However, climate simulations require long term predictions, thus I think they cannot be based on the same underlying mathematical equations.
From the video: "The climate models that are run at the NCCS are numerical expression of the various processes that make up the climate."
Are different numerical climate models compared on the basis of the underlying mathematical equations?
Are these models at all always based on mathematical equations or do they contain subroutines, which only the team which implemented it understands?
Are the underlying numerical methods stable?
Bringing data from observations together is important, but it creates an database and not necessary an physical simulation.