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In ERA-Interim, and often in meteorology, altitudes (the altitude of the land and sea surface, or specific altitudes in the atmosphere) are not represented as geometric altitude (in metres above the spheroid), but as geopotential height (in metres above the geoid). However, ECMWF archive the geopotential (in  m2/s2), not the geopotential height.

How to calculate surface geopotential height

In order to calculate the geopotential height of the land and sea surface (the so called surface geopotential height, or orography):

Surface elevation datasets used by ERA-Interim

In order to define the surface geopotential in ERA-Interim, the ECMWF model uses surface elevation data interpolated from GTOPO30, with some fixes for Antarctica and Greenland. See Chapter 10 Climatological data, of Part IV. Physical processes, of the ERA-Interim model documentation at   https://www.ecmwf.int/search/elibrary/part?solrsort=sort_label%20asc&title=part&secondary_title=31r1.

Spatial reference systems

The ECMWF model assumes the Earth is a perfect sphere, but the geodetic latitude/longitude of the surface elevation datasets are used as if they were the spherical latitude/longitude of the ECMWF model.

ECMWF data is referenced in the horizontal with respect to the WGS84 ellipse (which defines the major/minor axes) but in the vertical it is referenced to the Geoid (EGM96).

Earth model

For data in GRIB1 format (as is the case with ERA-Interim data) the earth model is a sphere with radius = 6367.47 km, as defined in the WMO GRIB Edition 1 specifications, Table 7, GDS Octet 17

For data in NetCDF format (i.e. converted from the native GRIB format to NetCDF), the earth model is inherited from the GRIB data.

Notes

  • The surface geopotential is also available on model levels (at level=1), where it is archived in spectral form.
  • Over oceans the surface geopotential field shows 'spectral ripples', which are a reflection of the fact that the ERA-Interim model is a spectral model and the grid point surface geopotential has been spectrally fitted.
  • For further documentation on surface and single level parameters see the ERA-Interim documentation, specifically Table 7.  
  • The model levels are hybrid pressure/sigma, eg for ERA-Interim. See Chapter 2 Basic equations and discretization of Part III. Dynamics and numerical procedures, of the ERA-Interim model documentation at   https://www.ecmwf.int/search/elibrary/part?solrsort=sort_label%20asc&title=part&secondary_title=31r1.
  • The definition of the 60 model levels, for  ERA-Interim, and the corresponding half-level, ph, and full-level, pf, values of pressure (for a standard atmosphere with a surface pressure of 1013.250 hPa), geopotential and geopotential heights can be found at http://www.ecmwf.int/en/forecasts/documentation-and-support/60-model-levels