Wednesday, October 31, 2018

In Pursuit of Plume Theory - 2

Fig. 1
I. Foreward Ho

Ah yes, when I say "all that 'plume theory' needs is another plume theory" may not excite many folks.

Plume theory deals with the dynamics that cause basal melt water (water flowing along the bottom of glaciers) to flow upwards from the grounding line (end point of an ice sheet / glacier where it turns into an ice shelf) as a "plume".

Fig. 2
As the plume flows upward it is said to melt the face or front of the glacier and possibly the bottom of the ice shelf or tongue of the glacier (e.g. Jenkins, Slater, O'Leary).

That is not the type of plume I am focusing on and modeling.

The hypothetical plume I am focusing on and modeling is: 1) generated all along the entire glacier face that is underwater, 2) all the way down to the grounding line, and 3) all along the entire width of the glacier face.

II. Big Totten

In Totten's case that would be big:
"Totten, which lies due south of Western Australia, currently reaches the ocean in the form of a floating shelf of ice that’s 90 miles by 22 miles in area.

Fig. 3
But the entire region, or what scientists call a "catchment", that could someday flow into the sea in this area is over 200,000 square miles in size — bigger than California.

Moreover, in some areas that ice is close to 2.5 miles thick, with over a mile of that vertical extent reaching below the surface of the ocean. It’s the very definition of vast."
(Antarctica's Totten Glacier, emphasis added). Concerning one of the deeper areas of Totten, it is said that "a deep trough in front of the western TIS cavity, with a maximum depth of 1097 m and a maximum width of 10 km at a depth of 600 m" (Science Direct, emphasis added).

But none of the plume I am hypothesizing is generated by basal melt, it is all generated by a cyclical melt dynamic composed entirely of melt water generated by the melting of the face of the ice.

Just for that one cavity 1097 m x 10 km = a melt zone that is anywhere from 6,000,000 m2 to  10,970,000 m2.

III. The Melt Engine

Every inch of that area has melt potential because ambient seawater is touching it, which as I will elaborate, creates an upward flowing stream, a plume.

Fig. 4
That melt water plume is sandwiched between the ice and the ambient water that "melted it" pursuant to the Second Law of Thermodynamics which holds that heat flows from a warmer source (seawater) to a cooler source (glacial ice).

The resulting melt water stream is less dense than the water that melted it.

So, the melted water is buoyant enough to begin to float toward the surface in a stream that, from all appearances in the model, has an impact as significant, or more, than a basal melt plume has.

My hypothetical plume is only found in deep and wide tidewater glaciers like Totten Glacier in Antarctica (e.g. "IV. Totten's Prime Plume", In Pursuit of Plume Theory).

IV. Relevant TEOS-10 Functions

The functionality is a simple construct which can be described by a small number of TEOS-10 toolkit functions.

I have described the more elementary ones in previous posts (Proof of Concept - 10).

The technique I chose to generate data used in today's graphs (the buoyancy factor) is not overly complicated.

One of the numerical values that the TEOS-10 library (function "gsw_melting_ice_into_seawater") computes is "w_ih_final."

When "w_ih_final" is zero the ice has become plume water, located between the glacier face and the ambient sea water.

At that place and time one can calculate the density of the plume with the TEOS-10 library function "gsw_rho" using two other values ("sa_final" & "ct_final") calculated by the aforesaid TEOS-10 library function "gsw_melting_ice_into_seawater."

The code now in my model is "gsw_rho(sa_final, ct_final, P)" (density of the plume at that depth) and "gsw_rho(SA, CT, P)" (density of the seawater which melted the ice at that depth).

The only thing left to do is subtract the plume density from the seawater density, and that difference gives us a buoyancy factor.

V. Buoyancy Factor Graphs

The graphs today concern the buoyancy factor, which is the difference in density.

The graph at Fig. 1 shows the buoyancy factor at the three shallowest pelagic depths (epi-, meso-, and bathy-) for the Amundsen Sea area.

The other three graphs (Fig. 2, Fig. 3, and Fig. 4) feature the three pelagic depths, one depth for each graph.

The big story is in the Buoyancy F. pane (lower left) in each graph.

Notice that the buoyancy factor grows more over time than any other element.

That is, the increase is more than Specific Enthalpy, more than Conservative Temperature, and more than Absolute Salinity.

This indicates that a strong stream of an upward moving melt water plume at the glacier face may be taking place even in the absence of a basal melt plume.

VI. Conclusion

This may be an important factor as my hypothesis indicates.

There is more work to be done, such as quantifying the melt in terms of mass, graphing the other five areas of Antarctica, and some other issues.

Meanwhile, check out this robust paper (Grounding line retreat of Totten Glacier).

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

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