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Thursday, January 10, 2019

The Ghost Plumes - 7

Weighing The Ghost Plumes
Without transparency, readers may not be able to fully grasp how I have detected and "weighed" the ghost thermal 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 PpH (m)pC (m3)pW (m)pF1 (m3 hr)pF2 (m3 hr)
3603 0.0688403 34.6443 860.482100.7637759480627.6377530.0923
3604 -0.0231401 34.6164 766.395100.63429810703506.3429820.7417
3605 0.281317 34.6431 721.175100.64837112359506.4837121.6679
3606 0.229139 34.6526 715.644100.63245310903206.3245320.6153
3700 -1.39607 34.1851 257.933100.5757747148015.7577417.0374
3701 -0.824565 34.5352 617.485100.6109718584636.1097119.2002
3702 -1.34776 34.3152 209.88100.6209418092446.2094119.8261

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 PpH (m)pC (m3)pW (m)pF1 (m3 hr)pF2 (m3 hr)
3607 0.0606724 34.6163 710.323100.7463479307017.4634728.7078
3608 0.197879 34.6518 722.062100.6555056501466.5550522.1463
3609 -0.0960948 34.6559 690.421100.6219817716466.2198119.9411
3610 0.13065 34.6431 710.405100.6267017610756.2670120.2404
3611 0.340791 34.6676 692.437100.61190813257406.1190819.2913
3612 0.464802 34.6562 686.502100.6331398462276.3313920.6589
3613 0.462862 34.6709 814.429100.6300847073316.3008420.4692
3614 0.382971 34.6757 726.101100.6211129693896.2111219.8797
3615 0.664067 34.6687 640.668100.6025729229606.0257218.7081

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 PpH (m)pC (m3)pW (m)pF1 (m3 hr)pF2 (m3 hr)
3616 0.575825 34.6883 645.103100.749875610407.4987528.9786
3716 -1.51096 34.812 320.717100.66017543239606.6017522.4296
3717 -0.612367 34.6914 473.067100.6331662370066.3316620.6436
5715 -0.0492717 34.6465 848.63100.64087311193406.4087321.1724
5816 -2.02866 34.719 425100.5045418964805.0454113.1103
5817 -0.249046 34.0439 156.846100.5878844939015.8788417.7525

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 PpH (m)pC (m3)pW (m)pF1 (m3 hr)pF2 (m3 hr)
5711 -0.142688 34.5161 627.237100.72680711637107.2680727.2197
5712 0.152066 34.4572 697.369100.6948984111506.9489824.8867
5713 -0.218251 34.5294 563.099100.7000944830607.0009425.2328
5714 0.192419 34.6324 830.27100.64369717611406.4369721.35

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 PpH (m)pC (m3)pW (m)pF1 (m3 hr)pF2 (m3 hr)
5606 0.758933 34.6004 777.199100.7655650207607.655630.2175
5706 -1.85698 34.7307 223.625100.5225232235705.225214.0417
5707 -0.0153308 34.0506 260.114100.62231423699806.2231419.9132
5708 -0.0261752 34.4337 442.97100.61388619667006.1388619.3924
5709 0.207656 34.4117 569.652100.6012178899636.0121718.6163
5710 0.290395 34.4819 702.498100.65687713496206.5687722.2264

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 PpH (m)pC (m3)pW (m)pF1 (m3 hr)pF2 (m3 hr)
5605 -0.0927532 34.6689 730.356100.7607117892647.6071129.8246
5700 -1.09699 34.4706 404.068100.62475110123506.2475120.0853
5701 -0.642563 34.6466 814.246100.63125213257706.3125220.5449
5702 -0.83651 34.6347 655.306100.6457658332406.4576521.4902
5703 -1.26299 34.6922 516.555100.602635733346.026318.7041
5705 -1.04155 34.7681 520.785100.662964176406.6296422.6464

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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