On Thermal Expansion & Thermal Contraction - 20

Fig. 1 A fusion of GISTEMP & WOD data

I. Some History

The notion of thermal expansion being the major cause of sea level volume change in the 19th, 20th and 21st centuries (over 200 years?) has little substantive support in the scientific literature record.

The records I review indicate a conflicting series of opinions based on a conflicting series of computer software models, even in the official government version of this issue:

A variety of ocean models have been employed for estimates of ocean thermal expansion ... the best estimate of thermal expansion from 1880 to

Fig. 2

1990 was 43 mm (with a range of 31 to 57 mm) (Warrick et al., 1996) ... De Wolde et al. (1995, 1997) developed a two dimensional (latitude-depth, zonally averaged) ocean model, with similar physics to the UD model. Their best estimate of ocean thermal expansion in a model forced by observed sea surface temperatures over the last 100 years was 35 mm (with a range of 22 to 51 mm) ...

(IPCC). The non-government view of the issue is somewhat similar:

The AOGCMs agree that sea-level rise is expected to be geographically

Fig. 3 PSMSL data

non-uniform, with some regions experiencing as much as twice the global average, and others practically zero, but they do not agree about the geographical pattern. The lack of agreement indicates that we cannot currently have con®dence in projections of local sea-level changes, and reveals a need for detailed analysis and intercomparison in order to understand and reduce the disagreements.

(Climate Dynamics, 2001). They seem to be utterly unaware of Woodward 1888, or more recently, Harvard Professor Mitrovica's work (Weekend Rebel Science Excursion - 47).

Thus, the equation given, is missing something hidden in plain sight:

Because GMSL and estimates of the steric and mass components have different uncertainties and the potential for systematic errors, one often investigates the sea level budget to see how well it closes:

GMSL(t) = GMSL_mass(t) + GMSL_steric(t)

At any particular time, t, the residual (GMSL(t) - GMSL_mass(t) - GMSL_steric(t)) is unlikely to be exactly zero due to random and short-period errors. However, over the long-term, the residual differences should be small. When they are not, it indicates a problem in one or more of the terms in Eq. (1).

(Evaluation of the Global Mean Sea Level Budget). IMO the complete formula is GMSL(t) = GMSL_mass(t) + GMSL_steric(t) + GMSL_{relocated mass}(t), where "relocated mass" is the ocean portion that is hidden in plain sight and therefore what I call "ghost

Fig. 4

water" (The Ghost-Water Constant, 2, 3, 4, 5, 6, 7, 8, 9; The Gravity of Sea Level Change, 2, 3, 4).

II. One Helpful Technique

For that reason, as regular readers know, I have been working on some techniques that allow us to have a better handle on the matter.

Since I like to use in situ measurements whenever possible, I have figured a way to fuse GISTEMP temperature records (1880-2016) with World Ocean Database (WOD) records (1956-2016).

Fig. 5

This allows us to generate a thermal expansion / contraction mapping of those same years (Fig. 1).

The basic concept is that currently some percentage of the heat entering the Earth ecosystem cannot escape back into space because of green house gases.

In terms of temperature, currently 93% of it enters the oceans.

We can follow that 93% because it leaves "fingerprints," in the form of warming ocean temperatures, as it makes its way into the ocean, leaving some 7% in the atmosphere and land above sea level.

Before I discovered this technique (yesterday) I did it this way: The World According To Measurements - 6.

III. How The Fusion Is Done

I combine the GISS temperature data with the WOD ocean temperature data using:

GISS + WOD
-------------------
2

That is, the GISS temperature for a given year (of which 93% is headed to the ocean anyway) is added to the WOD temperature already in the ocean, and then the average of the two is derived by division.

The actual C++ source code line in the module looks like this:
"T = (wodData[ypos+1].avgT + gissData[ypos+1].temperatureAnomaly) / 2 ;"

To see how this is reasonable notice this arithmetic:

(1880) -0.2 (GISS) + -0.136533 (WOD) = −0.336533
−0.336533 ÷ 2 = −0.1682665
(ocean temp increase of: -0.1682665 minus -0.136533 = −0.0317335)

(2016) 0.98 (GISS) + 0.597801 (WOD) = 1.577801
1.577801 ÷ 2 = 0.7889005
(ocean temp increase of: 0.7889005 minus 0.597801 = 0.1910995)

The 93% of recent larger temperatures (year 2016) blends, during the process, with 93% of increasingly smaller temperatures (year 1880).

So the "fusion" balances itself out over time (I will work on perfecting the percentages as time goes on).

The pattern of the GISS temperature anomaly shown in Fig. 1 (top) is reasonably closely aligned with the thermal expansion / contraction pattern also shown in Fig. 1 (bottom), and with the sea level change reported by tide gauge stations around the world (Fig. 3).

The graphs at Fig. 2, Fig. 4, and Fig. 5 show the TEOS-10 components (Absolute Salinity, Conservative Temperature, and Sea Pressure, which are factors that pull the pattern in various conflicting directions).

The thermal coefficient is generated by the TEOS-10 toolbox function gsw_alpha, and the steric volume changes are generated using the formula for volumetric, or cubical, expansion:

V = volume
T = temperature
β = thermal expansion coefficient

ΔV = V0 β ΔT
or
V₁ = V₀ * β * (T₀ - T₁)

(Physics Hypertextbook). The good thing to remember is that the numbers used are actual ocean and atmospheric data, not merely numbers generated by models.

IV. Conclusion

The thermosteric volume change percentage that is derived using this technique is smaller than the percentage generated with the technique I was using previously (The World According To Measurements - 6).

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

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