Let me shown you the implications of resolution using the WRF model used at the UW.
Here is 36-km resolution--representative of the best we had roughly in the late 1990s--for surface air temperature.
Really just the major features: no hint of valleys, Puget Sound is not apparent. No volcanic peaks.
Here is 12-km, the main resolution run by the National Weather Service today. A bit better, with more definition. No Puget Sound really.
Next 4-km. Far more structure and the valleys are much better defined.
And finally, the best--4/3 km. Run here at the UW for Washington and nearby states, the detail is extraordinary. Much of Puget Sound is defined. Individual river drainages are clearly resolved. You need this resolution to get realistic flow in the Columbia Gorge.
Mount Rainier and other volcanic peaks are clearly evident. In five years or so such resolution will be operational throughout the nation. This image is really beautiful too....you could hang it on the wall as art.
Right now the National Weather Service runs a global model at roughly 25-km resolution, and regionally at 4-km grid spacing. To be able to explicitly simulate thunderstorms one needs to do better than 4-km resolution, with more being better.
In the vertical, the resolution is dependent on the number of layers we have. For our local WRF model we used 37, with more layers near the surface where we really need the detail.
It takes a lot more computer power to make even modest improvements in resolution--every time you double horizontal resolution you need roughly 8 times more computer power. It is not surprising that weather forecasting uses some of the most powerful computers in the world.
Here in the Pacific Northwest we run 36, 12, 4 and 4/3 km resolution forecasts twice a day on clusters of commodity-off the shelf--processors (Intel Nehalem cores). This activity is sponsored by the Northwest Modeling Consortium, a group of Federal, State, and Local Agencies and some private sector firms.