任至涵,倪長(zhǎng)健,陳云強(qiáng),楊 泓

基于Copula函數(shù)的成都夏季O3污染潛勢(shì)模型

任至涵1,2,倪長(zhǎng)健1,2,陳云強(qiáng)3*,楊 泓3

(1.成都信息工程大學(xué)大氣科學(xué)學(xué)院,四川 成都 610225；2.高原大氣與環(huán)境四川省重點(diǎn)實(shí)驗(yàn)室,四川 成都 610225；3.四川省氣象服務(wù)中心,四川 成都 610072)

利用成都市2016～2019年6～8月O3濃度的逐時(shí)監(jiān)測(cè)數(shù)據(jù)以及該時(shí)段同時(shí)次的地面氣象觀測(cè)資料,構(gòu)建了O3污染潛勢(shì)3維(紫外輻射、相對(duì)濕度和氣溫)Copula聯(lián)合概率分布模型,并開展了模型的適用性研究.首先,通過對(duì)SciPy庫(kù)概率分布函數(shù)的優(yōu)選,確定了不同O3濃度等級(jí)條件下紫外輻射、氣溫和相對(duì)濕度的最優(yōu)邊緣概率分布函數(shù)(均通過了顯著性水平=0.05的K-S檢驗(yàn));其次,計(jì)算了3種Copula聯(lián)合概率分布函數(shù)的均方根誤差(RMSE值)、赤池信息準(zhǔn)則(AIC值)、貝葉斯信息量(BIC值),并借助Anderson-Darling檢驗(yàn),發(fā)現(xiàn)非對(duì)稱3維frank Copula聯(lián)合概率分布函數(shù)(M3Copula)可以最佳地表征不同O3濃度等級(jí)條件下紫外輻射、相對(duì)濕度和氣溫的聯(lián)合概率分布特征;最后,將不同O3濃度等級(jí)條件下M3Copula聯(lián)合概率密度作為對(duì)應(yīng)O3濃度等級(jí)的隸屬度,O3污染潛勢(shì)的分類結(jié)果對(duì)實(shí)際O3濃度等級(jí)具有較好的指示意義,模擬的平均準(zhǔn)確率為63%,其中優(yōu)等級(jí)、良等級(jí)、輕度污染等級(jí)以及中度及以上污染等級(jí)的模擬準(zhǔn)確率分別為82%、64%、48%和75%.

O3；污染潛勢(shì)；Copula函數(shù)；隸屬度；成都；污染特征

十三五期間,我國(guó)整體環(huán)境空氣質(zhì)量得到明顯改善,全國(guó)及重點(diǎn)區(qū)域PM2.5濃度顯著下降,重污染天數(shù)大幅減少,但近地面O3濃度和超標(biāo)天數(shù)持續(xù)上升,O3污染呈持續(xù)加重趨勢(shì),嚴(yán)重影響當(dāng)前環(huán)境空氣質(zhì)量[1-4].高濃度O3不僅危害人體的健康以及植物的生長(zhǎng),而且可通過改變大氣的氧化性,進(jìn)而加劇大氣復(fù)合污染的復(fù)雜性和不確定性[5-8].

研究表明[9-10],平流層輸入是對(duì)流層O3的天然源,但近地面O3主要來源于O3的光化學(xué)反應(yīng).氮氧化物(NO)和揮發(fā)性有機(jī)物(VOCs)等前體物在光照等適宜氣象條件下發(fā)生一系列光化學(xué)反應(yīng)產(chǎn)生O3,使得前體物和氣象要素與O3濃度之間構(gòu)成了一個(gè)復(fù)雜的非線性動(dòng)力系統(tǒng)[11].針對(duì)長(zhǎng)江三角洲地區(qū)代表城市杭州市臭氧濃度影響因素的研究指出,前體物濃度和氣象要素對(duì)O3濃度均存在顯著影響[12].良好的天氣條件如強(qiáng)輻射、低風(fēng)速有利于臭氧及其前體物的積累,從而有利于光化學(xué)反應(yīng)的發(fā)生[13].在O3前體物排放相對(duì)固定的條件下,近地面O3濃度變化主要與表征O3污染潛勢(shì)的氣象條件密切相關(guān).太陽(yáng)輻射和氣溫均與O3濃度之間存在顯著的正相關(guān)關(guān)系,強(qiáng)太陽(yáng)輻射和高溫能促進(jìn)光化學(xué)反應(yīng)速率,有利于O3濃度的升高[14-16].總云量、低云量和相對(duì)濕度則與O3濃度呈現(xiàn)出負(fù)相關(guān)關(guān)系,一方面,水汽的增加會(huì)減弱太陽(yáng)輻射的強(qiáng)度并降低日最高氣溫,另一方面,水汽能與O3發(fā)生反應(yīng)并消耗近地面O3[17-18].對(duì)中國(guó)典型城市O3濃度與多種氣象要素之間的復(fù)雜關(guān)系分析表明太陽(yáng)輻射、相對(duì)濕度和氣溫是影響O3光化學(xué)反應(yīng)生成的關(guān)鍵要素[19-21].任至涵等[22]針對(duì)成都地區(qū)的進(jìn)一步研究表明,11:00～19:00的氣象要素對(duì)逐日O3污染潛勢(shì)具有最優(yōu)的指示意義.由上述分析可見,氣象要素顯著影響O3光化學(xué)反應(yīng)的進(jìn)程,是O3光化學(xué)反應(yīng)非線性動(dòng)力系統(tǒng)的重要驅(qū)動(dòng)因子.

