区域集合预报基于SKEB和多物理过程的混合模式扰动方法研究
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摘要
为了研究随机动能后向散射(stochastic kinetic energy backscatter,SKEB)模式扰动方法在区域集合预报中的应用效果,基于WRF模式构建了集合预报系统,针对SKEB的扰动振幅进行了敏感性试验,以了解SKEB扰动的作用特征;发展了一种多物理过程组合(multi-physics,MPHY)与SKEB相结合的混合模式扰动方法(SKEB-MPHY),并对比了SKEB、MPHY以及SKEB-MPHY的预报效果,以探索区域集合预报的最优模式扰动实现方案。试验结果表明:SKEB方法通过固定的动能耗散率计算出流函数及温度扰动,从而对模式积分产生影响,且耗散率大小与预报离差正相关,垂直结构扰动不利于预报离差的发展。SKEB、MPHY以及SKEB-MPHY方法的对比试验表明,对于高空动力场预报离散度的增长,SKEB方法比MPHY方法占优,而低层温度预报离散度增长,MPHY比SKEB扰动方法占优,混合模式扰动方法的扰动增长能力在三种方案中表现最好。集合预报检验结果表明SKEB-MPHY方法评分优于单独的SKEB和MPHY方法。降水个例分析及降水评分结果表明与单独采用MPHY方法相比,引入SKEB方法可以对大雨预报有所改进。本文研究结果表明SKEB方法及在其基础上建立的混合模式扰动方法具有较好的应用前景。
To investigate the application effect of stochastic kinetic energy backscatter(SKEB) perturbation scheme, a regional ensemble forecast system(REFS) is constructed based on the WRF model. Sensitivity experiments on perturbation amplitude are conducted to find the functional characteristic of SKEB. Additionally, a synthetic model perturbation scheme which combines multi-physics(namely MPHY) and SKEB, called SKEB-MPHY, is developed, and the forecast effects of the three schemes of SKEB, MPHY and SKEB-MPHY are compared and evaluated. The results show that the SKEB scheme can estimate the stream function and temperature perturbation through a constant kinetic dissipation rate, and the exhibited difference of model integration is correlated to the amplitude of the kinetic dissipation rate. Perturbing the vertical structure is not helpful to the difference growth. The comparison results of SKEB, MPHY and SKEB-MPHY schemes indicate that the SKEB has advantage on upper-air wind spread growth compared to MPHY while MPHY has larger spread for low-level temperature than SKEB. The SKEB-MPHY scheme exhibits the best perturbation growth characteristic of the three schemes not only for upper-air variables but also for low-level variables. In addition, the SKEB-MPHY scheme has the most skillful performance of the three schemes in terms of ensemble verifications. Furthermore, compared with single MPHY scheme,applying the SKEB scheme will improve precipitation forecast skill of heavy rain. All the results from this study indicate that the SKEB scheme and the SKEB-based synthetic scheme are promising.
To investigate the application effect of stochastic kinetic energy backscatter(SKEB) perturbation scheme, a regional ensemble forecast system(REFS) is constructed based on the WRF model. Sensitivity experiments on perturbation amplitude are conducted to find the functional characteristic of SKEB. Additionally, a synthetic model perturbation scheme which combines multi-physics(namely MPHY) and SKEB, called SKEB-MPHY, is developed, and the forecast effects of the three schemes of SKEB, MPHY and SKEB-MPHY are compared and evaluated. The results show that the SKEB scheme can estimate the stream function and temperature perturbation through a constant kinetic dissipation rate, and the exhibited difference of model integration is correlated to the amplitude of the kinetic dissipation rate. Perturbing the vertical structure is not helpful to the difference growth. The comparison results of SKEB, MPHY and SKEB-MPHY schemes indicate that the SKEB has advantage on upper-air wind spread growth compared to MPHY while MPHY has larger spread for low-level temperature than SKEB. The SKEB-MPHY scheme exhibits the best perturbation growth characteristic of the three schemes not only for upper-air variables but also for low-level variables. In addition, the SKEB-MPHY scheme has the most skillful performance of the three schemes in terms of ensemble verifications. Furthermore, compared with single MPHY scheme,applying the SKEB scheme will improve precipitation forecast skill of heavy rain. All the results from this study indicate that the SKEB scheme and the SKEB-based synthetic scheme are promising.
