Weighing The Ghost Plumes |
Today I want to share the formulas used to determine plume flow.
I say "formulas" (plural) because there are three that I have used.
The first was alluded to in The Ghost Plumes - 3, but some time after using it I ran across a Phd. dude's post which gave me pause (link to formula discussion).
As a result, I decided to use two formulas, so, today I am making both formulas known.
At this time I am using the one that produces the lesser amount of plume flow volume (pF1).
Both formulas and their results are shown below as applied in each Antarctica Area and relevant Zone.
Descriptions of symbols:
Basic plume formula: pF = pH * pC * pW
pF = plume flow (m3 hr)
pH = plume segment height (m)
pW = Zone grounding line length (m)
pC = plume flow coefficient (m3)
The two formulas (#4 and #10):
Flow formula pF1 (#10): vT = sqrt( ( g*(md-m) )/0.5/p/CD/A )
Flow formula pF2 (#4): a = g * (m - md) / m
West Indian Ocean (Area A)
Zone # | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF1 (m3 hr) | pF2 (m3 hr) |
3603 | 0.0688403 | 34.6443 | 860.482 | 10 | 0.763775 | 948062 | 7.63775 | 30.0923 |
3604 | -0.0231401 | 34.6164 | 766.395 | 10 | 0.634298 | 1070350 | 6.34298 | 20.7417 |
3605 | 0.281317 | 34.6431 | 721.175 | 10 | 0.648371 | 1235950 | 6.48371 | 21.6679 |
3606 | 0.229139 | 34.6526 | 715.644 | 10 | 0.632453 | 1090320 | 6.32453 | 20.6153 |
3700 | -1.39607 | 34.1851 | 257.933 | 10 | 0.575774 | 714801 | 5.75774 | 17.0374 |
3701 | -0.824565 | 34.5352 | 617.485 | 10 | 0.610971 | 858463 | 6.10971 | 19.2002 |
3702 | -1.34776 | 34.3152 | 209.88 | 10 | 0.620941 | 809244 | 6.20941 | 19.8261 |
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 pF1: 44.8658 m3 hr
Area pF2: 149.181 m3 hr
East Indian Ocean (Area B)
Zone # | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF1 (m3 hr) | pF2 (m3 hr) |
3607 | 0.0606724 | 34.6163 | 710.323 | 10 | 0.746347 | 930701 | 7.46347 | 28.7078 |
3608 | 0.197879 | 34.6518 | 722.062 | 10 | 0.655505 | 650146 | 6.55505 | 22.1463 |
3609 | -0.0960948 | 34.6559 | 690.421 | 10 | 0.621981 | 771646 | 6.21981 | 19.9411 |
3610 | 0.13065 | 34.6431 | 710.405 | 10 | 0.626701 | 761075 | 6.26701 | 20.2404 |
3611 | 0.340791 | 34.6676 | 692.437 | 10 | 0.611908 | 1325740 | 6.11908 | 19.2913 |
3612 | 0.464802 | 34.6562 | 686.502 | 10 | 0.633139 | 846227 | 6.33139 | 20.6589 |
3613 | 0.462862 | 34.6709 | 814.429 | 10 | 0.630084 | 707331 | 6.30084 | 20.4692 |
3614 | 0.382971 | 34.6757 | 726.101 | 10 | 0.621112 | 969389 | 6.21112 | 19.8797 |
3615 | 0.664067 | 34.6687 | 640.668 | 10 | 0.602572 | 922960 | 6.02572 | 18.7081 |
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 pF1: 57.4935 m3 hr
Area pF2: 190.043 m3 hr
Ross Sea (Area C)
Zone # | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF1 (m3 hr) | pF2 (m3 hr) |
3616 | 0.575825 | 34.6883 | 645.103 | 10 | 0.749875 | 61040 | 7.49875 | 28.9786 |
