1. Introduction In 1904, Bjerknes pointed out that the future state of the atmosphere could be predicted by integrating the partial differential equations that govern the behavior of the atmosphere, using the observed state of the atmosphere at a particular time as initial fields. In 1922, Lewis Frey Richardson did a numerical prediction by hands and got 1 order larger of pressure change (surface pressure change of 145 mb in 6 hours). (Estimated that it would require a team of 64000 persons to carry out a 24 hours forecast in 24 hours.

2. Introduction In 1928, Courant, Friedrichs and Lewy found that space and time increments chosen to discretize the differential equations have to meet a certain stability requirement (“CFL” criteria). In 1930’s, Rossby and his collaborators found that the large-scale motions in the atmosphere could be represented approximately by a rather simple equation expressing the conservation of absolute vorticity following the motion of air columns.

3. Introduction At the end of World War II, the first electronic computer ENIAC (Electronic Numerical Integrator And Computer) was constructed at Princeton University. In the late 1940’s, Charney, Fjortoft, and Von Neumann used this computer for the first successful numerical forecast, based on integration of the absolute vorticity conservation equation (Charney et al. 1950).

4. Numerical Modeling Components Equations/variables Vertical coordinate Grid staggering Time integration schemes Advection schemes Initial conditions Physics schemes