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| Fig. 1 Tidewater Glacier Areas and Zones |
I. A Brief Review
I began this series by pointing out that, like ghost water around ice sheets, ghost plumes are in effect hidden in plain sight (The Ghost Plumes).
I went on, in subsequent posts in this series, to explain that I think that the "bathtub model" and "thermal expansion model" thinking is what hides the ghost plumes from contemplation (thermal expansion is the "go to guy" when the ice mass loss and sea level data is insufficient to explain sea level change).
That state of being "hidden" is most likely caused by the catch-all buffer hypothesis which says the ocean expands when warmed, so if we can't find enough ice mass loss to account for sea level rise quantities, then we blame it on the mysterious catch-all "thermal expansion".
It is a convenient way out, like what was used to explain sea level fall before we remembered Newton sitting under the apple tree and until NASA caught mean old Mr. Gravity in the act of hiding a great big horde of ghost water (NASA Busts The Ghost).
Finding additional ways the ice could be melting was left by the wayside and the thermal half-truth took charge (On Thermal Expansion & Thermal Contraction - 39).
Then, along came the R. Bindschadler et al. 2011 paper which gave us a good handle on the extent of the grounding lines of tidewater glaciers.
Bindschadler et al. 2011 was recently was followed up by Rignot et al. 2019 which used multi-faceted analyses to tell us more about glacial melt in the tidewaters of Antarctica (Four decades of Antarctic Ice Sheet mass balance from 1979–2017).
II. Measurements, Measurements and Measurements
The gist of the two papers I cited above is that Antarctica is so vast that we have to find non-conventional ways of using measurements to detect what is happening in Antarctica, in terms of tidewater glacial disintegration and their melting.
The Bindschadler crew used photographs of coastal areas taken by satellites to identify where the grounding lines of tidewater glaciers are, then measured the cumulative length of the grounding lines.
The Rignot crew used gravitational readings along with photos to calculate the retreat of tidewater glacier grounding lines to calculate the amount of ice mass loss.
I use both of their research conclusions to try to develop a cognitive radar with which to surmise potential melt in all areas where grounding lines have been detected.
The analysis is basically: "1) if the grounding lines are "X" meters long in a particular zone; 2) if we can reasonably estimate the amount of the ice face of the glaciers contacted by the tidewater; 3) if we can calculate, using in situ measurements, whether the tidewater is of sufficient Conservative Temperature (CT) and Absolute Salinity (SA) values, as calculated using the TEOS-10 software; then 4) we can make reasonable estimates of plume volume potential."
III. Finding Basic Values
I am still perfecting the calculations concerning the grounding lines, so today I present an updated view of those calculations that were presented in the previous post: The Ghost Plumes - 8.
One thing to remember is that the glacial ice is much closer to pure water than it is to seawater because, among other things, the saltiness is ejected during the freezing process.
For that reason, I believe it is more accurate to use today's 361.841 Gt value as the equivalent of 361,841 m3 of melt water.
Previously I used 365 Gt, so that is not much of a change to cause a redo (but there are also commas in the most recent big numbers!).
The bottom line is that in the final result, shown below, the cubic meter melt water values and the gigaton ice mass values have the same digits (but have a different decimal point location).
The graphic at Fig. 1 shows the geographical locations of the "Areas" and the "Zones" listed below.
Remember that this is a display of the values that would be derived in each Area and in each Zone WHEN the ghost plumes cause one millimeter of global mean sea level rise (1 mm GMSL).
IV. The Results
Note that the Area ("A-F") totals are presented at the end of each area's table, and the grand totals of all those Areas combined is presented after all the Areas have been presented.