3716 | -1.51096 | 34.812 | 320.717 | 10 | 0.660175 | 4323960 | 6.60175 | 22.4296 |
3717 | -0.612367 | 34.6914 | 473.067 | 10 | 0.633166 | 237006 | 6.33166 | 20.6436 |
5715 | -0.0492717 | 34.6465 | 848.63 | 10 | 0.640873 | 1119340 | 6.40873 | 21.1724 |
5816 | -2.02866 | 34.719 | 425 | 10 | 0.504541 | 896480 | 5.04541 | 13.1103 |
5817 | -0.249046 | 34.0439 | 156.846 | 10 | 0.587884 | 493901 | 5.87884 | 17.7525 |
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 pF1: 37.7652 m3 hr
Area pF2: 124.087 m3 hr
Amundsen Sea (Area D)
Zone # | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF1 (m3 hr) | pF2 (m3 hr) |
5711 | -0.142688 | 34.5161 | 627.237 | 10 | 0.726807 | 1163710 | 7.26807 | 27.2197 |
5712 | 0.152066 | 34.4572 | 697.369 | 10 | 0.694898 | 411150 | 6.94898 | 24.8867 |
5713 | -0.218251 | 34.5294 | 563.099 | 10 | 0.700094 | 483060 | 7.00094 | 25.2328 |
5714 | 0.192419 | 34.6324 | 830.27 | 10 | 0.643697 | 1761140 | 6.43697 | 21.35 |
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 pF1: 27.655 m3 hr
Area pF2: 98.6893 m3 hr
Bellingshausen Sea (Area E)
Zone # | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF1 (m3 hr) | pF2 (m3 hr) |
5606 | 0.758933 | 34.6004 | 777.199 | 10 | 0.76556 | 5020760 | 7.6556 | 30.2175 |
5706 | -1.85698 | 34.7307 | 223.625 | 10 | 0.52252 | 3223570 | 5.2252 | 14.0417 |
5707 | -0.0153308 | 34.0506 | 260.114 | 10 | 0.622314 | 2369980 | 6.22314 | 19.9132 |
5708 | -0.0261752 | 34.4337 | 442.97 | 10 | 0.613886 | 1966700 | 6.13886 | 19.3924 |
5709 | 0.207656 | 34.4117 | 569.652 | 10 | 0.601217 | 889963 | 6.01217 | 18.6163 |
5710 | 0.290395 | 34.4819 | 702.498 | 10 | 0.656877 | 1349620 | 6.56877 | 22.2264 |
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 pF1: 37.8237 m3 hr
Area pF2: 124.408 m3 hr
Weddell Sea (Area F)
Zone # | CT | SA | P | pH (m) | pC (m3) | pW (m) | pF1 (m3 hr) | pF2 (m3 hr) |
5605 | -0.0927532 | 34.6689 | 730.356 | 10 | 0.760711 | 789264 | 7.60711 | 29.8246 |
5700 | -1.09699 | 34.4706 | 404.068 | 10 | 0.624751 | 1012350 | 6.24751 | 20.0853 |
5701 | -0.642563 | 34.6466 | 814.246 | 10 | 0.631252 | 1325770 | 6.31252 | 20.5449 |
5702 | -0.83651 | 34.6347 | 655.306 | 10 | 0.645765 | 833240 | 6.45765 | 21.4902 |
5703 | -1.26299 | 34.6922 | 516.555 | 10 | 0.60263 | 573334 | 6.0263 | 18.7041 |
5705 | -1.04155 | 34.7681 | 520.785 | 10 | 0.662964 | 17640 | 6.62964 | 22.6464 |
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 pF1: 39.2807 m3 hr
Area pF2: 133.296 m3 hr
If anyone wants to comment on the two formulas discussed in this post, (preferring one or the other, along with some logic as to why), please feel free to do so.
The data used to produce the tables above was discussed in the previous post of this series.
The next post in this series is here, the previous post in this series is here.
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