The Ghost-Water Constant - 4

Fig. 1 USGS table: sea level rise potential
from ice sheet collapse (no ghost-water)

I. A Short Review

I found a recent video (see below), featuring Dr. Mitrovica, concerning both sea level rise (SLR), fall (SLF) and sea level change (SLC) "fingerprinting."

It is a long video, so I added a few comments just above the video, which begin with a time frame reference so that you can go directly to that location if you want to, so as to listen to that detail, if you would rather.

It is probably better to watch the whole shebang if you have the time (the first 30 min. discusses ice sheet gravity issues, the question / answer session at the end is maybe half of it).

In that video he mentions a factor that helps to calculate ghost-water volume: "if the entire Greenland ice sheet were to melt / disintegrate, sea level would fall 100 meters around the coastline of Greenland" (paraphrased).

"Finally," I thought, "now I can redo the ghost-water formula and have it relate, not to just a one meter portion of ice loss," as was done previously (The Ghost-Water Constant, 2, 3; The Gravity of Sea Level Change - 4).

Instead, we can now calculate the full spectrum of ghost-water, as well as being able to fingerprint it the Dredd Blog way (both geographically and geophysically).

II. The Table Revisited

The argument for ghost-water is based on my interpretation of the USGS calculation as to what happens when ice sheet volume on a land mass is dislocated into the ocean which surrounds that land mass.

The USGS's use of the abstract global mean average concept is based ONLY on ice sheet volume loss.

In other words, if you lose "x" volume of ice, then there will be "y" amount of sea level rise.

Notice carefully the implications of the USGS Table featured at Fig. 1, because it does not contain any notion of what happens to cause sea level change (SLC), in terms of ice sheet gravity dynamics.

It does not contain any notion of ocean water that was once held close to the coast by that ice sheet gravity.

Nor does it contain any notion of what happens to sea level when that ghost-water is relocated to the bulge area of the Earth, the bulge caused by the Earth's rotation.

Nor does it mention thermal expansion, land subsidence, or land rebound from the weight of the ice sheet after the ice sheet goes away.

It only includes the dynamic of the ice sheet becoming sea water when that ice leaves the land mass, by melting or by calving, and then enters the sea.

Fig. 2 USGS table modifications (13.95% version)

Since the USGS Table (Fig. 1) has no detail about all of that, I have created a table which contains the foundational concept for displaying that information (Fig. 2).

We know that ice sheet gravity pulls ocean water up against the coastline like a perpetual lunar or solar caused high tide, or like a wind-driven storm surge caused by onshore winds.

The difference is that this "ghost-water high tide" never goes away unless and until the ice mass gravity goes away.

Remember, the foundational concept of ghost-water is that as the ice sheet loses its mass, it also loses its gravitational power associated with that mass (The Gravity of Sea Level Change).

As that gravitational power is distributed elsewhere, along with the mass of the water that was once ice, what happens to the ghost-water?

The answer to that question is: concurrent with the ice melt-water and icebergs, the ghost-water which had been pulled up tight against the shore, is also released.

Both are then free to flow toward the equator (Mitrovica says in the video that it takes about 2 weeks to reach its destination).

As it flows to where ever the geophysical dynamics take it, it has an impact on SLC. along the way, like a tide.

Like all the other ocean water already there at the new location, it too contributes to the Earth's equatorial bulge and global SLC.

III. The Formula Revisited (Greenland)

The wedge formula is a simple, abstract way of finding the volume of the wedge shaped ghost-water area surrounding Greenland and Antarctica (see Fig. 3).

By extrapolation we can use it to roughly estimate the volume of gravity-captured water along Greenland's coast::

Fig. 3 The ghost-water in place (blue wedge)

V = (b * h * l) ÷ 2

where:

b = 2000 km
h = 100 m (full amount)
l = 44,087 km (Greenland coastline length)

Now, let's proceed on to normalizing all of the values into meters:

2,000 km = 2,000,000 m (km * 1000)
44,087 km = 44,087,000 m (km * 1000)

thus:

b = 2,000,000 m
h = 100 m
l = 44,087,000 m

V = (2,000,000 * 100 * 44,087,000) ÷ 2
V = (8.8174 × 10¹⁵ m³) ÷ 2
V = 4.4087 × 10¹⁵ m³

V = 4.4087 × 10¹² km³

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The next thing to do is figure out how much SLC is generated by this seawater once it is relocated:

2.78 x 10^-6 m = 0.00000278 m (1 km³ = 2.78 x 10^-6 m of SLR)
(to convert mm << m, ÷ by 1000 = 0.00000000278 mm)
so: 4.4087 × 10¹² km³ × 0.00000000278 mm = 12,256.186 mm
12,256.186 mm (12.26 m) = 40.21 ft. (÷ mm by 304.8 to get ft.)

