A Tale of Two Glaciers

Fig. 1 Where The Money Melt Is

There was a conversation between a lawman and a lawless man.

It went something like this: "Why do you rob banks?" asked the lawman, to which the lawless man replied "That is where the money is!"

Readers of Dredd Blog may wonder why I care about a minority class of glaciers (tidewater glaciers) and a minor section of those glaciers (their terminus) which are found in tidewaters along the coasts of Greenland and Antarctica (e.g. The Ghost Plumes, 2, 3, 4; In Pursuit of Plume Theory, 2, 3).

The answer to that wonder is illustrated in Fig. 1, which shows two glaciers in Greenland.

One of those glaciers is melting rapidly, the other one which is next to it, is melting very slowly by comparison.


The melt-rate difference between the two side-by-side glaciers is not questioned:

"Tracy and Heilprin, marine-terminating glaciers that drain into the eastern end of Inglefield Gulf in northwest Greenland, exhibit remarkably different behaviors despite being adjacent systems. Losing mass since 1892, Tracy Glacier has dramatically accelerated, thinned, and retreated. Heilprin has retreated only slightly during the last century and has remained almost stationary in the most recent decade. Previous studies suggest that Tracy’s base is deeper than Heilprin’s at the calving front (over 600 m, as opposed to the 350 m depth at Heilprin), which exposes it to warmer subsurface waters, resulting in more rapid retreat. We investigate the local oceanographic conditions in Inglefield Gulf and their interactions with Tracy and Heilprin using data collected in 2016 and 2017 as part of NASA’s Oceans Melting Greenland mission. Based on improved estimates of the fjord geometry and 20 temperature and salinity profiles near the fronts of these two glaciers, we find clear evidence that fjord waters are modified by ocean-ice interactions with Tracy Glacier. We find that Tracy thinned by 9.9 m near its terminus between 2016 and 2017, while Heilprin thinned by only 1.8 m."

(Willis et al. 2018, Oceanography, Volume 31, No. 2, emphasis added). But the explanation for the contrast in the two glaciers is questioned.

The authors of that paper adopt basal melt plume theory (BPT) to try to explain the phenomenon.

They do so even when the basal melt water volume of Heilprin is much larger than that of Tracy:

"Heilprin Glacier has a much larger runoff catchment [than Tracy], resulting in higher peak subglacial discharge [but less melt loss and retreat]"

(ibid). Furthermore, the BPT theory is not robust.

Nevertheless, it is in universal use when researchers try to explain tidewater glacial melt.

Using BPT alone, they are evidently unaware of the hypothesis of thermodynamic forcing (ghost plumes).

They also do so even though the following statement is found in the literature:

"However, without direct observations of subglacial channels/outlets or their upwelling plumes, the geometries used in these [BPT] plume models are unvalidated ... Although [BPT] plume theory is idealized, it is currently the primary (almost exclusive) tool for tuning or parameterizing plumes in numerical models."

(Surveying subglacial discharge plumes, emphasis added). There is no consideration that I am aware of for the thermodynamic forces I have set forth in previous Dredd Blog posts outlining the hypothesis of the ghost plumes, or Ghost Plume Theory (GPT).


The essence of general "ocean heat" or specific "tidewater heat" and its impact on tidewater glaciers is not properly addressed by analyzing atmospheric-temperature-caused glacial surface melt, mixed with basal friction melt, as is typically done in current research papers (In Pursuit of Plume Theory, 2, 3; The Ghost Plumes, 2, 3, 4).

Those basal melt dynamics produce fresh basal melt water that exits at the glacier's grounding line, but IMO that is not sufficient to explain the contrast between Tracy and Heilprin.

When we search for "ocean heat"the place to look and analyze is ocean water instead of basal melt water (In Search Of Ocean Heat, 2, 3).

The specific thermodynamic property to look for in ocean water is potential enthalpy (Patterns: Conservative Temperature & Potential Enthalpy, 2).

The specific quantity of potential enthalpy to look for in seawater that comes in contact with tidewater glaciers is the amount of potential enthalpy required to melt the glacial ice.


The proper tool to use in order to determine the potential enthalpy amount (the heat content) is the Thermodynamic Equation Of Seawater - 2010 (TEOS-10).

When basal melt, calving, and the thermodynamic melt of the ghost plumes are added together, then we are where we need to be.

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The following print-out concerns potential enthalpy and melt rates in WOD Zone 7706 where Tracy and Heilprin glaciers are located.

Annual mean averages for the zone are at the end of the Appendix.

Remember that variations from year to year are due to the quantity of in situ measurements, ocean heat variations due to currents, as well as glacial and other changes.

Similar appendices for tidewater glaciers in Antarctica are set forth in The Ghost Plumes - 4.

