In accordance with a new compensation principle of discrete computations,the traditional meteo- rological global (pseudo-) spectral schemes of barotropic primitive equation (s) are transformed into perfect energy cons...In accordance with a new compensation principle of discrete computations,the traditional meteo- rological global (pseudo-) spectral schemes of barotropic primitive equation (s) are transformed into perfect energy conservative fidelity schemes,thus resolving the problems of both nonlinear computa- tional instability and incomplete energy conservation,and raising the computational efficiency of the traditional schemes. As the numerical tests of the new schemes demonstrate,in solving the problem of energy conser- vation in operational computations,the new schemes can eliminate the (nonlinear) computational in- stability and,to some extent even the (nonlinear) computational diverging as found in the traditional schemes,Further contrasts between new and traditional schemes also indicate that,in discrete opera- tional computations,the new scheme in the case of nondivergence is capable of prolonging the valid in- tegral time of the corresponding traditional scheme,and eliminating certain kind of systematical com- putational“climate drift”,meanwhile increasing its computational accuracy and reducing its amount of computation.The working principle of this paper is also applicable to the problem concerning baroclin- ic primitive equations.展开更多
In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discreti...In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discretized schemes given as special cases.These two theorems can provide new mathematical basis for solving basic formulation problems of more types of conservative time- discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schemes.Besides.the two theorems can also solve two large categories of problems about linear and nonlinear computational instability. The traditional global spectral-vertical finite-difference semi-implicit model for baroclinic primitive equations is currently used in many countries in the world for operational weather forecast and numerical simulations of general circulation.The present work,however,based on Theorem 2 formulated in this paper,develops and realizes a high-order total energy conserving semi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model of baroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved for long,whether in terms of theory or practice.The total energy conserving semi-implicit scheme formulated here is applicable to real data long-term numerical integration. The experiment of thirteen FGGE data 30-day numerical integration indicates that the new type of total energy conserving semi-implicit fidelity scheme can surely modify the systematic deviation of energy and mass conserving of the traditional scheme.It should be particularly noted that,under the experiment conditions of the present work,the systematic errors induced by the violation of physical laws of conservation in the time-discretized process regarding the traditional scheme designs(called type Z errors for short)can contribute up to one-third of the total systematic root-mean-square(RMS)error at the end of second week of the integration and exceed one half of the total amount four weeks afterwards.In contrast,by realizing a total energy conserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors, roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reduced at the end of second week of the integration,and averagely more than one-third reduced at integral time of four weeks afterwards.In addition,experiment results also reveal that,in a sense,the effects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging.展开更多
To improve the energetics in the life cycle of an ideal baroclinic instability case, we develop a Physical Conserving Fidelity model (F-model), and we compare the simulations from the F-model to those of the traditi...To improve the energetics in the life cycle of an ideal baroclinic instability case, we develop a Physical Conserving Fidelity model (F-model), and we compare the simulations from the F-model to those of the traditional global spectral semi-implicit model (control model). The results for spectral kinetic energy and its budget indicate different performances at smaller scales in the two models. A two-way energy flow emerges in the generation and rapid growth stage of the baroclinic disturbance in the F-model. However, only a downscale mechanism dominates in the control model. In the F-model, the meso- and smaller scales are energized initially, and then an active upscale nonlinear cascade occurs. Thus, disturbances at prior scales are forced by both downscale and upscale energy cascades and by conversion from potential energy. An analysis of the eddy kinetic energy budget also shows remarkable enhancement of the energy conversion rate in the F-model. As a result, characteristics of the ideal baroclinic wave are greatly improved in the F-model, in terms of both intensity and time of formation.展开更多
Based on the principle of total energy conservation, we give two important algorithms, the total energy conservation algorithm and the symplectic algorithm, which are established for the spherical shallow water equati...Based on the principle of total energy conservation, we give two important algorithms, the total energy conservation algorithm and the symplectic algorithm, which are established for the spherical shallow water equations. Also, the relation between the two algorithms is analyzed and numerical tests show the efficiency of the algorithms.展开更多
基金Sponsored partly by Priority-Scientific-Projects for China's 7th and 8th Five-Year Plana Priority Project of the Director's Foundation of the Institute of Atmospheric PhysicsChinese Academy of Sciences.
