馬旭林,周勃旸,時(shí)洋②,計(jì)燕霞,和杰

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B08RDP區(qū)域集合預(yù)報(bào)溫度場(chǎng)質(zhì)量評(píng)估與綜合偏差訂正

馬旭林①*,周勃旸①,時(shí)洋①②,計(jì)燕霞①,和杰①

① 南京信息工程大學(xué) 氣象災(zāi)害教育部重點(diǎn)實(shí)驗(yàn)室,江蘇 南京 210044;

② 廣東省氣象臺(tái),廣東 廣州 510080

2014-11-24收稿，2015-06-21接受

國(guó)家自然科學(xué)基金資助項(xiàng)目(41275111;91437113);公益性行業(yè)(氣象)科研專項(xiàng)(GYHY201506005)

針對(duì)B08RDP(The Beijing 2008 Olympics Research and Development Project)5套區(qū)域集合預(yù)報(bào)資料,系統(tǒng)分析了各套集合預(yù)報(bào)溫度場(chǎng)的預(yù)報(bào)質(zhì)量。在此基礎(chǔ)上運(yùn)用集合預(yù)報(bào)的綜合偏差訂正方法對(duì)溫度場(chǎng)進(jìn)行偏差訂正,并對(duì)其效果進(jìn)行了分析討論。結(jié)果顯示:5套B08RDP區(qū)域集合預(yù)報(bào)中,美國(guó)國(guó)家環(huán)境預(yù)報(bào)中心(NCEP)區(qū)域集合預(yù)報(bào)溫度場(chǎng)的整體預(yù)報(bào)質(zhì)量最高,平均預(yù)報(bào)誤差最小,離散度也最為合理,預(yù)報(bào)可信度和可辨識(shí)度均較優(yōu);而中國(guó)氣象科學(xué)研究院(CAMS)的溫度預(yù)報(bào)誤差過大,預(yù)報(bào)質(zhì)量最差。整體上看,除NCEP之外的4套集合預(yù)報(bào)的溫度場(chǎng)均存在集合離散度偏小的問題;綜合偏差訂正能有效減小各集合預(yù)報(bào)溫度場(chǎng)的集合平均均方根誤差,改善集合離散度的質(zhì)量,顯示出綜合偏差訂正方案對(duì)集合預(yù)報(bào)溫度場(chǎng)偏差訂正的良好能力。

數(shù)值預(yù)報(bào)

集合預(yù)報(bào)

偏差訂正

質(zhì)量評(píng)估

B08RDP

數(shù)值預(yù)報(bào)模式及其初始場(chǎng)的不確定性,導(dǎo)致非線性運(yùn)動(dòng)大氣的確定性預(yù)報(bào)技巧受到限制。集合預(yù)報(bào)能夠較好地反映實(shí)際大氣運(yùn)動(dòng)不確定性特征,有效彌補(bǔ)了確定性預(yù)報(bào)的不足,已成為提高預(yù)報(bào)準(zhǔn)確性的有效方式,既是概率預(yù)報(bào)的基礎(chǔ)(智協(xié)飛等,2014a),也是目前集合——變分混合資料同化的前提(馬旭林等,2014)。集合預(yù)報(bào)的關(guān)鍵問題之一是集合初始擾動(dòng)的構(gòu)造,主要包括基于初值或模式不確定性的構(gòu)造方案。前者主要有歐洲中期天氣預(yù)報(bào)中心(ECMWF)的集合同化——奇異向量法、美國(guó)環(huán)境預(yù)報(bào)中心(NCEP)的重新尺度化集合變換法(ETR,Ensemble Transform with Rescaling)和加拿大氣象中心的集合卡爾曼濾波法(EnKF),以及基于集合卡爾曼理論發(fā)展的集合卡爾曼變換(ETKF)初始擾動(dòng)方法(Wang and Bishop,2003;馬旭林等,2008;Ma et al.,2009)等;后者通常可分為單模式多物理過程、多模式單物理過程以及多模式多物理過程(超級(jí)集合預(yù)報(bào))等,其中超級(jí)集合預(yù)報(bào)方法的預(yù)報(bào)效果多優(yōu)于單模式和多模式的集合平均(Krishnamurti et al.,2007;智協(xié)飛等,2013;崔慧慧和智協(xié)飛,2013)。

