The Ghost-Water Constant

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Fig. 1USGS sea level rise potential

In a previous post of a Dredd Blog series, I did some calculations concerning the sea level change (SLC) impact of ice sheet gravity (The Gravity of Sea Level Change - 4).

The result was an additional 11.32 ft. of sea level rise (SLR) for the two locations considered (Antarctica & Greenland).

The description of the phenomenon was "ghost-water" because an additional amount of SLR will take place without any additional calving or melting of ice sheets.

It is totally the result of losing something that can't be seen, ghostly gravity.

The ghost-water is water initially pulled up against the land mass (Greenland) all along the coastline, by the power of the Greenland ice sheet's gravity.

That ghost-water is released to flow elsewhere as the "ghost-gravity" is lost incrementally when the ice sheet mass decreases due to either ice melt or glaciers calving (The Gravity of Sea Level Change).


As it turns out, this ghost-water thingy is a constant which I am naming "gW".

I am going to apply it to all ice (Fig. 1) today, and determine its full value.

The numbers seem scary, so I want to double check the figures that Dr. Mitrovica gave us in the video (see video below).

So, we will start from scratch, initially leaving out Antarctica:

V = (b * h * l) / 2 (the formula)

b = 2000 km
h = 20 m
l = 44,087 km (Greenland coastline length)
...
V = (2,000,000 m * 20 m * 44,087,000 m) / 2
V = (1.76348 × 10¹⁵ m³) / 2 (meters)
V = (1.76348 × 10¹² km³) / 2 (kilometers)
...
(1.76348 × 10¹² km³× 0.00000000278 mm = 4902.4744 mm) / 2
((4902.4744 mm = 16.08 ft. (divide mm by 304.8 to derive feet)) / 2
8.042 feet (2.451m) of additional SLR (by Greenland ghost-water)

(see formula description @ The Gravity of Sea Level Change - 4). Ok, so now let's do Antarctica:

V = (b * h * l) / 2 (the formula)

b = 2000 km
h = 20 m
l = 17,968 km (Antarctica coastline length)
...
V = (2,000,000 m * 20 m * 17,968,000 m) / 2
V = (7.1872 × 10¹⁴ m³) / 2 (meters)
V = (3.5936 × 10¹¹ km³) / 2 (kilometers)
...
(3.5936 × 10¹¹ km³× 0.00000000278 mm = 999.0208 mm) / 2
((999.0208 mm = 3.278 ft. (divide mm by 304.8 to derive feet)) / 2
1.639 feet (0.5m) of additional SLR (by Antarctica ghost-water)

(see  The Gravity of Sea Level Change - 4 ... notice that Greenland and Antarctica were combined in that post). The lesson is that the circumference, i.e. the length of the coastline (e.g. jagged vs. smooth) has an effect on the outcome of the calculation.

According to Fig. 1, having done Greenland and Antarctica, that leaves only 0.45m to consider.

In other words, the non-ice sheet ice reservoirs - e.g. Glacier Bay that are mainly local impact.



The ghost-water is quite real, and should always be considered in SLC / SLR scenarios, it would seem.

To make the ghost-water reality more useful, we must link it to the full potential SLR of 80.32m (Fig. 1).

Nevertheless, there may not be an overarching constant at work here.

I mean a mathematical constant like G, the gravitational constant, and the thingy that the Masons put on their rings and stuff.


I am going to keep thinking about this, because there is at least a ratio of ice mass loss to ghost-water action on SLR in other parts of the globe where ghost-water ends up.

So far, the only place it does not end up is in the declarations of those who talk about "king tide""storm surge""unusual wa wa in my yard" and "God-water!! says Inhofe" ... "you can't tell one Atlantis from another by just one weather event."

We shall see the gravity of all of this.

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Professor Jerry X. Mitrovica on the gravity / axis bulge SLR / SLF issues we don't hear about often enough:

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