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Basic plume formula: p^F = p^H * p^C * p^W
p^F = plume flow (m³ hr)
p^H = plume height (m)
p^C = plume flow coefficient (m³ hr)
p^W = plume width (m)

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WOD Zone 7706

Year 1925
p^H = 145 m
p^C = 0.00402374 m³ hr
p^W = 286400 m
p^F = 145 * 0.00402374 * 286400
1925 zone plume potential: 167098 m³ hr

Year 1928
p^H = 990 m
p^C = 0.0177538 m³ hr
p^W = 286400 m
p^F = 990 * 0.0177538 * 286400
1928 zone plume potential: 5.03383e+06 m³ hr

Year 1940
p^H = 995 m
p^C = 0.0174987 m³ hr
p^W = 286400 m
p^F = 995 * 0.0174987 * 286400
1940 zone plume potential: 4.98656e+06 m³ hr

Year 1946
p^H = 245 m
p^C = 0.00540238 m³ hr
p^W = 286400 m
p^F = 245 * 0.00540238 * 286400
1946 zone plume potential: 379074 m³ hr

Year 1948
p^H = 25 m
p^C = 0.000323834 m³ hr
p^W = 286400 m
p^F = 25 * 0.000323834 * 286400
1948 zone plume potential: 2318.65 m³ hr

Year 1949
p^H = 10 m
p^C = 7.07012e-05 m³ hr
p^W = 286400 m
p^F = 10 * 7.07012e-05 * 286400
1949 zone plume potential: 202.488 m³ hr

Year 1950
p^H = 120 m
p^C = 0.00161231 m³ hr
p^W = 286400 m
p^F = 120 * 0.00161231 * 286400
1950 zone plume potential: 55412 m³ hr

Year 1951
p^H = 395 m
p^C = 0.00895653 m³ hr
p^W = 286400 m
p^F = 395 * 0.00895653 * 286400
1951 zone plume potential: 1.01323e+06 m³ hr

Year 1952
p^H = 705 m
p^C = 0.0104964 m³ hr
p^W = 286400 m
p^F = 705 * 0.0104964 * 286400
1952 zone plume potential: 2.11934e+06 m³ hr

Year 1953
p^H = 710 m
p^C = 0.00913512 m³ hr
p^W = 286400 m
p^F = 710 * 0.00913512 * 286400
1953 zone plume potential: 1.85757e+06 m³ hr

Year 1954
p^H = 295 m
p^C = 0.00554813 m³ hr
p^W = 286400 m
p^F = 295 * 0.00554813 * 286400
1954 zone plume potential: 468750 m³ hr

Year 1955
p^H = 75 m
p^C = 0.00132919 m³ hr
p^W = 286400 m
p^F = 75 * 0.00132919 * 286400
1955 zone plume potential: 28551 m³ hr

Year 1956
p^H = 80 m
p^C = 0.00141936 m³ hr
p^W = 286400 m
p^F = 80 * 0.00141936 * 286400
1956 zone plume potential: 32520.3 m³ hr

Year 1957
p^H = 230 m
p^C = 0.00379981 m³ hr
p^W = 286400 m
p^F = 230 * 0.00379981 * 286400
1957 zone plume potential: 250301 m³ hr

Year 1958
p^H = 120 m
p^C = 0.00280033 m³ hr
p^W = 286400 m
p^F = 120 * 0.00280033 * 286400
1958 zone plume potential: 96241.7 m³ hr

Year 1959
p^H = 775 m
p^C = 0.014103 m³ hr
p^W = 286400 m
p^F = 775 * 0.014103 * 286400
1959 zone plume potential: 3.1303e+06 m³ hr

Year 1960
p^H = 1120 m
p^C = 0.0231861 m³ hr
p^W = 286400 m
p^F = 1120 * 0.0231861 * 286400
1960 zone plume potential: 7.43737e+06 m³ hr

Year 1961
p^H = 695 m
p^C = 0.0145681 m³ hr
p^W = 286400 m
p^F = 695 * 0.0145681 * 286400
1961 zone plume potential: 2.89975e+06 m³ hr

Year 1962
p^H = 500 m
p^C = 0.0104896 m³ hr
p^W = 286400 m
p^F = 500 * 0.0104896 * 286400
1962 zone plume potential: 1.50211e+06 m³ hr

Year 1963
p^H = 1125 m
p^C = 0.015773 m³ hr
p^W = 286400 m
p^F = 1125 * 0.015773 * 286400
1963 zone plume potential: 5.08206e+06 m³ hr

Year 1964
p^H = 870 m
p^C = 0.0168553 m³ hr
p^W = 286400 m
p^F = 870 * 0.0168553 * 286400
1964 zone plume potential: 4.1998e+06 m³ hr

Year 1965
p^H = 845 m
p^C = 0.0194328 m³ hr
p^W = 286400 m
p^F = 845 * 0.0194328 * 286400
1965 zone plume potential: 4.7029e+06 m³ hr

