楊雙等
摘要:采用分位數(shù)回歸的縱向離散系數(shù)研究方法和雙站點(diǎn)濃度時(shí)間數(shù)據(jù),對(duì)突發(fā)水污染事故中河渠的水質(zhì)進(jìn)行預(yù)測(cè),并對(duì)比分析了分位數(shù)回歸與最小二乘法回歸效果。實(shí)例研究結(jié)果顯示,運(yùn)用分位數(shù)回歸法確定河渠縱向離散系數(shù)效果好,第一站點(diǎn)的回歸參數(shù)通過(guò)了97.5%置信水平下的假設(shè)檢驗(yàn),第二站點(diǎn)的預(yù)測(cè)值與實(shí)際值相關(guān)系數(shù)最高達(dá)到了0.928。同時(shí),分位數(shù)回歸法在解決偏態(tài)分布問(wèn)題時(shí)較最小二乘法有明顯優(yōu)勢(shì)。
關(guān)鍵詞:突發(fā)水污染;縱向離散系數(shù);偏態(tài)分布;示蹤試驗(yàn);分位數(shù)回歸;R軟件
中圖分類號(hào):TV131.2;X143 文獻(xiàn)標(biāo)志碼:A 文章編號(hào):
16721683(2014)05006304
Quantile regression method to determine longitudinal dispersion coefficient of river channel
YANG Shuang, YANG Haidong, WANG Zhuomin, XIAO Yi, SHAO Dongguo
(State Key laboratory of Water Resources and Hydropower Engineering Science,
Wuhan University,Wuhan 430072,China)
Abstract:The determination method of longitudinal dispersion coefficient based on the quantile regression and the concentrationtime data of two sites were used to predict the water quality in the river channel.Moreover,the results determined by the quantile regression and least squares regression methods were compared.The example results showed that the quantile regression method is feasible and effective to determine the longitudinal dispersion coefficient of river channel.The quantile regression parameters passed the hypothesis test in the 97.5% confidence level at the first site,and the highest correlation coefficient of the predicted and actual values at the second site reached up to 0.928.In addition,quantile regression method has more advantage in solving the problems with skewed distribution than the least squares regression method.
Key words:sudden water pollution;longitudinal dispersion coefficient;skewed distribution; tracer experiment;quantile regression;R software
南水北調(diào)中線總干渠上橋梁等水工建筑物眾多,存在發(fā)生突發(fā)水污染事故的風(fēng)險(xiǎn)。水污染事故發(fā)生時(shí)需要對(duì)渠道水質(zhì)進(jìn)行快速預(yù)測(cè),并提出應(yīng)急處置對(duì)策[12]。為了反映污染物在水流中運(yùn)動(dòng)的基本特征,人們?cè)谒鞯牧鲃?dòng)狀態(tài)穩(wěn)定、均勻,且污染物的分布只隨污染源變化等假設(shè)條件的基礎(chǔ)上建立了很多水質(zhì)模型[3]。在這些水質(zhì)模型的應(yīng)用過(guò)程中,確定縱向離散系數(shù)是一個(gè)關(guān)鍵工作,也是環(huán)境和流體力學(xué)領(lǐng)域研究的熱點(diǎn)[45]。
