GRAPES全球集合预报系统模式扰动随机动能补偿方案初步探究
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摘要
为了体现次网格尺度能量升尺度转换过程中存在的不确定性,文中将随机动能补偿(Stochastic Kinetic Energy Backscatter,SKEB)方案应用于GRAPES(Global/Regional Assimilation and Prediction System)全球集合预报系统(GRAPES-GEPS),以更好地表征模式误差并且增大集合离散度。使用的SKEB方案基于具有一定时、空相关特征的随机型以及由数值扩散导致的局地动能耗散率来构造随机流函数强迫。并根据流函数与水平风速旋转分量的关系,将SKEB方案中的流函数强迫转化为适用于GRAPES全球模式的水平风速扰动。结果表明,SKEB方案的使用一方面能够提高GRAPES对大气动能谱的模拟能力;另一方面能够改善GRAPES-GEPS的集合离散度与集合平均误差的关系,增加了集合离散度,并在一定程度上减小了集合平均误差,尤其是在热带地区这种改进更为显著。而且该方案使得热带地区连续分级概率评分(CRPS评分)显著减小。就降水预报而言,从Brier评分与相对作用特征面积(AROC,Area under the Relative Operating Characteristics)的结果来看,SKEB方案有助于改善中国地区小雨[0.1 mm,10 mm)、中雨[10 mm,25 mm)与大雨[25 mm,50 mm)量级降水的概率预报技巧,而对暴雨[50 mm,∞)量级降水预报技巧影响很小(24 h降水量)。总体上,模式扰动随机动能补偿方案提高了GRAPES-GEPS的概率预报技巧。
For describing uncertainties in the subgrid-scale energy upscaling transfer, a Stochastic Kinetic Energy Backscatter(SKEB) scheme has been introduced into the Global/Regional Assimilation and Prediction System(GRAPES) global ensemble prediction system(GEPS) to represent model errors more reasonably and increase the ensemble spread. In this research, the SKEB scheme employs the stochastic patterns with temporally and spatially correlated characteristics along with the estimated local kinetic energy dissipation rates caused by numerical diffusion to construct the stochastic stream function forcing. According to the relationship between the streamfunction and the rotational component of horizontal wind, the streamfunction forcing in the SKEB scheme is then transformed into horizontal wind perturbations, which are suitable for the GRAPES global model. The results indicate that, on the one hand, the application of the SKEB scheme improves the simulations of the atmospheric kinetic-energy spectra in the GRAPES model; on the other hand, it leads to a better spread-error relationship, increases the spread of the ensemble and reduces the root mean square error of the ensemble mean to some extent and the improvement is the most pronounced in the tropics. This scheme also contributes to a significant improvement of the continuous rank probability score(CRPS) in the tropics. In terms of precipitation forecast, the results from the Brier score and Area under the Relative Operating Characteristics(AROC) show that the SKEB scheme helps to improve probabilistic forecast skills of rainfall in China for light rain [0.1 mm, 10 mm), moderate rain [10 mm, 25 mm) and heavy rain [25 mm, 50 mm); however, it has little impact on the forecast of rainstorm [50 mm, ∞)(24 h precipitation). On the whole, the introduction of the SKEB scheme ameliorates the probabilistic prediction skills of the GRAPES-GEPS.
