[ecco-support] Global integral of vertical momentum flux not zero?

[Jean-Michel Campin]

Hi Paola and Fabien,

Ou is right, the horizontal integral of wVel is not zero because of z*.
With z*, wVel(k) (which corresponf to (H+Eta)/H*w* in the 2004 paper eq 11) is computed
by integrating eq.11 from bottom to level k, 
but because the depth H is not uniform everywhere (not a flat bottom)
this second contribution is not zero when integrated vertically to interface k, and this
is the case even if the global integral of d.Eta/dt was zero (which I am not sure it is,
with frrsh water input and seaice, but it's an other story).

Cheers,
Jean-Michel

On Fri, Jun 28, 2024 at 03:07:53PM +0000, Menemenlis, Dimitris (US 329B) wrote:
> Paola, Ou, and Fabien, I wonder if non-zero Evaporation minus Precipitation minus Runoff (EmPmR), including freshwater exchange with sea ice, could be the cause of non-zero WVELMASS in a ???realfreshwaterflux??? MITgcm configuration?
> 
> But these realfreshwaterflux volume fluxes could probably not explain ???order several Sv??? of horizontal integral of w.  Back of the envelope, a 2-cm sea level seasonal cycle of land-to-ocean mass transfer is a ~0.2 Sv vertical velocity at surface.  The Greenland and Antarctic mass loss is of order ~0.01 Sv at the surface.  The seasonal cycle of freshwater exchange with sea ice is ~1 Sv around Antarctica and 0.5 Sv in Arctic.  Subsurface WVELMASS would be proportionately smaller in z* coordinates.
> 
> Dimitris
> 
> 
> On Jun 28, 2024, at 1:51???AM, Paola Cessi <pcessi at ucsd.edu> wrote:
> 
> Hi Ou,
> 
> could you please elaborate of why this is the case? When I look at Adcroft & Campin 2004 (A&C04), even in z* coordinates WVELMASS should have zero horizontal integral. If you look at eq 11 of A&C04, the continuity eqn has an extra term (independent of z) given by \eta_t, but I believe it also has zero area average, when you compare it to (12) in A&C04, because the area integral of E-P is also made to be zero in ECCO. Unless there is something to do with the ice, which is not covered in A&C04, I don???t see why <w> is not zero.
> 
> Can you please enlighten us?
> 
> Many thanks,
> Paola
> 
> On Jun 27, 2024, at 2:17???AM, Wang, Ou (US 329B) <ou.wang at jpl.nasa.gov> wrote:
> 
> Hello Fabien,
> 
> You haven???t missed anything in your calculation. The horizontal integral of area-weighted vertical velocity (WVELMASS) across a particular vertical level does not necessarily equal zero.
> 
> Best regards,
> Ou Wang
> 
> From: ecco-support <ecco-support-bounces at mit.edu<mailto:ecco-support-bounces at mit.edu>> on behalf of Fabien Roquet <fabien.roquet at gu.se<mailto:fabien.roquet at gu.se>>
> Date: Monday, June 24, 2024 at 1:15???PM
> To: ecco-support at mit.edu<mailto:ecco-support at mit.edu> <ecco-support at mit.edu<mailto:ecco-support at mit.edu>>
> Subject: [EXTERNAL] [ecco-support] Global integral of vertical momentum flux not zero?
> Hello ECCO team,
> I have downloaded ECCO from PO.DAAC.
> Using WVELMASS from ECCO_L4_OCEAN_3D_VOLUME_FLUX_LLC0090GRID_DAILY_V4R4, multiplying with rA and summing along i, j, and tiles, I find the horizontal integral of w is not zero. Am I missing something?
> See picture for the vertical profile of w, which is of order several Sv.
> Thanks for your help,
> Fabien
> 
> 

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