Sunday, September 1, 2019

On Thermal Expansion & Thermal Contraction - 42

Fig. 1a SLC All Quads
Fig. 1b Thermal Proportion (All Quads, 10m)
Fig. 1c Thermal Proportion (All Quads, 300m)
Fig. 1d Thermal Proportion (All Quads, 1400m)
I. Child's Play

The sixth grade level explanation for the hypothesis of thermal expansion as 'the' major or even 'a' major cause of sea level rise (SLR) is about the same as the current Phd. level explanation:
"Using a plastic water bottle, food coloring, a straw, and a ruler, Connor was able to measure the water rising inside the water bottle. By shining a heat lamp on the water bottle, he was able to track the water’s height as time went on. After 45 minutes, the temperature rose from 72 degrees Fahrenheit to 113 degrees Fahrenheit causing the water to rise seven centimeters. This experiment clearly showed how the thermal expansion of water can lead to rising sea levels."
(Sixth Grade Science, emphasis added).  The same thermal expansion, if not more, would have happened if the water had been frozen in a freezer (On Thermal Expansion & Thermal Contraction - 37).

Tide gauge station data, teamed up with TEOS-10, offers a more exacting hypothesis (Fig. 1a).

Tide gauge stations, operating for a hundred years prior to the time plastic bottles filled the ocean, tell us that thermosteric sea level rise is a minor player in the sea level change game (On Thermal Expansion & Thermal Contraction, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41).

The current Ocean Heat Content (OHC) models lose the trail of thermal footprints when they confront strong ocean currents and turbulent seawater mixing.

That is because they have not yet adapted to the new standards for oceanography in the grown-up world (Patterns: Conservative Temperature & Potential Enthalpy - 4).

NE Quad (Proportion @ 10m)
NE Quad (Proportion @ 3000m)
NE Quad (Proportion @ 1400m)
II. In Situ Science

To the contrary, when we run 5.5 billion or so in situ measurements through the TEOS-10 toolkit, which is based on the thermodynamics of oceanography advanced by Josiah Gibbs, we come up with a different perspective, which we call reality (The World According To Measurements - 12).
Fig. 2a NW Quad (Proportion @ 10m)
Fig. 2b NW Quad (Proportion @ 300m)
Fig. 2c NW Quad (Proportion @ 1400m)

Fig. 1a shows a TEOS-10 calculated thermal expansion graph compared to a tide gauge station records graph (It's those damn facts messing up a "really fun" hypothesis again).
Fig. 3a SE Quad (Proportion @ 10m)
Fig. 3b SE Quad (Proportion @ 300m)
Fig. 3c SE Quad (Proportion @ 1400m)

III. Logic & Proportion Discovered

Fig. 1b through Fig. 1d show the proportionality patterns among thermal expansion / contraction, Conservative Temperature (CT), and Potential Enthalpy (hO).

Yes, OHC, hO, and CT are the synchronized, proportional thermodynamic properties in seawater that, when properly calculated, produce a scientific trail of thermodynamic equilibrium over the years, at all depths of the ocean.

These dynamics support a more robust hypothesis than the plastic bottle in the bathtub hypothesis does (McDougall, T. J., 2003: Potential enthalpy : A conservative oceanic variable for evaluating heat content and heat fluxes. Journal of Physical Oceanography, 33, 945-963).

IV. Natch
Fig. 4a SW Quad (Proportion @ 10m)
Fig. 4b SW Quad (Proportion @ 300m)
Fig. 4c SW Quad (Proportion @ 1400m)

It is natch and perhaps even intuitive that OHC, Ocean Heat Flux (OHF), CT, and hO are synchronized when measured and calculated properly.

I mean when it is done in the same exact in situ location of the ocean (same depth, same mass & volume of ocean water, same latitude & longitude, and same time) these factors should present the same pattern (not the same digits) when measured and calculated properly.

This is exactly what is shown in today's graphs at Fig. 1b - Fig. 1d, Fig. 2a - Fig. 2c, Fig. 3a - Fig. 3c, and Fig. 4a - Fig. 4c.

I have only recently figured out the exact sequence to use when calculating thermal expansion so as to synchronize the patterns.

Anyway, the quadrants shown in the graphs cover the entire globe of WOD Zones as pointed out here.

Only two of the thermal related values were synchronized in the past, but now we have the ability to show the full panorama of proportion in seawater thermodynamics.

V. Absolute Salinity (SA)

I should point out that the non-thermal property SA is also graphed along with the thermal components mentioned earlier.

As you can see, the non-thermal component SA does not follow the thermal component pattern.

However, it is used when calculating the other components:

z = gsw_z_from_p (depth, lat);
p = gsw_p_from_z (z, lat);
sa = gsw_sa_from_sp (sp, p, lon, lat);
ct = gsw_ct_from_t (sa, t, p);
tec = gsw_alpha (sa, ct, p)
vc = mu * (1 + (tec * (ct - prev_ct)))

[mu is "mass unit"; vc is "volume change per mass unit"; tec is "thermal expansion coefficient"]

(Build Your Own Thermosteric Computational System). The composition of seawater is such that all components are relevant, however, the thermal components are the proportional, synchronized factors being focused on today.

Probably the most difficult to follow is the "ct - prev-ct" portion, which is the timeline oriented part of calculating a thermal expansion and contraction continuum.

When there are gaps of in situ measurements, in terms of a missing year or two every now and then in the timeline, it takes careful consideration to properly fill in the years, or to skip them.

To preserve the pattern of proportion one must deal with each component in the same manner.

In other words, a gap in one is processed as a gap in all of them, so they must be calculated alike and together.

That process generates the synchronization so that when CT goes up, OHC, OHF, hO and thermal expansion also go up.

Likewise, when CT goes down, OHC, OHF, hO, and thermal expansion also go down.

This is not so for the non-thermal components such as SA, because they are not heat-specific parameters.

VI. Closing Comments

I intend to detail more depths, using appendices, in future posts (only 10m, 300m, and 1400m depths are shown today) .

Until then, take five.

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


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  3. Linking thermal components (thermal slc) with heat content (hO) and temperature (CT) at various depths makes scientific sense.

    It is a break through ...

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