In Pursuit of Plume Theory - 4

The Antarctica

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.


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.


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, S_A, P, p^F, p^H, p^C, and p^W value in each table below.

The software that generated the values begins with a 10 m plume height (p^H).

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 (p^H) 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 (p^H) in the tables below, indicating that 10 m of glacial ice exposure is sufficient.

This is because the width of the plumes (p^W) (grounding lines) is so large that a 10 m height of glacial ice in contact with ambient tidewater is sufficient.


The basic plume computations and variables for each table are as follows:

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)

Here are the area by area and zone by zone calculation results:

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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

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^F: 44.8658 m³ hr

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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

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^F: 57.4935 m³ hr

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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

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^F: 37.7652 m³ hr

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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

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^F: 27.655 m³ hr

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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

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^F: 37.8237 m³ hr

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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

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^F: 39.2807 m³ hr

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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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