Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directl...Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the effciency of the characteristic constrained interpolation profile （CIP） method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.展开更多
This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows（EWEIF...This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows（EWEIF） uses dynamic constraints in conjunction with projections of data onto parabolic cylinder functions to determine the amplitude of all equatorial waves.EWEIF allows us to decompose an instantaneous wave flow into individual equatorial waves with a presumed equivalent depth without using temporal or spatial filtering a priori.Three sets of EWEIF analyses are presented. The first set is to confirm that EWEIF is capable of recovering the individual waves constructed from theoretical equatorial wave solutions under various scenarios. The other two sets demonstrate the ability of the EWEIF method to derive time series of individual equatorial waves from instantaneous wave fields without knowing a priori exactly which waves exist in the data as well as their spatial and temporal scales using outputs of an equatorial β-channel shallow-water model and ERA-Interim data. The third set of demonstrations shows, for the first time, the continuous evolutions of individual equatorial waves in the stratosphere whose amplitude is synchronized with the background zonal wind as predicted by quasi-biennial oscillation theory.展开更多
基于前后张驰逼近(Back and Forth Nudging,简称BFN)和集合卡尔曼滤波(En KF)方法,构建了一种新的同化方法 HBFNEn KF(Hybrid Back and Forth Nudging En KF)混合同化方法,并将此同化系统分别与通道浅水模式(shallow water model)和全...基于前后张驰逼近(Back and Forth Nudging,简称BFN)和集合卡尔曼滤波(En KF)方法,构建了一种新的同化方法 HBFNEn KF(Hybrid Back and Forth Nudging En KF)混合同化方法,并将此同化系统分别与通道浅水模式(shallow water model)和全球浅水模式对接,检验了HBFNEn KF同化方法的有效性。同时,对比了集合均方根滤波(En SRF)、HNEn KF(Hybrid Nudging En KF)、HBFNEn KF三种方法在有误差模式中的同化效果。试验结果表明:HBFNEn KF同化方法保留了HNEn KF方法的同化连续性,解决了En KF同化不连续不平滑的问题,同时还有着更快的收敛速度;当采用单变量分析试验时,HBFNEn KF方法的优势最为明显,表明HBFNEn KF能够较好地保持不同模式变量间的平衡。此外,增量场尺度分析结果表明:相比En SRF,HBFNEn KF在大尺度范围有更好的同化效果,同时能够避免在中小尺度范围内出现大量的虚假增量。展开更多
A strategy for evaluating a global shallow water model based on aspects of kinetic energy spectra and nonlinear vorticity dynamics is proposed in this study.The kinetic energy spectra and nonlinear vorticity dynamics ...A strategy for evaluating a global shallow water model based on aspects of kinetic energy spectra and nonlinear vorticity dynamics is proposed in this study.The kinetic energy spectra and nonlinear vorticity dynamics of a recently developed global shallow water model on an unstructured mesh are evaluated in comparison with the benchmark solutions from a global high-resolution spectral model.The results show that the kinetic energy spectra,the rotational and divergent components,the stationary and transient components,and the nonlinear spectral fluxes of the developed shallow water model agree well with those generated by the reference model.In addition,the influence of different flux operators for transporting the potential vorticity(PV)is assessed specifically.It is indicated that the second-order flux operator leads to a spurious increase in the kinetic energy at the tail of the spectrum,whereas the upwind third-order flux operator does not support this behavior owing to implicit numerical diffusion.Moreover,the nonlinear vorticity dynamics is studied by using colliding modons.It is found that the grid-point model maintains the symmetrical pattern of vortices,and generates similar kinetic energy spectra and nonlinear spectral fluxes to the reference model.The evaluation provides a reference for assessing the shallow water model in terms of nonlinear dynamics,and the developed global shallow water model presents a good example.展开更多
基金supported by National Natural Science Foundation of China (NSFC) projects (Grant Nos. 40875065 and 40805045)the research projects 2008R001 at Chinese Academy of Meteorological Sciences (CAMS) and 2008 LASWZI05 at the State Key Laboratory of Severe Weather, CAMS
文摘Semi-implicit algorithms are popularly used to deal with the gravitational term in numerical models. In this paper, we adopt the method of characteristics to compute the solutions for gravity waves on a sphere directly using a semi-Lagrangian advection scheme instead of the semi-implicit method in a shallow water model, to avoid expensive matrix inversions. Adoption of the semi-Lagrangian scheme renders the numerical model always stable for any Courant number, and which saves CPU time. To illustrate the effciency of the characteristic constrained interpolation profile （CIP） method, some numerical results are shown for idealized test cases on a sphere in the Yin-Yang grid system.