目前有關(guān)縱向離散系數(shù)的確定方法中,理論公式法和經(jīng)驗(yàn)公式法都有相當(dāng)嚴(yán)格的適用條件,示蹤試驗(yàn)方法則能夠較準(zhǔn)確地?cái)M定河渠的縱向離散系數(shù)[6],但對(duì)濃度隨時(shí)間偏態(tài)分布的情況適用性不好。根據(jù)瞬時(shí)點(diǎn)源一維水質(zhì)模型,污染物遷移擴(kuò)散屬于高斯正態(tài)分布,而I.Guymer[7]通過(guò)大量試驗(yàn)研究發(fā)現(xiàn),天然河流或不規(guī)則斷面渠道中瞬時(shí)點(diǎn)源污染物的遷移擴(kuò)散呈現(xiàn)正偏態(tài)分布。南水北調(diào)中線渠道明渠段以梯形斷面為主,但是也存在彎道段、倒虹吸、渡槽和漸變段,沿程斷面形狀不規(guī)則,因此其污染物遷移擴(kuò)散規(guī)律應(yīng)為偏態(tài)分布。另外,最小二乘法過(guò)分注重整體擬合效果,使得其擬合后污染物重心和峰值往往偏離實(shí)際情況較遠(yuǎn);優(yōu)化類算法只需一個(gè)斷面的時(shí)間濃度過(guò)程數(shù)據(jù),無(wú)法避免初始段未均勻混合的影響,如非線性逼近法、單純形加速法、相關(guān)系數(shù)極值法和快速SA法[810]??梢?jiàn),現(xiàn)有方法研究沿程斷面不規(guī)則的河渠污染物擴(kuò)散偏態(tài)分布問(wèn)題時(shí),無(wú)法準(zhǔn)確確定污染團(tuán)峰值大小、重心位置等信息,因此亟待提出一種能夠解決這種問(wèn)題的新方法。
就擬合效果而言,如果示蹤劑濃度隨時(shí)間變化符合正態(tài)分布,則可以直接運(yùn)用中位數(shù)回歸或最小二乘法對(duì)第一站點(diǎn)的擬合參數(shù)值進(jìn)行預(yù)測(cè);如果濃度隨時(shí)間變化為偏態(tài)分布,則分位數(shù)回歸能夠提供更加準(zhǔn)確的信息。因此,分位數(shù)回歸相比最小二乘法回歸具有明顯優(yōu)勢(shì)。
[BT2][STHZ]4 結(jié)語(yǔ)
本文提出了基于分位數(shù)回歸的河渠縱向離散系數(shù)研究方法,并在R軟件中進(jìn)行了算例應(yīng)用,結(jié)果顯示,第一站點(diǎn)處各分位數(shù)回歸參數(shù)結(jié)果通過(guò)了975%置信水平下的假設(shè)檢驗(yàn),第二站點(diǎn)處預(yù)測(cè)值與實(shí)際值相關(guān)系數(shù)最高達(dá)到了0928。通過(guò)對(duì)比,發(fā)現(xiàn)中位數(shù)回歸參數(shù)結(jié)果可以近似代替最小二乘法回歸結(jié)果,且在濃度隨時(shí)間偏態(tài)分布的情況下,分位數(shù)回歸更具優(yōu)勢(shì),充分地顯示了其優(yōu)越性。分位數(shù)回歸方法利用雙站點(diǎn)濃度時(shí)間數(shù)據(jù)確定縱向離散系數(shù),減弱了初始段未均勻混合過(guò)程對(duì)預(yù)測(cè)效果的影響,解決了目前研究方法在研究沿程斷面不規(guī)則的河渠縱向離散系數(shù)中,無(wú)法準(zhǔn)確提供污染團(tuán)峰值大小、重心位置的問(wèn)題。endprint
分位數(shù)回歸結(jié)果具有很好的穩(wěn)健性,能夠?yàn)檠芯空咛峁┴S富的信息,在解決偏態(tài)分布問(wèn)題時(shí)優(yōu)點(diǎn)尤為突出。因此分位數(shù)回歸方法的應(yīng)用為縱向離散系數(shù)研究領(lǐng)域以及水文水資源其他方向的研究提供了一個(gè)新思路。
參考文獻(xiàn)(References):
[1] 曹倩,邵東國(guó),張 華,等.梯形斷面明渠縱向離散系數(shù)的分析[J].南水北調(diào)與水利科技,2012,10(6):1417.(CAO Qian,SHAO Dongguo,ZHANG Hua,et al.Determination of longitudinal dispersion coefficient of trapezoidal open channels[J].SouthtoNorth Water Transfers and Water Science & Technology,2012,10(6):1417.(in Chinese))
[2] SHAO Dongguo,YANG Haidong,XIAO Yi,et al.Water quality model parameter identification of an open channel in a long distance water transfer project based on finite difference,difference evolution and Monte Carlo[J].Water Science & Technology,2014,69(3):587594.
