Abstract
The last decades are characterized by significant progress in the development and operational use of modern numerical hydrodynamic methods of the Earth's weather and climate. This was made possible primarily due to modern understanding of the laws governing the basic physical and thermodynamic processes in the atmosphere and the emergence of more advanced mathematical models and effective methods of their implementation. In this chapter, we develop new numerical techniques used to solve the non-stationary problem of general circulation of the atmosphere with a prehistory and the problem of planetary weather forecast.