## 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 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.

## Wednesday, January 9, 2019

### In Pursuit of Plume Theory - 4

 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.

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 * pW
pF = plume flow (m3 hr)
pH = plume segment height (m)
pW = Zone grounding-line length (m)
pC = plume flow coefficient (m3)
Here are the area by area and zone by zone calculation results:

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.