The Ghost Plumes - 7

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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 (p^F₁).

Both formulas and their results are shown below as applied in each Antarctica Area and relevant Zone.

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Descriptions of symbols:

Basic plume formula: p^F = p^H * p^C * p^W
p^F = plume flow (m³ hr)
p^H = plume segment height (m)
p^W = Zone grounding line length (m)
p^C = plume flow coefficient (m³)

The two formulas (#4 and #10):

Flow formula p^F₁ (#10):  vT = sqrt( ( g*(md-m) )/0.5/p/CD/A )
Flow formula p^F₂ (#4):    a = g * (m - md) / m

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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

Zones in area: 10

Zones with...
... 1) a grounding line (p^W)
... 2) in situ data: 7

Area average CT: -0.43032 (deg C)

Area average S_A: 34.5131 (g/kg)

Area average P: 592.713 (dbar)

Combined Zone p^W: 6727190 (m)

Years with in situ data: 198

Area p^F₁: 44.8658 m³ hr

Area p^F₂: 149.181 m³ hr

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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

Zones in area: 9

Zones with...
... 1) a grounding line (p^W)
... 2) in situ data: 9

Area average CT: 0.289844 (deg C)

Area average S_A: 34.6562 (g/kg)

Area average P: 710.372 (dbar)

Combined Zone p^W: 7885215 (m)

Years with in situ data: 445

Area p^F₁: 57.4935 m³ hr

Area p^F₂: 190.043 m³ hr

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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

Zones in area: 15

Zones with...
... 1) a grounding line (p^W)
... 2) in situ data: 6

Area average CT: -0.645747 (deg C)

Area average S_A: 34.6002 (g/kg)

Area average P: 478.227 (dbar)

Combined Zone p^W: 7131727 (m)

Years with in situ data: 170

Area p^F₁: 37.7652 m³ hr

Area p^F₂: 124.087 m³ hr

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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

Zones in area: 8

Zones with...
... 1) a grounding line (p^W)
... 2) in situ data: 4

Area average CT: -0.00411329 (deg C)

Area average S_A: 34.5338 (g/kg)

Area average P: 679.494 (dbar)

Combined Zone p^W: 3819060 (m)

Years with in situ data: 44

Area p^F₁: 27.655 m³ hr

Area p^F₂: 98.6893 m³ hr

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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

Zones in area: 10

Zones with...
... 1) a grounding line (p^W)
... 2) in situ data: 6

Area average CT: -0.106917 (deg C)

Area average S_A: 34.4515 (g/kg)

Area average P: 496.01 (dbar)

Combined Zone p^W: 14820593 (m)

Years with in situ data: 120

Area p^F₁: 37.8237 m³ hr

Area p^F₂: 124.408 m³ hr

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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

Zones in area: 12

Zones with...
... 1) a grounding line (p^W)
... 2) in situ data: 6

Area average CT: -0.828893 (deg C)

Area average S_A: 34.6469 (g/kg)

Area average P: 606.886 (dbar)

Combined Zone p^W: 4551598 (m)

Years with in situ data: 177

Area p^F₁: 39.2807 m³ hr

Area p^F₂: 133.296 m³ hr

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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 previous post in this series is here.