GRAPES的新初始化方案
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摘要
四维变分同化由于引入预报模式作为一项约束,理论上它的分析场已经具有较好的平衡性,但实施时还会有诸多因重力波导致的高频振荡过程,因此,四维变分同化(4DVar)分析仍需要初始化。文中描述了GRAPES全球四维变分同化系统(GRAPES-4DVar)的新初始化方案的科学设计、公式演绎以及试验结果。GRAPES-4DVar的新初始化方案采用数字滤波方案作为代价函数的一项约束控制重力波引发的不平衡结构,约束强加在分析增量上与极小化迭代过程同步进行。新的初始化方案是变分同化系统的一部分,数字滤波的积分时间与4DVar的同化时间窗一致,不会对4DVar产生额外的计算资源消耗;并能适应长时间窗的同化,不会因为时间窗的延长而削弱慢波过程。新初始化方案中,模式轨迹的光滑程度可在变分同化中通过重力波控制项的权重系数方便控制。GRAPES全球四维变分同化的理想和循环同化批量试验都表明,在四维变分同化中,重力波的控制依然非常重要,具有初始化的GRAPES试验,无论分析还是预报技巧都较无初始化的有明显优势。与以前分析和滤波独立实施的旧初始化方案相比,新方案的分析和预报效果略优,同时有效地节省循环同化系统的运行时间,这对四维变分同化来说非常重要。
Theoretically, the analysis of a four-dimensional variational(4 DVar) data assimilation system is in better balance as the forecast model is its constraint. In actual implementation of 4 DVar, however, there are many processes that can lead to high-frequency gravity waves. Thus, the initialization process is still necessary for 4 DVar. In the present paper, the scientific design and formula derivation of the new initialization scheme of GRAPES(Global and Regional Assimilation Prediction System) numerical weather prediction system and experiments using the new scheme are presented. The four-dimensional variational data assimilation system of GRAPES(hereafter GRAPES-4 DVar) adopts the digital filter scheme for initialization. The digital filter is added to the penalty function as a weak constraint to efficiently diminish the unbalanced structure associated with gravity-inertia waves. The constraint is only imposed on the incremental analysis and run synchronously with the minimization. The weak constraining term does not add extra computation cost since the integration period of the digital filter is the same as the 4 DVar's time window. Furthermore, the new initialization scheme is suitable for long time window assimilation and will not weaken slow wave processes as the time window extends. It is easy to control the smoothness of model trajectory by tuning digital filter coefficient in the variational assimilation procedure. Results of GRAPES-4 DVar assimilation cycling experiments show that the initialization is necessary in the 4 DVar analysis, and the analysis and forecast skills have been improved significantly in the experiments with initialization compared to those without initialization. Compared to the old initialization scheme, in which the analysis and filter are two independent procedures, the new scheme efficiently saves the running time of assimilation cycling, although its impact on analysis and forecast is similar to that of the old scheme.
Theoretically, the analysis of a four-dimensional variational(4 DVar) data assimilation system is in better balance as the forecast model is its constraint. In actual implementation of 4 DVar, however, there are many processes that can lead to high-frequency gravity waves. Thus, the initialization process is still necessary for 4 DVar. In the present paper, the scientific design and formula derivation of the new initialization scheme of GRAPES(Global and Regional Assimilation Prediction System) numerical weather prediction system and experiments using the new scheme are presented. The four-dimensional variational data assimilation system of GRAPES(hereafter GRAPES-4 DVar) adopts the digital filter scheme for initialization. The digital filter is added to the penalty function as a weak constraint to efficiently diminish the unbalanced structure associated with gravity-inertia waves. The constraint is only imposed on the incremental analysis and run synchronously with the minimization. The weak constraining term does not add extra computation cost since the integration period of the digital filter is the same as the 4 DVar's time window. Furthermore, the new initialization scheme is suitable for long time window assimilation and will not weaken slow wave processes as the time window extends. It is easy to control the smoothness of model trajectory by tuning digital filter coefficient in the variational assimilation procedure. Results of GRAPES-4 DVar assimilation cycling experiments show that the initialization is necessary in the 4 DVar analysis, and the analysis and forecast skills have been improved significantly in the experiments with initialization compared to those without initialization. Compared to the old initialization scheme, in which the analysis and filter are two independent procedures, the new scheme efficiently saves the running time of assimilation cycling, although its impact on analysis and forecast is similar to that of the old scheme.