So here we go:
(1 mm yr due to 361.841 Gt yr Ice mass loss
caused by plumes of melt water)
RE: Global Mean Sea Level (GMSL)
Melt Water at 361,841 m3 raises GMSL one millimeter
(current total GMSL is ~3.4 mm yr)
RE: Relevant Antarctica Grounding Line (AGL)
AGL length: 47,455,400 m (Bindschadler et al. 2011)
West Indian Ocean (Area A)
Area's Percent of AGL (APGL): 14.1758%
Breakdown by WOD Zones in Area A:
| WOD Zone # | Grounding Line Length (meters) | Zone % of APGL | Zone Plume Volume (m3) | Zone Ice Loss (gigatons) |
| 3603 | 948,062 | 14.093 | 8,192.69 yr 22.4304 day 0.934598 hr | 8.19269 yr 0.0224304 day 0.000934598 hr |
| 3604 | 1,070,350 | 15.9108 | 9,249.44 yr 25.3236 day 1.05515 hr | 9.24944 yr 0.0253236 day 0.00105515 hr |
| 3605 | 1,235,950 | 18.3725 | 10,680.5 yr 29.2416 day 1.2184 hr | 10.6805 yr 0.0292416 day 0.0012184 hr |
| 3606 | 1,090,320 | 16.2077 | 9,422.01 yr 25.7961 day 1.07484 hr | 9.42201 yr 0.0257961 day 0.00107484 hr |
| 3700 | 714,801 | 10.6256 | 6,176.96 yr 16.9116 day 0.70465 hr | 6.17696 yr 0.0169116 day 0.00070465 hr |
| 3701 | 858,463 | 12.7611 | 7,418.42 yr 20.3105 day 0.846272 hr | 7.41842 yr 0.0203105 day 0.000846272 hr |
| 3702 | 809,244 | 12.0295 | 6,993.09 yr 19.146 day 0.797752 hr | 6.99309 yr 0.019146 day 0.000797752 hr |
Area A Totals: Meltwater volume: 58,133.1 m3; Ice Loss: 58.1331 Gt
East Indian Ocean (Area B)
Area's Percent of AGL (APGL): 16.6161%
Breakdown by WOD Zones in Area B:
| WOD Zone # | Grounding Line Length (meters) | Zone % of APGL | Zone Plume Volume (m3) | Zone Ice Loss (gigatons) |
| 3607 | 930,701 | 11.8031 | 8,042.67 yr 22.0196 day 0.917484 hr | 8.04267 yr 0.0220196 day 0.000917484 hr |
| 3608 | 650,146 | 8.24512 | 5,618.25 yr 15.3819 day 0.640913 hr | 5.61825 yr 0.0153819 day 0.000640913 hr |
| 3609 | 771,646 | 9.78598 | 6,668.19 yr 18.2565 day 0.760688 hr | 6.66819 yr 0.0182565 day 0.000760688 hr |
| 3610 | 761,075 | 9.65192 | 6,576.84 yr 18.0064 day 0.750267 hr | 6.57684 yr 0.0180064 day 0.000750267 hr |
| 3611 | 1,325,740 | 16.813 | 11,456.4 yr 31.3659 day 1.30691 hr | 11.4564 yr 0.0313659 day 0.00130691 hr |
| 3612 | 846,227 | 10.7318 | 7,312.68 yr 20.021 day 0.83421 hr | 7.31268 yr 0.020021 day 0.00083421 hr |
| 3613 | 707,331 | 8.97034 | 6,112.41 yr 16.7349 day 0.697286 hr | 6.11241 yr 0.0167349 day 0.000697286 hr |
| 3614 | 969,389 | 12.2937 | 8,376.99 yr 22.9349 day 0.955623 hr | 8.37699 yr 0.0229349 day 0.000955623 hr |
| 3615 | 922,960 | 11.7049 | 7,975.77 yr 21.8365 day 0.909853 hr | 7.97577 yr 0.0218365 day 0.000909853 hr |
Area B Totals: Meltwater volume: 68,140.2 m3; Ice Loss: 68.1402 Gt
Ross Sea (Area C)
Area's Percent of AGL (APGL): 20.3385%
Breakdown by WOD Zones in Area C:
| WOD Zone # | Grounding Line Length (meters) | Zone % of APGL | Zone Plume Volume (m3) | Zone Ice Loss (gigatons) |
| 3616 | 61,040 | 0.632426 | 527.478 yr 1.44416 day 0.0601732 hr | 0.527478 yr 0.00144416 day 6.01732e-05 hr |
| 3716 | 4,323,960 | 44.7999 | 37,365.6 yr 102.301 day 4.26256 hr | 37.3656 yr 0.102301 day 0.00426256 hr |
| 3717 | 237,006 | 2.45558 | 2,048.09 yr 5.60737 day 0.23364 hr | 2.04809 yr 0.00560737 day 0.00023364 hr |
| 3816 | 1,050,520 | 10.8843 | 9,078.08 yr 24.8544 day 1.0356 hr | 9.07808 yr 0.0248544 day 0.0010356 hr |
| 3817 | 257,695 | 2.66994 | 2,226.87 yr 6.09685 day 0.254035 hr | 2.22687 yr 0.00609685 day 0.000254035 hr |
