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2m temperature is a diagnostic, not a direct output from the atmospheric model.  Forecast screen level variables are not directly evaluated but are determined via knowledge of the the lowest model level temperature (at 10m) and the "skin" temperature of the underlying surface.  In turn the skin temperature is determined via the land surface scheme HTESSEL, or the lake surface scheme FLake, or the sea-surface temperature (through NEMO).  Temperatures at 2m are then derived by interpolation between the forecast 10m temperature and the forecast surface skin temperature.

Fig9.2.-1:  Values at the 2m level (e.g. temperature) are not taken from a model level as such but are computed via interpolation between skin temperature and the level of the lowest atmospheric model level (level 137). 2m dew point is derived from the humidity interpolated in a similar way.  The nature of the interpolation profile used depends on other factors, such as wind speed.

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