近年來,在全球氣候變化以及城市化進(jìn)程不斷加快的背景下,以高溫?zé)崂藶榇淼臉O端天氣氣候事件多發(fā)且頻發(fā),由此導(dǎo)致O3光化學(xué)反應(yīng)關(guān)鍵氣象因子的組合模態(tài)愈加復(fù)雜[23].目前空氣污染潛勢(shì)研究大多以天氣形勢(shì)及影響大氣擴(kuò)散能力的氣象要素指標(biāo)為依據(jù),對(duì)未來大氣環(huán)境質(zhì)量進(jìn)行定性或半定量的預(yù)報(bào),這顯然不足以表征O3光化學(xué)反應(yīng)污染潛勢(shì)的高維、非線性以及不確定性等特點(diǎn)[24].建立多變量聯(lián)合分布的傳統(tǒng)方法要求變量間不能存在較強(qiáng)的相關(guān)性,且邊際分布屬于同一類型或是需要轉(zhuǎn)換為同一類型;另外,在對(duì)數(shù)據(jù)進(jìn)行多次處理與變換過程中,還可能導(dǎo)致數(shù)據(jù)信息的失真[25-26].而金融領(lǐng)域運(yùn)用成熟的Copula函數(shù)為構(gòu)建聯(lián)合分布提供了一種應(yīng)用潛力巨大的新方法,它在建立聯(lián)合結(jié)構(gòu)的同時(shí),能夠有機(jī)結(jié)合隨機(jī)變量間不同的相關(guān)程度和相關(guān)模式,建立聯(lián)合分布的過程可以分解為邊緣分布和聯(lián)合分布,這兩個(gè)互相獨(dú)立的部分分別加以處理[27-28].Copula函數(shù)模型的形式靈活多樣,且不受邊際分布形式的限制,具有客觀、定量、準(zhǔn)確以及實(shí)用性強(qiáng)等優(yōu)點(diǎn),已被廣泛應(yīng)用于多領(lǐng)域復(fù)雜問題的研究[29-34],這也為多指標(biāo)O3污染潛勢(shì)模型的建立提供了方法論.

成都位于四川盆地的西部,是中國(guó)西南地區(qū)社會(huì)、經(jīng)濟(jì)和文化中心.成都人口稠密,工業(yè)發(fā)達(dá),O3前體污染物排放量大,加之特殊地形和氣候條件的綜合影響,該區(qū)域一直是四川盆地夏季O3濃度的高值中心[35].本文利用成都市2016～2019年6～8月O3逐時(shí)監(jiān)測(cè)數(shù)據(jù)以及該時(shí)段同時(shí)次的地面氣象觀測(cè)資料,基于不同O3濃度等級(jí)分別構(gòu)建了O3污染潛勢(shì)3維(紫外輻射、相對(duì)濕度和氣溫)Copula聯(lián)合概率分布函數(shù),進(jìn)而分析了該模型的特點(diǎn)和適用性,據(jù)此深化對(duì)成都地區(qū)O3光化學(xué)氣象成因的認(rèn)知.

1 數(shù)據(jù)與方法

1.1 數(shù)據(jù)來源及處理

數(shù)據(jù)來源:采用資料包括成都市溫江區(qū)氣象觀測(cè)站(103.83°E,30.70°N)所提供的2016～2019年6～8月逐時(shí)O3連續(xù)監(jiān)測(cè)數(shù)據(jù)和氣象觀測(cè)數(shù)據(jù).氣象數(shù)據(jù)包括常規(guī)地面觀測(cè)氣象資料氣溫和相對(duì)濕度以及地面輻射觀測(cè)資料(紫外A輻射輻照度(UVA),以下簡(jiǎn)稱紫外輻射),并對(duì)監(jiān)測(cè)數(shù)據(jù)進(jìn)行嚴(yán)格的質(zhì)量控制.

數(shù)據(jù)處理:根據(jù)《環(huán)境空氣質(zhì)量指數(shù)技術(shù)規(guī)定》(HJ633—2012)標(biāo)準(zhǔn)[36],對(duì)逐時(shí)O3數(shù)據(jù)進(jìn)行8h滑動(dòng)平均處理,以表征O3濃度等級(jí)的O3日最大8h滑動(dòng)平均濃度(O3-8)構(gòu)建O3濃度的日序列;基于成都地區(qū)關(guān)鍵時(shí)段的研究成果[22],在研究時(shí)段內(nèi)逐日求取11:00～19:00氣象要素的平均值,據(jù)此得到氣象要素的日序列.

1.2 研究方法

1.2.1 邊緣分布函數(shù)的優(yōu)選 紫外輻射、相對(duì)濕度和氣溫的概率分布函數(shù)源于Python的SciPy包,Fitter函數(shù)可以遍歷其中的104種概率分布函數(shù).利用極大似然估計(jì)法進(jìn)行參數(shù)估計(jì),基于Kolmogorov-Smirnov檢驗(yàn)(K-S檢驗(yàn))、RMSE值、AIC值和BIC值的綜合分析,對(duì)紫外輻射、相對(duì)濕度和氣溫的概率分布函數(shù)進(jìn)行優(yōu)選.RMSE值、AIC值和BIC值越小,表征該概率分布函數(shù)的擬合效果越好.

