact comes from precipitation in the evolutionof ambient PCDD/PCDFs in Hong Kong at the long-termtime scaling(about one years). Meantime, no signicant relationships are foundbetweenambientdioxinsandaveragetemperatureatlong-termtimescale(about15years). Thehighlong-termcross-correlatedbetweenambient dioxins andprecipitation(andPM10) maybecome from the strong inuence of the Asian monsoon system. Theclear seasonality crossover point is consistent with the atmosphericcirculation and regional transport hypothesis. We have noticed thatitisthersttimethatthelong-termcross-correlationbetweenambient dioxins and precipitation(temperature, PM10) is quanti-ed, bywayofDCCA. Thisstudycanbeextendedtotreatotherdomains of environmental science, due the generality of DCCA.AcknowledgmentsWe acknowledgenancial supports from the National NaturalScience Foundation of China (41105118), Hunan Provincial NaturalScienceFoundationof China(13JJB012) andScientic ResearchFund of Hunan Provincial Education Department (13B089).Fig. 7. DCCA plot of total dioxins and average PM10 concentrations in Tsuen Wan site.K. Shi / Atmospheric Environment 97 (2014) 130e135 134ReferencesChi, K.H., Hsu, S.C., Wang, S.H., Chang, M.B., 2008. Increase of ambient PCDD/F andPCBconcentrations innorthern TaiwanduringAsianduststormepisode. 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