Constructions and Applied Examinations of a Kind of Square-Conservative Schemes in High Precision in the Time Direction

In order to meet the needs of work in numerical weather forecast and in numerical simulations for climate change and ocean current, a kind of difference scheme in high precision in the time direction developed from the completely square-conservative difference scheme in explicit way is built by means of the Taylor expansion. A numerical test with 4-wave Rossby-Haurwitz waves on them and an application of them on the monthly mean current the of South China Sea are carried out, from which, it is found that not only do the new schemes have high harmony and approximate precision but also can the time step of the schemes be lengthened and can much computational time be saved. Therefore, they are worth generalizing and applying.