由于全球集合預(yù)報(bào)分辨率較低,難以有效捕獲中小尺度天氣系統(tǒng)的信息,從而具有較高分辨率的區(qū)域集合預(yù)報(bào)得到了快速發(fā)展(Bowler et al.,2009),并在數(shù)值天氣預(yù)報(bào)業(yè)務(wù)中得到廣泛應(yīng)用。如NCEP早期采用增長(zhǎng)模繁殖法構(gòu)造初始擾動(dòng)的短時(shí)區(qū)域集合預(yù)報(bào)系統(tǒng)(Du et al.,2003),目前由基于ETR方法的NCEP全球集合預(yù)報(bào)提供邊界條件(麻巨慧等,2011),并考慮了模式不確定性(Du et al.,2006)。由ECMWF全球集合預(yù)報(bào)降尺度構(gòu)造的COSMO-LEPS區(qū)域集合預(yù)報(bào)系統(tǒng)也具有較好的預(yù)報(bào)性能(Marsigli et al.,2008)。加拿大采用集合卡爾曼濾波(EnKF)方法發(fā)展了區(qū)域集合預(yù)報(bào)系統(tǒng),并對(duì)不同的對(duì)流凝結(jié)參數(shù)和次網(wǎng)格尺度物理傾向進(jìn)行隨機(jī)擾動(dòng)(Li et al.,2008;Charron et al.,2010)。英國(guó)氣象局則由ETKF初始擾動(dòng)的全球集合預(yù)報(bào)降尺度形成了區(qū)域集合預(yù)報(bào)系統(tǒng)MOGREPS(The Met Office Global and Regional Ensemble Prediction System),同時(shí)使用隨機(jī)對(duì)流渦度考慮次網(wǎng)格不確定性(Bowler et al.,2009)?；诔叨然旌戏椒?Wang et al.,2010,2014)構(gòu)造的奧地利區(qū)域集合預(yù)報(bào)系統(tǒng)(Wang et al.,2011),將全球集合預(yù)報(bào)大尺度擾動(dòng)信息與區(qū)域集合預(yù)報(bào)的中小尺度信息相結(jié)合,較好地反映了實(shí)際大氣多尺度的不確定性特征,也有效改善了預(yù)報(bào)性能。日本氣象廳則在非靜力模式的基礎(chǔ)上利用奇異向量法作為初始擾動(dòng)方案建立了區(qū)域集合預(yù)報(bào)系統(tǒng)(Saito et al.,2006),也表現(xiàn)出良好的效果。

2008年為北京奧運(yùn)會(huì)提供支撐的B08RDP(The Beijing 2008 Olympics Research and Development Project)項(xiàng)目(Duan et al.,2012)集中了6個(gè)預(yù)報(bào)中心的區(qū)域集合預(yù)報(bào)系統(tǒng)制作同一時(shí)間、相同區(qū)域的中尺度集合預(yù)報(bào),其中客觀評(píng)估各中心區(qū)域集合預(yù)報(bào)的整體預(yù)報(bào)質(zhì)量和比較其預(yù)報(bào)性能是B08RDP項(xiàng)目的主要目標(biāo)之一(Duan et al.,2012)。集合預(yù)報(bào)質(zhì)量評(píng)估已開展了諸多研究(智協(xié)飛等,2014b),但評(píng)估物理量多選取海平面氣壓、500 hPa高度場(chǎng)或2 m溫度等(Johnson and Swinbank,2009;Alexander et al.,2009),較少關(guān)注對(duì)流層低層的集合預(yù)報(bào)質(zhì)量。對(duì)于區(qū)域集合預(yù)報(bào),對(duì)流層低層的溫度、位勢(shì)高度以及濕度等對(duì)中小尺度天氣系統(tǒng)的發(fā)生發(fā)展通常起著關(guān)鍵作用,也是反映區(qū)域集合預(yù)報(bào)性能的重要方面。因此,本文利用B08RDP項(xiàng)目的區(qū)域集合預(yù)報(bào)資料,首先對(duì)反映集合預(yù)報(bào)整體質(zhì)量的對(duì)流層低層(850 hPa)溫度預(yù)報(bào)質(zhì)量進(jìn)行多角度評(píng)估分析。然后,運(yùn)用基于自適應(yīng)卡爾曼濾波的遞減平均方法(Du et al.,2007;Cui et al.,2012;馬旭林等,2015),分別對(duì)各套集合預(yù)報(bào)的溫度變量進(jìn)行綜合偏差訂正,合理調(diào)整集合平均預(yù)報(bào)誤差和集合離散度,進(jìn)一步改善區(qū)域集合預(yù)報(bào)的整體質(zhì)量,為實(shí)際預(yù)報(bào)業(yè)務(wù)中更好的應(yīng)用區(qū)域集合預(yù)報(bào)產(chǎn)品提供參考。

