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.

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.

III. About The Relevant Values

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 PpH (m)pC (m3)pW (m)pF (m3 hr)
3603 0.0688403 34.6443 860.482100.7637759480627.63775
3604 -0.0231401 34.6164 766.395100.63429810703506.34298
3605 0.281317 34.6431 721.175100.64837112359506.48371
3606 0.229139 34.6526 715.644100.63245310903206.32453
3700 -1.39607 34.1851 257.933100.5757747148015.75774
3701 -0.824565 34.5352 617.485100.6109718584636.10971
3702 -1.34776 34.3152 209.88100.6209418092446.20941

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 PpH (m)pC (m3)pW (m)pF (m3 hr)
3607 0.0606724 34.6163 710.323100.7463479307017.46347
3608 0.197879 34.6518 722.062100.6555056501466.55505
3609 -0.0960948 34.6559 690.421100.6219817716466.21981
3610 0.13065 34.6431 710.405100.6267017610756.26701
3611 0.340791 34.6676 692.437100.61190813257406.11908
3612 0.464802 34.6562 686.502100.6331398462276.33139
3613 0.462862 34.6709 814.429100.6300847073316.30084
3614 0.382971 34.6757 726.101100.6211129693896.21112
3615 0.664067 34.6687 640.668100.6025729229606.02572

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 PpH (m)pC (m3)pW (m)pF (m3 hr)
3616 0.575825 34.6883 645.103100.749875610407.49875
3716 -1.51096 34.812 320.717100.66017543239606.60175
3717 -0.612367 34.6914 473.067100.6331662370066.33166
5715 -0.0492717 34.6465 848.63100.64087311193406.40873
5816 -2.02866 34.719 425100.5045418964805.04541
5817 -0.249046 34.0439 156.846100.5878844939015.87884

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 PpH (m)pC (m3)pW (m)pF (m3 hr)
5711 -0.142688 34.5161 627.237100.72680711637107.26807
5712 0.152066 34.4572 697.369100.6948984111506.94898
5713 -0.218251 34.5294 563.099100.7000944830607.00094
5714 0.192419 34.6324 830.27100.64369717611406.43697

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 PpH (m)pC (m3)pW (m)pF (m3 hr)
5606 0.758933 34.6004 777.199100.7655650207607.6556
5706 -1.85698 34.7307 223.625100.5225232235705.2252
5707 -0.0153308 34.0506 260.114100.62231423699806.22314
5708 -0.0261752 34.4337 442.97100.61388619667006.13886
5709 0.207656 34.4117 569.652100.6012178899636.01217
5710 0.290395 34.4819 702.498100.65687713496206.56877

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 PpH (m)pC (m3)pW (m)pF (m3 hr)
5605 -0.0927532 34.6689 730.356100.7607117892647.60711
5700 -1.09699 34.4706 404.068100.62475110123506.24751
5701 -0.642563 34.6466 814.246100.63125213257706.31252
5702 -0.83651 34.6347 655.306100.6457658332406.45765
5703 -1.26299 34.6922 516.555100.602635733346.0263
5705 -1.04155 34.7681 520.785100.662964176406.62964

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.