GRAPES全球奇异向量方法改进及试验分析
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摘要
基于总能量模的奇异向量扰动常用于构造集合预报的初始条件。以建立GRAPES(Global and Regional Assimilation PrEdiction System)全球集合预报系统为目的,基于前期研发的GRAPES全球模式奇异向量方法,在GRAPES全球切线性模式和伴随模式2.0版的框架下,开展了引入线性化边界层方案来改善奇异向量结构,并提高奇异向量计算效率的研究。通过连续试验,从奇异向量的扰动能量结构、扰动能量谱及扰动空间分布等方面,综合分析改进GRAPES全球奇异向量的结构及演变特征。试验结果表明,改进后的GRAPES奇异向量方法有效抑制了之前扰动能量在近地面层不合理的快速增长,同时,奇异向量最优扰动的结构更客观地体现了中高纬度区域大气初始条件中的斜压不稳定扰动及其演变,如在初始时刻奇异向量扰动能量主要位于对流层中层,并呈现出随高度向西倾斜的大气斜压特征;经过线性化演变,扰动能量向较大水平尺度转移,并在垂直结构上表现出向对流层高层上传及向对流层低层下传的特征等。针对GRAPES奇异向量迭代求解中伴随模式计算耗时为主的情况,改进伴随模式中广义共轭余差方案的调用方式,并采用大内存存储法来提高其计算效率,进而将奇异向量总计算时间缩短了25%。总之,改进后的GRAPES奇异向量方法,可应用于构建面向业务应用的GRAPES全球集合预报系统。
The singular vectors(SVs) based on total-energy norm are generally used to represent initial uncertainty in ensemble forecasting. The GRAEPE SV method based on the total-energy norm using the GRAPES dynamical core model has been developed. Impacts and importance of linearized physical processes on the SVs have been widely studied in the literature. To improve the GRAPES SVs, based on the recently developed GRAPES tangent linear model(TLM) and adjoint model(ADM) version 2.0, the implementation of linearized planetary boundary layer(PBL) parameterization on the calculation of extratropical SVs is conducted. The characteristics of SVs and their linear evolutions are measured by energy partition, energy spectra and spatial distribution through continuous experiments over 1-month period. The unreasonable quick energy growth near the surface that was observed previously in the structure of SVs without linearized physics has been greatly improved. Furthermore, the structures of the upgraded SVs are more consistent with those of previous studies, which exhibit the characteristics of typical total-energy based SVs, i.e., the energy maximum is located in the middle troposphere with obvious westward tilt with height in the spatial structure of SVs at initial time; during their growth, there are upward energy transfer to the upper troposphere and downward energy transfer to the surface, and an upscale energy transfer is shown in the energy spectra. The results show that the upgraded SVs are capable of capturing the baroclinic instability in the troposphere. In order to improve the computation efficiency of GRAPES SVs, the ADM that is most computationally expensive is optimized by reducing the use of GCR(Generalized Conjugate-Residual) in the ADM and increasing computational memory. As a result, the total computation time of GRAPES SVs can be reduced by up to 25%. Overall, the upgraded GRAPES SVs are able to meet the expectation for constructing the initial perturbation for GRAPES global ensemble prediction.
The singular vectors(SVs) based on total-energy norm are generally used to represent initial uncertainty in ensemble forecasting. The GRAEPE SV method based on the total-energy norm using the GRAPES dynamical core model has been developed. Impacts and importance of linearized physical processes on the SVs have been widely studied in the literature. To improve the GRAPES SVs, based on the recently developed GRAPES tangent linear model(TLM) and adjoint model(ADM) version 2.0, the implementation of linearized planetary boundary layer(PBL) parameterization on the calculation of extratropical SVs is conducted. The characteristics of SVs and their linear evolutions are measured by energy partition, energy spectra and spatial distribution through continuous experiments over 1-month period. The unreasonable quick energy growth near the surface that was observed previously in the structure of SVs without linearized physics has been greatly improved. Furthermore, the structures of the upgraded SVs are more consistent with those of previous studies, which exhibit the characteristics of typical total-energy based SVs, i.e., the energy maximum is located in the middle troposphere with obvious westward tilt with height in the spatial structure of SVs at initial time; during their growth, there are upward energy transfer to the upper troposphere and downward energy transfer to the surface, and an upscale energy transfer is shown in the energy spectra. The results show that the upgraded SVs are capable of capturing the baroclinic instability in the troposphere. In order to improve the computation efficiency of GRAPES SVs, the ADM that is most computationally expensive is optimized by reducing the use of GCR(Generalized Conjugate-Residual) in the ADM and increasing computational memory. As a result, the total computation time of GRAPES SVs can be reduced by up to 25%. Overall, the upgraded GRAPES SVs are able to meet the expectation for constructing the initial perturbation for GRAPES global ensemble prediction.