| 5715 | 1,119,340 | 11.5973 | 9,672.79 yr 26.4827 day 1.10344 hr | 9.67279 yr 0.0264827 day 0.00110344 hr |
| 5815 | 1,211,780 | 12.5551 | 10,471.6 yr 28.6697 day 1.19457 hr | 10.4716 yr 0.0286697 day 0.00119457 hr |
| 5816 | 896,480 | 9.28829 | 7,746.94 yr 21.21 day 0.883749 hr | 7.74694 yr 0.02121 day 0.000883749 hr |
| 5817 | 493,901 | 5.11723 | 4,268.05 yr 11.6853 day 0.486887 hr | 4.26805 yr 0.0116853 day 0.000486887 hr |
Area C Totals: Meltwater volume: 83,405.5 m3; Ice Loss: 83.4055 Gt
Amundsen Sea (Area D)
Area's Percent of AGL (APGL): 8.04768%
Breakdown by WOD Zones in Area D:
| WOD Zone # | Grounding Line Length (meters) | Zone % of APGL | Zone Plume Volume (m3) | Zone Ice Loss (gigatons) |
| 5711 | 1,163,710 | 30.4711 | 10,056.2 yr 27.5324 day 1.14718 hr | 10.0562 yr 0.0275324 day 0.00114718 hr |
| 5712 | 411,150 | 10.7657 | 3,552.96 yr 9.72747 day 0.405311 hr | 3.55296 yr 0.00972747 day 0.000405311 hr |
| 5713 | 483,060 | 12.6487 | 4,174.37 yr 11.4288 day 0.4762 hr | 4.17437 yr 0.0114288 day 0.0004762 hr |
| 5714 | 1,761,140 | 46.1145 | 15,218.9 yr 41.6671 day 1.73613 hr | 15.2189 yr 0.0416671 day 0.00173613 hr |
Area D Totals: Meltwater volume: 33,002.4 m3; Ice Loss: 33.0024 Gt
Bellingshausen Sea (Area E)
Area's Percent of AGL (APGL): 31.2306%
Breakdown by WOD Zones in Area E:
| WOD Zone # | Grounding Line Length (meters) | Zone % of APGL | Zone Plume Volume (m3) | Zone Ice Loss (gigatons) |
| 5606 | 5,020,760 | 33.8769 | 43,387 yr 118.787 day 4.94946 hr | 43.387 yr 0.118787 day 0.00494946 hr |
| 5706 | 3,223,570 | 21.7506 | 27,856.5 yr 76.267 day 3.17779 hr | 27.8565 yr 0.076267 day 0.00317779 hr |
| 5707 | 2,369,980 | 15.9911 | 20,480.2 yr 56.0718 day 2.33632 hr | 20.4802 yr 0.0560718 day 0.00233632 hr |
| 5708 | 1,966,700 | 13.27 | 16,995.3 yr 46.5305 day 1.93877 hr | 16.9953 yr 0.0465305 day 0.00193877 hr |
| 5709 | 889,963 | 6.00491 | 7,690.63 yr 21.0558 day 0.877325 hr | 7.69063 yr 0.0210558 day 0.000877325 hr |
| 5710 | 1,349,620 | 9.10638 | 11,662.8 yr 31.9309 day 1.33045 hr | 11.6628 yr 0.0319309 day 0.00133045 hr |
Area E Totals: Meltwater volume: 128,072 m3; Ice Loss: 128.072 Gt
Weddell Sea (Area F)
Area's Percent of AGL (APGL): 9.5913%
Breakdown by WOD Zones in Area F:
| WOD Zone # | Grounding Line Length (meters) | Zone % of APGL | Zone Plume Volume (m3) | Zone Ice Loss (gigatons) |
| 5605 | 789,264 | 17.3404 | 6,820.44 yr 18.6733 day 0.778056 hr | 6.82044 yr 0.0186733 day 0.000778056 hr |
| 5700 | 1,012,350 | 22.2417 | 8,748.24 yr 23.9514 day 0.997974 hr | 8.74824 yr 0.0239514 day 0.000997974 hr |
| 5701 | 1,325,770 | 29.1276 | 11,456.7 yr 31.3666 day 1.30694 hr | 11.4567 yr 0.0313666 day 0.00130694 hr |
| 5702 | 833,240 | 18.3066 | 7,200.45 yr 19.7138 day 0.821407 hr | 7.20045 yr 0.0197138 day 0.000821407 hr |
| 5703 | 573,334 | 12.5963 | 4,954.47 yr 13.5646 day 0.565192 hr | 4.95447 yr 0.0135646 day 0.000565192 hr |
| 5705 | 17,640 | 0.387557 | 152.436 yr 0.417348 day 0.0173895 hr | 0.152436 yr 0.000417348 day 1.73895e-05 hr |
Area F Totals: Meltwater volume: 39,332.7 m3; Ice Loss: 39.3327 Gt
Antarctica Annual Totals: Meltwater volume: 410,086 m3; Ice Loss: 410.086 Gt
Note: Rignot et al. calculated ice loss at 252 +- 26 Gt/y during 2009-2017 (PNAS)
V. Closing Comments
Note that the Rignot team's value for total gigatons of ice loss is less than that which 1 mm of SLR would compel by my calculations.