Thus, there is an additional 12.26 m (40.21 ft) of global mean average SLC caused by the ghost-water, should all of the Greenland ice sheet melt / collapse into the sea.

On to Antarctica.

IV. The Formula Revisited (Antarctica)

The only thing different with applying the concepts and formulas to Antarctica is the fact that the coastline length and the drop in sea level are different quantities compared to Greenland.

Let's calculate Antarctica's contribution while using the same technique I used with the Greenland data.

But first, we must derive the drop in sea level at Antarctica's coastline, because Mitrovica did not mention that value in the video.

We can do that by comparing Antarctica's magnitude to Greenland's magnitude using the figures recorded @ Fig. 1.

I used all of Greenland's ice volume in the calculation above, so I must also use all of Antarctica's ice volume.

Antarctica's total SLC contribution, per Fig. 1, is: 64.80 m + 8.06 m + 0.46 m = 73.32 m, used as follows:

Let's apply a "Greenland = Antarctica" ratio:

Calculation of Antarctica area SLF

so:

b = 2000 km
h = 1119.39 m (total Antarctica SLF)
l = 17,968 km (Antarctica coastline length)

normalize to meters:

V = (2,000,000 * 1119.39 * 17,968,000) ÷ 2
V = (4.022639904 × 10¹⁶) ÷ 2
V = 2.01 × 10¹⁶ m³

V = 2.01 × 10¹³ km³ 

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The next thing to do is to figure out how much SLC is generated by this quantity of seawater once it is relocated:

2.78 x 10^-6 m = 0.00000278 m (1 km³ = 2.78 x 10^-6 m of SLR)
(for mm << m we divide by 1000, to derive 0.00000000278 mm)
so: 2.01 × 10¹³ km³ × 0.00000000278 mm = 55,914.69 mm
55,914.69 mm (55.92 m) = 183.45 ft. (÷ mm by 304.8 to get ft.)

There is an additional 55.92 m (183.45 ft) of global mean average SLR caused by the ghost-water, should all of Antarctica's ice sheet melt / collapse into the sea.

To use this in SLC fingerprinting, the new estimated ghost-water constant must be calculated.

80.32 m (total SLC due to ice sheet collapsing into ocean per Fig. 1)
68.18 m (total ghost-water: Antarctica (55.92 m) + Greenland (12.26 m))

68.18 ÷ 80.32 = 0.848854582 (* 100 = 84.89)

The new ghost constant for all ice sheet volume is 84.89%.

V. Ramifications

This seems to be an unreal number because it increases the SLC from ice sheet loss by an enormous amount (from 13.95% to 84.89%).

Fig. 4 U.S. East Coast

But, unless the USGS changes its figures or says it included gravity and ghost-water values in its estimations @ Fig. 1, that constant is real in the abstract (they did not know about Woodward / Mitrovica concepts IMO).

The constant will naturally prove to be an imperfect estimate as time goes on, in the sense that the Greenland and Antarctica coastlines are not perfect lines (the figures I used are the currently known values for those coastlines).

For example, those real, geographical coastlines are not that smooth, because they contain zigs and zags, varying depths of water near their shores, and the like.

Fig. 5 Geographical fingerprint

Nevertheless, the basic principle is sound IMO.

Note that one recent figure for thermal expansion was doubled (100% increase compared to my lower 84.89%).

Note also that my lower increase is based on Mitrovica statements made in the video lecture below.

Statements which are more recent, indicating that 100 m of SLF at the Greenland coastline will take place if the Greenland ice sheet completely goes away.

I hope I didn't make any typo and/or math errors.

Check it out to see if I did.

VI. Some New Fingerprints?

So, how does all of this ghost-water stuff change the historical record, made for us by a couple of hundred years of tide gauge station records?