引文
陈静,矫梅燕,龚建东,等,2006.非绝热物理过程对北京暴雨数值预报不确定性影响[J].应用气象学报,17(S1):18-27. Chen J,Jiao M Y,Gong J D,et al,2006. The impact of diabatic physics on the uncertainty of heavy rainfall ensemble simulations in Beijing[J]. J Appl Meteor Sci, 17(S1):18-27(in Chinese).
陈静,薛纪善,颜宏,2003.华南中尺度暴雨数值预报的不确定性与集合预报试验[J].气象学报,61(4):432-446.Chen J,Xue J S,Yan H,2003. The uncertainty of mesoscale numerical prediction ofSouth China heavy rain and the ensemble simulations[J]. Acta Meteor Sinica, 61(4),432-446(in Chinese).
邓国,龚建东,邓莲堂,等,2010.国家级区域集合预报系统研发和性能检验[J].应用气象学报,21(5):513-523. Deng G,Gong J D,Deng L T,et al,2010. Development of mesoscale ensemble predication system at National Meteorological Center[J]. J Appl Meteor Sci,21(5):513-523(in Chinese).
段明铿,王盘兴,吴洪宝,等,2009.夏季亚欧中高纬度环流的集合预报效果检验[J].应用气象学报,20(1):56-61. Duan M K,Wang P X,Wu II B,et al,2009. The ensemble forecasting verification on the summer eurasian middle high latitude circulation[J]. J Appl Meter Sci,20(1):56-61(in Chinese).
黄红艳,齐琳琳,刘健文,等,2016.多物理ETKF在暴雨集合预报中的初步应用[J].大气科学,40(4):657-668. Huang II Y,Qi L L,Liu J W,et al,2016. Preliminary application of a multi-physical ensemble transform Kalman filter in precipitation ensemble prediction[J]. Chinese J Atmos Sci, 40(4):657-668(in Chinese).
李俊,杜钧,刘羽,2015.北京“7. 21”特大暴雨不同集合预报方案的对比试验[J].气象学报,73(1):50-71. Li J,Du J,Liu Y,2015. A comparison of initial condition,multi-physics and stochastic physicsbased ensembles in predicting Beijing “7. 21” excessive storm rain event[J]. Acta Meteor Sinica,73(1):50-71(in Chinese)
任志杰,陈静,田华,2011. T213全球集合预报系统物理过程随机扰动方法研究[J].气象,37(9):1049-1059. Ren Z J,Chen J,Tian H,2011. Research on T213 Ensemble Prediction System stochastic physics perturbation[J]. Meteor Mon, 37(9):1049-1059(in Chinese).
谭宁,陈静,田华,2013.两种模式随机扰动方案比较及扰动传播分析[J].气象,39(5):543-555. Tan N,Chen J,Tian II,2013. Comparision between two global model stochastic perturbation schemes and analysis of perturbation propagation[J]. Meteor Mon,39(5):543-555(in Chinese).
谭燕,陈葆德,2014.多种扰动组合的热带气旋路径集合预报技术研究[J].高原气象,33(4):1012-1021. Tan Y,Chen B D,2014.Study of multiple perturb tropical cyclone ensemble forecast[J].Plateau Meteor,33(4):1012-1021(in Chinese).
谭燕,陈德辉,2007.基于非静力模式物理扰动的中尺度集合预报试验[J].应用气象学报,18(3):386-406. Tan Y,Chen D II,2007.Mesoscale ensemble forecasts on physical perturbation using a non-hydrostatic model[J]. J Appl Meter Sci, 18(3):386-406(in Chinese).
袁月,李晓莉,陈静,等,2016. GRAPES区域集合预报系统模式不确定性的随机扰动技术研究[J].气象,42(10):1161-1175. Yuan Y,Li X L,Chen J,et al,2016. Stochastic parameterization toward model uncertainty for the GRAPES mesoscale ensemble prediction system[J]. Meteor Mon,42(10):1161-1175(in Chinese).
张涵斌,陈静,智协飞,等,2014a.基于GRAPES_Meso的集合预报扰动方案设计与比较[J].大气科学学报,37(3):276-284. Zhang H B, Chen J, Zhi X F, et al, 2014a. Design and comparison of perturbation schemes for GRAPES_Meso based ensemble forecast[J]. Trans Atmos Sci,37(3):276-284(in Chinese).