在常用的Copula函數(shù)當(dāng)中,Archimedean Copula具有形式簡(jiǎn)單且適用性強(qiáng)等特點(diǎn),已被廣泛地應(yīng)用于研究金融和水文水資源等方面的復(fù)雜現(xiàn)象[38-39].由于二維以上對(duì)稱Archimedean Copula只能描述變量間正的相依性并且要求變量間相關(guān)系數(shù)非常接近,本研究選用非對(duì)稱Archimedean Copula函數(shù)中的Frank Copula函數(shù)、Clayton Copula函數(shù)和AMH Copula函數(shù),分析它們作為紫外輻射、相對(duì)濕度和氣溫聯(lián)合分布函數(shù)的適用性.

(1)Frank Copula函數(shù)

(2)Clayton Copula函數(shù)

(3)AMH Copula函數(shù)

式中:參數(shù)1和2所體現(xiàn)的相關(guān)程度是逐層遞減的,即1和2的相關(guān)性比1和3、2和3的相關(guān)性都強(qiáng)[40].

利用邊緣函數(shù)推斷法估算三維不對(duì)稱Copula函數(shù)的參數(shù)[41],進(jìn)而通過RMSE值、AIC值和BIC值開展Copula函數(shù)的優(yōu)選[38],最終基于Anderson- Darling檢驗(yàn)統(tǒng)計(jì)量(AD統(tǒng)計(jì)量)對(duì)最優(yōu)Copula函數(shù)進(jìn)行擬合度檢驗(yàn)[42-43].經(jīng)驗(yàn)累積聯(lián)合概率計(jì)算公式為:

2 結(jié)果與分析

2.1 成都夏季O3濃度分級(jí)及建模樣本的確定

根據(jù)《環(huán)境空氣質(zhì)量指數(shù)技術(shù)》(HJ633—2012)[36],按O3-8濃度空氣質(zhì)量分指數(shù)逐年統(tǒng)計(jì)2016～2019年6～8月優(yōu)、良、輕度污染、中度污染以及重度污染的日數(shù),如表1所示. 2016～2019年6～8月優(yōu)、良、輕度污染、中度污染以及重度污染的日數(shù)分別為61, 140, 118, 31和9d,對(duì)應(yīng)占比是16.99%、39.00%、32.87%、8.64%和2.51%.由于重度污染日數(shù)較少,單獨(dú)建模會(huì)導(dǎo)致模型代表性不強(qiáng),將中度污染日和重度污染日并稱為中度及以上污染日,據(jù)此得到4個(gè)O3濃度等級(jí),即優(yōu)等級(jí)、良等級(jí)、輕度污染等級(jí)和中度及以上污染等級(jí),對(duì)應(yīng)建模的樣本量分別為61,140,118和40.

表1 2016～2019 年5個(gè)O3濃度等級(jí)的天數(shù)(d)

2.2 不同O3濃度等級(jí)下紫外輻射、相對(duì)濕度和氣溫概率分布函數(shù)的優(yōu)選

表2 4個(gè)O3濃度等級(jí)下3種氣象要素的最優(yōu)概率分布函數(shù)

注:概率分布函數(shù)及其參數(shù)來源于https://docs.scipy.org/doc/scipy/reference/stats.html SciPy庫(kù).

2.3 不同O3濃度等級(jí)下紫外輻射、相對(duì)濕度和氣溫3維Copula模型

基于不同O3濃度等級(jí)下紫外輻射、相對(duì)濕度和氣溫概率分布函數(shù)的優(yōu)選結(jié)果,利用clayton Copula、frank Copula和AMH Copula函數(shù)進(jìn)行完全嵌套以構(gòu)建3維O3污染潛勢(shì)模型,并通過邊緣函數(shù)推斷法(二階段法)估計(jì)Copula聯(lián)合概率分布函數(shù)的參數(shù),結(jié)果如表3所示. AMH Copula函數(shù)的參數(shù)估計(jì)結(jié)果雖然收斂,但4個(gè)O3濃度等級(jí)參數(shù)值均存在超出規(guī)定參數(shù)取值范圍的情況[37],非對(duì)稱frank Copula函數(shù)(M3Copula)和clayton Copula函數(shù)(M4Copula)的參數(shù)估計(jì)結(jié)果則符合構(gòu)建條件.針對(duì)M3Copula和M4Copula函數(shù)的進(jìn)一步計(jì)算表明,不同O3濃度等級(jí)下M3Copula的RMSE值、AIC值和BIC值均相對(duì)較小,即M3Copula能夠最佳地描述紫外輻射、相對(duì)濕度和氣溫之間的相關(guān)關(guān)系.另外,圖2給出了4個(gè)O3濃度等級(jí)的M3Copula聯(lián)合概率分布函數(shù)的理論累積概率分布和實(shí)測(cè)累積概率分布散點(diǎn)圖. M3Copula聯(lián)合概率分布函數(shù)的理論累積概率和實(shí)測(cè)累積概率點(diǎn)均勻分布在45°對(duì)角線附近,決定系數(shù)2位于0.8641～0.9750之間.綜上,非對(duì)稱3維frank Copula聯(lián)合概率分布函數(shù)(M3Copula)能最佳地表征不同O3濃度等級(jí)下紫外輻射、相對(duì)濕度和氣溫的相關(guān)關(guān)系.