引文
纪立人.2011.数值天气预报发展进程中若干亮点的回顾及其启迪.气象科技进展,1(1):40-43.Ji L R.2011.Some highlights and their implication in the early progress of numerical weather prediction:A review.Adv Meteor Sci Technol,1(1):40-43 (in Chinese)
刘艳,薛纪善,张林等.2016.GRAPES全球三维变分同化系统的检验与诊断.应用气象学报,27(1):1-15.Liu Y,Xue J S,Zhang L,et al.2016.Verification and diagnostics for data assimilation system of global GRAPES.J Appl Meteor Sci,27(1):1-15(in Chinese)
马旭林,庄照荣,薛纪善等.2009.GRAPES非静力数值预报模式的三维变分资料同化系统的发展.气象学报,67(1):50-60.Ma X L,Zhuang Z R,Xue J S,et al.2009.Development of 3-D variational data assimilation system forthe nonhydrostatic numerical weather prediction model-GRAPES.Acta Meteor Sinica,67(1):50-60(in Chinese)
张林,刘永柱.2017.GRAPES全球四维变分同化系统极小化算法预调节.应用气象学报,28(2):168-176.Zhang L,Liu Y Z.2017.The Preconditioning of minimization algorithm in GRAPES global four-dimensional variational data assimilation system.J Appl Meteor Sci,28(2):168-176 (in Chinese)
刘永柱,张林,金之雁.2017.GRAPES全球切线性和伴随模式的调优.应用气象学报,28(1):62-71.Liu Y Z,Zhang L,Jin Z Y.2017.The optimization of GRAPES global tangent linear model and adjoint model.J Appl Meteor Sci,28(1):62-71 (in Chinese)
薛纪善,庄世宇,朱国富等.2008.GRAPES新一代全球/区域变分同化系统研究.科学通报,53(20):2408-2417.Xue J S,Zhuang S Y,Zhu G F,et al.2008.Scientific design and preliminary results of three-dimensional variational data assimilation system of GRAPES.Chinese Sci Bull,53(20):2408-2417 (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 GRAPES.Beijing:Science Press,383pp (in Chinese)
张华,薛纪善,庄世宇等.2004.GRAPES三维变分同化系统的理想试验.气象学报,62(1):31-41.Zhang H,Xue J S,Zhuang S Y,et al.2004.Idea experiments of GRAPES three-dimensional variational data assimilation system.Acta Meteor Sinica,62(1):31-41(in Chinese)
庄世宇,薛纪善,朱国富等.2005.GRAPES全球三维变分同化系统:基本设计方案与理想试验.大气科学,29(6):872-884.Zhuang S Y,Xue J S,Zhu G F,et al.2005.GRAPES global 3D-Var System:Basic scheme design and single observation test.Chinese J Atmos Sci,29(6):872-884 (in Chinese)
Arakawa A,Schubert W H.1974.Interaction of a cumulus cloud ensemble with the large-scale environment,Part I.J Atmos Sci,31(3):674-701
Ballish B,Cao X H,Kalnay E,et al.1992.Incremental nonlinear normal-mode initialization.Mon Wea Rev,120(8):1723-1734
Courtier P,Thépaut J N,Hollingsworth A.1994.A strategy for operational implementation of 4D-Var,using an incremental approach.Quart J Roy Meteor Soc,120(519):1367-1387
Daley R.1997.Atmospheric Data Analysis.New York:Cambridge University Press,457pp
Dee D P,Uppala S M,Simmons A J,et al.2011.The ERA-Interim reanalysis:Configuration and performance of the data assimilation system.Quart J Roy Meteor Soc,137(656):553-597
Ehrendorfer M,Errico R M,Raeder K D.1999.Singular-vector perturbation growth in a primitive equation model with moist physics.J Atmos Sci,56(11):1627-1648
Errico R M.2000.Interpretations of the total energy and rotational energy norms applied to determination of singular vectors.Quart J Roy Meteor Soc,126(566):1581-1599
Gauthier P,Thépaut J N.2001.Impact of the digital filter as a weak constraint in the preoperational 4DVAR assimilation system of Météo-France.Mon Wea Rev,129(8):2089-2102
Hong S Y,Lim J O J.2006.The WRF single-moment 6-class microphysics scheme (WSM6).J Korean Meteor Soc,42:129-151
Liu K,Chen Q Y,Sun J.2015.Modification of cumulus convection and planetary boundary layer schemes in the GRAPES global model.J Meteor Res,29(5):806-822
Liu Y Z,Zhang L,Lian ZH.2018.Conjugate gradient algorithm in the four-dimensional variational data assimilation system in GRAPES.J Meteor Res,32(6):974-984