张涵斌,陈静,智协飞,等,2014b. GRAPES区域集合预报系统应用研究[J].气象,40(9):1076-1087. Zhang H B,Chen J,Zhi X F,et al,2014b. Study on the application of GRAPES regional ensemble prediction system[J]. Meteor Mon,40(9):1076-1087(in Chinese).
赵鸣,2008.边界层和陆面过程对中国暴雨影响研究的进展[J].暴雨灾害,27(2):186-190. Zhao M,2008. A review of the research on the effects of boundary layer and land surface process on heavy rain in China[J]. Torrential Rain Disasters, 27(2):186-190(in Chinese).
智协飞,孙晶,周文友,2015a. 2009年夏季西太平洋台风的集合预报和多模式集成预报试验[J].大气科学学报,38(5):633-640. Zhi X F,Sun J,Zhou W Y,2015a. Ensemble and multimodel ensemble forecasts of Western Pacific typhoons during summer 2009[J]. Trans Atmos Sci,38(5):633-640(in Chinese).
智协飞,朱寿鹏,孙晶,等,2015b.基于BGM与ETKF的台风“苏拉”(1209)集合预报的对比试验Ⅰ:路径预报[J].大气科学学报,38(6):776-784. Zhi X F,Zhu S P,Sun J,et al,2015b. Comparative experiments of ensemble forecasting of Typhoon Saola(1209)based on BGM and ETKF,Part I:track forecast[J]. Trans Atmos Sci, 38(6):776-784(in Chinese).
Berner J,Ha S Y,Hacker J P,et al,2011. Model uncertainty in a mesoscale ensemble prediction system:stochastic versus multiphysics representations[J]. Mon Wea Rev,139(6):1972-1995.
Berner J,Shutts G J,Leutbecher M,et al,2009. A spectral stochastic kinetic energy backscatter scheme and its impact on flow-dependent predictability in the ECMWF ensemble prediction system[J].J Atmos Sci, 66(3):603-626.
Bouttier F,Vie B,Nuissier O,et al,2012. Impact of stochastic physics in a convection-permitting ensemble[J]. Mon Wea Rev, 140(11):3706-3721.
Bowler N E, Arribas A, Mylne K R, et al, 2008. The MOGREPS short-range ensemble prediction system[J]. Quart J Roy Meteor Soc,134(632):703-722.
Bowler N F, Arribas A,Sarah E,et al,2009. The local ETKF and SKEB:upgrades to the MOGREPS short-range ensemble prediction system[J]. Quart J Roy Meteor Soc,135(640):767-776.
Buizza R,Miller M,Palmer T N,1999. Stochastic representation of model uncertainties in the ECMWF ensemble prediction system[J]. Quart J Roy Meteor Soc, 125(560):2887-2908.
Du J,Mullen S L,Sanders F,1997. Short-range ensemble forecasting of quantitative precipitation[J]. Mon Wea Rev,125(10):2427-2459.
Duda J D, Wang X G,Kong F Y,et al,2016. Impact of a stochastic kinetic energy backscatter scheme on warm season convectionallowing ensemble forecasts[J]. Mon Wea Rev,144(5):1887-1908.
Epstein E S, 1969. Stochastic dynamic prediction[J]. Tellus,21(6):739-759.
Frogner I L,Haakenstad H,Iversen T,2006. Limited-area ensemble predictions at the Norwegian Meteorological Institute[J]. Quart J Roy Meteor Soc, 132(621):2785-2808.
Hersbach H,2000. Decomposition of the continuous ranked probability score for ensemble prediction systems[J]. Wea Forecasting,15(5):559-570.Houtekamer P L,Lefaivre L,Derome J,et al,1996. A system simula-
tion approach to ensemble prediction[J]. Mon Wea Rev, 124(6):1225-1242.
Krishnamurti T N, Kishtawal C M,LaRow T E,et al,1999. Improved weather and seasonal climate forecasts from multimodel superensemble[J]. Science,285(5433):1548-1550.
Leith C E,1974. Theoretical skill of Monte Carlo forecasts[J]. Mon Wea Rev,102(6):409-418.
Li X L,Charron M,Spacek L,et al,2008. A regional ensemble prediction system based on moist targeted singular vectors and stochastic parameter perturbations[J]. Mon Wea Rev, 136(2):443-462.
Lin J W B,Neelin J D,2000. Influence of a stochastic moist convective parameterization on tropical climate variability[J]. Geophys Res Lett,27(22):3691-3694.
