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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?
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<div>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.
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<div>Dimitris</div>
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<div>On Jun 28, 2024, at 1:51 AM, Paola Cessi <pcessi@ucsd.edu> wrote:</div>
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Hi Ou,
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<div>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. </div>
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<div>Can you please enlighten us?</div>
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<div>Many thanks,<br class="Apple-interchange-newline">
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<span style="font-style: normal;">Paola<br>
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<div>On Jun 27, 2024, at 2:17 AM, Wang, Ou (US 329B) <ou.wang@jpl.nasa.gov> wrote:</div>
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<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Hello Fabien,<o:p></o:p></span></div>
<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div>
<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">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.<o:p></o:p></span></div>
<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div>
<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Best regards,<o:p></o:p></span></div>
<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;">Ou Wang<o:p></o:p></span></div>
<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 11pt;"><o:p> </o:p></span></div>
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<b><span style="font-size: 12pt;">From:<span class="Apple-converted-space"> </span></span></b><span style="font-size: 12pt;">ecco-support <<a href="mailto:ecco-support-bounces@mit.edu">ecco-support-bounces@mit.edu</a>> on behalf of Fabien Roquet <<a href="mailto:fabien.roquet@gu.se">fabien.roquet@gu.se</a>><br>
<b>Date:<span class="Apple-converted-space"> </span></b>Monday, June 24, 2024 at 1:15</span><span style="font-size: 12pt; font-family: Arial, sans-serif;"> </span><span style="font-size: 12pt;">PM<br>
<b>To:<span class="Apple-converted-space"> </span></b><a href="mailto:ecco-support@mit.edu">ecco-support@mit.edu</a><span class="Apple-converted-space"> </span><<a href="mailto:ecco-support@mit.edu">ecco-support@mit.edu</a>><br>
<b>Subject:<span class="Apple-converted-space"> </span></b>[EXTERNAL] [ecco-support] Global integral of vertical momentum flux not zero?<o:p></o:p></span></p>
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<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">Hello ECCO team,<o:p></o:p></span></div>
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<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">I have downloaded ECCO from PO.DAAC.<o:p></o:p></span></div>
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<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">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?<o:p></o:p></span></div>
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<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">See picture for the vertical profile of w, which is of order several Sv.<o:p></o:p></span></div>
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<div style="margin: 0in; font-size: 10pt; font-family: Aptos, sans-serif;"><span style="font-size: 12pt;">Thanks for your help,<br>
Fabien<o:p></o:p></span></div>
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