1　B08RDP區(qū)域集合預(yù)報(bào)資料

B08RDP項(xiàng)目是中國(guó)氣象局為2008年北京奧運(yùn)會(huì)的成功舉辦提供天氣預(yù)報(bào)支持,充分發(fā)揮多個(gè)集合預(yù)報(bào)中心的區(qū)域集合預(yù)報(bào)的優(yōu)勢(shì),提高天氣預(yù)報(bào)準(zhǔn)確性而建立的聯(lián)合項(xiàng)目。該項(xiàng)目共有國(guó)家氣象中心(NMC)、中國(guó)氣象科學(xué)院(CAMS)、美國(guó)國(guó)家環(huán)境預(yù)報(bào)中心(NCEP)、日本氣象廳(JMA)氣象研究所、奧地利氣象局(ZAMG)、加拿大環(huán)境部數(shù)值預(yù)報(bào)研究中心等6家單位組成。其中,CAMS使用我國(guó)自行研發(fā)的非靜力中尺度全球/區(qū)域同化預(yù)報(bào)系統(tǒng)GRAPES(陳德輝等,2008;馬旭林等,2009)作為集合預(yù)報(bào)的預(yù)報(bào)模式,而NMC使用WRF作為區(qū)域集合預(yù)報(bào)模式,二者的初始擾動(dòng)構(gòu)造方案同為增長(zhǎng)模繁殖法,邊界條件均由NCEP全球ETR初始擾動(dòng)集合預(yù)報(bào)提供,同時(shí)采用多積云對(duì)流參數(shù)、邊界層及陸面過程方案構(gòu)造模式擾動(dòng)。其他中心的區(qū)域集合預(yù)報(bào)系統(tǒng)的配置參考文獻(xiàn)Duan et al.(2012)。

因加拿大環(huán)境部數(shù)值預(yù)報(bào)中心的資料不完整,研究中只選取B08RDP項(xiàng)目中其余5套區(qū)域集合預(yù)報(bào)850 hPa溫度場(chǎng)資料進(jìn)行預(yù)報(bào)質(zhì)量的評(píng)估分析和綜合偏差訂正,并考察偏差訂正后各集合預(yù)報(bào)質(zhì)量的改善程度。NMC的集合擾動(dòng)成員數(shù)為15個(gè),CAMS為9個(gè),NCEP、JMA和ZAMG分別為15、11和17個(gè)集合擾動(dòng)成員。共同的預(yù)報(bào)區(qū)域?yàn)?90～140°E,25～50°N),模式分辨率為15 km,預(yù)報(bào)時(shí)效為36 h,時(shí)間間隔為6 h。資料的時(shí)間長(zhǎng)度為2008年6月24日—8月24日,共62 d。檢驗(yàn)分析資料為ECMWF高分辨率再分析資料,其分辨率與資料區(qū)域均與集合預(yù)報(bào)資料一致。

2　質(zhì)量評(píng)估

集合預(yù)報(bào)的質(zhì)量主要可以從預(yù)報(bào)可靠性及預(yù)報(bào)可辨識(shí)度兩個(gè)方面衡量。預(yù)報(bào)可靠性用來評(píng)價(jià)集合預(yù)報(bào)對(duì)不同預(yù)報(bào)概率對(duì)應(yīng)的觀測(cè)頻率無偏估計(jì)的能力,主要反映集合預(yù)報(bào)與相應(yīng)觀測(cè)在統(tǒng)計(jì)學(xué)上的一致性(Wilks,2006),可用集合平均均方根誤差(RMSE)、可信度曲線以及Talagrand分布等評(píng)價(jià);而集合預(yù)報(bào)可辨識(shí)度是指集合預(yù)報(bào)區(qū)分未來不同天氣事件的能力,一般采用可信度曲線、ROC(Relative Operating Characteristic)曲線等進(jìn)行評(píng)價(jià)。

圖1　850 hPa溫度集合預(yù)報(bào)的RMSE(a)和r比值(b)Fig.1　The (a)RMSE and (b)r scores of temperature at 850 hPa for the five sets of ensemble forecasts

2.1集合預(yù)報(bào)可信度

RMSE可以用來對(duì)比各集合預(yù)報(bào)的預(yù)報(bào)準(zhǔn)確性,即衡量集合平均的預(yù)報(bào)可靠性。圖1a為5套集合預(yù)報(bào)資料的850 hPa溫度場(chǎng)集合平均均方誤差在36 h預(yù)報(bào)時(shí)效內(nèi)的分布。可以看出,CAMS與NMC兩套資料的RMSE較大,而JMA、NCEP、ZAMG三套資料則相對(duì)較小,其中CAMS的6 h集合平均預(yù)報(bào)偏差約為ZAMG的5倍,說明不同中心的集合平均預(yù)報(bào)的可靠性具有明顯的差異。另外,CAMS的RMSE幾乎是NMC近兩倍,而CAMS與NMC兩套集合預(yù)報(bào)除預(yù)報(bào)模式不同、集合成員數(shù)略有差異之外,其余集合預(yù)報(bào)系統(tǒng)特征均一致,可以說明集合預(yù)報(bào)中預(yù)報(bào)模式和集合成員數(shù)對(duì)集合預(yù)報(bào)平均的可靠性具有重要影響。