Marsigli C,Boccanera F,Montani A,et al,2005. The COSMO-LEPS mesoscale ensemble system:validation of the methodology and verification[J]. Nonlin Processes Geophys,12(4):527-536.
Molteni F,Buizza R,Palmer T N,et al, 1996. The ECMWF ensemble prediction system:methodology and validation[J]. Quart J Roy Meteor Soc, 122(529):73-119.
Posselt D J, Vukicevic T,2010. Robust characterization of model physics uncertainty for simulations of deep moist convection[J].Mon Wea Rev, 138(5):1513-1535.
Shutts G,2005. A kinetic energy backscatter algorithm for use in ensemble prediction systems[J]. Quart J Roy Meteor Soc,131(612):3079-3102.
Sindic-Rancic G,Toth Z,Kalnay E, 1998. Storm scale ensemble experiments with the ARPS model preliminary results[C]//Proceedings of the 12th Conference on Numerical Weather Prediction. Phoenix, Arizona:American Meteorological Society:279-280.
Stensrud D J,Bao J W,Warner T T,2000. Using initial condition and model physics perturbations in short-range ensemble simulations of mesoscale convective systems[J]. Mon Wea Rev,128(7):2077-2107.
Stensrud D J,Fritsch J M,1994. Mesoscale convective systems in weakly forced large-scale environments. Part H:Generation of a mesoscale initial condition[J]. Mon Wea Rev, 122(9):2068-2083.
Toth Z,Kalnay E,1993. Ensemble forecasting at NMC:The generation of perturbations[J]. Bull Amer Meteor Soc,74(12):2317-2330.
Toth Z, Kalnay E,1997. Ensemble forecasting at NCEP and the breeding method[J]. Mon Wea Rev,125(12):3297-3319.
Vie B,Nuissier O,Ducrocq V,2011. Cloud-resolving ensemble simulations of Mediterranean heavy precipitating events:uncertainty on initial conditions and lateral boundary conditions[J]. Mon Wea Rev,139(2):403-423.
Wang Y,Bellus M,Wittmann C,et al,2011. The Central Euro-pean limited-area ensemble forecasting system:ALADIN-LAEF[J].Quart J Roy Meteor Soc,137(655):483-502.
Zhi X F,Qi II X,Bai Y Q,et al,2012. A comparison of three kinds of multimodel ensemble forecast techniques based on the TIGGE data[J]. Acta Meteor Sinica,26(1):41-51.
陈静,薛纪善,颜宏,2003.华南中尺度暴雨数值预报的不确定性与集合预报试验[J].气象学报,61(4):432-446.Chen J,Xue J S,Yan H,2003. The uncertainty of mesoscale numerical prediction ofSouth China heavy rain and the ensemble simulations[J]. Acta Meteor Sinica, 61(4),432-446(in Chinese).
邓国,龚建东,邓莲堂,等,2010.国家级区域集合预报系统研发和性能检验[J].应用气象学报,21(5):513-523. Deng G,Gong J D,Deng L T,et al,2010. Development of mesoscale ensemble predication system at National Meteorological Center[J]. J Appl Meteor Sci,21(5):513-523(in Chinese).
段明铿,王盘兴,吴洪宝,等,2009.夏季亚欧中高纬度环流的集合预报效果检验[J].应用气象学报,20(1):56-61. Duan M K,Wang P X,Wu II B,et al,2009. The ensemble forecasting verification on the summer eurasian middle high latitude circulation[J]. J Appl Meter Sci,20(1):56-61(in Chinese).
黄红艳,齐琳琳,刘健文,等,2016.多物理ETKF在暴雨集合预报中的初步应用[J].大气科学,40(4):657-668. Huang II Y,Qi L L,Liu J W,et al,2016. Preliminary application of a multi-physical ensemble transform Kalman filter in precipitation ensemble prediction[J]. Chinese J Atmos Sci, 40(4):657-668(in Chinese).
李俊,杜钧,刘羽,2015.北京“7. 21”特大暴雨不同集合预报方案的对比试验[J].气象学报,73(1):50-71. Li J,Du J,Liu Y,2015. A comparison of initial condition,multi-physics and stochastic physicsbased ensembles in predicting Beijing “7. 21” excessive storm rain event[J]. Acta Meteor Sinica,73(1):50-71(in Chinese)
任志杰,陈静,田华,2011. T213全球集合预报系统物理过程随机扰动方法研究[J].气象,37(9):1049-1059. Ren Z J,Chen J,Tian H,2011. Research on T213 Ensemble Prediction System stochastic physics perturbation[J]. Meteor Mon, 37(9):1049-1059(in Chinese).