Fig. 6 Geophysical fingerprint

Not a drop higher or lower.

History is history.

The SLC record is a matter of historical reality which the new perspective has nothing to do with.

I mean, in terms of changing the values in historical records, it does nothing.

It will not change the geographical footprints, that is, where the SLC originated (Greenland ice sheet, Antarctica ice sheet, or glaciers).

It will change the geophysical fingerprint, which is the nature of the SLC in terms of

Fig. 7  US West Coast

displacement percentage, ghost-water percentage, and the percentage of other factors, such as thermal expansion, cooling expansion, land-mass subsidence, and land-mass rebound.

But, as you can see in Fig. 4 - Fig. 9, history is neither changed by the error of leaving ghost-water out of the previous understanding, or by the accuracy of including it.

It is a matter of whether or not we grasp the history, or whether we make it up as we go.

Fig. 8 Geographical fingerprint

Scientific discovery takes place as we go, but it does not change history, it merely makes it more understandable.

The largest impact I see from this discovery is its impact on acceleration of SLC in the near future and beyond.

There are countless times when discoveries were rejected then grasped like a cat does when falling through limbs of a tree.

They reject gravity, head downtown, then with eyes very wide open, grasp the gravity of

Fig. 9 Geophysical Fingerprint

their situation.

I expect regular readers to scrutinize this closely.

I have not plugged in the full 84.89% of ghost-water into the module of the Dredd Blog model that does the geophysical fingerprint.

What I did do is double the 13.95% to 27.9%, and I subtracted that 13.95% increase from the displacement percentage (percent calculations have to add up to 100%).

As you can see from Fig. 6, and Fig. 9, it does not change the tide gauge sea level history.

The historical pattern is the same in all cases.

I will await some peer-review comments from regular readers, and will double check the data for awhile.

VII. Conclusion

Fig. 10 USGS table modifications (27.9% version)

Please hurry and make any comments "for" or "against" as soon as possible (if you have any).

But don't go off half cocked, half baked, or any other form of cluelessness.

This is serious business, and as the Dredd Blog "About page" says:

"But for those who submit articles for posting, or who comment, be sure to note that Dredd Blog does not suffer foolishness lightly, so please back up your contrary, or other assertions, with links to evidence which indicates that what you are saying is more than merely unfounded personal opinion (not that it would or would not be accepted for that reason)."

(About Page). Let's not tread too much on logic here, rather, let's use it.

In closing, let me say three things: 1) you can quickly notice the potential changes to SLC by comparing Fig. 2 with Fig. 10; 2) the zone and PSMSL stations featured in the graphs at Fig. 4, 5, and 6 are: Zone AH.SE.NW (East Coast USA: CAMBRIDGE II, Stn. #1295; WASHINGTON DC, Stn. #360; SOLOMON'S ISLAND (BIOL. LAB.), Stn. #412; ANNAPOLIS (NAVAL ACADEMY), Stn. #311; BALTIMORE, Stn. #148; LEWES (BREAKWATER HARBOR), Stn. #224; PHILADELPHIA (PIER 9N), Stn. #135; REEDY POINT, Stn. #786); 3) the zone and PSMSL stations featured in the graphs at Fig. 7, 8, and 9 are: Zone AG.SE.NE (West Coast USA: SOUTH BEACH., Stn. #1196; CHARLESTON II., Stn. #1269; PORT ORFORD., Stn. #1640; CRESCENT CITY., Stn. #378 ; N. SPIT @ HUMBOLDT BAY., Stn. #1639; ARENA COVE @ CALIFORNIA., Stn. #2125; POINT REYES., Stn. #1394; SAN FRANCISCO., Stn. #10; ALAMEDA (NAVAL AIR STATION), Stn. #437).

The next post in this series is here, the previous post in this series is here.

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Another Mitrovica video:

08:00 The use of global mean average has led us astray for 100 years.
15:20 Taking the average assumes the imaginary bathtub model.
16:30 It is completely wrong.
21:00 100m of SLF @ Greenland's coast when all ice sheet is gone.
26:40 The Dutch government did not understand the scenario.
28:40 When the ice sheet melts, all the water is distributed in 2 weeks.
29:30 It is error to say that SLF is due only to the land rising.

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