Abstract: One of important features in the numerical modelling of motions of atmosphere or ocean consists in the long period prediction.A key point in such simulations is to maintain the intrinsic physical features of the original problem and to preveant the distortion due to the accumulation of numerical errors.This paper takes into account the traditional Semi-Lagrangian integration scheme.A scheme is constructed so as to keep the conservation of total energy and enlarge the time step to one decade times.Besides it is an explicit scheme,it avoids complex matrices.Several preliminary numerical tests show good perspective of this scheme.

Key words: Semi-Lagrangian integration scheme, conservation of total energy, unconditional stability, explicit difference scheme