Lynch P,Huang X Y.1992.Initialization of the HIRLAM model using a digital filter.Mon Wea Rev,120(6):1019-1034
Lynch P,Huang X Y.2010.Initialization//Lahoz W,Khattatov B,Menard R.Data Assimilation:Making Sense of Observations.Berlin,Heidelberg:Springer,241-259
Mlawer E J,Taubman S J,Brown P D,et al.1997.Radiative transfer for inhomogeneous atmospheres:RRTM,a validated correlated-k model for the longwave.J Geophys Res,102(D14):16663-16682
Polavarapu S,Tanguay M,Fillion L.2000.Four-dimensional variational data assimilation with digital filter initialization.Mon Wea Rev,128(7):2491-2510
Rabier F.2005.Overview of global data assimilation developments in numerical weather-prediction centres.Quart J Roy Meteor Soc,131(613):3215-3233
Rawlins F,Ballard S P,Bovis K J,et al.2007.The Met Office global four-dimensional variational data assimilation scheme.Quart J Roy Meteor Soc,133(623):347-362
Temperton C.1988.Implicit normal mode initialization.Mon Wea Rev,116(5):1013-1031
Temperton C.1989.Implicit normal mode initialization for spectral models.Mon Wea Rev,117(2):436-451
Troen I B,Mahrt L.1986.A simple model of the atmospheric boundary layer;sensitivity to surface evaporation.Bound-Layer Meteor,37(1-2):129-148
Wee T K,Kuo Y H.2004.Impact of a digital filter as a weak constraint in MM5 4DVAR:An observing system simulation experiment.Mon Wea Rev,132(2):543-559
Williamson D L,Temperton C.1981.Normal mode initialization for a multilevel grid-point model.Part II:Nonlinear aspects.Mon Wea Rev,109(4):744-757
①薛纪善,刘艳,张林等.2012.GRAPES全球三维变分同化系统模式变量分析版科学文档.中国气象局数值预报中心内部技术手册.北京:中国气象局,1-105
①薛纪善,刘艳,张林等.2012.GRAPES全球三维变分同化系统模式变量分析版科学文档.中国气象局数值预报中心内部技术手册.北京:中国气象局,1-105
①薛纪善,刘艳,张林等.2012.GRAPES全球三维变分同化系统模式变量分析版科学文档.中国气象局数值预报中心内部技术手册.北京:中国气象局,1-105
刘艳,薛纪善,张林等.2016.GRAPES全球三维变分同化系统的检验与诊断.应用气象学报,27(1):1-15.Liu Y,Xue J S,Zhang L,et al.2016.Verification and diagnostics for data assimilation system of global GRAPES.J Appl Meteor Sci,27(1):1-15(in Chinese)
马旭林,庄照荣,薛纪善等.2009.GRAPES非静力数值预报模式的三维变分资料同化系统的发展.气象学报,67(1):50-60.Ma X L,Zhuang Z R,Xue J S,et al.2009.Development of 3-D variational data assimilation system forthe nonhydrostatic numerical weather prediction model-GRAPES.Acta Meteor Sinica,67(1):50-60(in Chinese)
张林,刘永柱.2017.GRAPES全球四维变分同化系统极小化算法预调节.应用气象学报,28(2):168-176.Zhang L,Liu Y Z.2017.The Preconditioning of minimization algorithm in GRAPES global four-dimensional variational data assimilation system.J Appl Meteor Sci,28(2):168-176 (in Chinese)
刘永柱,张林,金之雁.2017.GRAPES全球切线性和伴随模式的调优.应用气象学报,28(1):62-71.Liu Y Z,Zhang L,Jin Z Y.2017.The optimization of GRAPES global tangent linear model and adjoint model.J Appl Meteor Sci,28(1):62-71 (in Chinese)
薛纪善,庄世宇,朱国富等.2008.GRAPES新一代全球/区域变分同化系统研究.科学通报,53(20):2408-2417.Xue J S,Zhuang S Y,Zhu G F,et al.2008.Scientific design and preliminary results of three-dimensional variational data assimilation system of GRAPES.Chinese Sci Bull,53(20):2408-2417 (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 GRAPES.Beijing:Science Press,383pp (in Chinese)
张华,薛纪善,庄世宇等.2004.GRAPES三维变分同化系统的理想试验.气象学报,62(1):31-41.Zhang H,Xue J S,Zhuang S Y,et al.2004.Idea experiments of GRAPES three-dimensional variational data assimilation system.Acta Meteor Sinica,62(1):31-41(in Chinese)
庄世宇,薛纪善,朱国富等.2005.GRAPES全球三维变分同化系统:基本设计方案与理想试验.大气科学,29(6):872-884.Zhuang S Y,Xue J S,Zhu G F,et al.2005.GRAPES global 3D-Var System:Basic scheme design and single observation test.Chinese J Atmos Sci,29(6):872-884 (in Chinese)