[3] 程聲通.環(huán)境系統(tǒng)分析教程[M].北京:化學(xué)工業(yè)出版社.2006:3638.(CHENG Shengtong.Environmental system analysis tutorial[M].Beijing:Chemical Industry Press.2006:3638.(in Chinese))
[4] Zhang Wei.A 2D numerical simulation study on longitudinal solute transport and longitudinal dispersion coefficient [J].Water Resources Research,2011,47(7).
[5] 陳永燦,王志剛,朱德軍,等.冰封河道縱向離散系數(shù)計(jì)算研究[J].水力發(fā)電學(xué)報(bào),2012,31(5):173177.(CHEN Yongcan,Wang Zhigang,ZHU Dejun,et al.Study on longitudinal dispersion coefficient for icecovered rivers[J].Journal of Hydroelectric Engineering,2012,31(5):173177.(in Chinese))
[6] 高偉,楊中華.彎道縱向離散系數(shù)研究進(jìn)展[J].中國(guó)農(nóng)村水利水電,2009,2:58.(GAO Wei,YANG Zhonghua.Advance in longitudinal dispersion coefficient of river bends[J].China Rural and Hydropower,2009,2:58.(in Chinese))
[7] I Guymer.Longitudinal Dispersion in Sinuous Channels with Changes in Shape[J].Journal of Hydraulic Engineering,1998,124:3340.
[8] 顧莉,華祖林.天然河流縱向離散系數(shù)確定方法的研究進(jìn)展[J].水利水電科技進(jìn)展,2007,27(2):8589.(GU Li,HUA Zulin.Advance in determination of longitudinal dispersion coefficient of natural rivers[J].Advances in Science Technology of Water Resources,2007,27(2):8589.(in Chinese))
[9] 顧莉,華祖林,何 偉,等.河流污染物縱向離散系數(shù)確定的演算優(yōu)化法[J].水利學(xué)報(bào),2007,38(12):14211425.(GU Li,HUA Zulin,HE Wei,et al.Routingopimization method for determination of longitudinal dispersion coefficient in river[J].Journal of Hydraulic Engineering,2007,38(12):14211425.(in Chinese))[ZK)]
[10] [ZK(#]楊海東,肖 宜,王卓民,等.突發(fā)性水污染事件溯源方法[J].水科學(xué)進(jìn)展,2014,25(1):122129.(YANG Haidong,XIAO Yi,WANG Zhuomin,et al.On source identification method
for sudden water pollution accidents[J].Advances in Water Science,2014,25(1):122129.(in Chinese))
[11] Roger Koenker,Gilbert Bassett,Jr.Regression Quantiles[J].Econometrica,1978,46(1):3350.
[12] 喬艦,李再興.分位數(shù)回歸的理論再說(shuō)明及實(shí)例分析[J].統(tǒng)計(jì)與決策,2012,19:104107.(QIAO Jian,LI Zaixing.Quantile regression theory to explain and instance analysis[J].Statistics and Decision,2012,19:104107.(in Chinese))
[13] 陳建寶,丁軍軍.分位數(shù)回歸技術(shù)綜述[J].統(tǒng)計(jì)與信息論壇,2008,3:8996.(CHEN Jianbao,DING Junjun.A review of technologies on quantile regression[J].Statistics & Information Forum,2008,3:8996.(in Chinese))
[14] Lingxin Hao,Daniel Q Naiman.分位數(shù)回歸模型[M].肖東亮,譯.上海:上海人民出版社,2012.(Lingxin Hao,Daniel Q.Naiman.Quantile regression model[M].XIAO Dongliang,translation.Shanghai:Shanghai People′s Publishing House,2012.)
