Vorticity and divergence can be calculated using wind field in numerical forecast. The issue involves the problem of calculating differentiation using observation data, and it is ill-posed in mathematics. In a limited domain, the one-dimensional numerical differentiation can be used to calculate vorticity and divergence, but the method requires that the data along the boundary be accurate. This paper suggests a new method of calculating vorticity and divergence using the periodical function's one-dimensional numerical differentiation algorithm, and comparison is made with usually used difference method. The stream function and velocity potential are calculated using vorticity and divergence, and the initial wind field is reconstructed using the stream function and velocity potential. Results show that the algorithm proposed in this paper is stable, feasible, and its accuracy is superior to the difference method. It provides a new idea that the method mag be used in global meteorology data diagnosis analysis and forecast.