Unification of the Anelastic and Quasi-Hydrostatic Systems of Equations

被引:51
作者
Arakawa, Akio [2 ]
Konor, Celal S. [1 ]
机构
[1] Colorado State Univ, Dept Atmospher Sci, Ft Collins, CO 80523 USA
[2] Univ Calif Los Angeles, Dept Atmospher & Ocean Sci, Los Angeles, CA USA
关键词
TERRAIN-FOLLOWING COORDINATE; ELASTIC EQUATIONS; NUMERICAL-METHODS; SCALE ANALYSIS; MODEL; PRESSURE; APPROXIMATION; ATMOSPHERE; CONVECTION; MOTION;
D O I
10.1175/2008MWR2520.1
中图分类号
P4 [大气科学(气象学)];
学科分类号
0706 ; 070601 ;
摘要
A system of equations is presented that unifies the nonhydrostatic anelastic system and the quasi-hydrostatic compressible system for use in global cloud-resolving models. By using a properly defined quasi-hydrostatic density in the continuity equation, the system is fully compressible for quasi-hydrostatic motion and anelastic for purely nonhydrostatic motion. In this way, the system can cover a wide range of horizontal scales from turbulence to planetary waves while filtering vertically propagating sound waves of all scales. The continuity equation is primarily diagnostic because the time derivative of density is calculated from the thermodynamic ( and surface pressure tendency) equations as a correction to the anelastic continuity equation. No reference state is used and no approximations are made in the momentum and thermodynamic equations. An equation that governs the time change of total energy is also derived. Normal-mode analysis on an f plane without the quasigeostrophic approximation and on a midlatitude beta plane with the quasigeostrophic approximation is performed to compare the unified system with other systems. It is shown that the unified system reduces the westward retrogression speed of the ultra-long barotropic Rossby waves through the inclusion of horizontal divergence due to compressibility.
引用
收藏
页码:710 / 726
页数:17
相关论文
共 67 条
[1]  
[Anonymous], 1997, Atmosphere-Ocean, DOI DOI 10.1080/07055900.1997.9687359
[2]  
[Anonymous], 1959, NOTICE MON WEA REV, DOI DOI 10.1175/1520-0493(1959)087,0042:N.2.0.CO
[3]  
2
[4]   Mass conservation and the anelastic approximation [J].
Bannon, Peter R. ;
Chagnon, Jeffrey M. ;
James, Richard P. .
MONTHLY WEATHER REVIEW, 2006, 134 (10) :2989-3005
[5]  
BANNON PR, 1995, J ATMOS SCI, V52, P2302, DOI 10.1175/1520-0469(1995)052<2302:PVCHAA>2.0.CO
[6]  
2
[7]  
BOLIN B, 1956, TELLUS, V8, P61
[8]  
BUBNOVA R, 1995, MON WEATHER REV, V123, P515, DOI 10.1175/1520-0493(1995)123<0515:IOTFEE>2.0.CO
[9]  
2
[10]  
Cote J, 1998, MON WEATHER REV, V126, P1373, DOI 10.1175/1520-0493(1998)126<1373:TOCMGE>2.0.CO