In this paper, the writer has found the solutions of the two horizontal dimension waves by use of parameter explaining method with respect to the barotropic vorticity equation of atmospheric motions. It was pointed out that when the air flow was resisted by the forest or mountain areas with forest, the unlike horizontal wind speed shear would be formed on both sides of the central line of the forest. The wind speed shear would result in special precipitation distribution for the forest regions by producing unstable wave energy. When the basic flow was west, for flat forest regions, the rain fall in the north area of the central line was heavier than that in the south area; while in the mountain regions this unstable energy provided by the wind speed shear would produce much more rainy days on the north slope of the mountains than those on the south slope, even though where the moisture is abundant. A check was made against the theory which was derived above by use of the preciptation data of the Xiao Xin An mountains forest to represent the data for flat forest regions located in the eastern low mountain area of the Northeast, and of the Chang Bai Mountains forest for mountain forest regions respectively. The agreement of the theory and observation data was quite satisfactory.