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I am trying to understand the actual meaning of the ECMWF L137 model levels. In the link I provided, both pressures (in hPa) and heights (in m) are given for every level. But which actually defines the model level, and which is merely included as an indicative value?

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Since it discusses the pressure values setup first, then says:

Also provided are the Geopotential and Geometric heights, the temperature and density of the level based on the 1976 version of the International Civil Aviation Organization (ICAO) Standard Atmosphere...

I would take that to indicate that the vertical coordinates are defined by pressure, which is how I've always believed it to be. And then the other values are just estimates from the standard atmosphere approximation.

In addition https://rda.ucar.edu/datasets/ds115.4/docs/levels.hybrid.html looks to give more details on the vertical setup...

The vertical coordinate parameters define the edges of the atmospheric layers in terms of the surface pressure (in Pascals). The parameters can be considered as being true at the mid-point (in pressure) of a layer for each point. The formula to use to determine edges of the layers is $P_{k+1/2} = A_{k+1/2} + B_{k+1/2}P_s$, where $P_s$ is the surface pressure and $A$ and $B$ are defined in the table.

So others who work on modeling may be able to offer further input on the setup, but from my casual understanding, it looks to definitely be based on pressure :-)

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