The idea is nice but weather prediction is a rather complex process. Lets assume you are able to get all the raw data from the weather stations which might be a challenge on its own and a considerable amount of data. After each model run you have a data assimilation process which introduces the new measurements from the time since the last run. And it is not that easy to just throw more processing power on it. The model parameters have to be set carefully. For example you have to fulfill the CFL criterion to get a numerical stable model. That means you have to change the time resolution once you change the space resolution accordingly. There are also parameterisations in weathermodels which replace otherwise very expensive computations. So if you have more processing power available you might want to replace these with a more accurate calculation. But that would mean you had to change the code. And the main problem might be that I am not sure how you would parallelize the model without waiting for other clients to finish their computations.
I think implementing wheather modeling in BOINC is a big challenge.
But there might be areas other than numerical weather prediction better suited for BOINC.
Climate predicion (like climateprediction.net already does) for example is much easier done on BOINC. The difference with climate modeling is that the state of the atmosphere you start your computation with is not important (as it is with weather prediction). In climate modeling you run a model with a certain set of parameters until it is in a equilibrium state. Each host calculates the model with a different set of parameters. Way easier to handle in a BOINC environment than weather forecasting.