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The implementation of the sigma pressure hybrid coordinate into the GFS
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    "The derivation of the hybrid coordinate is based on ECMWF's publications. The distance between the set of equations and the corresponding computer code is considerable and many details have to be specified and expanding. These overly detailed notes attempt to provide a DOCUMENTATION of what was actually derived and coded into the existing GFS over-structure. Attached to these notes is a calling tree of the various key routines of the hybrid GFS with accents on the new hybrid code or the replacement of the old sigma codes. Some of the equations contain partial vertical sums which may be delicate to code. In these cases a detailed exposition of the code is provided for a four level model so that all terms, especially near boundaries are accounted for. It is pointed out that they hybrid sigma-pressure coordinate presented here does not become a pure sigma structure as defined in the current GFS. Comparison of the tendencies produced by NCEP's sigma definition and the corresponding ECMWF definition reveals very similar forecasts at most model levels except at the very top of the model, as expected"--Page 1, paragraphs 1-2.

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