谭宁,陈静,田华,2013.两种模式随机扰动方案比较及扰动传播分析[J].气象,39(5):543-555. Tan N,Chen J,Tian II,2013. Comparision between two global model stochastic perturbation schemes and analysis of perturbation propagation[J]. Meteor Mon,39(5):543-555(in Chinese).
谭燕,陈葆德,2014.多种扰动组合的热带气旋路径集合预报技术研究[J].高原气象,33(4):1012-1021. Tan Y,Chen B D,2014.Study of multiple perturb tropical cyclone ensemble forecast[J].Plateau Meteor,33(4):1012-1021(in Chinese).
谭燕,陈德辉,2007.基于非静力模式物理扰动的中尺度集合预报试验[J].应用气象学报,18(3):386-406. Tan Y,Chen D II,2007.Mesoscale ensemble forecasts on physical perturbation using a non-hydrostatic model[J]. J Appl Meter Sci, 18(3):386-406(in Chinese).
袁月,李晓莉,陈静,等,2016. GRAPES区域集合预报系统模式不确定性的随机扰动技术研究[J].气象,42(10):1161-1175. Yuan Y,Li X L,Chen J,et al,2016. Stochastic parameterization toward model uncertainty for the GRAPES mesoscale ensemble prediction system[J]. Meteor Mon,42(10):1161-1175(in Chinese).
张涵斌,陈静,智协飞,等,2014a.基于GRAPES_Meso的集合预报扰动方案设计与比较[J].大气科学学报,37(3):276-284. Zhang H B, Chen J, Zhi X F, et al, 2014a. Design and comparison of perturbation schemes for GRAPES_Meso based ensemble forecast[J]. Trans Atmos Sci,37(3):276-284(in Chinese).
张涵斌,陈静,智协飞,等,2014b. GRAPES区域集合预报系统应用研究[J].气象,40(9):1076-1087. Zhang H B,Chen J,Zhi X F,et al,2014b. Study on the application of GRAPES regional ensemble prediction system[J]. Meteor Mon,40(9):1076-1087(in Chinese).
赵鸣,2008.边界层和陆面过程对中国暴雨影响研究的进展[J].暴雨灾害,27(2):186-190. Zhao M,2008. A review of the research on the effects of boundary layer and land surface process on heavy rain in China[J]. Torrential Rain Disasters, 27(2):186-190(in Chinese).
智协飞,孙晶,周文友,2015a. 2009年夏季西太平洋台风的集合预报和多模式集成预报试验[J].大气科学学报,38(5):633-640. Zhi X F,Sun J,Zhou W Y,2015a. Ensemble and multimodel ensemble forecasts of Western Pacific typhoons during summer 2009[J]. Trans Atmos Sci,38(5):633-640(in Chinese).
智协飞,朱寿鹏,孙晶,等,2015b.基于BGM与ETKF的台风“苏拉”(1209)集合预报的对比试验Ⅰ:路径预报[J].大气科学学报,38(6):776-784. Zhi X F,Zhu S P,Sun J,et al,2015b. Comparative experiments of ensemble forecasting of Typhoon Saola(1209)based on BGM and ETKF,Part I:track forecast[J]. Trans Atmos Sci, 38(6):776-784(in Chinese).
Berner J,Ha S Y,Hacker J P,et al,2011. Model uncertainty in a mesoscale ensemble prediction system:stochastic versus multiphysics representations[J]. Mon Wea Rev,139(6):1972-1995.
Berner J,Shutts G J,Leutbecher M,et al,2009. A spectral stochastic kinetic energy backscatter scheme and its impact on flow-dependent predictability in the ECMWF ensemble prediction system[J].J Atmos Sci, 66(3):603-626.
Bouttier F,Vie B,Nuissier O,et al,2012. Impact of stochastic physics in a convection-permitting ensemble[J]. Mon Wea Rev, 140(11):3706-3721.
Bowler N E, Arribas A, Mylne K R, et al, 2008. The MOGREPS short-range ensemble prediction system[J]. Quart J Roy Meteor Soc,134(632):703-722.
Bowler N F, Arribas A,Sarah E,et al,2009. The local ETKF and SKEB:upgrades to the MOGREPS short-range ensemble prediction system[J]. Quart J Roy Meteor Soc,135(640):767-776.