a:優(yōu)等級(jí);b:良等級(jí);c:輕度污染等級(jí);d:中度及以上污染等級(jí)

表3 4個(gè)O3濃度等級(jí)下3種Copula聯(lián)合概率分布函數(shù)擬合結(jié)果

注:AMH函數(shù)的參數(shù)估計(jì)結(jié)果均超出規(guī)定參數(shù)取值范圍,””表示未進(jìn)行后續(xù)檢驗(yàn)結(jié)果計(jì)算.

由上分析可知,M3Copula分布函數(shù)可以最佳地表征不同O3濃度等級(jí)條件下紫外輻射強(qiáng)度、相對(duì)濕度和氣溫的聯(lián)合概率分布.如圖3所示, O3優(yōu)等級(jí)下M3Copula聯(lián)合概率密度高值對(duì)應(yīng)紫外輻射、相對(duì)濕度和氣溫的主要分布區(qū)間分別為0～12W/m2、80%～100%和18～27℃,計(jì)算的聯(lián)合概率分布為59%;O3良等級(jí)下M3Copula聯(lián)合概率密度高值對(duì)應(yīng)紫外輻射、相對(duì)濕度和氣溫的主要分布區(qū)間分別為10～24W/m2、55%～90%和23～30℃,計(jì)算的聯(lián)合概率分布為57%;O3輕度污染等級(jí)下M3Copula聯(lián)合概率密度高值對(duì)應(yīng)紫外輻射、相對(duì)濕度和氣溫的主要分布區(qū)間分別為15～28W/m2、40%～80%和27～33℃,計(jì)算的聯(lián)合概率分布為58%;O3中度及以上污染等級(jí)下M3Copula聯(lián)合概率密度高值對(duì)應(yīng)紫外輻射、相對(duì)濕度和氣溫的主要分布區(qū)間分別為20～30W/ m2、37%～65%和30～35℃,計(jì)算的聯(lián)合概率分布為60%.即隨著O3濃度等級(jí)的提高,M3Copula聯(lián)合概率密度函數(shù)的高值區(qū)域?qū)?yīng)的紫外輻射強(qiáng)度、相對(duì)濕度和氣溫也呈現(xiàn)出顯著的響應(yīng)特征.

基于構(gòu)建的O3污染潛勢(shì)3維(紫外輻射、相對(duì)濕度和氣溫)Copula聯(lián)合概率分布模型,進(jìn)一步開展了模型的適用性研究.利用成都市2016～2019年6～8月期間合計(jì)359個(gè)樣本數(shù)據(jù),在不同O3濃度等級(jí)(優(yōu)、良、輕度污染和中度及以上污染)條件下分別計(jì)算紫外輻射強(qiáng)度、相對(duì)濕度和氣溫的M3Copula聯(lián)合概率密度值,并將計(jì)算結(jié)果作為相應(yīng)O3濃度等級(jí)的隸屬度,據(jù)此判定O3的污染潛勢(shì),結(jié)果如表5所示. O3污染潛勢(shì)Copula模型的模擬準(zhǔn)確率為63%.就模擬準(zhǔn)確率在不同濃度等級(jí)下的分布而言,優(yōu)等級(jí)和中度及以上污染等級(jí)的模擬準(zhǔn)確率較高,分別為82%和75%,良等級(jí)和輕度污染等級(jí)的模擬正確率略低,分別為64%和48%.

表4 4個(gè)O3濃度等級(jí)下M3Copula聯(lián)合概率分布函數(shù)擬合度檢驗(yàn)結(jié)果

注:”AD2”代表樣本量為的實(shí)測(cè)樣本AD檢驗(yàn)統(tǒng)計(jì)量.

