I. Foreward
Nonintuitive situations in scientific research can cause
communication problems (e.g.
The Gravity of Sea Level Change) .
One example is when one is trying to communicate the answer to the question: "
Why does the TEOS10 function gsw_enthalpy_t_exact indicate that there is more "heat" in deep ocean water than there is in shallow ocean water, even when they are both at the same temperature?"
II. The Area of Concern
I modified a graphic (
Fig. 1) of a tidewater glacier terminus in order to focus on the ocean depth at which the subsurface "face" of such glaciers begin and end.

Fig. 2 Area A (W. Indian Ocean) 
In this case the "face" is the glacial ice from the top of the glacier to the glacier's grounding line below sea level.
For example, the face of Totten Glacier in Antarctica (
WOD Zone 3611) reaches 2,500 meters below sea level (from grounding line up to sea level is ~2500m).

Fig. 3 Area B (E. Indian Ocean) 
With less of a face, Thwaites Glacier in Antarctica (
WOD Zone 5710) is nicknamed "the Doomsday Glacier".
I am providing graphs of the Antarctic areas of those two zones.
They are graphs that detail the
specific enthalpy of those areas.
Today's graph that features Thwaites Glacier's specific enthalpy is at
Fig. 6, and the graph that features Totten Glacier's specific enthalpy is at
Fig. 3.
There are many other glaciers in those graphed areas.
I am mentioning Thwaites and Totten because they represent enough sea level rise to destroy our current global seatradebased civilization (
The Extinction of Robust Sea Ports  10).
III. Enthalpy or Specific Enthalpy?
These entities (enthalpy and specific enthalpy) are described in various and sundry ways:
Simple English view
A chemistry view
The definition of enthalpy Encyclopedia Britannica.
Enthalpy reflects "the capacity to release heat." (Quora).
But, since I use
the TEOS10 toolkit for my seawater thermodynamic computations, that is where I focus my efforts.
One of the TEOS10 documents states: "
The specific enthalpy is therefore a measure of the heat content of the system" (
TEOS10 Primer, p. 8, emphasis added).
That there is "specific enthalpy" as well as "enthalpy" necessitates some clarification:

Fig. 4 Area C (Ross Sea) 
"[formula for enthalpy:] "H = U + pV, where H is the enthalpy of the system, U is the internal energy of the system, p is the pressure of the system, V is the volume of the system.
...
[formula for specific enthalpy:] h = u + pv, where u is the specific internal energy, p is the pressure, and v is specific volume."
(
Wikipedia, emphasis added). Ok, but are capital letters vs lower case letters the only difference?
Either way, since "p is the pressure", it is easy to see that both
enthalpy and
specific enthalpy tend to encapsulate a quantity increase (J / kg) as
the ocean depth (and therefore pressure) increases.
But, is that the gravamen, the essential matter of the situation?
No, because once again "mass unit" comes to the forefront:
"A common practice in sea level research is to analyze separately the variability

Fig. 5 Area D (Amundsen Sea) 
of the steric and mass components of sea level. However, there are conceptual and practical issues that have sometimes been misinterpreted, leading to erroneous and contradictory conclusions on regional sea level variability. The crucial point to be noted is that the steric component does not account for volume changes but does for volume changes per mass unit (i.e., density changes). This indicates that the steric component only represents actual volume changes when the mass of the considered water body remains constant."
(
On Thermal Expansion & Thermal Contraction  38). And this factor dovetails quite well with the "specific enthalpy" vs "enthalpy" consideration:
"Specific Enthalpy is the total energy in a system due to pressure and temperature per unit of mass in that system. Specific enthalpy is used in thermodynamic equations when one wants to know the energy for a given single unit mass of a substance. The SI units for specific enthalpy are kJ/kg (kilojoules per kilogram).
Specific enthalpy is calculated by taking the total enthalpy of the system

Fig. 6 Area E (Bellingshausen Sea) 
and dividing it by the total mass of the system. It is written mathematically as:
h = H/m
where h is the specific enthalpy, H is the enthalpy of the system, and m is the total mass of the system. Specific enthalpy can also be written in terms of specific energy, pressure, and specific volume such that the following equation is true:
h = u + pv
where u is the specific energy, p is the pressure and v is the volume. This is to be seen as the specific enthalpy version of, and not to be confused with, the enthalpy equation:
H = U + pV
where H is the total enthalpy, U is the energy of the work done in the system, p is pressure, and V is the volume of the system."
(
Calcularor Org). It is fundamental that the mass unit (in this case a zone bounded by latitude and longitude lines at various depth slices ... e.g. 1020m) be identified and quantified prior to doing thermal expansion or specific enthalpy calculations.
IV. What About The Graphs?
As we peruse today's graphs, note that they not only concern the context of
specific enthalpy, they also concern the context of thermosteric sea level change (a.k.a. thermal expansion / contraction).

Fig. 7 Area F (Weddell Sea) 
Notice that the graphs are the exact opposite of what is hypothesized in the "
thermal expansion is the greatest cause of sea level rise in the 20th century" myth.
The deepest waters, way down far away from warming sunlight and the global warming induced greenhouse effect at the ocean's surface, is where specific enthalpy (
"a measure of the heat content of the system
") is strongest (
Fig. 2 
Fig. 7).
In other words, all things being the same, the deeper water is where the "heat" is most abundant in terms of Joules per kilogram (J / kg).
The depths and names of depth layers are explained
here.
V. Conclusion
The main cause of that nonintuitive factor
is the pressure at deep depths, where the glacial iceface is most vulnerable to Antarctic current driven warming.
It takes just a little warming down there to cause a lot of melt water to flow upwards in a plume (
Frontal processes on tidewater glaciers).
Other
Conservative Temperature graphs indicate that, in places, those deep waters have warmed about a degree Celsius, like the Earth's atmosphere way above those waters has (
GISS).
The previous post in this series is
here.