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<p class="MsoNormal"><span style="font-size:11.0pt">Hi Xinfeng,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">In terms of z* and the real freshwater flux boundary condition, there is no change between v4r1 and v4r4. The smaller horizontal integral of the Eulerian vertical velocity We (i.e. WVELMASS) in Figure 6 of
your paper is probably because you were looking at the time-mean value. I did a quick calculation of the horizontal integrals of WVELMASS for v4r1. The time-mean value is only a few percent of Sv's, one to two orders of magnitude smaller than that for a particular
month.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Best,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">Ou<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">ecco-support <ecco-support-bounces@mit.edu> on behalf of Xinfeng Liang <xfliang@udel.edu><br>
<b>Date: </b>Saturday, June 29, 2024 at 11:49</span><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:black"> </span><span style="font-size:12.0pt;color:black">AM<br>
<b>To: </b>ecco-support@mit.edu <ecco-support@mit.edu><br>
<b>Subject: </b>[EXTERNAL] Re: [ecco-support] ecco-support Digest, Vol 99, Issue 13<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Hi All,<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">Is it possible that this issue depends on the version of ECCO? I did a similar calculation a long time ago with ECCO v4r1, and the horizontal integrals of We and Wb were both zero (almost). Check out Figure
6 of this paper </span><a href="https://urldefense.us/v3/__https:/agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2017JC012985__;!!PvBDto6Hs4WbVuu7!Ok-hcWt9TcG88ixQI97cvH1tO3Wyfbv4MWBEgUQ0Yn8ECStDb286q4K2C-ErGViPIykRlhk-AF7wmRo7T_Iu-A$"><span style="font-size:12.0pt">https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2017JC012985</span></a><span style="font-size:12.0pt">.
Has anything changed since then that could affect this?<br clear="all">
<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:Helvetica;color:black"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:Helvetica;color:black">Best,<br>
Xinfeng<br>
---------------------------<br>
Xinfeng Liang<br>
Associate Professor<o:p></o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt;font-family:Helvetica;color:black">School of Marine Science and Policy<br>
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<p class="MsoNormal"><span style="font-size:12.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal"><span style="font-size:12.0pt">On Fri, Jun 28, 2024 at 12:00</span><span style="font-size:12.0pt;font-family:"Arial",sans-serif"> </span><span style="font-size:12.0pt">PM <</span><a href="mailto:ecco-support-request@mit.edu"><span style="font-size:12.0pt">ecco-support-request@mit.edu</span></a><span style="font-size:12.0pt">>
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Today's Topics:<br>
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1. Re: Global integral of vertical momentum flux not zero?<br>
(Jean-Michel Campin)<br>
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----------------------------------------------------------------------<br>
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Message: 1<br>
Date: Fri, 28 Jun 2024 11:44:40 -0400<br>
From: Jean-Michel Campin <</span><a href="mailto:jmc@mit.edu" target="_blank"><span style="font-size:12.0pt">jmc@mit.edu</span></a><span style="font-size:12.0pt">><br>
To: "ECCO support list, wider membership" <</span><a href="mailto:ecco-support@mit.edu" target="_blank"><span style="font-size:12.0pt">ecco-support@mit.edu</span></a><span style="font-size:12.0pt">><br>
Subject: Re: [ecco-support] Global integral of vertical momentum flux<br>
not zero?<br>
Message-ID: <</span><a href="mailto:20240628154440.GA20988@ocean.mit.edu" target="_blank"><span style="font-size:12.0pt">20240628154440.GA20988@ocean.mit.edu</span></a><span style="font-size:12.0pt">><br>
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Hi Paola and Fabien,<br>
<br>
Ou is right, the horizontal integral of wVel is not zero because of z*.<br>
With z*, wVel(k) (which corresponf to (H+Eta)/H*w* in the 2004 paper eq 11) is computed<br>
by integrating eq.11 from bottom to level k, <br>
but because the depth H is not uniform everywhere (not a flat bottom)<br>
this second contribution is not zero when integrated vertically to interface k, and this<br>
is the case even if the global integral of d.Eta/dt was zero (which I am not sure it is,<br>
with frrsh water input and seaice, but it's an other story).<br>
<br>
Cheers,<br>
Jean-Michel<br>
<br>
On Fri, Jun 28, 2024 at 03:07:53PM +0000, Menemenlis, Dimitris (US 329B) wrote:<br>
> 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?<br>
> <br>
> 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.<br>
> <br>
> Dimitris<br>
> <br>
> <br>
> On Jun 28, 2024, at 1:51???AM, Paola Cessi <</span><a href="mailto:pcessi@ucsd.edu" target="_blank"><span style="font-size:12.0pt">pcessi@ucsd.edu</span></a><span style="font-size:12.0pt">> wrote:<br>
> <br>
> Hi Ou,<br>
> <br>
> 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.<br>
> <br>
> Can you please enlighten us?<br>
> <br>
> Many thanks,<br>
> Paola<br>
> <br>
> On Jun 27, 2024, at 2:17???AM, Wang, Ou (US 329B) <</span><a href="mailto:ou.wang@jpl.nasa.gov" target="_blank"><span style="font-size:12.0pt">ou.wang@jpl.nasa.gov</span></a><span style="font-size:12.0pt">> wrote:<br>
> <br>
> Hello Fabien,<br>
> <br>
> 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.<br>
> <br>
> Best regards,<br>
> Ou Wang<br>
> <br>
> From: ecco-support <</span><a href="mailto:ecco-support-bounces@mit.edu" target="_blank"><span style="font-size:12.0pt">ecco-support-bounces@mit.edu</span></a><span style="font-size:12.0pt"><mailto:</span><a href="mailto:ecco-support-bounces@mit.edu" target="_blank"><span style="font-size:12.0pt">ecco-support-bounces@mit.edu</span></a><span style="font-size:12.0pt">>>
on behalf of Fabien Roquet <</span><a href="mailto:fabien.roquet@gu.se" target="_blank"><span style="font-size:12.0pt">fabien.roquet@gu.se</span></a><span style="font-size:12.0pt"><mailto:</span><a href="mailto:fabien.roquet@gu.se" target="_blank"><span style="font-size:12.0pt">fabien.roquet@gu.se</span></a><span style="font-size:12.0pt">>><br>
> Date: Monday, June 24, 2024 at 1:15???PM<br>
> To: </span><a href="mailto:ecco-support@mit.edu" target="_blank"><span style="font-size:12.0pt">ecco-support@mit.edu</span></a><span style="font-size:12.0pt"><mailto:</span><a href="mailto:ecco-support@mit.edu" target="_blank"><span style="font-size:12.0pt">ecco-support@mit.edu</span></a><span style="font-size:12.0pt">>
<</span><a href="mailto:ecco-support@mit.edu" target="_blank"><span style="font-size:12.0pt">ecco-support@mit.edu</span></a><span style="font-size:12.0pt"><mailto:</span><a href="mailto:ecco-support@mit.edu" target="_blank"><span style="font-size:12.0pt">ecco-support@mit.edu</span></a><span style="font-size:12.0pt">>><br>
> Subject: [EXTERNAL] [ecco-support] Global integral of vertical momentum flux not zero?<br>
> Hello ECCO team,<br>
> I have downloaded ECCO from PO.DAAC.<br>
> 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?<br>
> See picture for the vertical profile of w, which is of order several Sv.<br>
> Thanks for your help,<br>
> Fabien<br>
> <br>
> <br>
<br>
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End of ecco-support Digest, Vol 99, Issue 13<br>
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