本次研究得出，在條件允許的情況下盡量應(yīng)用多種方法聯(lián)用進(jìn)行診斷，以減少偽影干擾及患者個(gè)人病癥發(fā)展?fàn)顩r對(duì)診斷的影響，而MRI結(jié)合MRA的篩查方案價(jià)格可能對(duì)于部分患者來說，存在一定的經(jīng)濟(jì)負(fù)擔(dān)，此外，患者圖像的判斷也需要醫(yī)師的經(jīng)驗(yàn)，所以應(yīng)盡可能選擇經(jīng)驗(yàn)較為豐富的醫(yī)師進(jìn)行圖像分析，以保證診斷的準(zhǔn)確性。

集合離散度主要反映集合成員描述實(shí)際大氣運(yùn)動(dòng)狀態(tài)不確定性的能力,理論上其量值應(yīng)與集合平均預(yù)報(bào)誤差相當(dāng)。r是集合平均的預(yù)報(bào)誤差(RMSE)與集合離散度(spread)的比值,可用來衡量集合離散度相對(duì)于集合平均預(yù)報(bào)誤差的合理程度,理想情況下r為1。比較5套集合預(yù)報(bào)資料的850 hPa溫度場(chǎng)r評(píng)分(圖1b)可知,NCEP的集合離散度最為合理,6～36 h預(yù)報(bào)的r均位于1附近,而其余集合預(yù)報(bào)均明顯大于1,尤其CAMS更為顯著。這說明,除NCEP的集合預(yù)報(bào)外,其余集合預(yù)報(bào)的集合離散度均顯著偏小。另外,CAMS、NMC和JMA集合預(yù)報(bào)的r值隨著預(yù)報(bào)時(shí)間的增加有明顯減小的趨勢(shì),而RMSE(圖1a)并未有相應(yīng)的顯著增長(zhǎng)或下降,說明這三套集合預(yù)報(bào)的集合離散度隨預(yù)報(bào)時(shí)間的增加有增大趨勢(shì),顯示出集合預(yù)報(bào)的不確定性越來越大,但仍未能反映實(shí)際大氣運(yùn)動(dòng)的不確定性特征大小的程度。另外也反映出,這三個(gè)中心的集合預(yù)報(bào)平均預(yù)報(bào)偏差過大,可能主要與預(yù)報(bào)模式性能或模式初值的質(zhì)量相關(guān)。

Talagrand圖主要用來評(píng)價(jià)集合離散度代表觀測(cè)不確定性的程度,即評(píng)估集合成員與觀測(cè)之間的一致性(Wilks,2006)。Talagrand通過統(tǒng)計(jì)觀測(cè)落在由大到小排列的集合成員區(qū)間內(nèi)的頻率而獲得,理想的集合預(yù)報(bào)各集合成員與觀測(cè)滿足一致性條件,所有次序統(tǒng)計(jì)值相同(圖中橫直線),呈水平均一形態(tài)。圖2為5套集合預(yù)報(bào)資料的Talagrand分布,圖中橫坐標(biāo)的區(qū)間數(shù)與各自不同的集合成員數(shù)相對(duì)應(yīng)。由圖可知,NCEP集合預(yù)報(bào)各成員之間基本呈水平分布,相對(duì)為最優(yōu);ZAMG與JMA各集合成員間過于相似且不同于觀測(cè)值,呈明顯的U型分布,說明集合離散度偏小,不能代表實(shí)際觀測(cè)的不確定性特征;而CAMS則呈L型,表明預(yù)報(bào)值偏大,使得觀測(cè)值時(shí)常處于最小次序的位置,同時(shí)離散度偏小,在預(yù)報(bào)質(zhì)量上則具有顯著的高溫預(yù)報(bào)偏差,即空?qǐng)?bào)較多;NMC的U型分布也有一定的高溫預(yù)報(bào)偏差。

圖2　5組集合預(yù)報(bào)的850 hPa溫度24 h預(yù)報(bào)的 Talagrand分布　　a.NCEP;b.ZAMG;c.JMA;d.CAMS;e.NMCFig.2　Talagrand distribution for the 850-hPa 24-h temperature forecast of the five sets of ensemble forecasts:(a)NCEP;(b)ZAMG;(c)JMA;(d)CAMS;(e)NMC

