On The More Robust Sea Level Computation Techniques

Measurements of change

I. Background

The scientific literature contains some debate. or at least different methodologies, concerning the proper way to calculate the quantity of thermal expansion and contraction of ocean water.

Which means that you can expect, based on the same evidence, different statements about the portion of sea level rise or fall that is considered to be thermosteric (thermal expansion / contraction) in nature, compared to what is considered to be eustatic in nature (scientific literature reflects that unwanted reality).

II. Some Clarification

Thermosteric warming (thermal expansion) does not add atoms to the ocean water, but it does move the atoms further apart from one another, so, the ocean volume increases (even though the number of atoms remains the same).

Thermosteric cooling (thermal contraction) draws the atoms closer together, so, the ocean volume decreases (even though the number of atoms remains the same).

Mass-volume (eustatic) increase  is a different dynamic, because it is a function of adding more atoms to the ocean water (via ice berg calving, or by melt water from ice sheets or glaciers on land flowing into the ocean).

Mass-volume (eustatic) decrease is caused, among other things, by evaporation of ocean water into the atmosphere, and the eventual placement of that water on land by rain.

III. Some Variations In Values

I won't belabor the issue of variation of analysis of steric vs eustatic in the published literature (because there is a lot of it), but I will quote from two papers which are at odds as to "who dunnit" (steric man or eustatic man):

"We examine the relationship between 50-year-long records of global sea level (GSL) calculated from 1023 tide gauge stations and global ocean heat

Fig. 1a All Zones, Constant Volume

content (GOHC), glacier and ice sheet melting. The lack of consistent correlation between changes in GOHC and GSL during the period 1955–2003 argues against GOHC being the dominant factor in GSL as is often thought. [IOW eustatic man dunnit] We provide clear evidence of the substantial and increasing role in GSL from the eustatic component (47%) compared with the contribution from increasing heat content (25%), suggesting that the primary role is being played by the melting glaciers and ice sheets. There remains about 1/4 of GSL rise unaccounted for by the best estimates of both eustatic and thermosteric effects [BTW that is the ghost water constant].  This fraction also exhibits large variability that is not readily associated with known causes of sea level variability. The most likely explanation of this unknown fraction is underestimated melting, climate-driven changes in terrestrial storage components, and decadal timescale variability in global water cycle. This argues for a concerted effort to quantify changes in these reservoirs" (JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, D08105, doi:10.1029/2007JD009208, 2008, PDF).
...
"Over the years 2002–2014, we find a global mean steric trend of 1.38 ± 0.16 mm/y, compared with a total trend of 2.74 ± 0.58 mm/y [steric man dunnit]. This is

Fig. 1b G23 Zones, Constant Volume

significantly larger than steric trends derived from in situ temperature/salinity profiles and models which range from 0.66 ± 0.2 to 0.94 ± 0.1 mm/y. Mass contributions from ice sheets and glaciers (1.37 ± 0.09 mm/y, accelerating with 0.03 ± 0.02 mm/y2) are offset by a negative hydrological component (−0.29 ± 0.26 mm/y). The combined mass rate (1.08 ± 0.3 mm/y) is smaller than previous GRACE estimates (up to 2 mm/y), but it is consistent with the sum of individual contributions (ice sheets, glaciers, and hydrology) found in literature" (Revisiting the contemporary sea-level budget on global and regional scales, 2015, PDF).

The ongoing exercise to unify the research into which factors contribute most to ocean volume change (steric or eustatic), must be bolstered with unification of both research and analysis.

One effort in that direction is the TEOS-10 toolkit, which I use.

But, the major factor in unification will be to unify the conceptual framework IMO.

IV. Some Procedural Inconsistencies

One paper expands upon the proper techniques and procedures involved in steric vs eustatic analysis:

"A common practice in sea level research is to analyze separately the variability 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."

(JOURNAL OF GEOPHYSICAL RESEARCH: OCEANS, VOL. 118, 953–963, doi:10.1002/jgrc.20060, by Gabriel Jordà and Damià Gomis, 2013; @p. 953, 954, emphasis added). One way to remember mass volume compared to steric / spatial volume is that mass volume is how many atoms the water column contains, but steric / spatial volume refers to how far apart from one another those atoms are.

V. A Dredd Blog Solution

In light of ("the steric component only represents actual volume changes when the mass of the considered water body remains constant") I decided to modify the software module to calculate both situations.

Fig. 2a All Zones, Variable Volume

That is, to calculate based on both the mass remaining constant, as well as the mass quantity changing.

(Of course the mass is constantly changing in the real world, but I digress.)

I decided to do both the constant scenario and the variable scenario because it would be helpful for detecting situations where presentations are at odds as a result of the use of these  two different techniques as if they were the same.

Fig. 2b G23 Zones, Variable Volume

Notice Fig. 1a and Fig. 1b, which graph the situations in both the Golden 23 as well as All Zones as to the situation where the mass remains constant.

They both use the constant mass volume technique.

Then compare those two with Fig. 2a and Fig. 2b, which use the variable mass volume technique to graph those situations in both the Golden 23 as well as All Zones.

VI. Conclusion

The situation where the mass remains constant generates less thermal expansion and contraction than the variable mass situation does.

The constant mass is more accurate, in terms of calculating actual thermosteric volume change, than the variable volume scenario is.

That is because using the variable volume assumes a volume amount that has been increased or decreased because of an increase or decrease in the total amount of water in the oceans, rather than being based only on the temperature and salinity changes.

Thermosteric change can only be isolated by using a fixed quantity of water that experiences changing water temperatures.

Using the varying mass-volume quantity each year will mix steric with eustatic to produce a conflated thermal expansion analysis.

It is, in that respect, the same as using a combination of zones that are biased toward either sea level fall or sea level rise.

One must choose both carefully with an unswerving goal of having a balanced input of data.

In future posts I will use the same PSMSL tide gauge stations that the authors in journal papers used in their papers, in order to further expand upon the concepts addressed in today's post.

The next post in this series is here.

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