基金supported by grants from the National Science Foundation(Grant No.AGS-1354834)the NASA Interdisciplinary Studies Program(Grant No.NNH12ZDA001NIDS)
文摘This paper presents a method for expanding horizontal flow variables in data using the free solutions to the shallow-water system as a basis set. This method for equatorial wave expansion of instantaneous flows（EWEIF） uses dynamic constraints in conjunction with projections of data onto parabolic cylinder functions to determine the amplitude of all equatorial waves.EWEIF allows us to decompose an instantaneous wave flow into individual equatorial waves with a presumed equivalent depth without using temporal or spatial filtering a priori.Three sets of EWEIF analyses are presented. The first set is to confirm that EWEIF is capable of recovering the individual waves constructed from theoretical equatorial wave solutions under various scenarios. The other two sets demonstrate the ability of the EWEIF method to derive time series of individual equatorial waves from instantaneous wave fields without knowing a priori exactly which waves exist in the data as well as their spatial and temporal scales using outputs of an equatorial β-channel shallow-water model and ERA-Interim data. The third set of demonstrations shows, for the first time, the continuous evolutions of individual equatorial waves in the stratosphere whose amplitude is synchronized with the background zonal wind as predicted by quasi-biennial oscillation theory.
文摘基于前后张驰逼近(Back and Forth Nudging,简称BFN)和集合卡尔曼滤波(En KF)方法,构建了一种新的同化方法 HBFNEn KF(Hybrid Back and Forth Nudging En KF)混合同化方法,并将此同化系统分别与通道浅水模式(shallow water model)和全球浅水模式对接,检验了HBFNEn KF同化方法的有效性。同时,对比了集合均方根滤波(En SRF)、HNEn KF(Hybrid Nudging En KF)、HBFNEn KF三种方法在有误差模式中的同化效果。试验结果表明:HBFNEn KF同化方法保留了HNEn KF方法的同化连续性,解决了En KF同化不连续不平滑的问题,同时还有着更快的收敛速度;当采用单变量分析试验时,HBFNEn KF方法的优势最为明显,表明HBFNEn KF能够较好地保持不同模式变量间的平衡。此外,增量场尺度分析结果表明:相比En SRF,HBFNEn KF在大尺度范围有更好的同化效果,同时能够避免在中小尺度范围内出现大量的虚假增量。
基金Supported by the National Key Research and Development Program of China(2017YFC1502202)National Natural Science Foundation of China(41875135)Basic Research and Operation Founds of Chinese Academy of Meteorological Sciences(2018Y004).
文摘A strategy for evaluating a global shallow water model based on aspects of kinetic energy spectra and nonlinear vorticity dynamics is proposed in this study.The kinetic energy spectra and nonlinear vorticity dynamics of a recently developed global shallow water model on an unstructured mesh are evaluated in comparison with the benchmark solutions from a global high-resolution spectral model.The results show that the kinetic energy spectra,the rotational and divergent components,the stationary and transient components,and the nonlinear spectral fluxes of the developed shallow water model agree well with those generated by the reference model.In addition,the influence of different flux operators for transporting the potential vorticity(PV)is assessed specifically.It is indicated that the second-order flux operator leads to a spurious increase in the kinetic energy at the tail of the spectrum,whereas the upwind third-order flux operator does not support this behavior owing to implicit numerical diffusion.Moreover,the nonlinear vorticity dynamics is studied by using colliding modons.It is found that the grid-point model maintains the symmetrical pattern of vortices,and generates similar kinetic energy spectra and nonlinear spectral fluxes to the reference model.The evaluation provides a reference for assessing the shallow water model in terms of nonlinear dynamics,and the developed global shallow water model presents a good example.
