Abstract
The system of hydrodynamic equations on the rotating earth, which are the equations of motion, the continuity equation of mass and the thermo-dynamical equation, is derived from the variational principle for the field of the meteorological motion. Another conservative quantities of the absolute vorticity are discussed as a whole on the foundation of variational principle which shall become to be available for the numerical prediction.
The merit of the numerical prediction based on Hamilton's canonical equations of the “meteorological field” may be exceedingly remarkable in the long range forecasting. There are some technical “uncertainty” in the long range forecasting. Then, it is necessary to eliminate the small scale disturbances which cause the technical “uncertainty property”. We show the graphical method of numerical prediction based on the Hamilton's canonical equations which take initially space average of the vorticities around the each vortex centre to eliminate the small scale disturbances, as the fundamental study for the extended and long range forecasting.