Year 1966
p^H = 1530 m
p^C = 0.0364881 m³ hr
p^W = 286400 m
p^F = 1530 * 0.0364881 * 286400
1966 zone plume potential: 1.59888e+07 m³ hr

Year 1967
p^H = 90 m
p^C = 0.00207688 m³ hr
p^W = 286400 m
p^F = 90 * 0.00207688 * 286400
1967 zone plume potential: 53533.6 m³ hr

Year 1968
p^H = 110 m
p^C = 0.00229481 m³ hr
p^W = 286400 m
p^F = 110 * 0.00229481 * 286400
1968 zone plume potential: 72295.7 m³ hr

Year 1969
p^H = 965 m
p^C = 0.0182011 m³ hr
p^W = 286400 m
p^F = 965 * 0.0182011 * 286400
1969 zone plume potential: 5.03034e+06 m³ hr

Year 1970
p^H = 505 m
p^C = 0.0100456 m³ hr
p^W = 286400 m
p^F = 505 * 0.0100456 * 286400
1970 zone plume potential: 1.45292e+06 m³ hr

Year 1971
p^H = 90 m
p^C = 0.00165645 m³ hr
p^W = 286400 m
p^F = 90 * 0.00165645 * 286400
1971 zone plume potential: 42696.6 m³ hr

Year 1972
p^H = 550 m
p^C = 0.00997612 m³ hr
p^W = 286400 m
p^F = 550 * 0.00997612 * 286400
1972 zone plume potential: 1.57144e+06 m³ hr

Year 1977
p^H = 135 m
p^C = 0.00214996 m³ hr
p^W = 286400 m
p^F = 135 * 0.00214996 * 286400
1977 zone plume potential: 83126.3 m³ hr

Year 1980
p^H = 180 m
p^C = 0.00385248 m³ hr
p^W = 286400 m
p^F = 180 * 0.00385248 * 286400
1980 zone plume potential: 198603 m³ hr

Year 1984
p^H = 655 m
p^C = 0.0110339 m³ hr
p^W = 286400 m
p^F = 655 * 0.0110339 * 286400
1984 zone plume potential: 2.06988e+06 m³ hr

Year 1987
p^H = 140 m
p^C = 0.00252381 m³ hr
p^W = 286400 m
p^F = 140 * 0.00252381 * 286400
1987 zone plume potential: 101195 m³ hr

Year 1990
p^H = 770 m
p^C = 0.0146518 m³ hr
p^W = 286400 m
p^F = 770 * 0.0146518 * 286400
1990 zone plume potential: 3.23113e+06 m³ hr

Year 1997
p^H = 415 m
p^C = 0.00624194 m³ hr
p^W = 286400 m
p^F = 415 * 0.00624194 * 286400
1997 zone plume potential: 741892 m³ hr

Year 1998
p^H = 280 m
p^C = 0.00528193 m³ hr
p^W = 286400 m
p^F = 280 * 0.00528193 * 286400
1998 zone plume potential: 423569 m³ hr

Year 1999
p^H = 445 m
p^C = 0.00636883 m³ hr
p^W = 286400 m
p^F = 445 * 0.00636883 * 286400
1999 zone plume potential: 811694 m³ hr

Year 2001
p^H = 310 m
p^C = 0.00691392 m³ hr
p^W = 286400 m
p^F = 310 * 0.00691392 * 286400
2001 zone plume potential: 613846 m³ hr

Year 2003
p^H = 820 m
p^C = 0.0162267 m³ hr
p^W = 286400 m
p^F = 820 * 0.0162267 * 286400
2003 zone plume potential: 3.81081e+06 m³ hr

Year 2006
p^H = 930 m
p^C = 0.0131433 m³ hr
p^W = 286400 m
p^F = 930 * 0.0131433 * 286400
2006 zone plume potential: 3.50074e+06 m³ hr

Year 2007
p^H = 595 m
p^C = 0.00983588 m³ hr
p^W = 286400 m
p^F = 595 * 0.00983588 * 286400
2007 zone plume potential: 1.67611e+06 m³ hr

Year 2016
p^H = 570 m
p^C = 0.00950065 m³ hr
p^W = 286400 m
p^F = 570 * 0.00950065 * 286400
2016 zone plume potential: 1.55096e+06 m³ hr

Year 2017
p^H = 535 m
p^C = 0.012462 m³ hr
p^W = 286400 m
p^F = 535 * 0.012462 * 286400
2017 zone plume potential: 1.90947e+06 m³ hr

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Annual Mean Averages

plume flow (p^F): 2.10187e+06 m³ hr
plume height (p^H): 504.419 (m)
plume flow coefficient (p^C): 0.00943033 (m³ hr)
plume width (p^W): 286400 (m)