2.2預(yù)報(bào)可辨識(shí)度

ROC曲線是不同檢驗(yàn)閾值的命中率與誤報(bào)率對(duì)應(yīng)各點(diǎn)的連線,該曲線以下覆蓋的面積稱為ROC面積,代表集合預(yù)報(bào)區(qū)分未來不同天氣事件能力的大小。理想集合預(yù)報(bào)的ROC曲線由x=0和y=1組成,對(duì)應(yīng)的面積為1。對(duì)于實(shí)際的集合預(yù)報(bào),ROC面積愈接近于1,說明該集合預(yù)報(bào)區(qū)分天氣事件的能力就越好。通過對(duì)比12 h預(yù)報(bào)的850 hPa溫度的ROC曲線的形態(tài)和ROC面積(圖3a)可見,NCEP與ZAMG的ROC面積較大,分別達(dá)到0.94和0.95,說明二者對(duì)未來不同天氣事件的區(qū)分能力較優(yōu);而JMA與NMC的ROC面積分別僅為0.89和0.80,CAMS的ROC面積更低至0.65,反映了這些集合預(yù)報(bào)相對(duì)較低的區(qū)分未來不同天氣事件的能力。對(duì)于24 h預(yù)報(bào)(圖3b)而言,ZAMG、NCEP和JMA的ROC面積均在0.90以上,具有同12 h預(yù)報(bào)接近的質(zhì)量。NMC的則為0.83,比12 h預(yù)報(bào)略有升高,而CAMS的預(yù)報(bào)能力依然最差。從ROC面積指標(biāo)來看,無論12 h還是24 h的區(qū)域集合預(yù)報(bào),NMC和CAMS對(duì)未來不同天氣事件的區(qū)分能力相對(duì)于其他三者都明顯偏低。

2.3綜合評(píng)分

圖3　850 hPa溫度集合預(yù)報(bào)的ROC評(píng)分　　a.12 h預(yù)報(bào);b.24 h預(yù)報(bào)Fig.3　ROC curves for the 850-hPa temperature forecasts of five sets of ensemble forecasts:(a)12 h;(b)24 h

圖4　850 hPa溫度集合預(yù)報(bào)的可信度　　a.12 h預(yù)報(bào);b.24 h預(yù)報(bào)Fig.4　Reliability diagram for the 850-hPa temperature forecasts of five sets of ensemble forecasts:(a)12 h;(b)24 h

可信度曲線為綜合評(píng)價(jià)集合預(yù)報(bào)可信度(reliability)和可辨識(shí)度(resolution)的綜合反映,是通過對(duì)不同檢驗(yàn)閾值的預(yù)報(bào)概率分類中觀測(cè)事件發(fā)生的相對(duì)頻率進(jìn)行統(tǒng)計(jì)而得到的結(jié)果(Hartmann et al.,2002)。理想的預(yù)報(bào)概率與觀測(cè)事件的頻率相同,此時(shí)可信度曲線為x=y的對(duì)角線。從5個(gè)中心集合預(yù)報(bào)溫度降溫2 ℃預(yù)報(bào)的可信度曲線(圖4)來看,無論12 h(圖4a)還是24 h(圖4b)預(yù)報(bào),NCEP集合預(yù)報(bào)的可信度曲線總體上穩(wěn)定處于對(duì)角線附近兩側(cè),顯示出較高質(zhì)量的預(yù)報(bào)可信度與可辨識(shí)度,只是24 h預(yù)報(bào)中在低預(yù)報(bào)概率(0～0.4)區(qū)間的預(yù)報(bào)概率略大于觀測(cè)頻率,導(dǎo)致可辨識(shí)度略低;從JMA的可信度曲線可以發(fā)現(xiàn),其24 h預(yù)報(bào)的可信度曲線分布優(yōu)于12 h預(yù)報(bào),基本上與NCEP的預(yù)報(bào)可信度和可辨識(shí)度相當(dāng)。說明隨著預(yù)報(bào)時(shí)間的延長(zhǎng),集合預(yù)報(bào)的可信度和可辨識(shí)度的變化與預(yù)報(bào)模式的性能具有重要的關(guān)系;ZAMG的可信度曲線顯示,在兩個(gè)預(yù)報(bào)時(shí)效內(nèi)其在中高預(yù)報(bào)概率區(qū)間的預(yù)報(bào)值均偏大,且可信度曲線中間部分斜率偏小,可辨識(shí)度偏低;CAMS的可信度曲線分布明顯偏離x=y的對(duì)角線,說明其在整個(gè)預(yù)報(bào)概率分布區(qū)間內(nèi)的預(yù)報(bào)可辨識(shí)度均較差。尤其在24 h預(yù)報(bào)中都呈現(xiàn)預(yù)報(bào)概率遠(yuǎn)低于觀測(cè)頻率,說明其預(yù)報(bào)值顯著小于實(shí)際觀測(cè)值,類似的情形也出現(xiàn)在NMC的中低預(yù)報(bào)概率(0～0.5)區(qū)間。