[15] 蘇瑜,萬(wàn)宇艷.分位數(shù)回歸思想與簡(jiǎn)單應(yīng)用[J].統(tǒng)計(jì)教育,2009(10):5861.(SU Yu,WAN Yuyan.The idea and application of quantile regression[J].Statistical Thinktank,2009(10):5861.(in Chinese))
[16] 溫季,郭建青,宰松梅,等.河流水團(tuán)示蹤試驗(yàn)數(shù)據(jù)分析的雙站直線解析法[J].水利學(xué)報(bào),2008,39(5):618622.(WEN Ji,GUO Jianqing,ZAI Songmei,et al.Linear analytic method for determining water quality parameters of river according to the observation data obtained from two sections[J].Journal of Hydraulic Engineering,2008,39(5):618622.(in Chinese))endprint
分位數(shù)回歸結(jié)果具有很好的穩(wěn)健性,能夠?yàn)檠芯空咛峁┴S富的信息,在解決偏態(tài)分布問(wèn)題時(shí)優(yōu)點(diǎn)尤為突出。因此分位數(shù)回歸方法的應(yīng)用為縱向離散系數(shù)研究領(lǐng)域以及水文水資源其他方向的研究提供了一個(gè)新思路。
參考文獻(xiàn)(References):
[1] 曹倩,邵東國(guó),張 華,等.梯形斷面明渠縱向離散系數(shù)的分析[J].南水北調(diào)與水利科技,2012,10(6):1417.(CAO Qian,SHAO Dongguo,ZHANG Hua,et al.Determination of longitudinal dispersion coefficient of trapezoidal open channels[J].SouthtoNorth Water Transfers and Water Science & Technology,2012,10(6):1417.(in Chinese))
[2] SHAO Dongguo,YANG Haidong,XIAO Yi,et al.Water quality model parameter identification of an open channel in a long distance water transfer project based on finite difference,difference evolution and Monte Carlo[J].Water Science & Technology,2014,69(3):587594.
[3] 程聲通.環(huán)境系統(tǒng)分析教程[M].北京:化學(xué)工業(yè)出版社.2006:3638.(CHENG Shengtong.Environmental system analysis tutorial[M].Beijing:Chemical Industry Press.2006:3638.(in Chinese))
[4] Zhang Wei.A 2D numerical simulation study on longitudinal solute transport and longitudinal dispersion coefficient [J].Water Resources Research,2011,47(7).
[5] 陳永燦,王志剛,朱德軍,等.冰封河道縱向離散系數(shù)計(jì)算研究[J].水力發(fā)電學(xué)報(bào),2012,31(5):173177.(CHEN Yongcan,Wang Zhigang,ZHU Dejun,et al.Study on longitudinal dispersion coefficient for icecovered rivers[J].Journal of Hydroelectric Engineering,2012,31(5):173177.(in Chinese))
[6] 高偉,楊中華.彎道縱向離散系數(shù)研究進(jìn)展[J].中國(guó)農(nóng)村水利水電,2009,2:58.(GAO Wei,YANG Zhonghua.Advance in longitudinal dispersion coefficient of river bends[J].China Rural and Hydropower,2009,2:58.(in Chinese))
[7] I Guymer.Longitudinal Dispersion in Sinuous Channels with Changes in Shape[J].Journal of Hydraulic Engineering,1998,124:3340.
[8] 顧莉,華祖林.天然河流縱向離散系數(shù)確定方法的研究進(jìn)展[J].水利水電科技進(jìn)展,2007,27(2):8589.(GU Li,HUA Zulin.Advance in determination of longitudinal dispersion coefficient of natural rivers[J].Advances in Science Technology of Water Resources,2007,27(2):8589.(in Chinese))
[9] 顧莉,華祖林,何 偉,等.河流污染物縱向離散系數(shù)確定的演算優(yōu)化法[J].水利學(xué)報(bào),2007,38(12):14211425.(GU Li,HUA Zulin,HE Wei,et al.Routingopimization method for determination of longitudinal dispersion coefficient in river[J].Journal of Hydraulic Engineering,2007,38(12):14211425.(in Chinese))[ZK)]
[10] [ZK(#]楊海東,肖 宜,王卓民,等.突發(fā)性水污染事件溯源方法[J].水科學(xué)進(jìn)展,2014,25(1):122129.(YANG Haidong,XIAO Yi,WANG Zhuomin,et al.On source identification method
for sudden water pollution accidents[J].Advances in Water Science,2014,25(1):122129.(in Chinese))
[11] Roger Koenker,Gilbert Bassett,Jr.Regression Quantiles[J].Econometrica,1978,46(1):3350.
