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| The Antarctica |
I. Background
I pointed out in a previous post that calculating thermal plume volume and flow is just about impossible without knowing how far below sea level the grounding line is (In Pursuit of Plume Theory, 2, 3).
To begin with, the reason for the difficulty I just mentioned is that it can't be known precisely at this time how much tidewater glacier ice is in contact with the ambient tidewater (to know that info we must know precisely how much of the ice is in contact with the ambient seawater).
So, today I am presenting a follow-up to the calculations previously presented.
II. A Workaround
Antarctica is such a harsh environment that determining the missing tidewater ice exposure information even once is difficult, but doing so again and again is prohibitive at this time.
Remember that the height value can and does change due to grounding line movement caused by tidewater glacier ice melting, and/or glacier grounding lines retreating (or advancing) from year to year.
To try an end-run around that knowledge barrier, I calculated how much plume volume and flow would be required to raise global mean sea level (GMSL) by ~1.13 mm.
I chose that amount because it is one third of the current annual GMSL rise (GMSLR), which is ~3.4 mm (On Thermal Expansion & Thermal Contraction - 40).
Today I present more calculations showing that with only a ten meter (10 m) vertical ice contact height (plume height), the 10 m amount is more than sufficient to cause a GMSLR of ~1.33 m per year.
Remember that "the rubber meets the road" where ambient tidewater contacts any tidewater glacier's ice at or above the grounding line.
III. About The Relevant Values
The result of the calculations presented later on in this post are based on all in situ measurements contained in the WOD that relate to Antarctica tidewaters.
Additionally, the grounding line values come from the ASAID database as described by a previous post linking to and quoting R. Bindschadler et al. 2011.
Those WOD and ASAID values are converted into TEOS-10 values by software routines in the TEOS-10 toolbox as described previously in this series.
The tables below are summaries of all seawater temperature, salinity, and depth values in all of the zones and areas set forth in them.
"All" means all measurements for every year going back as far as measurements have been taken in Antarctica at a particular zone.
All of those values are combined together, then averaged into one CT, SA, P, pF, pH, pC, and pW value in each table below.
The software that generated the values begins with a 10 m plume height (pH).
But it increases, in increments of 10 m at a time, if the software analysis determines that the hourly volume value is too small.
Those hourly volume values for "Zone's Plume Volume" are displayed in On Thermal Expansion & Thermal Contraction - 40.
They must be matched or exceeded to equate to a ~1.13 mm GMSLR value.
If a "10" is the plume height (pH) in the tables below, it indicates that the minimum value (10 m) was sufficient to produce the hourly plume volume required to raise sea level by ~1.13 mm during a given year.
Note that there are no values higher than the 10 m plume height (pH) in the tables below, indicating that 10 m of glacial ice exposure is sufficient.
This is because the width of the plumes (pW) (grounding lines) is so large that a 10 m height of glacial ice in contact with ambient tidewater is sufficient.
IV. The Calculation Results
The basic plume computations and variables for each table are as follows:
Basic plume formula: pF = pH * pC * pWHere are the area by area and zone by zone calculation results:
pF = plume flow (m3 hr)
pH = plume segment height (m)
pW = Zone grounding-line length (m)
pC = plume flow coefficient (m3)
West Indian Ocean (Area A)
| Zone | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF (m3 hr) |
| 3603 | 0.0688403 | 34.6443 | 860.482 | 10 | 0.763775 | 948062 | 7.63775 |
| 3604 | -0.0231401 | 34.6164 | 766.395 | 10 | 0.634298 | 1070350 | 6.34298 |
| 3605 | 0.281317 | 34.6431 | 721.175 | 10 | 0.648371 | 1235950 | 6.48371 |
| 3606 | 0.229139 | 34.6526 | 715.644 | 10 | 0.632453 | 1090320 | 6.32453 |
| 3700 | -1.39607 | 34.1851 | 257.933 | 10 | 0.575774 | 714801 | 5.75774 |
| 3701 | -0.824565 | 34.5352 | 617.485 | 10 | 0.610971 | 858463 | 6.10971 |
| 3702 | -1.34776 | 34.3152 | 209.88 | 10 | 0.620941 | 809244 | 6.20941 |
Area Summary:
Zones in area: 10
Zones with...
... 1) a grounding line (pW)
... 2) in situ data: 7
Area average CT: -0.43032 (deg C)
Area average SA: 34.5131 (g/kg)
Area average P: 592.713 (dbar)
Combined Zone pW: 6727190 (m)
Years with in situ data: 198
Area pF: 44.8658 m3 hr
East Indian Ocean (Area B)
| Zone | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF (m3 hr) |
| 3607 | 0.0606724 | 34.6163 | 710.323 | 10 | 0.746347 | 930701 | 7.46347 |
| 3608 | 0.197879 | 34.6518 | 722.062 | 10 | 0.655505 | 650146 | 6.55505 |
| 3609 | -0.0960948 | 34.6559 | 690.421 | 10 | 0.621981 | 771646 | 6.21981 |
| 3610 | 0.13065 | 34.6431 | 710.405 | 10 | 0.626701 | 761075 | 6.26701 |
| 3611 | 0.340791 | 34.6676 | 692.437 | 10 | 0.611908 | 1325740 | 6.11908 |
| 3612 | 0.464802 | 34.6562 | 686.502 | 10 | 0.633139 | 846227 | 6.33139 |
| 3613 | 0.462862 | 34.6709 | 814.429 | 10 | 0.630084 | 707331 | 6.30084 |
| 3614 | 0.382971 | 34.6757 | 726.101 | 10 | 0.621112 | 969389 | 6.21112 |
| 3615 | 0.664067 | 34.6687 | 640.668 | 10 | 0.602572 | 922960 | 6.02572 |
Area Summary:
Zones in area: 9
Zones with...