3　綜合偏差訂正

理想集合預(yù)報(bào)的集合平均預(yù)報(bào)誤差為零,集合離散度能夠合理表征實(shí)際大氣運(yùn)動(dòng)的不確定性特征。由于數(shù)值預(yù)報(bào)模式存在預(yù)報(bào)偏差,很大程度上導(dǎo)致了集合預(yù)報(bào)的偏差;另外,初始擾動(dòng)構(gòu)造方案的不盡合理也通常會(huì)造成集合離散度偏低,這都會(huì)限制集合預(yù)報(bào)的整體性能。因此,在業(yè)務(wù)應(yīng)用前,一般都會(huì)對(duì)集合預(yù)報(bào)進(jìn)行偏差訂正和離散度的合理調(diào)整。本文采用基于卡爾曼濾波的遞減平均后驗(yàn)訂正的綜合偏差訂正方法(馬旭林等,2015),對(duì)5套集合預(yù)報(bào)進(jìn)行偏差訂正,以改善其整體質(zhì)量,提高應(yīng)用能力。

3.1綜合偏差訂正方案

集合預(yù)報(bào)的綜合偏差訂正包括一階矩及二階矩訂正,其中一階矩偏差訂正是訂正集合平均預(yù)報(bào)偏差以增加預(yù)報(bào)可靠性,二階矩訂正通過改善集合預(yù)報(bào)概率密度函數(shù)與觀測(cè)值的概率分布一致性,實(shí)現(xiàn)集合離散度的調(diào)整。綜合偏差訂正則是在一階矩訂正的基礎(chǔ)上加入二階矩訂正,先后調(diào)整集合預(yù)報(bào)偏差和集合離散度,以改善集合預(yù)報(bào)質(zhì)量。因綜合偏差訂正方案中的一階矩與二階矩偏差訂正相互獨(dú)立并先后進(jìn)行,故單獨(dú)試驗(yàn)的最優(yōu)權(quán)重系數(shù)適用于綜合偏差訂正。

由于B08RDP項(xiàng)目資料時(shí)長(zhǎng)的限制,試驗(yàn)中選取20 d的集合預(yù)報(bào)作為一階矩和二階矩訂正的訓(xùn)練資料。綜合偏差訂正共分為兩步:首先進(jìn)行一階矩偏差訂正以去除集合平均預(yù)報(bào)偏差;然后使用一階矩偏差訂正后的集合平均預(yù)報(bào)誤差調(diào)整集合離散度。綜合偏差訂正方案的詳細(xì)說明請(qǐng)參見馬旭林等(2015)文獻(xiàn)。

圖5　850 hPa溫度集合預(yù)報(bào)訂正前(虛線)、后(實(shí)線)的RMSE(a)和r比值(b)Fig.5　The (a)RMSE and (b)r scores for the 850-hPa temperature of five sets of ensemble forecasts without(dashed line) and with(solid line) BC

3.2綜合偏差訂正效果

圖6　850 hPa溫度24 h集合預(yù)報(bào)偏差訂正前(灰色)、后(黑色)的Talagrand分布a.NCEP;b.ZAMG;c.JMA;d.CAMS;e.NMCFig.6　Talagrand distribution for the 850-hPa temperature at 24 h of five sets of ensemble forecasts without(gray bars) and with(black bars) BC:(a)NCEP;(b)ZAMG;(c)JMA;(d)CAMS;(e)NMC

圖5為各中心集合預(yù)報(bào)綜合訂正前后850 hPa溫度預(yù)報(bào)的RMSE和r的分布。各中心集合預(yù)報(bào)訂正后(實(shí)線)的RMSE評(píng)分均較訂正前(虛線)評(píng)分更優(yōu)(圖5a),說明綜合偏差訂正能夠有效減小集合平均預(yù)報(bào)偏差。特別是,訂正前集合平均預(yù)報(bào)偏差越大,其訂正效果更加顯著。其中,CAMS集合預(yù)報(bào)平均偏差減小134.3%,而偏差較小的NCEP集合預(yù)報(bào)也減小了8.2%。綜合偏差訂正后的CAMS集合平均預(yù)報(bào)偏差仍明顯大于其他集合預(yù)報(bào),這也說明若集合預(yù)報(bào)平均偏差過大,綜合偏差訂正也僅能起到一定程度的改善,并不能完全去除。訂正后各集合預(yù)報(bào)的r曲線均位于1附近(圖5b),表明綜合偏差訂正對(duì)集合離散度的調(diào)整效果較為明顯。進(jìn)一步分析可知,綜合偏差訂正對(duì)NCEP的集合離散度調(diào)整幅度最小,而對(duì)CAMS的調(diào)整幅度最大,這也顯示出NCEP的集合預(yù)報(bào)相對(duì)于CAMS而言具有更高的質(zhì)量。

