Ask HN: Interesting papers on weather prediction?

The other day I was watching the weather forecast on TV, and started wondering exactly what kind of algorithms those meteorological boffins are running on their supercomputers to predict whether or not it will rain tomorrow.

Can anyone suggest some good papers to serve as a technical introduction to information processing/algorithms for weather prediction?

(Target audience: I'm a professional software developer with a working knowledge of data mining and related fields, and a barely-remembered knowledge of high school physics.)