The Ghost Plumes - 2

Fig. 1 Current Events

Regular readers know that Dredd Blog has been checking out tidewater glaciers in Antarctica.

That is because, among other things, they are impacted by the world's largest current (Fig. 1, cf. The Ghost Plumes).

Recently this study has been focusing on spontaneous plumes.

The spontaneous plumes that are not associated with basal melt plumes are being focused on because they are ghost plumes in the sense that they are not yet finding their way into scientific literature (In Pursuit of Plume Theory, 2, 3).

Even the complete dimensions of tidewater glaciers that are being studied are not finding their way into that literature in a way that would assist in furthering the hypothesis of ghost plumes.

I haven't been able to find datasets that include the width of tidewater glaciers at the point where they contact the ocean (terminus).

There are mentions here and there of the width of some tidewater glaciers on a ad hoc or sporadic basis, but for the most part when dimensions are mentioned it is the length of a glacier, or how far it has receded or advanced.

Fig. 2a

Fig. 2b

Fig. 2c

Fig. 2d

Fig. 2e

Thus, at this time I am not able to report on any specific tidewater glacier's plume width or, therefore,  any specific glacier's plume volume.

At this point I am left with the meta-level computations which I am blogging about at this time. 

The potential plume volume diagram at Fig. 3 depicts a plume as a triangle "P" located between the glacier "G" and the ocean water "O".

If you follow the formula link at Fig. 3 you will note that the calculation for the ghost plume's volume is the same arithmetic and math as the formula used for ice-sheet-gravity based ghost water.

So, I have generated graphs of the melt water volume of ghost plumes at tidewater glaciers based on five arbitrary widths (1km, 5km, 10km, 20km, and 50km).

The depth at the top of the plume is also arbitrary at one meter (1m).

I have, however, calculated the  height or span of potential plumes by processing the conditions (temperature, salinity, and pressure) of the seawater at each Zone in each area (see Appendices A, B, C, D, E, F).

Those values, as regular readers know, are calculated using the world standard TEOS-10 library functions.

The graphs at Fig. 2a - Fig. 2e are graphs of the potential plume volume at one Zone (3611) in one Area (E. Indian Ocean).

I am using that geographic region because that us where Totten glacier is located.

The left hand vertical values on the graphs represent real volumes of plumes (x 10³ m³) at the plume height/span shown in Appendix B, and the width depicted (km) in each graph.

Fig. 3 V = (b * h * l) ÷ 2

The horizontal values represent years in which there are recorded in situ measurements available in various datasets that I use (e.g. WOD, SOCCOM, OMG, WHI).

Note that the volume calculations are only for a "fixed volume".

But, in reality these spontaneous plumes are not "fixed", because they are flowing like a river, or like the basal melt plumes.

So, obviously the next phase in fully presenting this hypothesis is to calculate the velocity of the upward lift (flow) from the bottom of the plume to the top of the plume.

That is a function of the buoyancy or upthrust exerted against the less dense plume melt water.

Since I have found no specific software functions to calculate spontaneous ghost plume velocity, and there are no functions to handle this in the TEOS-10 library or anywhere else I have looked, I must construct those software functions myself.

The Buoyancy Plume Theorists (basal melt scientists) use various hybrid formulas depending on whether they are of the opinion that basal melt water plumes are cone shaped or prism shaped.

I am exploring their prism-shape formulas, and also looking at fundamental hydrology formulas in order to hammer out a solution.

Solving for the velocity of the plume flow is essential for determining the amount of melt water that is entering the ocean so as to contribute to sea level rise.

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