Vertically integrated northward energy flux fields

Datasets and Usage
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I’m doing some atmospheric energy budget work and have some questions about the vertically integrated energy flux fields in ERA5 and ERA-Interim. The specific fields I’m using are:

  • Vertical integral of northward heat flux
  • Vertical integral of northward water vapor flux
  • Vertical integral of northward geopotential flux
  • Vertical integral of northward kinetic energy flux
  • Vertical integral of northward total energy flux

I’d like to know more about how these fields are produced. Here are the specific things I’m wondering:

  1. Does using these fields reduce the numerical error involved compared to doing the product and vertical integral myself? For example, if I took 1-hourly temperature (T) and meridional wind (v) in ERA5, multiplied them together (with a factor of c_p), and then column-integrated, would I get a result that’s lower quality than what’s in the “vertical integral of northward heat flux” field? If so, why?
  2. Is the vertical integral done in the model’s native hybrid coordinate (rather than first interpolating to standard pressure levels)?
  3. Have any of these fields had a mass-flux correction applied to them? The ECMWF technical memorandum located here says in section 4.4 that “It is still necessary to mass adjust energy fluxes and their divergence in [ERA-Interim],” but has that been done for the output fields I listed above? If so, what method was used?
  4. ERA5 includes a “mass-consistent” product containing the same fields I listed above, but with a mass-flux adjustment applied to the wind field. Is the only difference between the mass-consistent versions of these output fields and the base ERA5 versions the fact that the former has had a mass-flux adjustment applied, and the latter hasn’t?
  5. Finally: Are the monthly-mean versions of the fields listed above simply produced by taking a mean of the 1-hourly (or 6-hourly, in ERA-Interim) versions in each calendar month, or is there something more complicated being done?

I know this is a lot to ask, but I’d be happy even with partial answers to the above. I’m just trying to understand exactly where these vertically integrated fields come from. Thanks a lot for any help you can provide!