綜上分析可見,紫外輻射強(qiáng)度、相對(duì)濕度和氣溫的變化會(huì)導(dǎo)致同一O3等級(jí)下M3Copula聯(lián)合概率密度的改變,而相同的紫外輻射強(qiáng)度、相對(duì)濕度和氣溫在不同O3等級(jí)下M3Copula聯(lián)合概率密度的計(jì)算結(jié)果也呈現(xiàn)規(guī)律性差異.構(gòu)建的成都夏季O3污染潛勢(shì)模型表征了紫外輻射強(qiáng)度、相對(duì)濕度和氣溫對(duì)O3濃度變化的綜合影響,該模型的分類結(jié)果對(duì)實(shí)際O3濃度等級(jí)具有較好的指示意義,但也存在一定偏差,其中原因主要有以下幾個(gè)方面.(1)O3濃度的演化與氮氧化物(NO)和揮發(fā)性有機(jī)物(VOCs)等前體污染物的變化密切相關(guān),本文假定這些前體物的排放相對(duì)固定,只考慮紫外輻射強(qiáng)度、相對(duì)濕度和氣溫等氣象因子對(duì)O3的作用,這是基于該模型進(jìn)行O3濃度等級(jí)分類誤差的重要來源.(2)本文構(gòu)建的O3污染潛勢(shì)指標(biāo)體系只包括紫外輻射、相對(duì)濕度和氣溫3個(gè)氣象因子,這主要考慮到近地面O3是光化學(xué)反應(yīng)的產(chǎn)物以及研究區(qū)主要為靜小風(fēng)的環(huán)境背景,但實(shí)際風(fēng)場(chǎng)、降水以及其它相關(guān)氣象因子也會(huì)在一定程度上對(duì)O3濃度造成影響,由此導(dǎo)致模型的不確定性.(3)值得一提的是,每日O3濃度還取決于前一日O3濃度狀況.另外,O3濃度等級(jí)之間的模糊不確定性也會(huì)在很大程度上降低分類的準(zhǔn)確性,這可能是良等級(jí)尤其是輕度污染等級(jí)分類精度相對(duì)較差的重要成因.若將O3優(yōu)等級(jí)和良等級(jí)聚為一類,輕度污染等級(jí)和中度及以上污染等級(jí)聚為一類,該模型對(duì)二者的分類準(zhǔn)確率分別為82%和83%.因此,模型分類結(jié)果是判定會(huì)否出現(xiàn)O3污染的重要依據(jù).

圖3 4個(gè)O3濃度等級(jí)M3Copula聯(lián)合概率密度分布圖

Fig.3 Joint probability density distribution of M3Copula at four O3 concentration levels

a:優(yōu)等級(jí);b:良等級(jí);c:輕度污染等級(jí);d:中度及以上污染等級(jí)

表5 2016～2019年O3污染潛勢(shì)分類結(jié)果

3 結(jié)論

3.1 紫外輻射、相對(duì)濕度和氣溫在不同O3濃度等級(jí)條件下的最優(yōu)邊緣概率分布函數(shù)及其統(tǒng)計(jì)參數(shù)均存在顯著的差異,體現(xiàn)了氣象條件變化及其耦合效應(yīng)對(duì)O3濃度演化影響的復(fù)雜性和不確定性.

3.2 M3Copula聯(lián)合概率分布函數(shù)可以最佳地表征不同O3濃度等級(jí)條件下紫外輻射、相對(duì)濕度和氣溫的聯(lián)合概率分布特征.M3Copula聯(lián)合概率密度函數(shù)高值區(qū)域?qū)?yīng)的紫外輻射強(qiáng)度、相對(duì)濕度和氣溫隨著O3濃度等級(jí)的增加均呈現(xiàn)出顯著的響應(yīng)特征.

3.3 O3污染潛勢(shì)模型M3Copula聯(lián)合概率分布函數(shù)的分類模擬結(jié)果對(duì)實(shí)際O3濃度等級(jí)具有較好的指示意義,平均準(zhǔn)確率為63%,其中優(yōu)等級(jí)和中度及以上污染等級(jí)的模擬準(zhǔn)確率較高,分別為82%和75%,良等級(jí)和輕度污染等級(jí)的模擬正確率略低,分別為64%和48%.

[1] 劉 建,吳 兌,范紹佳,等.前體物與氣象因子對(duì)珠江三角洲臭氧污染的影響[J]. 中國(guó)環(huán)境科學(xué), 2017,37(3):813-820.

Liu J, Wu D, Fan S J, et al. Impacts of precursors and meteorological factors on ozone pollution in Pearl River Delta [J]. China Environmental Science, 2017,37(3):813-820.

[2] 姜 華,常宏咪.我國(guó)臭氧污染形勢(shì)分析及成因初探 [J]. 環(huán)境科學(xué)研究, 2021,34(7):1576-1582.

Jiang H, Chang H M. Analysis of China's Ozone Pollution Situation, Preliminary Investigation of Causes and Prevention and Control Recommendations [J]. Research of Environmental Sciences, 2021, 34(7):1576-1582.

[3] Zhang Z Y, Zhang X L, Gong D Y, et al. Evolution of surface O3and PM2.5concentrations and their relationships with meteorological conditions over the last decade in Beijing [J]. Atmospheric Environment, 2015,108:67-75.

[4] 栗澤苑,楊雷峰,華道柱,等.2013～2018年中國(guó)近地面臭氧濃度空間分布特征及其與氣象因子的關(guān)系 [J]. 環(huán)境科學(xué)研究, 2021,34(9): 2094-2104.

Li Z Y, Yang L F, Hua D Z, et al. Spatial Pattern of Surface Ozone and its Relationship with Meteorological Variables in China during 2013～2018 [J]. Research of Environmental Sciences, 2021,34(9): 2094-2104.

[5] Liu Y M, Wang T. Worsening urban ozone pollution in China from 2013 to 2017–Part 2: The effects of emission changes and implications for multi-pollutant control [J]. Atmospheric Chemistry and Physics, 2020,20(11):6323-6337.

[6] 張?zhí)煸?沈楠馳,趙 雪,等.2015～2019年成渝城市群臭氧濃度時(shí)空變化特征及人口暴露風(fēng)險(xiǎn)評(píng)價(jià) [J]. 環(huán)境科學(xué)學(xué)報(bào), 2021,41(10): 4188-4199.