That is a good sign because the real scientists always underestimate ;-) ... just kidding ... these values today do not include the "Conservative Temperature (CT) and Absolute Salinity (SA) values, as calculated using the TEOS-10 software" mentioned in Section II above.
These are merely calculations showing what ice melt values would derive @ 1 mm of GMSLR.
I am in the process of fusing the TEOS-10 calculations in The Ghost Plumes - 7
with this calculation set and the Countries With Sea Level Change - 2 set.
But, before it can be universally applied (i.e. include Greenland etc.) I have to derive Greenland etc. values.
In an earlier paper (9 years earlier), Rignot seems to allude to ghost plumes and gives some indication of those values:
"These rates of submarine melting are two orders of magnitude larger than surface melt rates, but comparable to rates of iceberg discharge. We conclude that ocean waters melt a considerable, but highly variable, fraction of the calving fronts of glaciers before they disintegrate into icebergs, and suggest that submarine melting must have a profound influence on grounding-line stability and ice-flow dynamics ... The widespread two to threefold acceleration of the glaciers cannot be explained solely by enhanced lubrication of the bed from surface meltwater, for seasonal variations in glacier velocity do not exceed 8–10%, independent of latitude. Glacier acceleration is instead probably caused by the ungrounding of ice fronts from the bed, which reduces buttressing of inland ice and entrains faster rates of ice flow to the ocean. To unground glaciers from the bed, they must melt and thin. Warmer air temperatures thin the glaciers from the surface and allow the ice flotation margin to migrate inland. Such surface melting is well documented in Greenland. However, melting can also occur along the submarine termini of the glaciers. A warmer ocean will erode submerged grounded ice and cause the grounding line to retreat. In contrast, we know very little about rates of submarine melting along calving fronts. The only measurements of submarine glacier melting so far have been conducted in Alaska"(Rignot et al. 2010, Nature Geoscience, emphasis added). He may have been the first to contemplate ghost plumes.
...
"Surface melt rates in the lower 5 km of the three glacier systems averaged 4–18 cm d−1 in July–August 2008 (highest value in July; refs 12, 14). Our inferred submarine melting rates are two orders of magnitude larger [than 'Surface melt rates']. Submarine melting is therefore a major ablation process across tidewater glacier fronts. This has several important consequences for glacier dynamics. First, submarine melting is more likely to dislodge glaciers from their beds than surface melting. Enhanced submarine melting, either from warmer ocean waters or enhanced forced convection by increased subglacial discharge, will melt grounded ice directly and cause grounding-line retreat. Our data show that a thermal forcing of 3 ◦ C melts ice at a rate of several metres per day, that is, hundreds of metres in one summer. In comparison, an increase in surface melting will be effective at ungrounding a glacier only if the glacier surface slope is low so that the line of hydrostatic equilibrium retreats rapidly with a small change in ice thickness. Furthermore, if the glacier retreats into deeper waters, submarine melting will increase because the submerged area and the pressure-dependent melting point of ice will both increase, two positive feedbacks. Moreover, submarine melting must have an enormous influence on ice calving mechanics. Pronounced submarine melting will undercut the submerged ice faces and promote calving from below the water surface, a mode of calving frequently observed at tidewater termini."
Anyway, I am marshaling their Greenland data for future inclusion along with the Antarctica data shown in the Section IV. tables above.
The previous post in this series is here.
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