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Weather forecast models do include current climatology
Let me expand upon that... weather forecast models use current datasets as inputs to their calculations, this includes amongst other things sea surface temperature, windspeeds, precipitation and so on. They implicitly represent current climatology as the current observation data points includes any changes to date , e.g. look at North Atlantic basin sea surface temps, they have been rising for a while now (outside of El Niño/La Niña).
Weather forecast modelling does not include climate forcing due to the short time frames, so any complaints about the assumptions of stationarity of the climate aren't that relevant. They do not predict future climate as they are not that forward looking.
Re: AI forecast models, some good results are coming out but AI forecast models will not replace the standard ones any time soon. Expect to see hybridised models in the near future. Like any new tech they need iterations to become really useful and the current ones do not capture the extreme weather we can see such as storms. The future might look very different though
What does all this mean? We live on a big wet windy rock in the NE Atlantic expect lots of weather and sometimes the forecast isn't perfect
Meteo de France expalined that in the past they had a regional specialists who checked over the weather forecasts to confirm they were plausible. Cuts mean that's gone down to one for the whole of France so the computer predictions are mostly unchecked and go out raw, with some forecasts that an experienced human would call bollocks on.
@Edukator - they probably thought that as the forecast models improved, they could use less of the experienced (i.e. expensive) staff and save money.
Most of the utility companies did that here in and around the Millennium and quickly found out that they needed to get them back in to tell them the stuff that wasn't in computer models or documented. A lot of people in their mid-50s were suddenly earning good consultancy fees 🤦♂️