I agree that Machine Learning is not always the right approach but wouldn't it be a relatively inexpensive experiment to see if it could be used for more accurate predictions? I'm surprised that topographical patterns are mapped that precisely when ASOS and AWOs stations are so far apart. Also the weather data from commercial airplanes is so far above the surface that modeling small buildings would be meaningless.
I heard a talk from ex-Googler climate.com (now Monsanto) guys. Their forecasts were accurate enough to build a very profitable insurance business. I bet they used Bayesian rather than FEM techniques.
Is it that 'physics simulation' forecasting is best for short timescales (e.g. < 1 week in the uk), whilst ML can be better for estimating next year's weather statistics in some particular place? (Because your butterfly effect means that simulating the actual weather out to 1 year 'accurately' is not possible).
Presumably any short-term ML forecasting would use the physics simulation as it's main input, and then try to improve slightly on it (e.g. maybe you observe that in a particular small area, the rainfall is on average 10% more than the physics simulation, so your ML method would add 10%, giving you a slight forecast improvement)?
I heard a talk from ex-Googler climate.com (now Monsanto) guys. Their forecasts were accurate enough to build a very profitable insurance business. I bet they used Bayesian rather than FEM techniques.