For describing uncertainties in the subgrid-scale energy upscaling transfer, a Stochastic Kinetic Energy Backscatter(SKEB) scheme has been introduced into the Global/Regional Assimilation and Prediction System(GRAPES) global ensemble prediction system(GEPS) to represent model errors more reasonably and increase the ensemble spread. In this research, the SKEB scheme employs the stochastic patterns with temporally and spatially correlated characteristics along with the estimated local kinetic energy dissipation rates caused by numerical diffusion to construct the stochastic stream function forcing. According to the relationship between the streamfunction and the rotational component of horizontal wind, the streamfunction forcing in the SKEB scheme is then transformed into horizontal wind perturbations, which are suitable for the GRAPES global model. The results indicate that, on the one hand, the application of the SKEB scheme improves the simulations of the atmospheric kinetic-energy spectra in the GRAPES model; on the other hand, it leads to a better spread-error relationship, increases the spread of the ensemble and reduces the root mean square error of the ensemble mean to some extent and the improvement is the most pronounced in the tropics. This scheme also contributes to a significant improvement of the continuous rank probability score(CRPS) in the tropics. In terms of precipitation forecast, the results from the Brier score and Area under the Relative Operating Characteristics(AROC) show that the SKEB scheme helps to improve probabilistic forecast skills of rainfall in China for light rain [0.1 mm, 10 mm), moderate rain [10 mm, 25 mm) and heavy rain [25 mm, 50 mm); however, it has little impact on the forecast of rainstorm [50 mm, ∞)(24 h precipitation). On the whole, the introduction of the SKEB scheme ameliorates the probabilistic prediction skills of the GRAPES-GEPS.
引文
蔡沅辰,闵锦忠,庄潇然.2017.不同随机物理扰动方案在一次暴雨集合预报中的对比研究.高原气象,36(2):407-423.Cai Y C,Min J Z,Zhuang X R.2017.Comparison of different stochastic physics perturbation schemes on a storm-scale ensemble forecast in a heavy rain event.Plateau Meteor,36(2):407-423 (in Chinese)
刘畅,闵锦忠,冯宇轩等.2018.不同模式扰动方案在风暴尺度集合预报中的对比试验研究.气象学报,76(4):605-619.Liu C,Min J Z,Feng Y X,et al.2018.Comparison of different model perturbation schemes on storm-scale ensemble forecast.Acta Meteor Sinica,76(4):605-619(in Chinese)
刘永柱,沈学顺,李晓莉.2013.基于总能量模的GRAPES全球模式奇异向量扰动研究.气象学报,71(3):517-526.Liu Y Z,Shen X S,Li X L.2013.Researeh on the singular vector perturbation of the GRAPES global model based on the total energy norm.Acta Meteor Sinica,71(3):517-526 (in Chinese)
麻巨慧,朱跃建,王盘兴等.2011.NCEP、ECMWF及CMC全球集合预报业务系统发展综述.大气科学学报,34(3):370-380.Ma J H,Zhu Y J,Wang P X,et al.2011.A review on the developments of NCEP,ECMWF and CMC global ensemble forecast system.Trans Atmos Sci,34(3):370-380 (in Chinese)
马旭林,薛纪善,陆维松.2008.GRAPES全球集合预报的集合卡尔曼变换初始扰动方案初步研究.气象学报,66(4):526-536.Ma X L,Xue J S,Lu W S.2008.Preliminary study on ensemble transform Kalman filter-based initial perturbationscheme in GRAPES global ensemble prediction.Acta Meteor Sinica,66(4):526-536 (in Chinese)
闵锦忠,刘畅,王世璋等.2018.随机物理倾向扰动(SPPT)在风暴尺度集合预报中的影响研究.气象学报,76(4):590-604.Min J Z,Liu C,Wang S Z,et al.2018.Impact of stochastically perturbed parameterization tendencies (SPPT) on storm-scale ensemble forecast.Acta Meteor Sinica,76(4):590-604(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.气象,37(9):1049-1059.Ren Z J,Chen J,Tian H.2011.Research on T213 ensemble prediction system stochastic physics perturbation.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.气象,39(5):543-555.Tan N,Chen J,Tian H.2013.Comparison between two global model stochastic perturbation schemes and analysis of perturbation propagation.Meteor Mon,39(5):543-555 (in Chinese)