... 1) a grounding line (pW)
... 2) in situ data: 9
Area average CT: 0.289844 (deg C)
Area average SA: 34.6562 (g/kg)
Area average P: 710.372 (dbar)
Combined Zone pW: 7885215 (m)
Years with in situ data: 445
Area pF: 57.4935 m3 hr
Ross Sea (Area C)
| Zone | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF (m3 hr) |
| 3616 | 0.575825 | 34.6883 | 645.103 | 10 | 0.749875 | 61040 | 7.49875 |
| 3716 | -1.51096 | 34.812 | 320.717 | 10 | 0.660175 | 4323960 | 6.60175 |
| 3717 | -0.612367 | 34.6914 | 473.067 | 10 | 0.633166 | 237006 | 6.33166 |
| 5715 | -0.0492717 | 34.6465 | 848.63 | 10 | 0.640873 | 1119340 | 6.40873 |
| 5816 | -2.02866 | 34.719 | 425 | 10 | 0.504541 | 896480 | 5.04541 |
| 5817 | -0.249046 | 34.0439 | 156.846 | 10 | 0.587884 | 493901 | 5.87884 |
Area Summary:
Zones in area: 15
Zones with...
... 1) a grounding line (pW)
... 2) in situ data: 6
Area average CT: -0.645747 (deg C)
Area average SA: 34.6002 (g/kg)
Area average P: 478.227 (dbar)
Combined Zone pW: 7131727 (m)
Years with in situ data: 170
Area pF: 37.7652 m3 hr
Amundsen Sea (Area D)
| Zone | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF (m3 hr) |
| 5711 | -0.142688 | 34.5161 | 627.237 | 10 | 0.726807 | 1163710 | 7.26807 |
| 5712 | 0.152066 | 34.4572 | 697.369 | 10 | 0.694898 | 411150 | 6.94898 |
| 5713 | -0.218251 | 34.5294 | 563.099 | 10 | 0.700094 | 483060 | 7.00094 |
| 5714 | 0.192419 | 34.6324 | 830.27 | 10 | 0.643697 | 1761140 | 6.43697 |
Area Summary:
Zones in area: 8
Zones with...
... 1) a grounding line (pW)
... 2) in situ data: 4
Area average CT: -0.00411329 (deg C)
Area average SA: 34.5338 (g/kg)
Area average P: 679.494 (dbar)
Combined Zone pW: 3819060 (m)
Years with in situ data: 44
Area pF: 27.655 m3 hr
Bellingshausen Sea (Area E)
| Zone | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF (m3 hr) |
| 5606 | 0.758933 | 34.6004 | 777.199 | 10 | 0.76556 | 5020760 | 7.6556 |
| 5706 | -1.85698 | 34.7307 | 223.625 | 10 | 0.52252 | 3223570 | 5.2252 |
| 5707 | -0.0153308 | 34.0506 | 260.114 | 10 | 0.622314 | 2369980 | 6.22314 |
| 5708 | -0.0261752 | 34.4337 | 442.97 | 10 | 0.613886 | 1966700 | 6.13886 |
| 5709 | 0.207656 | 34.4117 | 569.652 | 10 | 0.601217 | 889963 | 6.01217 |
| 5710 | 0.290395 | 34.4819 | 702.498 | 10 | 0.656877 | 1349620 | 6.56877 |
Area Summary:
Zones in area: 10
Zones with...
... 1) a grounding line (pW)
... 2) in situ data: 6
Area average CT: -0.106917 (deg C)
Area average SA: 34.4515 (g/kg)
Area average P: 496.01 (dbar)
Combined Zone pW: 14820593 (m)
Years with in situ data: 120
Area pF: 37.8237 m3 hr
Weddell Sea (Area F)
| Zone | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF (m3 hr) |
| 5605 | -0.0927532 | 34.6689 | 730.356 | 10 | 0.760711 | 789264 | 7.60711 |
| 5700 | -1.09699 | 34.4706 | 404.068 | 10 | 0.624751 | 1012350 | 6.24751 |
| 5701 | -0.642563 | 34.6466 | 814.246 | 10 | 0.631252 | 1325770 | 6.31252 |
| 5702 | -0.83651 | 34.6347 | 655.306 | 10 | 0.645765 | 833240 | 6.45765 |
| 5703 | -1.26299 | 34.6922 | 516.555 | 10 | 0.60263 | 573334 | 6.0263 |
| 5705 | -1.04155 | 34.7681 | 520.785 | 10 | 0.662964 | 17640 | 6.62964 |
Area Summary:
Zones in area: 12
Zones with...
... 1) a grounding line (pW)
... 2) in situ data: 6
Area average CT: -0.828893 (deg C)
Area average SA: 34.6469 (g/kg)
Area average P: 606.886 (dbar)
Combined Zone pW: 4551598 (m)
Years with in situ data: 177
Area pF: 39.2807 m3 hr
V. Conclusion
As you can see, the thermal plumes themselves can easily account for one third of GMSLR based on the available WOD and ASAID data.
The previous post in this series is here.
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