相对垂直加速度和中尺度大气运动方程组

Relative Vertical Acceleration and the Mesoscale Atmospheric Motion Equations

对具有强对流性质的中尺度系统运动的描写,直接采用包含准静力假设的p坐标系或σ坐标系大气运动方程组是不精确又不合理的。因此,必须发展更精确的非静力中尺度大气运动方程组。本文通过引入相对垂直加速度δ和通用(x,y,ζ,t)坐标系(简称ζ坐标系),导出了ζ坐标系中的非静力大气运动方程组。该方程组的垂直运动方程是非静力的,相对垂直加速度δ是可预报的;垂直加速度可由δ直接求得;而δ既直接影响速度场、位势场、质量场和地面气压场,还间接影响温度场。通过对通用ζ坐标系中非静力大气运动方程组的应用,可以很容易地获得p坐标系或σ坐标系及其它垂直坐标系中的非静力大气运动方程组;当δ为零时,则简化为一般包含准静力假设的p坐标系或σ坐标系及其它垂直坐标系中的大气运动方程组。在一般广泛使用的p坐标系或σ坐标系大气运动方程组中,因未考虑δ的贡献,对一些场的预报就会产生误差,较长时间的数值积分会使这种误差积累愈来愈大。显然,新发展的非静力大气运动方程组考虑了δ的贡献,从而消除了这种误差,所以就更为精确,也更适用于对中尺度系统运动的描写和预报。

It is not precise and unreasonable to describe for the motion of the mesoscale systems with severe convective character adopting directly the motion equations in pressure (\%p\%) and sigma (\%σ\%) coordinates included assumption of quasi\|hydrostatic approximation. Therefore the more precise non\|hydrostatic mesoscale atmospheric motion equations must be developed. In this paper, the non\|hydrostatic atmospheric motion equations in (\%x, y, ζ, t\%) (abbreviation \%ζ\%) coordinates has been derived through inducting a relative vertical acceleration delta (\%δ\%) and a generalized \%ζ\% coordinates. In the equations, the vertical motion equation is the non\|hydrostatic; the relative vertical acceleration delta (\%δ\%) is predictable; the vertical acceleration may get directly from \%δ\%; the \%δ\% has directly effect on the fields of the velocity, geopotential height and mass, while the \%δ\% also has indirectly effect on the temperature field. It is quite easy to get the non\|hydrostatic motion equations in the \%p\%\| or the \%σ\%\| as well as other vertical coordinates through the use of the non\|hydrostatic motion equations in the \%ζ\% coordinates. The motion equations in \%p\%\| and σ\| coordinates included assumption of quasi\|hydrostatic approximation are simplifying results of corresponding to the equations when the \%δ\%=0. Because this effect of the \%δ\% did not considered in the atmospheric motion equations in the coordinates included assumption of quasi\|hydrostatic approximation, therefore, the error must be generated for predicting a few fields. This error accumulation must be increased with time increasing of numerical integration. Obviously, the contribution of the \%δ\% has been considered in the developed new non\|hydrostatic atmospheric motion equations, the errors have been removed in the equations. Therefore the equations are more precise and also suitable to describe and predict the motion of the mesoscale systems.