王亚华,臧增亮,潘晓滨等.2015.高分辨率GRAPES-GFS的动能谱及其转折特征分析.气象学报,73(5):965-974.Wang Y H,Zang Z L,Pan X B,et al.2015.The kinetic energy spectrum and its transition characteristics analysis of the high-resolution GRAPES-GFS.Acta Meteor Sinica,73(5):965-974 (in Chinese)
薛纪善,陈德辉.2008.数值预报系统GRAPES的科学设计与应用.北京:科学出版社,383pp.Xue J S,Chen D H.2008.Scientific Design and Application of Numerical Prediction System GRAPES.Beijing:Science Press,383pp (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.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.Meteor Mon,42(10):1161-1175 (in Chinese)
Atger F.1999.The skill of ensemble prediction systems.Mon Wea Rev,127(9):1941-1953
Bengtsson L,Steinheimer M,Bechtold P,et al.2013.A stochastic parametrization for deep convection using cellular automata.Quart J Roy Meteor Soc,139(675):1533-1543
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 Atmos Sci,66(3):603-626
Berner J,Ha S Y,Hacker J P,et al.2011.Model uncertainty in a mesoscale ensemble prediction system:Stochastic versus multiphysics representations.Mon Wea Rev,139(6):1972-1995
Berner J,Fossell K R,Ha S Y,et al.2015.Increasing the skill of probabilistic forecasts:Understanding performance improvements from model-error representations.Mon Wea Rev,143(4):1295-1320
Berner J,Achatz U,Batté L,et al.2017.Stochastic parameterization:Toward a new view of weather and climate models.Bull Amer Meteor Soc,98(3):565-588
Bishop C H,Etherton B J,Majumdar S J.2001.Adaptive sampling with the ensemble transform Kalman filter.Part I:Theoretical aspects.Mon Wea Rev,129(3):420-436
Brier G W.1950.Verification of forecasts expressed in terms of probability.Mon Wea Rev,78(1):1-3
Buizza R,Palmer T N.1995.The singular-vector structure of the atmospheric global circulation.J Atmos Sci,52(9):1434-1456
Buizza R,Milleer M,Palmer T N.1999.Stochastic representation of model uncertainties in the ECMWF ensemble prediction system.Quart J Roy Meteor Soc,125(560):2887-2908
Candille G,C?té C,Houtekamer P L,et al.2007.Verification of an ensemble prediction system against observations.Mon Wea Rev,135(7):2688-2699
Charron M,Pellerin G,Spacek L,et al.2010.Toward random sampling of model error in the Canadian ensemble prediction system.Mon Wea Rev,138(5):1877-1901
Christensen H M,Moroz I M,Palmer T N.2015.Stochastic and perturbed parameter representations of model uncertainty in convection parameterization.J Atmos Sci,72(6):2525-2544
Duda J D,Wang X G,Kong F Y,et al.2016.Impact of a stochastic kinetic energy backscatter scheme on warm season convection-allowing ensemble forecasts.Mon Wea Rev,144(5):1887-1908
Hacker J P,Ha S Y,Snyder C,et al.2011.The U.S.Air Force Weather Agency’s mesoscale ensemble:Scientific description and performance results.Tellus A:Dyn Meteor Oceanogr,63(3):625-641
Hoffman R N,Kalnay E.1983.Lagged average forecasting,an alternative to Monte Carlo forecasting.Tellus A:Dyn Meteor Oceanogr,35(2):100-118
Houtekamer P L,Lefaivre L,Derome J,et al.1996.A system simulation approach to ensemble prediction.Mon Wea Rev,124(6):1225-1242
Kober K,Craig G C.2016.Physically based stochastic perturbations (PSP) in the boundary layer to represent uncertainty in convective initiation.J Atmos Sci,73(7):2893-2911
