Two schemes for vertical discretization of the model are proposed,one with equal △lnσ and the other in terms of Tschebyscheff polynomials.It is proved that in adiabatic and inviscid cases if the meteorological eleme...Two schemes for vertical discretization of the model are proposed,one with equal △lnσ and the other in terms of Tschebyscheff polynomials.It is proved that in adiabatic and inviscid cases if the meteorological elements and related physical quantities are continuous in time and in the horizontal,the total energy and total mass are conserved within a high approximation respectively, and there is a correct conversion between total kinetic and total potential energy.Numerical computations show that the schemes both have high accuracy.For example,in integrating the hydrostatic equation the computational errors of geopotential height resulting from the schemes are much less than those resulting from EC79 in a-coordinate.展开更多
A three-dimensional(3D)global adiabatic spectral primitive equation model has been designed.The main features are as follows. (1)Adoption of spherical harmonics and Tschebyscheff polynomials as the basis functions in ...A three-dimensional(3D)global adiabatic spectral primitive equation model has been designed.The main features are as follows. (1)Adoption of spherical harmonics and Tschebyscheff polynomials as the basis functions in the horizontal and vertical respectively,but the unknowns in the spectral equations are two- dimensional; (2)Inclusion of the tropopause,which may vary with time and space; (3)Suggestion of a spectral method for representing the vertical structure of the atmosphere applicable to the unsmoothed profile case; (4)In consideration of nonlinear vertical aliasing a technique is proposed to avoid it and nonlinear computational instability. Based on real data forecasts up to 48 hours have been performed.The results show that the statistical verifications with the model are superior on the average to those with the T42L9 used operationally before 1995 at NMC of China at the same mean resolution.展开更多
Through analysis and numerical computation of ECMWF's discrete scheme of hydrostatic equation (Baede et al. 1979),it has been found that in the case of equal △σ there exist systematic errors in the scheme.The er...Through analysis and numerical computation of ECMWF's discrete scheme of hydrostatic equation (Baede et al. 1979),it has been found that in the case of equal △σ there exist systematic errors in the scheme.The error E caused by taking the arithmetic mean of the geopotential heights of two adjacent half a-levels as the geopotential height of the cor- responding integer a-level,increases with height and has an unacceptable maximum in the vicinity of the top of the at- mosphere;however,the errors caused by the temperature treatment are generally small.On the other hand,if an uneven △σ-scheme in which the levels in the upper and lower atmosphere are denser than those in the middle atmosphere,is adopted,then E can be much reduced.However,if the resolution of the original equal Art-scheme doubles,then E can only be found to be much reduced in the troposphere and that in the vicinity of the atmospheric top is still unacceptable. Two numerical schemes for improvement have been presented.Of them one is the same as the ECMWF's scheme, but with equal △lnσ,and the other is to integrate the equation by the use of Tschebyscheff polynomials T and to adopt the zeros of TN as the atmospheric levels where N is the total number of levels.The results show that with both schemes the computational errors can be much reduced,especially the latter,due to the fact that the errors of three statistical types are generally less than the root mean square error of the geopotential heights reported in TEMP.展开更多
文摘Two schemes for vertical discretization of the model are proposed,one with equal △lnσ and the other in terms of Tschebyscheff polynomials.It is proved that in adiabatic and inviscid cases if the meteorological elements and related physical quantities are continuous in time and in the horizontal,the total energy and total mass are conserved within a high approximation respectively, and there is a correct conversion between total kinetic and total potential energy.Numerical computations show that the schemes both have high accuracy.For example,in integrating the hydrostatic equation the computational errors of geopotential height resulting from the schemes are much less than those resulting from EC79 in a-coordinate.
基金This study is supported by the National Natural Science Foundation of China under the program No.49575268.
文摘A three-dimensional(3D)global adiabatic spectral primitive equation model has been designed.The main features are as follows. (1)Adoption of spherical harmonics and Tschebyscheff polynomials as the basis functions in the horizontal and vertical respectively,but the unknowns in the spectral equations are two- dimensional; (2)Inclusion of the tropopause,which may vary with time and space; (3)Suggestion of a spectral method for representing the vertical structure of the atmosphere applicable to the unsmoothed profile case; (4)In consideration of nonlinear vertical aliasing a technique is proposed to avoid it and nonlinear computational instability. Based on real data forecasts up to 48 hours have been performed.The results show that the statistical verifications with the model are superior on the average to those with the T42L9 used operationally before 1995 at NMC of China at the same mean resolution.
文摘Through analysis and numerical computation of ECMWF's discrete scheme of hydrostatic equation (Baede et al. 1979),it has been found that in the case of equal △σ there exist systematic errors in the scheme.The error E caused by taking the arithmetic mean of the geopotential heights of two adjacent half a-levels as the geopotential height of the cor- responding integer a-level,increases with height and has an unacceptable maximum in the vicinity of the top of the at- mosphere;however,the errors caused by the temperature treatment are generally small.On the other hand,if an uneven △σ-scheme in which the levels in the upper and lower atmosphere are denser than those in the middle atmosphere,is adopted,then E can be much reduced.However,if the resolution of the original equal Art-scheme doubles,then E can only be found to be much reduced in the troposphere and that in the vicinity of the atmospheric top is still unacceptable. Two numerical schemes for improvement have been presented.Of them one is the same as the ECMWF's scheme, but with equal △lnσ,and the other is to integrate the equation by the use of Tschebyscheff polynomials T and to adopt the zeros of TN as the atmospheric levels where N is the total number of levels.The results show that with both schemes the computational errors can be much reduced,especially the latter,due to the fact that the errors of three statistical types are generally less than the root mean square error of the geopotential heights reported in TEMP.
