Weather and machine learning
Weather prediction should be an extremely good match for machine learning approaches, in fact. What machine learning likes is lots and lots of training data, and weather has a huge amount of that. For instance: if you want to predict what will happen in 24 hours, well, you make the prediction, then you wait 24 hours, and you have the actual data of what really did happen which you can now use to train the system. And that goes on for ever: there is always more training data arriving because you always have data telling you what the conditions are now. And there's just vast amounts of data being puked down from all the sensors. So you get to train the system for ever.
Of course, the problem is that any trained NN-based model will probably be entirely opaque: you can't look inside it and find the bit where it's modelling clouds or something. But, for weather (not climate), that's fine: what matters is only how good the forecasts are, not that the numerical model that made them be comprehensible.
In a previous job I made just this suggestion, although I don't think they did anything about it. Presumably someone will, at which point the people running the big GCMs are going to look a bit silly, if it's not them who moved to machine learning.