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

Fri Jul 12 12:12:12 EDT 2024

Hi Ou,

One thing to keep in mind with z* is that "wVel" does not match "w*" of the 2004 z* paper
but is instead "= w* x (H+Eta)/H".

Now with z* and useRealFreshWaterFlux=T :
1) at the surface: wVel is equal to EmPmR/rho_const (EmPmR in kg/m2/s), so it's not zero, 
  and my impression (to confirm) is that the fresh-water balancing that is used here is 
  applied at the top of ocean+seaice, so the horizontal integral of wVel at the surface 
  is not zero (but remains small).
2) at depth, the horizontal integral of wVel is not zero, because of z* and non uniform depth.
  It's probably easier to see it from eq. 11 of the 2004 paper, if you integrate vertically this
  eq from the zery bottom to the level k (at z* = zk*), as done in the model to compute wVel,
  the first term gives (zk* + H)/H d.Eta/dt ; the second term (divergence of horizontal transport)
  will not contribute to horizontal integral ; and the third term is just wVel at zk*.
  With a flat bottom, the depth scaling in the first term can be moved ouside the horizontal integral,
  so that the horizontal integral of wVel will scale as a fraction of the integral of d.Eta/dt
  (and will be small).
  But with a non uniform H (i.e., not a flat bottom), the horizontal integral of wVel 
  is not constrained by the horizontal integral of d.Eta/dt ; it depends on the product
  of d.Eta/dt with (zk* + H)/H and could be larger, especially if, locally, d.Eta/dt is larger
  (e.g. with tides or with higth frequency forcing).

Cheers,
Jean-Michel

On Sat, Jun 29, 2024 at 11:21:23PM +0000, Wang, Ou (US 329B) wrote:
> Hi Jean-Michel,
> 
> Thank you for your clarification regarding the question of non-zero horizontal integral of wVel.
> 
> Because of z* vertical coordinate, would Eta also contribute to non-zero horizontal integral of wVel, even for a level at depth? If so, would the Eta contribution be related to the freshwater exchanges at the ocean surface, including those between sea-ice and ocean, as Dimitris described in his reply to Fabien???s question?
> 
> Thanks,
> Ou
> 
> From: ecco-support <ecco-support-bounces at mit.edu> on behalf of Jean-Michel Campin <jmc at mit.edu>
> Date: Friday, June 28, 2024 at 8:45???AM
> To: ECCO support list, wider membership <ecco-support at mit.edu>
> Subject: [EXTERNAL] Re: [ecco-support] Global integral of vertical momentum flux not zero?
> 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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