Zhang T Y, Shen N C, Zhao X, et al. Spatiotemporal variation characteristics of ozone and its population exposure risk assessment in Chengdu-Chongqing urban agglomeration during 2015 to 2019 [J].Acta Scientiae Circumstantiae, 2021,41(10):4188-4199.

[7] 方笑堃,羅小三,張 丹,等.臭氧污染對(duì)水稻生長(zhǎng)、產(chǎn)量及礦質(zhì)金屬元素含量的影響 [J]. 環(huán)境科學(xué), 2020,41(8):3797-3803.

Fang X K, Luo X S, Zhang D, et al. Effects of Ozone Pollution on Growth, Yields, and Mineral Metallic Element Contents of Paddy Rice [J]. Environmental science, 2020,41(8):3797-3803.

[8] Xie B, Zhang H, Wang Z L, et al. A modeling study of effective radiative forcing and climate response due to tropospheric ozone [J]. Advances in Atmospheric Sciences, 2016,33(7):819-828.

[9] 林偉立,胡建信,唐孝炎.臭氧層耗損對(duì)對(duì)流層大氣質(zhì)量的影響和在中國(guó)的響應(yīng) [J]. 環(huán)境科學(xué)研究, 2002,(3):61-64.

Lin W L, Hu J X, Tang X Y. The Impact of Stratospheric Ozone Depletion on the Tropospheric Air Quality and Implications for China [J]. Research of Environmental Sciences, 2002,(3):61-64.

[10] 李嫣婷,孫天樂,何 龍,等.深圳市秋季大氣臭氧立體分布特征 [J]. 中國(guó)環(huán)境科學(xué), 2020,40(5):1975-1981.

Li Y T, Sun T L, He L, et al. Vertical distribution characteristics of ozone pollution in Shenzhen in autumn [J]. China Environmental Science, 2020,40(5):1975-1981.

[11] 唐孝嚴(yán),張遠(yuǎn)航,邵 敏.大氣環(huán)境化學(xué) [M]. 北京:高等教育出版社, 2006:272-273.

Tang X Y, Zhang Y H, Shao M. Atmosphere Environmental Chemistry [M]. Beijing: China Higher Education Press, 2006:272-273.

[12] Li K W, Chen L H, Ying F, et al. Meteorological and chemical impacts on ozone formation: A case study in Hangzhou, China [J]. Atmospheric Research, 2017:40-52.

[13] Tao W, Li X, Peter B, et al. Ozone pollution in China: A review of concentrations, meteorological influences, chemical precursors, and effects [J]. Science of the Total Environment, 2016:1582-1596.

[14] 易 睿,王亞林,張殷俊,等.長(zhǎng)江三角洲地區(qū)城市臭氧污染特征與影響因素分析 [J]. 環(huán)境科學(xué)學(xué)報(bào), 2015,35(8):2370-2377.

Yi R, Wang Y L, Zhang Y J, et al. Pollution characteristics and influence factors of ozone in Yangtze River Delta [J]. Acta Scientiae Circumstantiae, 2015,35(8):2370-2377.

[15] 曹庭偉,吳 鍇,康 平,等.成渝城市群臭氧污染特征及影響因素分析 [J]. 環(huán)境科學(xué)學(xué)報(bào), 2018,38(4):1275-1284.

Cao T W, Wu K, Kang P, et al. Study on ozone pollution characteristics and meteorological cause of Chengdu-Chongqing urban agglomeration [J]. Acta Scientiae Circumstantiae, 2018,38(4):1275- 1284.

[16] 黃 俊,廖碧婷,吳 兌,等.廣州近地面臭氧濃度特征及氣象影響分析 [J]. 環(huán)境科學(xué)學(xué)報(bào), 2018,38(1):23-31.

Huang J, Liao B T, Wu D, et al. Guangzhou ground level ozone concentration characteristics and associated meteorological factors [J]. Acta Scientiae Circumstantiae, 2018,38(1):23-31.

[17] 王 磊,劉端陽(yáng),韓桂榮,等.南京地區(qū)近地面臭氧濃度與氣象條件關(guān)系研究 [J]. 環(huán)境科學(xué)學(xué)報(bào), 2018,38(4):1285-1296.

Wang L, Liu D Y, Han G R, et al. Study on the relationship between surface ozone concentrations and meteorological conditions in Nanjing, China [J]. Acta Scientiae Circumstantiae, 2018,38(4):1285-1296.

[18] Ying Y T, Sze F L, Roland V G. The influence of meteorological factors and biomass burning on surface ozone concentrations at Tanah Rata, Malaysia [J]. Atmospheric Environment, 2013,70:435-446.

[19] 徐 錕,劉志紅,何沐全,等.成都市夏季近地面臭氧污染氣象特征[J]. 中國(guó)環(huán)境監(jiān)測(cè), 2018,34(5):36-45.

Xu K, Liu z h, He M Q, et al. Meteorological Characteristics of O3Pollution Near the Ground in Summer of Chengdu [J]. Environmental Monitoring in China, 2018,34(5):36-45.

[20] 胡成媛,康 平,吳 鍇,等.基于GAM模型的四川盆地臭氧時(shí)空分布特征及影響因素研究 [J]. 環(huán)境科學(xué)學(xué)報(bào), 2019,39(3):809-820.