由Talagrand分布(圖6)可以看出,訂正后各中心集合預(yù)報(bào)更趨于水平均勻分布,各次序統(tǒng)計(jì)值也與理想Talagrand評(píng)分(圖中橫直線)更加接近。ZAMG與JMA的集合預(yù)報(bào)訂正前的U型分布消失,兩邊次序統(tǒng)計(jì)值減小而中間各次序統(tǒng)計(jì)值增加,更接近于理想Talagrand分布;CAMS的高溫預(yù)報(bào)偏差基本去除,NMC的U型也消失,高溫預(yù)報(bào)偏差也基本去除。由于NCEP集合預(yù)報(bào)訂正前的Talagrand分布較較為合理,訂正后的調(diào)整并不顯著。綜上,綜合偏差訂正對(duì)于集合預(yù)報(bào)離散度的調(diào)整以及預(yù)報(bào)偏差的消除都具有較為明顯的效果。

對(duì)比綜合偏差訂正前(虛線)后(實(shí)線)各中心850 hPa溫度預(yù)報(bào)降溫2 ℃時(shí)的ROC評(píng)分(圖7)可以看出,綜合偏差訂正后,各集合預(yù)報(bào)的ROC面積均有不同程度的增加,表明綜合偏差訂正對(duì)于集合預(yù)報(bào)可辨識(shí)度的正向調(diào)整作用顯著。盡管訂正后各中心集合預(yù)報(bào)的ROC面積仍然差異較大,這很大程度上與訂正前集合預(yù)報(bào)的質(zhì)量不同有直接關(guān)系。其中訂正效果最明顯的為CAMS的集合預(yù)報(bào),其12 h和24 h降溫預(yù)報(bào)的ROC面積增長(zhǎng)幅度分別達(dá)到33.8%(圖7a)與29.4%(圖7b),而對(duì)于訂正前ROC面積較優(yōu)的JMA、NCEP與ZAMG,訂正后的ROC面積增長(zhǎng)幅度則相對(duì)較小。也就是說,對(duì)于質(zhì)量較差的集合預(yù)報(bào),綜合偏差訂正的效果尤佳。

圖8顯示,12 h(圖8a)和24 h(圖8b)的CAMS和NMC的集合預(yù)報(bào)訂正后的可信度曲線明顯更接近對(duì)角線,較訂正前預(yù)報(bào)值偏小的情況得到了明顯改善,其中24 h的NMC集合預(yù)報(bào),訂正前中低預(yù)報(bào)概率(0～0.6)事件的預(yù)報(bào)值偏大的情況在訂正后也得到了一定得緩解;同樣地,訂正后的NCEP、ZAMG與JMA集合預(yù)報(bào)的可信度曲線均更靠近對(duì)角線,其預(yù)報(bào)可信度和可辨識(shí)度均有不同程度的提高。

圖7　850 hPa溫度集合預(yù)報(bào)偏差訂正前(虛線)后(實(shí)線)的ROC評(píng)分　　a.12 h預(yù)報(bào);b.24 h預(yù)報(bào)Fig.7　ROC curves for the 850-hPa temperature of five sets of ensemble forecasts without(dashed line) and with(solid line) BC:(a)12 h;(b)24 h

圖8　850 hPa溫度集合預(yù)報(bào)偏差訂正前(虛線)后(實(shí)線)的可信度評(píng)分　　a.12 h預(yù)報(bào);b.24 h預(yù)報(bào)Fig.8　Reliability diagrams for the 850-hPa temperature of five sets of ensemble forecasts without(dashed line) and with(solid line) BC:(a)12 h;(b)24 h

綜上,綜合偏差訂正不僅可以減小集合平均預(yù)報(bào)偏差,而且還能有效地調(diào)整集合離散度,進(jìn)而改善集合預(yù)報(bào)的可信度與可辨識(shí)度,綜合提高了集合預(yù)報(bào)的整體質(zhì)量。值得注意的是,綜合偏差訂正對(duì)于質(zhì)量較好的NCEP區(qū)域集合預(yù)報(bào)的訂正效果較小(特別是離散度的調(diào)整),而對(duì)預(yù)報(bào)質(zhì)量欠佳的CAMS和NMC集合預(yù)報(bào)的訂正效果則較為明顯,尤其是集合平均預(yù)報(bào)偏差的訂正更加有效;對(duì)于ZAMG與JMA兩套資料而言,綜合偏差訂正對(duì)其集合離散度和預(yù)報(bào)可辨識(shí)度的調(diào)整效果均較顯著。