Leith C E.1974.Theoretical skill of Monte Carlo forecasts.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.Mon Wea Rev,136(2):443-462
Mason P J,Thomson D J.1992.Stochastic backscatter in large-eddy simulations of boundary layers.J Fluid Mech,242:51-78
Molteni F,Buizza R,Palmer T N,et al.1996.The ECMWF ensemble prediction system:Methodology and validation.Quart J Roy Meteor Soc,122(529):73-119
Nastrom G D,Gage K S.1985.A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft.J Atmos Sci,42(9):950-960
Ollinaho P,Lock S J,Leutbecher M,et al.2017.Towards process-level representation of model uncertainties:Stochastically perturbed parametrizations in the ECMWF ensemble.Quart J Roy Meteor Soc,143(702):408-422
Palmer T N,Shutts G J,Hagedorn R,et al.2005.Representing model uncertainty in weather and climate prediction.Annu Rev Earth Planet Sci,33:163-193
Palmer T N,Buizza R,Doblas-Reyes F,et al.2009.Stochastic parametrization and model uncertainty.ECMWF Technical Memoranda,598.Shinfield Park,Reading:ECMWF,42pp
Palmer T N.2012.Towards the probabilistic Earth-system simulator:A vision for the future of climate and weather prediction.Quart J Roy Meteor Soc,138(665):841-861
Plant R S,Craig G C.2008.A stochastic parameterization for deep convection based on equilibrium statistics.J Atmos Sci,65(1):87-105
Richardson D S.2000.Skill and relative economic value of the ECMWF ensemble prediction system.Quart J Roy Meteor Soc,126(563):649-667
Sanchez C,Williams K D,Collins M.2016.Improved stochastic physics schemes for global weather and climate models.Quart J Roy Meteor Soc,142(694):147-159
Shutts G.2005.A kinetic energy backscatter algorithm for use in ensemble prediction systems.Quart J Roy Meteor Soc,131(612):3079-3102
Talagrand O,Vautard R,Strauss B.1997.Evaluation of probabilistic prediction Systems//Proceedings of ECMWF Workshop on Predictability.Reading,United Kingdom:ECMWF,20-22
Tennant W J,Shutts G J,Arribas A,et al.2011.Using a stochastic kinetic energy backscatter scheme to improve MOGREPS probabilistic forecast skill.Mon Wea Rev,139(4):1190-1206
Tompkins A M,Berner J.2008.A stochastic convective approach to account for model uncertainty due to unresolved humidity variability.J Geophys Res,113(D18):D18101,doi:10.1029/2007JD009284
Toth Z,Kalnay E.1993.Ensemble forecasting at NMC:The generation of perturbations.Bull Amer Meteor Soc,74(12):2317-2330
Wang X G,Bishop C H.2003.A comparison of breeding and ensemble Transform Kalman Filter ensemble forecast schemes.J Atmos Sci,60(9):1140-1158
Wilks D S.2005.Effects of stochastic parametrizations in the Lorenz '96 system.Quart J Roy Meteor Soc,131(606):389-407
Yonehara H,Ujiie M.2011.A sochastic physics scheme for model uncertainties in the JMA one-week ensemble prediction system.CAS/JSC WGNE Res Activit Atmos Ocean Modell,41(6):9-10
刘畅,闵锦忠,冯宇轩等.2018.不同模式扰动方案在风暴尺度集合预报中的对比试验研究.气象学报,76(4):605-619.Liu C,Min J Z,Feng Y X,et al.2018.Comparison of different model perturbation schemes on storm-scale ensemble forecast.Acta Meteor Sinica,76(4):605-619(in Chinese)
刘永柱,沈学顺,李晓莉.2013.基于总能量模的GRAPES全球模式奇异向量扰动研究.气象学报,71(3):517-526.Liu Y Z,Shen X S,Li X L.2013.Researeh on the singular vector perturbation of the GRAPES global model based on the total energy norm.Acta Meteor Sinica,71(3):517-526 (in Chinese)
麻巨慧,朱跃建,王盘兴等.2011.NCEP、ECMWF及CMC全球集合预报业务系统发展综述.大气科学学报,34(3):370-380.Ma J H,Zhu Y J,Wang P X,et al.2011.A review on the developments of NCEP,ECMWF and CMC global ensemble forecast system.Trans Atmos Sci,34(3):370-380 (in Chinese)