引文
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.Research 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)
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)
刘永柱,龚建东,张林等.2019.线性化物理过程对GRAPES 4DVAR同化的影响.气象学报,77(2):196-209.Liu Y Z,Gong J D,Zhang L,et al.2019.Influence of linearized physical processes on the GRAPES 4DVAR.Acta Meteor Sinica,77(2):196-209 (in Chinese)
任迪生,沈学顺,薛纪善等.2011.GRAPES伴随模式底层数据栈优化.应用气象学报,22(3):362-366.Ren D S,Shen X S,Xue J S,et al.2011.Optimized design of stack for GRAPES's adjoint model.J Appl Meteor Sci,22(3):362-366 (in Chinese)
沈学顺,苏勇,胡江林等.2017.GRAPES_GFS全球中期预报系统的研发和业务化.应用气象学报,28(1):1-10.Shen X S,Su Y,Hu J L,et al.2017.Development and operation transformation of GRAPES global middle-range forecast system.J Appl Meteor Sci,28(1):1-10 (in Chinese)
张林,朱宗申.2008.GRAPES模式切线性垂直扩散方案的误差分析和改进.应用气象学报,19(2):194-200.Zhang L,Zhu Z S.2008.Estimation of linearized vertical diffusion scheme in GRAPES model.J Appl Meteor Sci,19(2):194-200 (in Chinese)
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
Buehner M,Zadra A.2006.Impact of flow-dependent analysis-error covariance norms on extratropical singular vectors.Quart J Roy Meteor Soc,132(615):625-646
Buizza R.1994.Sensitivity of optimal unstable structures.Quart J Roy Meteor Soc,120(516):429-451
Buizza R,Palmer T N.1995.The singular-vector structure of the atmospheric global circulation.J Atoms Sci,52(9):1434-1456
Coutinho M M,Hoskins B J,Buizza R.2004.The influence of physical processes on extratropical singular vectors.J Atmos Sci,61(2):195-209
Diaconescu E P,Laprise R.2012.Singular vectors in atmospheric sciences:A review.Earth-Sci Rev,113(3-4):161-175
Hartmann D L,Buizza R,Palmer T N.1995.Singular vectors:The effect of spatial scale on linear growth of disturbances.J Atmos Sci,52(22):3885-3894
Hong S Y,Pan H K L.1996.Nonlocal boundary layer vertical diffusion in a medium-range forecast model.Mon Wea Rev,124(10):2322-2339
Hoskins B,Buizza R,Badger J.2000.The nature of singular vector growth and structure.Quart J Roy Meteor Soc,126(566):1565-1580
Houtekamer P L,Mitchell H L.2005.Ensemble Kalman filtering.Quart J Roy Meteor Soc,31(613):3269-3289
Laroche S,Tanguay M,Delage Y.2002.Linearization of a simplified planetary boundary layer parameterization.Mon Wea Rev,130(8):2074-2087
Lawrence A R,Leutbecher M,Palmer T N.2009.The characteristics of Hessian singular vectors using an advanced data assimilation scheme.Quart J Roy Meteor Soc,135(642):1117-1132
Mahfouf J F.1999.Influence of physical processes on the tangent-linear approximation.Tellus A,51(2):147-166
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
Montani A,Thorpe A J.2002.Mechanisms leading to singular-vector growth for FASTEX cyclones.Quart J Roy Meteor Soc,128(579):131-148
Mu M,Duan W S,Wand B.2003.Conditional nonlinear optimal perturbation and its application.Nolin Processes Geophys,10(6):493-501
Mureau R,Molteni F,Palmer T N.1993.Ensemble prediction using dynamically conditioned perturbations.Quart J Roy Meteor Soc,119(510):299-323
Palmer T N,Molteni F,Mureau R,et al.1993.Ensemble Prediction//Proceedings of the ECMWF Seminar on Validation of Models over Europe.Reading,UK:Shinfield Park,21-66
Palmer T N,Gelaro R,Barkmeijer J,et al.1998.Singular vectors,metrics,and adaptive observations.J Atoms Sci,55(4):633-653
Toth Z,Kalnay E.1997.Ensemble forecasting at NCEP and the breeding method.Mon Wea Rev,125(12):3297-3319
Zadra A,Buehner M,Laroche S,et al.2004.Impact of the GEM model simplified physics on extratropical singular vectors.Quart J Roy Meteor Soc,130(602):2541-2569