文摘In accordance with a new compensation principle of discrete computations,the traditional meteo- rological global (pseudo-) spectral schemes of barotropic primitive equation (s) are transformed into perfect energy conservative fidelity schemes,thus resolving the problems of both nonlinear computa- tional instability and incomplete energy conservation,and raising the computational efficiency of the traditional schemes. As the numerical tests of the new schemes demonstrate,in solving the problem of energy conser- vation in operational computations,the new schemes can eliminate the (nonlinear) computational in- stability and,to some extent even the (nonlinear) computational diverging as found in the traditional schemes,Further contrasts between new and traditional schemes also indicate that,in discrete opera- tional computations,the new scheme in the case of nondivergence is capable of prolonging the valid in- tegral time of the corresponding traditional scheme,and eliminating certain kind of systematical com- putational“climate drift”,meanwhile increasing its computational accuracy and reducing its amount of computation.The working principle of this paper is also applicable to the problem concerning baroclin- ic primitive equations.
基金The work is supported by the National Natural Science Foundation of China(49675267).
文摘In this paper,two formulation theorems of time-difference fidelity schemes for general quadratic and cubic physical conservation laws are respectively constructed and proved,with earlier major conserving time-discretized schemes given as special cases.These two theorems can provide new mathematical basis for solving basic formulation problems of more types of conservative time- discrete fidelity schemes,and even for formulating conservative temporal-spatial discrete fidelity schemes by combining existing instantly conserving space-discretized schemes.Besides.the two theorems can also solve two large categories of problems about linear and nonlinear computational instability. The traditional global spectral-vertical finite-difference semi-implicit model for baroclinic primitive equations is currently used in many countries in the world for operational weather forecast and numerical simulations of general circulation.The present work,however,based on Theorem 2 formulated in this paper,develops and realizes a high-order total energy conserving semi-implicit time-difference fidelity scheme for global spectral-vertical finite-difference model of baroclinic primitive equations.Prior to this,such a basic formulation problem remains unsolved for long,whether in terms of theory or practice.The total energy conserving semi-implicit scheme formulated here is applicable to real data long-term numerical integration. The experiment of thirteen FGGE data 30-day numerical integration indicates that the new type of total energy conserving semi-implicit fidelity scheme can surely modify the systematic deviation of energy and mass conserving of the traditional scheme.It should be particularly noted that,under the experiment conditions of the present work,the systematic errors induced by the violation of physical laws of conservation in the time-discretized process regarding the traditional scheme designs(called type Z errors for short)can contribute up to one-third of the total systematic root-mean-square(RMS)error at the end of second week of the integration and exceed one half of the total amount four weeks afterwards.In contrast,by realizing a total energy conserving semi-implicit fidelity scheme and thereby eliminating corresponding type Z errors, roughly an average of one-fourth of the RMS errors in the traditional forecast cases can be reduced at the end of second week of the integration,and averagely more than one-third reduced at integral time of four weeks afterwards.In addition,experiment results also reveal that,in a sense,the effects of type Z errors are no less great than that of the real topographic forcing of the model.The prospects of the new type of total energy conserving fidelity schemes are very encouraging.
基金This research was supported by the National Basic Research Program of China (No. 2012CB957804) and the National Natural Science Foundation of China (Grant Nos. 41275109, 41075078 and 41175051).
文摘To improve the energetics in the life cycle of an ideal baroclinic instability case, we develop a Physical Conserving Fidelity model (F-model), and we compare the simulations from the F-model to those of the traditional global spectral semi-implicit model (control model). The results for spectral kinetic energy and its budget indicate different performances at smaller scales in the two models. A two-way energy flow emerges in the generation and rapid growth stage of the baroclinic disturbance in the F-model. However, only a downscale mechanism dominates in the control model. In the F-model, the meso- and smaller scales are energized initially, and then an active upscale nonlinear cascade occurs. Thus, disturbances at prior scales are forced by both downscale and upscale energy cascades and by conversion from potential energy. An analysis of the eddy kinetic energy budget also shows remarkable enhancement of the energy conversion rate in the F-model. As a result, characteristics of the ideal baroclinic wave are greatly improved in the F-model, in terms of both intensity and time of formation.
基金This project is supported by the National Key Planning Development Project for Basic tesearch(GrantNo.1999032801),the National Outstanding Youth Scientist Foundation of China(Grant No.49835109)and the Na-tional Natural Science Foundation of China(Grant
文摘Based on the principle of total energy conservation, we give two important algorithms, the total energy conservation algorithm and the symplectic algorithm, which are established for the spherical shallow water equations. Also, the relation between the two algorithms is analyzed and numerical tests show the efficiency of the algorithms.