You say you want "some good papers", but I think you need a book, not an article or articles.
It's a big field, very broad, very well-developed, and quite technical on many levels (physical modeling, numerical propagation of PDEs, filtering/data assimilation). An international cast has contributed results and ideas for decades.
You might be able to find a survey article, but such an article would tend to be written for specialists. It tends to look like this:
http://en.wikipedia.org/wiki/Numerical_weather_prediction
You say you want "some good papers", but I think you need a book, not an article or articles.
It's a big field, very broad, very well-developed, and quite technical on many levels (physical modeling, numerical propagation of PDEs, filtering/data assimilation). An international cast has contributed results and ideas for decades.
You might be able to find a survey article, but such an article would tend to be written for specialists. It tends to look like this:
http://people.sc.fsu.edu/~inavon/pubs/Springer_book.pdf [PDF]
The current state of the art in NWP is probably the ECMWF:
http://www.ecmwf.int/