Numerical weather models are simulations of the future state of the atmosphere out through time. Millions of observations are used as initial conditions in trillions of calculations which produce a three dimensional image of what the atmosphere might look like at sometime in the future.
The Global Forecast System (GFS) is a planetary numerical weather prediction system comprising of a global computer model and variational analysis run by the United States' National Weather Service (NWS).
Access this Model here from WeatherOnline: GFS
Access this Model here from WeatherOnline: GFS
ECMWF is the European Centre for Medium-Range Weather Forecasts.
It is both a research institute and a 24/7 operational service, producing global numerical weather predictions. The Centre has one of the largest supercomputer facilities and meteorological data archives in the world.
Access this Model here from WeatherOnline: ECMWF