马旭林,薛纪善,陆维松.2008.GRAPES全球集合预报的集合卡尔曼变换初始扰动方案初步研究.气象学报,66(4):526-536.Ma X L,Xue J S,Lu W S.2008.Preliminary study on ensemble transform Kalman filter-based initial perturbationscheme in GRAPES global ensemble prediction.Acta Meteor Sinica,66(4):526-536 (in Chinese)
闵锦忠,刘畅,王世璋等.2018.随机物理倾向扰动(SPPT)在风暴尺度集合预报中的影响研究.气象学报,76(4):590-604.Min J Z,Liu C,Wang S Z,et al.2018.Impact of stochastically perturbed parameterization tendencies (SPPT) on storm-scale ensemble forecast.Acta Meteor Sinica,76(4):590-604(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.气象,37(9):1049-1059.Ren Z J,Chen J,Tian H.2011.Research on T213 ensemble prediction system stochastic physics perturbation.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.气象,39(5):543-555.Tan N,Chen J,Tian H.2013.Comparison between two global model stochastic perturbation schemes and analysis of perturbation propagation.Meteor Mon,39(5):543-555 (in Chinese)
王亚华,臧增亮,潘晓滨等.2015.高分辨率GRAPES-GFS的动能谱及其转折特征分析.气象学报,73(5):965-974.Wang Y H,Zang Z L,Pan X B,et al.2015.The kinetic energy spectrum and its transition characteristics analysis of the high-resolution GRAPES-GFS.Acta Meteor Sinica,73(5):965-974 (in Chinese)
薛纪善,陈德辉.2008.数值预报系统GRAPES的科学设计与应用.北京:科学出版社,383pp.Xue J S,Chen D H.2008.Scientific Design and Application of Numerical Prediction System GRAPES.Beijing:Science Press,383pp (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.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.Meteor Mon,42(10):1161-1175 (in Chinese)
Atger F.1999.The skill of ensemble prediction systems.Mon Wea Rev,127(9):1941-1953
Bengtsson L,Steinheimer M,Bechtold P,et al.2013.A stochastic parametrization for deep convection using cellular automata.Quart J Roy Meteor Soc,139(675):1533-1543
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 Atmos Sci,66(3):603-626
Berner J,Ha S Y,Hacker J P,et al.2011.Model uncertainty in a mesoscale ensemble prediction system:Stochastic versus multiphysics representations.Mon Wea Rev,139(6):1972-1995
Berner J,Fossell K R,Ha S Y,et al.2015.Increasing the skill of probabilistic forecasts:Understanding performance improvements from model-error representations.Mon Wea Rev,143(4):1295-1320
Berner J,Achatz U,Batté L,et al.2017.Stochastic parameterization:Toward a new view of weather and climate models.Bull Amer Meteor Soc,98(3):565-588
Bishop C H,Etherton B J,Majumdar S J.2001.Adaptive sampling with the ensemble transform Kalman filter.Part I:Theoretical aspects.Mon Wea Rev,129(3):420-436
Brier G W.1950.Verification of forecasts expressed in terms of probability.Mon Wea Rev,78(1):1-3
Buizza R,Palmer T N.1995.The singular-vector structure of the atmospheric global circulation.J Atmos Sci,52(9):1434-1456
Buizza R,Milleer M,Palmer T N.1999.Stochastic representation of model uncertainties in the ECMWF ensemble prediction system.Quart J Roy Meteor Soc,125(560):2887-2908
Candille G,C?té C,Houtekamer P L,et al.2007.Verification of an ensemble prediction system against observations.Mon Wea Rev,135(7):2688-2699
Charron M,Pellerin G,Spacek L,et al.2010.Toward random sampling of model error in the Canadian ensemble prediction system.Mon Wea Rev,138(5):1877-1901
Christensen H M,Moroz I M,Palmer T N.2015.Stochastic and perturbed parameter representations of model uncertainty in convection parameterization.J Atmos Sci,72(6):2525-2544
Duda J D,Wang X G,Kong F Y,et al.2016.Impact of a stochastic kinetic energy backscatter scheme on warm season convection-allowing ensemble forecasts.Mon Wea Rev,144(5):1887-1908