4　結(jié)論

本文從多個(gè)角度評(píng)估分析了B08RDP項(xiàng)目中5套集合預(yù)報(bào)的質(zhì)量,在此基礎(chǔ)上采用綜合偏差訂正方法進(jìn)行綜合偏差訂正,并對(duì)其效果進(jìn)行了討論。

1)5套B08RDP集合預(yù)報(bào)資料中,NCEP集合預(yù)報(bào)的平均預(yù)報(bào)偏差最小,離散度最為合理,預(yù)報(bào)可信度以及可辨識(shí)度均較好,整體預(yù)報(bào)質(zhì)量為最高;CAMS集合預(yù)報(bào)存在的預(yù)報(bào)偏差明顯偏大,整體性能最弱,這應(yīng)該與數(shù)值預(yù)報(bào)模式的性能有一定的關(guān)系;

2)從整體上看,集合離散度偏小是除NCEP之外的4套集合預(yù)報(bào)普遍存在的問題;

3)綜合偏差訂正方法能夠有效地減小各集合預(yù)報(bào)的集合平均偏差,集合離散度的質(zhì)量也有明顯提高,較好地改善了離散度普遍偏小的問題,顯示出綜合偏差訂正方法具有改善集合預(yù)報(bào)整體質(zhì)量的良好能力。

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Five sets of regional ensemble forecasts with lead times of 36 h over two months from 24 June 2008 to 24 August 2008 from the Beijing 2008 Olympics Research and Development Project(B08RDP) are evaluated and analyzed.This is firstly done by means of standard probabilistic verification scores,including root-mean-square error(RMSE),ensemble spread,talagrand diagrams,reliability,and ROC(Relative Operating Characteristic) curves.Then,to improve the forecast quality,a combined decaying averaging bias correction scheme(BC) is applied to the ensemble forecasts of B08RDP to reduce the bias in the ensemble mean and to adjust the improper spread of ensembles with sufficient performance evaluation.The BC scheme is designed based on the original Kalman filter.It contains the first moment bias correction,mainly for correcting the bias in the ensemble mean to improve the reliability of the ensemble forecasts,and the second moment bias correction mainly for adjusting the ensemble spread to make the ensemble forecasts fully representative of the uncertainties in the observations.Lastly,the BC scheme’s capacity is evaluated and discussed by means of the verification scores mentioned above.Temperatures at 850 hPa are corrected and verified in this study,wherein ECMWF reanalysis data are used as the reference for the verification.

The results show that,among the five sets of regional ensemble forecasts in B08RDP,the regional ensemble forecasts from NCEP possess the best forecast quality,with minimal bias,the most appropriate spread,and the best performance in terms of reliability,resolution and talagrand distributions.Meanwhile,the regional ensemble forecast from CAMS demonstrates the worst forecast quality,due to its largest forecast bias.On the whole,a relatively small spread is a common problem for several of the ensemble forecasts,except those from NCEP.In general,the combined bias correction scheme is proven to be efficient in reducing the RMSE of the ensemble mean,and in generating a more appropriate ensemble spread,for the five sets of ensemble forecasts,revealing its ability to improve the quality of ensemble forecasts,especially for ensemble forecasts of an already low quality.

numerical weather prediction;ensemble weather forecast;combined bias correction;performance evaluation;B08RDP

(責(zé)任編輯：孫寧)

Evaluation and combined bias correction on temperature forecast of regional ensemble prediction system of B08RDP

MA Xulin1,ZHOU Boyang1,SHI Yang1,2,JI Yanxia1,He Jie1

1KeyLaboratoryofMeteorologicalDisaster,MinistryofEducation(KLME),NanjingUniversityofInformationScience&Technology,Nanjing210044,China;2GuangdongMeteorologicalObservatory,Guangzhou510080,China

10.13878/j.cnki.dqkxxb.20141124003

引用格式：馬旭林,周勃旸,時(shí)洋,等,2016.B08RDP區(qū)域集合預(yù)報(bào)溫度場(chǎng)質(zhì)量評(píng)估與綜合偏差訂正[J].大氣科學(xué)學(xué)報(bào),39(5):643-652.

Ma X L,Zhou B Y,Shi Y,et al.,2016.Evaluation and combined bias correction on temperature forecast of regional ensemble prediction system of B08RDP[J].Trans Atmos Sci,39(5):643-652.doi：10.13878/j.cnki.dqkxxb.20141124003.(in Chinese).

*聯(lián)系人，E-mail:xulinma@nuist.edu.cn