Arakawa A,Schubert W H.1974.Interaction of a cumulus cloud ensemble with the large-scale environment,Part I.J Atmos Sci,31(3):674-701
Ballish B,Cao X H,Kalnay E,et al.1992.Incremental nonlinear normal-mode initialization.Mon Wea Rev,120(8):1723-1734
Courtier P,Thépaut J N,Hollingsworth A.1994.A strategy for operational implementation of 4D-Var,using an incremental approach.Quart J Roy Meteor Soc,120(519):1367-1387
Daley R.1997.Atmospheric Data Analysis.New York:Cambridge University Press,457pp
Dee D P,Uppala S M,Simmons A J,et al.2011.The ERA-Interim reanalysis:Configuration and performance of the data assimilation system.Quart J Roy Meteor Soc,137(656):553-597
Ehrendorfer M,Errico R M,Raeder K D.1999.Singular-vector perturbation growth in a primitive equation model with moist physics.J Atmos Sci,56(11):1627-1648
Errico R M.2000.Interpretations of the total energy and rotational energy norms applied to determination of singular vectors.Quart J Roy Meteor Soc,126(566):1581-1599
Gauthier P,Thépaut J N.2001.Impact of the digital filter as a weak constraint in the preoperational 4DVAR assimilation system of Météo-France.Mon Wea Rev,129(8):2089-2102
Hong S Y,Lim J O J.2006.The WRF single-moment 6-class microphysics scheme (WSM6).J Korean Meteor Soc,42:129-151
Liu K,Chen Q Y,Sun J.2015.Modification of cumulus convection and planetary boundary layer schemes in the GRAPES global model.J Meteor Res,29(5):806-822
Liu Y Z,Zhang L,Lian ZH.2018.Conjugate gradient algorithm in the four-dimensional variational data assimilation system in GRAPES.J Meteor Res,32(6):974-984
Lynch P,Huang X Y.1992.Initialization of the HIRLAM model using a digital filter.Mon Wea Rev,120(6):1019-1034
Lynch P,Huang X Y.2010.Initialization//Lahoz W,Khattatov B,Menard R.Data Assimilation:Making Sense of Observations.Berlin,Heidelberg:Springer,241-259
Mlawer E J,Taubman S J,Brown P D,et al.1997.Radiative transfer for inhomogeneous atmospheres:RRTM,a validated correlated-k model for the longwave.J Geophys Res,102(D14):16663-16682
Polavarapu S,Tanguay M,Fillion L.2000.Four-dimensional variational data assimilation with digital filter initialization.Mon Wea Rev,128(7):2491-2510
Rabier F.2005.Overview of global data assimilation developments in numerical weather-prediction centres.Quart J Roy Meteor Soc,131(613):3215-3233
Rawlins F,Ballard S P,Bovis K J,et al.2007.The Met Office global four-dimensional variational data assimilation scheme.Quart J Roy Meteor Soc,133(623):347-362
Temperton C.1988.Implicit normal mode initialization.Mon Wea Rev,116(5):1013-1031
Temperton C.1989.Implicit normal mode initialization for spectral models.Mon Wea Rev,117(2):436-451
Troen I B,Mahrt L.1986.A simple model of the atmospheric boundary layer;sensitivity to surface evaporation.Bound-Layer Meteor,37(1-2):129-148
Wee T K,Kuo Y H.2004.Impact of a digital filter as a weak constraint in MM5 4DVAR:An observing system simulation experiment.Mon Wea Rev,132(2):543-559
Williamson D L,Temperton C.1981.Normal mode initialization for a multilevel grid-point model.Part II:Nonlinear aspects.Mon Wea Rev,109(4):744-757
①薛纪善,刘艳,张林等.2012.GRAPES全球三维变分同化系统模式变量分析版科学文档.中国气象局数值预报中心内部技术手册.北京:中国气象局,1-105
①薛纪善,刘艳,张林等.2012.GRAPES全球三维变分同化系统模式变量分析版科学文档.中国气象局数值预报中心内部技术手册.北京:中国气象局,1-105
①薛纪善,刘艳,张林等.2012.GRAPES全球三维变分同化系统模式变量分析版科学文档.中国气象局数值预报中心内部技术手册.北京:中国气象局,1-105