Hacker J P,Ha S Y,Snyder C,et al.2011.The U.S.Air Force Weather Agency’s mesoscale ensemble:Scientific description and performance results.Tellus A:Dyn Meteor Oceanogr,63(3):625-641
Hoffman R N,Kalnay E.1983.Lagged average forecasting,an alternative to Monte Carlo forecasting.Tellus A:Dyn Meteor Oceanogr,35(2):100-118
Houtekamer P L,Lefaivre L,Derome J,et al.1996.A system simulation approach to ensemble prediction.Mon Wea Rev,124(6):1225-1242
Kober K,Craig G C.2016.Physically based stochastic perturbations (PSP) in the boundary layer to represent uncertainty in convective initiation.J Atmos Sci,73(7):2893-2911
Leith C E.1974.Theoretical skill of Monte Carlo forecasts.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.Mon Wea Rev,136(2):443-462
Mason P J,Thomson D J.1992.Stochastic backscatter in large-eddy simulations of boundary layers.J Fluid Mech,242:51-78
Molteni F,Buizza R,Palmer T N,et al.1996.The ECMWF ensemble prediction system:Methodology and validation.Quart J Roy Meteor Soc,122(529):73-119
Nastrom G D,Gage K S.1985.A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft.J Atmos Sci,42(9):950-960
Ollinaho P,Lock S J,Leutbecher M,et al.2017.Towards process-level representation of model uncertainties:Stochastically perturbed parametrizations in the ECMWF ensemble.Quart J Roy Meteor Soc,143(702):408-422
Palmer T N,Shutts G J,Hagedorn R,et al.2005.Representing model uncertainty in weather and climate prediction.Annu Rev Earth Planet Sci,33:163-193
Palmer T N,Buizza R,Doblas-Reyes F,et al.2009.Stochastic parametrization and model uncertainty.ECMWF Technical Memoranda,598.Shinfield Park,Reading:ECMWF,42pp
Palmer T N.2012.Towards the probabilistic Earth-system simulator:A vision for the future of climate and weather prediction.Quart J Roy Meteor Soc,138(665):841-861
Plant R S,Craig G C.2008.A stochastic parameterization for deep convection based on equilibrium statistics.J Atmos Sci,65(1):87-105
Richardson D S.2000.Skill and relative economic value of the ECMWF ensemble prediction system.Quart J Roy Meteor Soc,126(563):649-667
Sanchez C,Williams K D,Collins M.2016.Improved stochastic physics schemes for global weather and climate models.Quart J Roy Meteor Soc,142(694):147-159
Shutts G.2005.A kinetic energy backscatter algorithm for use in ensemble prediction systems.Quart J Roy Meteor Soc,131(612):3079-3102
Talagrand O,Vautard R,Strauss B.1997.Evaluation of probabilistic prediction Systems//Proceedings of ECMWF Workshop on Predictability.Reading,United Kingdom:ECMWF,20-22
Tennant W J,Shutts G J,Arribas A,et al.2011.Using a stochastic kinetic energy backscatter scheme to improve MOGREPS probabilistic forecast skill.Mon Wea Rev,139(4):1190-1206
Tompkins A M,Berner J.2008.A stochastic convective approach to account for model uncertainty due to unresolved humidity variability.J Geophys Res,113(D18):D18101,doi:10.1029/2007JD009284
Toth Z,Kalnay E.1993.Ensemble forecasting at NMC:The generation of perturbations.Bull Amer Meteor Soc,74(12):2317-2330
Wang X G,Bishop C H.2003.A comparison of breeding and ensemble Transform Kalman Filter ensemble forecast schemes.J Atmos Sci,60(9):1140-1158
Wilks D S.2005.Effects of stochastic parametrizations in the Lorenz '96 system.Quart J Roy Meteor Soc,131(606):389-407
Yonehara H,Ujiie M.2011.A sochastic physics scheme for model uncertainties in the JMA one-week ensemble prediction system.CAS/JSC WGNE Res Activit Atmos Ocean Modell,41(6):9-10