Pretty much all of the AI weather prediction models are trained on ECMWF ERA5, which is kinda like a numerical weather prediction model run to forecast at t=0. ERA5 is historical weather data, but it’s a “reanalysis” of it.

Historical weather data is discrete. You need continuous state for weather modelling which is currently achieved through conventional reforecasts using those historical observations.

From a quick read: ECMWF and IBTrACS data - the former is model based (with measurement data crunched), the latter purely observational.