摘要
在高空大范围流型的数值预报中技术上的困难问题之一就是如何消去原始高度场或预报高度场里的小扰动.这种小扰动不论是真的,还是假的(原始场中的观测误差,预报场中的截平误差(Truncation error),地转风假定下原始小扰动的虚假发展等等),都不是预报的对象,因此必须用种种平滑化过程设法除去.
It is pointed out in this note that the procedure of smoothing according ■,(■the finite difference Laplacian)used in numerical analysis and forecasting,after every time step,is equivalent to introducing the turbulence term with k=AΔt/(Δs)^(2),where A is the austausch coefficient,Δt the time step and Δs the horizontal grid-size.It is also shown that the rate of damping of the wave for different wave length may be estimated from■,which is a solution of the equation■,with■.It is evident that the small-scale waves damp much more rapidly than the large-scale ones as the damping term involves L^(-2) in the exponential.Damping factor for 24hr with different values of A used by different authors are computed.A proper constant value of A seems to be 5×10^(9)(see tables)for Δs=300km and Δt=1 hr.Richardson’s result of enormous tendency is attributed to the week smoothing with small values of austausch(2×10^(8))for the scale of the motion choosen(l~Δs=400 km).It is easily seen that even with Richardson’s formula A=0.2l^(4/3)(10^(2)<1<10^(6)),the damping effect still increases with the decrease of wave length L,because in this case there is still a factor L^(-2/3)in the exponential of the damping term.Therefore small scale motion is damped very effectively with the value of A given by the above formula.It is emphasized that with turbulence term the smoothing of initial data ahead by a seperate program and the use of balance equation at the initial moment are all not neccessary;and the real instability of the inertiogravitational wave and the false instability in computation will be no longer a serious problem.Thus the work of numerical analysis and forecasting,even with primitive equations of motion,could be carried out with more success.
作者
顾震潮
KOO CHEN-CHAO(Institute of Geophysics and Meteorology,Academia Sinica)
出处
《气象学报》
1957年第4期319-323,共5页
Acta Meteorologica Sinica