Hu C Y, Kang P, Wu K, et al. Study of the spatial and temporal distribution of ozone and its influence factors over Sichuan Basin based on generalized additive model [J]. Acta Scientiae Circumstantiae, 2019,39(3):809-820.

[21] 嚴(yán)曉瑜,緱曉輝,楊 婧,等.中國(guó)典型城市臭氧變化特征及其與氣象條件的關(guān)系[J]. 高原氣象, 2020,39(2):416-430.

Xiao Y, GOU X H, YANG J, et al. The Variety of Ozone and its Relationship with Meteorological Conditions in Typical Cities in China [J]. Plateau Meteorology, 2020,39(2):416-430.

[22] 任至涵,倪長(zhǎng)健,花瑞陽(yáng),等.成都O3逐日污染潛勢(shì)關(guān)鍵時(shí)段優(yōu)選的GAM模型 [J]. 中國(guó)環(huán)境科學(xué), 2021,41(11):5079-5085.

Ren Z H, Ni C J, Hua R Y, et al. Optimization of the key period of daily ozone pollution potential in Chengdu based on Generalized Additive Model [J]. China Environmental Science, 2021,41(11):5079- 5085.

[23] 白瑩瑩,程炳巖,王 勇,等.城市化進(jìn)程對(duì)重慶夏季高溫炎熱天氣的影響 [J]. 氣象, 2015,41(3):319-327.

Bai Y Y, Cheng B Y, Wang Y, et al. Influences of Urbanization Speed on the Summer High Temperature and Sultry Weather in Chongqing [J]. Meteorological monthly, 2015,41(3):319-327.

[24] 黃曉嫻,王體健,江 飛.空氣污染潛勢(shì)-統(tǒng)計(jì)結(jié)合預(yù)報(bào)模型的建立及應(yīng)用 [J]. 中國(guó)環(huán)境科學(xué), 2012,32(8):1400-1408.

Huang X X, Wang T J, Jiang F, et al. An air pollution potential forecast model combined with statistical method and its application [J]. China Environmental Science, 2015,35(8):2370-2377.

[25] Mishra A K, Singh V P, Desai V R. Drought characterization: A probabilistic approach [J]. Stochastic Environment Research and Risk Assessment, 2009,23(1):41-55.

[26] Song S B, Singh V P. Meta-elliptical copulas for drought frequency analysis of periodic hydrologic data [J]. Stochastic Environmental Research and Risk Assessment, 2010,24(3):425-444.

[27] Longin F, Solnik B. Extreme correlations of international equity markets [J]. Journal of Finace, 2001,56:649-676.

[28] Hu L. Dependence patterns across financial markets: A mixed copula approach [J]. Applied Financial Economics, 2006,16(10):717-729.

[29] Zhang L, Singh V P. Trivariate flood frequency analysis using the Gumbel-Hougaard copula [J]. Journal of Hydrologic Engineering, 2007,12(4):431-439.

[30] Garcia-Portugues E, Crujeiras R M, Gonzalez-Manteiga W. Exploring wind direction and SO2concentration by circular-linear density estimation [J]. Stochastic Environmental Research & Risk Assessment, 2013,27(5):1055-1067.

[31] 李 寧,顧孝天,劉雪琴.沙塵暴災(zāi)害致災(zāi)因子三維聯(lián)合分布與重現(xiàn)期探索 [J]. 地球科學(xué)進(jìn)展, 2013,28(4):490-496.

Li N, Gu X T, Liu X Q. Return period analysis based on joint distribution of three hazards in dust storm disaster [J]. Advances in Earth Science, 2013,28(4):490-496.

[32] 陳子燊,黃 強(qiáng),劉曾美.基于非對(duì)稱Archimedean Copula的三變量洪水風(fēng)險(xiǎn)評(píng)估 [J]. 水科學(xué)進(jìn)展, 2016,27(5):763-771.

Chen Z Y, Huang Q, Liu Z M. Three-variable flood risk assessment based on asymmetric Archimedean Copula [J]. Advances in water Science, 2016,27(5):763-771.

[33] 許紅師,練繼建,賓零陵,等.臺(tái)風(fēng)災(zāi)害多元致災(zāi)因子聯(lián)合分布研究 [J]. 地理科學(xué), 2018,38(12):2118-2124.

Xu H S, Lian J J, Bin L L et al. Joint Distribution of Multiple Typhoon Hazard Factors [J]. Scientia Geographica Sinica, 2018,38(12):2118- 2124.

[34] Ji Z H, Liu X Q. Comparative analysis of PM2.5pollution risk in China using three-dimensional Archimedean copula method [J]. Geomatics, Natural Hazards and Risk, 2019,10(1):2368-2386.

[35] 汪可可,康 平,周明衛(wèi),等.四川盆地臭氧濃度空間分異及驅(qū)動(dòng)因子研究 [J]. 中國(guó)環(huán)境科學(xué), 2020,40(6):2361-2370.

Wang K K, Kang P, Zhou M W, et al. Spatial differentiation and driving factors of ozone concentration in Sichuan Basin [J]. China Environmental Science, 2020,40(6):2361-2370.

[36] HJ633-2012 環(huán)境空氣質(zhì)量指數(shù)技術(shù)規(guī)定(試行) [S].

