Please, I will like to know how to go about writing a proposal concerning my project on the topic "application of expert systems to weather forecasting in numerical weather prediction."

sori pal, never heard of it. Try the net

If you are writing a proposal, just read an abstract from a similar project you found from google search and make your own proposal from that. Remember, the proposal doesn't matter and your project does not necessarily have to follow everything laid out in your proposal.

I also assume that numerical weather prediction will involve some derivation from the Navier-Stokes equations.