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The models I have in mind are the major global models such as the Global Forecast System (GFS) and the European Center for Medium range Weather Forecasting (ECMWF).

These models produce numerous output and as such there are numerous ways to validate the forecast they produce. I've seen many plots that focus on specific heights on the 500 mb surface to gauge forecast accuracy, but that is all I'm familiar with.

How is model skill and forecast correctness measured? Is it an overall global skill, or are various skills in specific regions of the globe also evaluated? Are these validation results freely available on the internet?

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There are lots of articles that assess global models both locally and globally. They usually focus on a few parameters that are easily comparable with observations (e.g., temperature, wind, surface pressure). A couple of examples of the many available:

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