Abstract: By examining Semi-Lagrangian scheme in atmospheric dynamics,the main conclusions are obtained as follows.(1)The Semi-Lagrangian scheme by Robet is not of absolute stability.(2)The sufficient condition for computationally stability about Semi-Lagrangian scheme is obtained,which is similar with CFL condition.(3)According to characteristics of shallow-water equations,there are two kinds of characteristic surfaces:the stream lines(for slow process) and Monge cone (for fast process).However,the Semi-Lagrangian scheme only contains the first kind.Thus,the second kind and interaction between these kinds should be studied in the future.(4)As global classic solution in atmospheric dynamics equations does not exist generally,global backward integration is not carried out generally.

Key words: semi-Lagrangian scheme, characterististic, backward integration, absolute stability