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)
刘永柱,龚建东,张林等.2019.线性化物理过程对GRAPES 4DVAR同化的影响.气象学报,77(2):196-209.Liu Y Z,Gong J D,Zhang L,et al.2019.Influence of linearized physical processes on the GRAPES 4DVAR.Acta Meteor Sinica,77(2):196-209 (in Chinese)
任迪生,沈学顺,薛纪善等.2011.GRAPES伴随模式底层数据栈优化.应用气象学报,22(3):362-366.Ren D S,Shen X S,Xue J S,et al.2011.Optimized design of stack for GRAPES's adjoint model.J Appl Meteor Sci,22(3):362-366 (in Chinese)
沈学顺,苏勇,胡江林等.2017.GRAPES_GFS全球中期预报系统的研发和业务化.应用气象学报,28(1):1-10.Shen X S,Su Y,Hu J L,et al.2017.Development and operation transformation of GRAPES global middle-range forecast system.J Appl Meteor Sci,28(1):1-10 (in Chinese)
张林,朱宗申.2008.GRAPES模式切线性垂直扩散方案的误差分析和改进.应用气象学报,19(2):194-200.Zhang L,Zhu Z S.2008.Estimation of linearized vertical diffusion scheme in GRAPES model.J Appl Meteor Sci,19(2):194-200 (in Chinese)
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
Buehner M,Zadra A.2006.Impact of flow-dependent analysis-error covariance norms on extratropical singular vectors.Quart J Roy Meteor Soc,132(615):625-646
Buizza R.1994.Sensitivity of optimal unstable structures.Quart J Roy Meteor Soc,120(516):429-451
Buizza R,Palmer T N.1995.The singular-vector structure of the atmospheric global circulation.J Atoms Sci,52(9):1434-1456
Coutinho M M,Hoskins B J,Buizza R.2004.The influence of physical processes on extratropical singular vectors.J Atmos Sci,61(2):195-209
Diaconescu E P,Laprise R.2012.Singular vectors in atmospheric sciences:A review.Earth-Sci Rev,113(3-4):161-175
Hartmann D L,Buizza R,Palmer T N.1995.Singular vectors:The effect of spatial scale on linear growth of disturbances.J Atmos Sci,52(22):3885-3894
Hong S Y,Pan H K L.1996.Nonlocal boundary layer vertical diffusion in a medium-range forecast model.Mon Wea Rev,124(10):2322-2339
Hoskins B,Buizza R,Badger J.2000.The nature of singular vector growth and structure.Quart J Roy Meteor Soc,126(566):1565-1580
Houtekamer P L,Mitchell H L.2005.Ensemble Kalman filtering.Quart J Roy Meteor Soc,31(613):3269-3289
Laroche S,Tanguay M,Delage Y.2002.Linearization of a simplified planetary boundary layer parameterization.Mon Wea Rev,130(8):2074-2087
Lawrence A R,Leutbecher M,Palmer T N.2009.The characteristics of Hessian singular vectors using an advanced data assimilation scheme.Quart J Roy Meteor Soc,135(642):1117-1132
Mahfouf J F.1999.Influence of physical processes on the tangent-linear approximation.Tellus A,51(2):147-166
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
Montani A,Thorpe A J.2002.Mechanisms leading to singular-vector growth for FASTEX cyclones.Quart J Roy Meteor Soc,128(579):131-148
Mu M,Duan W S,Wand B.2003.Conditional nonlinear optimal perturbation and its application.Nolin Processes Geophys,10(6):493-501
Mureau R,Molteni F,Palmer T N.1993.Ensemble prediction using dynamically conditioned perturbations.Quart J Roy Meteor Soc,119(510):299-323
Palmer T N,Molteni F,Mureau R,et al.1993.Ensemble Prediction//Proceedings of the ECMWF Seminar on Validation of Models over Europe.Reading,UK:Shinfield Park,21-66
Palmer T N,Gelaro R,Barkmeijer J,et al.1998.Singular vectors,metrics,and adaptive observations.J Atoms Sci,55(4):633-653
Toth Z,Kalnay E.1997.Ensemble forecasting at NCEP and the breeding method.Mon Wea Rev,125(12):3297-3319
Zadra A,Buehner M,Laroche S,et al.2004.Impact of the GEM model simplified physics on extratropical singular vectors.Quart J Roy Meteor Soc,130(602):2541-2569