Buizza R,Miller M,Palmer T N,1999. Stochastic representation of model uncertainties in the ECMWF ensemble prediction system[J]. Quart J Roy Meteor Soc, 125(560):2887-2908.
Du J,Mullen S L,Sanders F,1997. Short-range ensemble forecasting of quantitative precipitation[J]. Mon Wea Rev,125(10):2427-2459.
Duda J D, Wang X G,Kong F Y,et al,2016. Impact of a stochastic kinetic energy backscatter scheme on warm season convectionallowing ensemble forecasts[J]. Mon Wea Rev,144(5):1887-1908.
Epstein E S, 1969. Stochastic dynamic prediction[J]. Tellus,21(6):739-759.
Frogner I L,Haakenstad H,Iversen T,2006. Limited-area ensemble predictions at the Norwegian Meteorological Institute[J]. Quart J Roy Meteor Soc, 132(621):2785-2808.
Hersbach H,2000. Decomposition of the continuous ranked probability score for ensemble prediction systems[J]. Wea Forecasting,15(5):559-570.Houtekamer P L,Lefaivre L,Derome J,et al,1996. A system simula-
tion approach to ensemble prediction[J]. Mon Wea Rev, 124(6):1225-1242.
Krishnamurti T N, Kishtawal C M,LaRow T E,et al,1999. Improved weather and seasonal climate forecasts from multimodel superensemble[J]. Science,285(5433):1548-1550.
Leith C E,1974. Theoretical skill of Monte Carlo forecasts[J]. Mon Wea Rev,102(6):409-418.
Li X L,Charron M,Spacek L,et al,2008. A regional ensemble prediction system based on moist targeted singular vectors and stochastic parameter perturbations[J]. Mon Wea Rev, 136(2):443-462.
Lin J W B,Neelin J D,2000. Influence of a stochastic moist convective parameterization on tropical climate variability[J]. Geophys Res Lett,27(22):3691-3694.
Marsigli C,Boccanera F,Montani A,et al,2005. The COSMO-LEPS mesoscale ensemble system:validation of the methodology and verification[J]. Nonlin Processes Geophys,12(4):527-536.
Molteni F,Buizza R,Palmer T N,et al, 1996. The ECMWF ensemble prediction system:methodology and validation[J]. Quart J Roy Meteor Soc, 122(529):73-119.
Posselt D J, Vukicevic T,2010. Robust characterization of model physics uncertainty for simulations of deep moist convection[J].Mon Wea Rev, 138(5):1513-1535.
Shutts G,2005. A kinetic energy backscatter algorithm for use in ensemble prediction systems[J]. Quart J Roy Meteor Soc,131(612):3079-3102.
Sindic-Rancic G,Toth Z,Kalnay E, 1998. Storm scale ensemble experiments with the ARPS model preliminary results[C]//Proceedings of the 12th Conference on Numerical Weather Prediction. Phoenix, Arizona:American Meteorological Society:279-280.
Stensrud D J,Bao J W,Warner T T,2000. Using initial condition and model physics perturbations in short-range ensemble simulations of mesoscale convective systems[J]. Mon Wea Rev,128(7):2077-2107.
Stensrud D J,Fritsch J M,1994. Mesoscale convective systems in weakly forced large-scale environments. Part H:Generation of a mesoscale initial condition[J]. Mon Wea Rev, 122(9):2068-2083.
Toth Z,Kalnay E,1993. Ensemble forecasting at NMC:The generation of perturbations[J]. Bull Amer Meteor Soc,74(12):2317-2330.
Toth Z, Kalnay E,1997. Ensemble forecasting at NCEP and the breeding method[J]. Mon Wea Rev,125(12):3297-3319.
Vie B,Nuissier O,Ducrocq V,2011. Cloud-resolving ensemble simulations of Mediterranean heavy precipitating events:uncertainty on initial conditions and lateral boundary conditions[J]. Mon Wea Rev,139(2):403-423.
Wang Y,Bellus M,Wittmann C,et al,2011. The Central Euro-pean limited-area ensemble forecasting system:ALADIN-LAEF[J].Quart J Roy Meteor Soc,137(655):483-502.
Zhi X F,Qi II X,Bai Y Q,et al,2012. A comparison of three kinds of multimodel ensemble forecast techniques based on the TIGGE data[J]. Acta Meteor Sinica,26(1):41-51.
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