[12] 喬艦,李再興.分位數(shù)回歸的理論再說(shuō)明及實(shí)例分析[J].統(tǒng)計(jì)與決策,2012,19:104107.(QIAO Jian,LI Zaixing.Quantile regression theory to explain and instance analysis[J].Statistics and Decision,2012,19:104107.(in Chinese))
[13] 陳建寶,丁軍軍.分位數(shù)回歸技術(shù)綜述[J].統(tǒng)計(jì)與信息論壇,2008,3:8996.(CHEN Jianbao,DING Junjun.A review of technologies on quantile regression[J].Statistics & Information Forum,2008,3:8996.(in Chinese))
[14] Lingxin Hao,Daniel Q Naiman.分位數(shù)回歸模型[M].肖東亮,譯.上海:上海人民出版社,2012.(Lingxin Hao,Daniel Q.Naiman.Quantile regression model[M].XIAO Dongliang,translation.Shanghai:Shanghai People′s Publishing House,2012.)
[15] 蘇瑜,萬(wàn)宇艷.分位數(shù)回歸思想與簡(jiǎn)單應(yīng)用[J].統(tǒng)計(jì)教育,2009(10):5861.(SU Yu,WAN Yuyan.The idea and application of quantile regression[J].Statistical Thinktank,2009(10):5861.(in Chinese))
[16] 溫季,郭建青,宰松梅,等.河流水團(tuán)示蹤試驗(yàn)數(shù)據(jù)分析的雙站直線解析法[J].水利學(xué)報(bào),2008,39(5):618622.(WEN Ji,GUO Jianqing,ZAI Songmei,et al.Linear analytic method for determining water quality parameters of river according to the observation data obtained from two sections[J].Journal of Hydraulic Engineering,2008,39(5):618622.(in Chinese))endprint
分位數(shù)回歸結(jié)果具有很好的穩(wěn)健性,能夠?yàn)檠芯空咛峁┴S富的信息,在解決偏態(tài)分布問(wèn)題時(shí)優(yōu)點(diǎn)尤為突出。因此分位數(shù)回歸方法的應(yīng)用為縱向離散系數(shù)研究領(lǐng)域以及水文水資源其他方向的研究提供了一個(gè)新思路。
參考文獻(xiàn)(References):
[1] 曹倩,邵東國(guó),張 華,等.梯形斷面明渠縱向離散系數(shù)的分析[J].南水北調(diào)與水利科技,2012,10(6):1417.(CAO Qian,SHAO Dongguo,ZHANG Hua,et al.Determination of longitudinal dispersion coefficient of trapezoidal open channels[J].SouthtoNorth Water Transfers and Water Science & Technology,2012,10(6):1417.(in Chinese))
[2] SHAO Dongguo,YANG Haidong,XIAO Yi,et al.Water quality model parameter identification of an open channel in a long distance water transfer project based on finite difference,difference evolution and Monte Carlo[J].Water Science & Technology,2014,69(3):587594.
[3] 程聲通.環(huán)境系統(tǒng)分析教程[M].北京:化學(xué)工業(yè)出版社.2006:3638.(CHENG Shengtong.Environmental system analysis tutorial[M].Beijing:Chemical Industry Press.2006:3638.(in Chinese))
[4] Zhang Wei.A 2D numerical simulation study on longitudinal solute transport and longitudinal dispersion coefficient [J].Water Resources Research,2011,47(7).
[5] 陳永燦,王志剛,朱德軍,等.冰封河道縱向離散系數(shù)計(jì)算研究[J].水力發(fā)電學(xué)報(bào),2012,31(5):173177.(CHEN Yongcan,Wang Zhigang,ZHU Dejun,et al.Study on longitudinal dispersion coefficient for icecovered rivers[J].Journal of Hydroelectric Engineering,2012,31(5):173177.(in Chinese))
[6] 高偉,楊中華.彎道縱向離散系數(shù)研究進(jìn)展[J].中國(guó)農(nóng)村水利水電,2009,2:58.(GAO Wei,YANG Zhonghua.Advance in longitudinal dispersion coefficient of river bends[J].China Rural and Hydropower,2009,2:58.(in Chinese))
[7] I Guymer.Longitudinal Dispersion in Sinuous Channels with Changes in Shape[J].Journal of Hydraulic Engineering,1998,124:3340.
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