HJ633-2012 Technical regulation on ambient air quality index (on trial) [S].

[37] Sklar A. Random variables, joint distribution functions and copulas [J]. Kybernetika-Praha, 1973,9(6):449-460.

[38] 宋松柏,蔡煥杰,金菊良,等.Copulas函數(shù)及其在水文中的應(yīng)用 [M]. 北京:科學(xué)出版社, 2012:112-113.

Song S B, Cai H J, Jin J L, et al. Copulas function and its application in hydrology [M]. Beijing: Science Press, 2012:112-113.

[39] 王 沁,呂王勇.基于非對(duì)稱阿基米德Copula模型的投資組合風(fēng)險(xiǎn)度量 [J]. 四川師范大學(xué)學(xué)報(bào)(自然科學(xué)版), 2019,42(2):260-268.

Wang Q, Lv W Y, et al. Portfolio risk measurement based on asymmetric Archimedes Copula model [J]. Journal of Sichuan Normal University (Natural Science), 2019,42(2):260-268.

[40] 王筱萍,高慧敏,曾建潮.基于嵌套Gumbel Copula函數(shù)的分布估計(jì)算法 [J]. 系統(tǒng)仿真學(xué)報(bào), 2013,25(10):2337-2342.

Wang Y P, Gao H M, Zeng J C, Estimation of Distribution Algorithms Based on Nested Gumbel Copula [J]. Journal of System Simulation, 2013,25(10):2337-2342.

[41] 楊益黨,羅羨華.Copula函數(shù)的參數(shù)估計(jì) [J]. 新疆師范大學(xué)學(xué)報(bào)(自然科學(xué)版), 2007,26(2):5.

Yang Y D, Luo X H. Parameter estimation of Copula function [J]. Journal of Xinjiang Normal University (Natural Sciences Edition), 2007,26(2):5.

[42] 馬明衛(wèi),宋松柏.橢圓型Copulas函數(shù)在西安站干旱特征分析中的應(yīng)用 [J]. 水文, 2010,30(4):36-42.

Ma M W, Song S B. Application of Elliptic Copulas Function in Analysis of Drought Characteristics in Xi 'an Station [J]. Journal of China Hydrology, 2010,30(4):36-42.

[43] Ma M W, Ren L L, Song S B, et al. Goodness-of-fit tests for multi-dimensional copulas: Expanding application to historical drought data [J]. Water Science and Engineering, 2013,6(1):18-30.

Summer O3pollution potential model based on copula function in Chengdu.

REN Zhi-han1,2, NI Chang-jian1,2,

CHEN Yun-qiang3*, YANG Hong3(1.School of Atmospheric Sciences, Chengdu University of Information Technology, Chengdu 610225, China；2.Plateau Atmosphere and Environment Key Laboratory of Sichuan Province, Chengdu 610225, China；3.Meteorological Service Center of Sichuan Province, Chengdu 610072, China)., 2022,42(9)：4009～4017

The evolution of Ozone (O3) concentration near the ground is closely related to the coupling effect of multiple meteorological factors, but the complexity and uncertainty keep still unclear . In order to explore the problem mentioned above, the hourly monitoring data of O3concentration as well as the surface meteorological observation data during the same time period in Chengdu from 2016 to 2019 during summer were collected, a three-dimensional copula joint probability distribution model of O3pollution potential (including UV radiation, relative humidity, and temperature) was constructed, and the applicability of the model was further explored. Firstly, the optimal marginal probability distributions of UV radiation, relative humidity and ambient temperature under different O3concentration levels were determined at significant level of=0.05 in K-S test based on the optimization of probability distributions belonging to SciPy package. Secondly, the root-mean-square-error (RMSE), Akaike Information Criterion (AIC), and Bayesian Information criterion (BIC) of three kinds of joint probability distribution functions were calculated, respectively. With the help of Anderson-Darling test (A-D test), it was found that asymmetric three-dimensional frank Copula joint probability distribution function (M3Copula) has better fitting effects on the joint probability distribution characteristics of UV radiation, relative humidity, and ambient temperature, respectively, under different O3concentration levels. Finally, Taking the joint probability density of M3Copula under different O3concentration levels as the membership of O3concentration levels, the classification results of O3pollution potential has a fairly good indication of the actual O3concentration levels, and the M3Copula can simulate the O3concentration levels with 63% accuracy, of which the simulation accuracy of excellent level, good level, light pollution level and moderate or higher pollution level were 82%, 64%, 48%, and 75%, respectively. Our findings demonstrated that the classification results of O3pollution potential have a fairly good instruction significance to actual O3concentration levels.

ozone；pollution potential；Copula function；membership degree；Chengdu；pollution characteristics

X515

A

1000-6923(2022)09-4009-09

2022-01-23

國(guó)家重點(diǎn)研發(fā)計(jì)劃項(xiàng)目(2018YFC0214004;2018YFC1506006);四川省科技廳應(yīng)用基礎(chǔ)研發(fā)項(xiàng)目(2021YJ0314)

*責(zé)任作者, 高級(jí)工程師, 179417919@qq.com

任至涵(1997-),女,四川閬中人,成都信息工程大學(xué)碩士研究生,主要從事大氣物理學(xué)與大氣環(huán)境方面研究.