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| Fig. 1 |
I. Background
In the previous two posts of this series (In Pursuit of Plume Theory, 2) I scratched the surface of the hypothesis about a type of glacial plume that is independent of melt water flowing out of the grounding line area of a glacier.
That type of melt water, as you know, is known as basal melt water.
Today I am going deeper into the hypothesis, using the graphic at Fig. 1 in order to depict the basic concept that a non-basal melt water plume spontaneously develops along the subsurface face or front of a tidewater glacier, even though no basal melt water stream may exist at that glacier.
Consider a glacier with a face or front that has one thousand meters under water, and is ten kilometers wide.
When only a one meter plume develops, the arithmetic for that plume looks like this: 1 m (average plume size between the ice and ambient seawater) x 1,000 m (portion of glacier under water) x 10,000 m (10 km wide glacier) = 10,000,000 m3 (ten million cubic meters).
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| Fig. 2 |
That water is continually replenished when it floats toward the ocean surface (or along the bottom of the ice shelf where an ice shelf exists).
It is replenished because the buoyancy created by the difference in density (between the fresher melt water and the ambient ocean saltwater) pushes the melt water upward out of the way.
Then, the ambient ocean saltwater makes contact with the glacial ice once again (since the plume water has floated upward), and the heat transfer & melt cycle repeats itself.
That takes place automatically because heat spontaneously flows from a warmer mass (ocean saltwater) into a cooler mass (glacial ice) pursuant to the Second Law of Thermodynamics.
II. The Test Zones
I have generated Appendices A, B, C, D, E, and F (locations shown @ Fig. 2 above) which have graphs that show the changes in buoyancy (ambient saltwater density minus plume melt water density) at various depths in the Southern Ocean around Antarctica.
The data and graphs indicate that the buoyancy factor has increased over time.
The only way buoyancy can show up in the analysis is that the in situ conditions have become conducive to melting the ice.
Increases in buoyancy indicate that melting conditions are becoming more extant.
This indicates IMO that the warming seawater in contact with Antarctic tidewater glaciers has, at some point in time, started generating plumes that did not exist prior to the warming.
III. Example Source Code
The following C++ source code calculates buoyancy by comparing the density of the melt water to the density of the ambient saltwater.
It is an excerpt from the model I am working on:
/** loop through annual data */
for (unsigned yrPos = 0; yrPos < maxMainYears; yrPos++)
{
/** skip empty years */
if (wodZone[yrPos].year != 0)
{
/** loop through depth data */
for (unsigned dpos = 0; dpos < maxWoddepths; dpos++)
{
/** extract Conservative Temperature & Absolute Salinity */
double CT = wodZone[yrPos].CT[dpos];
double SA = wodZone[yrPos].SA[dpos];
/** use only valid data */
if (CT != invalidWODvalue &&
SA != invalidWODvalue &&
testCT_SA(CT,SA,dpos))
{
/** extract pressure, w_Ih, & t_Ih */
double P = wodZone[yrPos].P[dpos];
double w_Ih = wodZone[yrPos].w_Ih[dpos];
double t_Ih = wodZone[yrPos].t_Ih[dpos];
/** init plume values (to be calculated) */
double sa_final = 0;
double ct_final = 0;
double w_ih_final = 0;
/** calculate plume values with TEOS-10 library function */
gsw_melting_ice_into_seawater(SA,CT,P,w_Ih,t_Ih,
&sa_final,&ct_final,
&w_ih_final);
/** store calculated plume values */
wodZone[yrPos].sa_final[dpos] = sa_final;
wodZone[yrPos].ct_final[dpos] = ct_final;
/*************************************
when w_ih_final is 0 the ice melted
------------------------------------
"Note that when w_Ih_final = 0, the
final seawater is not at the
freezing temperature." - TEOS lib
**************************************/
wodZone[yrPos].w_ih_final[dpos] = w_ih_final;
/*****************************************
ct_final and sa_final are plume values
when the w_id_final value equals zero
******************************************/
if (w_ih_final == 0.0)
{
/** isolate the density values (buoyancy) */
double plume_density = gsw_rho(sa_final, ct_final, P);
double ambient_density = gsw_rho(SA, CT, P);
double diff_density = ambient_density - plume_density;
/** store the bouyancy factor */
if (diff_density > 0.0)
{
wodZone[yrPos].buoyancy[dpos] = diff_density;
}
}
}
} /** for dpos */
} /** if year != 0 */
} /** for yrPos */
It creates the buoyancy factor data displayed in the graphs in Appendices A, B, C, D, E, and F.
IV. Conclusion
The TEOS-10 library functions indicate that, in any of those Appendices A-F detailing areas of Antarctica, the glacial ice (which the ambient tidewater comes in contact with) spontaneously melts at various speeds at various latitudes and longitudes (if they are deep enough, i.e. underwater enough).
I think this may be a source of tidewater glacier disintegration that has not been noticed.
I am going to continue with the WOD in situ measurements to investigate this possibility in full.
The previous post in this series is here.