Sunday, June 17, 2018

Build Your Own Thermosteric Computational System - 2

Fig. 1 WOD Zone 7513
I. Advantages

There are some advantages to having your own thermosteric computational system (Build Your Own Thermosteric Computational System).

"It's easy to do" isn't one of them.

But the fact that you can concentrate your research on one zone or one tide gauge station, or all WOD zones and all PSMSL tide gauge stations, is one of those advantages.

It makes it less of a hassle to check scientific, peer reviewed papers for true science, for
Fig. 2 Location of WOD Zone 7513
not so true science, and even for questionable hypotheses in those papers.

Today, once again let's do just that.

Let's take a look at one WOD Zone (7513) marked with the red square on the WOD Map at Fig. 2.

The relevant data taken from WOD and PSMSL datasets is displayed on the graph at Fig. 1), so that we can see how "the hypothesis that the main cause of sea level rise is that the ocean is warming" comports with the available evidence.

II. Fact vs Fiction

Of course, the warming of the oceans is something that we can confirm.

We can confirm as well that the cause of that ocean warming is global warming of the atmosphere due to the overuse of fossil fuels, and that most of that warming enters the oceans.

But does that ipso facto support the hypothesis that the ocean warming taking place is the main cause of sea level rise?

No, that part is fiction, but the word is beginning to spread:
"Observations from the Jason series have revolutionized scientists' understanding of contemporary sea level rise and its causes. We know that today's sea level rise is about one-third the result of the warming of existing ocean water, with the remainder [two-thirds] coming from melting land ice."
(Is Sea Level Science Above the Law?, quoting NASA). Even though I consider "one-third" to be an over-estimate, at least the direction the revolution is taking is the correct one.

But, these "revolutioniz[ing]" events take a while to peculate through the walls of bias generated by errors in text books and older, erroneous papers (Humble Oil-Qaeda - 2).

III. The Graphs

To put it bluntly, the graph at Fig. 1 shows that the mean average sea level of WOD Zone 7513 is falling, not rising.

It also shows that the sea level is not rising even though the mean average water temperature is rising.

This phenomenon takes place all around the Cryosphere where there are huge ice sheets and glacier fields (Proof of Concept, 2, 3, 4, 5, 6, 7, 8; The Evolution and Migration of Sea Level Hinge Points, 2The Gravity of Sea Level Change, 2, 3, 4; NASA Busts The Ghost).

Anyway, the relevant PSMSL stations in WOD Zone 7513 are:
Canada:
PRINCE RUPERT, station number: 167
QUEEN CHARLOTTE CITY, station number: 829

United States:
ELFIN COVE, station number: 2300
YAKUTAT, station number: 445
SITKA, station number: 426
PORT ALEXANDER, station number: 2299
SKAGWAY, station number: 495
JUNEAU, station number: 405
KETCHIKAN, station number: 225
Click on the station number to view the PSMSL records for that station.

The two stations in that zone which are in Canada show that as you move past and away from the gravitational-pull hinge-point, the sea level stops falling.

Note that Glacier Bay melting is the cause of the sea level fall ("The Park is named for its abundant tidewater and terrestrial glaciers, numbering 1,045 in total" - ibid, emphasis added).

IV. The Science

The original published paper that predicted that sea level would fall around the Cryosphere's ice sheets and large glacial fields was revealed by a scientific team led by Harvard Professor J. X. Mitrovica:
Woodward is evidently the first scientist to add robust concepts of physics a la Newton to sea level change science:
To our knowledge, Woodward (1888) was the first to demonstrate that the rapid melting of an ice sheet would lead to a geographically variable sea level change. Woodward (1888) assumed a rigid, non-rotating Earth, and therefore self-gravitation of the surface load was the only contributor to the predicted departure from a geographically uniform (i.e. eustatic) sea level rise. This departure was large and counter-intuitive. Specifically, sea level was predicted to fall within ∼2000 km of a melting ice sheet, and to rise with progressively higher amplitude at greater distances. The physics governing this redistribution is straightforward.
(The Warming Science Commentariat). At least Woodward was not committed to an insane asylum like Semmelweis was (for challenging conventional, but erroneous, dogmatic "science").

But, Woodward was ignored, at least until Mitrovica et al. (see video below) closely studied his work.

Not only did Mitrovica not ignore Woodward, he improved immensely upon Woodward's work, while at the same time giving Woodward credit for his work.
(The World According To Measurements - 5, quoting Dr. Mitrovica). Integrity is an important factor in good science, as the Mitrovica team has shown.

V. The Reality

The reality is that ideas can be more difficult to change than we would expect, as shown by a quick google of "what is the main cause of sea level rise."

The common myth is in error because the research of Sir Issac Newton seems to have been forgotten (On Thermal Expansion & Thermal Contraction - 8).

VI. The Conclusion

Build your own Thermosteric Computational System.

The previous post in this series is here.

Friday, June 15, 2018

Humble Oil-Qaeda - 2

Fig. 1 Merchants of Doubt
I. Oil-Qaeda

In the first post of this series the dark side of the Oil-Qaeda force was discussed (Humble Oil-Qaeda).

In today's post we will take a look at how Oil-Qaeda infects the minds via subversion of the educational system.

But more than that, let's also take a look at how they have done the same thing to the practice of science while we discuss some papers science organizations use to support the myth that thermal expansion is the main cause of sea level rise.

Oil-Qaeda's impact has been greater than the sum of its parts, in that, even though they have not infected every school and every science organization, they have spread a crippling amount of uncertainty and doubt (see e.g. Reading, Writing And Fracking? What The Oil Industry Teaches Oklahoma Students, Big Oil, Big Influence, Big Oil Goes to College).

It is not all consciously deliberate:
Fig. 2
"That’s something more scientists should probably be doing, because bias is very often completely unconscious. Few researchers will admit to being biased in their research, says Naomi Oreskes, a Harvard University researcher and the author of Merchants of Doubt, and they may not even be aware that their research is being influenced."
(Public Universities Get an Education in Private Industry, bold added). In other words, "In recent years ... understanding of science and respect for its role in decision making have declined ... science is easily drowned out by misinformation or manipulated for the benefit of private interests" (Why a Center for Science and Democracy?).

Now, let's move on to the topic of Oil-Qaeda's impact on scientific literature in the context of thermal expansion of the oceans.

II. My Review of Thermal Expansion Literature

The following list is offered by NOAA (an organization I respect) in support of the TECOSLR myth:
  • Antonov, J. I., S. Levitus, T. P. Boyer, 2002: Steric sea level variations during 1957–1994: Importance
    of salinity, J. Geophys. Res., 107, 8013, DOI: 10.1029/2001JC000964. [gravity=1, Woodward=0, TEOS-10=n/a]
  • Antonov, J. I., S. Levitus, T. P. Boyer, 2005: Thermosteric sea level rise, 1955–2003, Geophys. Res.
    Lett.
    , 32, L12602, DOI: 10.1029/2005GL023112. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Antonov, J. I., S. Levitus, T. P. Boyer, 2004: Climatological annual cycle of ocean heat content, Geophys.
    Res. Lett.
    , 31, L04304, DOI: 10.1029/2003GL018851. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Boyer, T. et al., 2007: Changes in freshwater content in the North Atlantic Ocean 1955–2006, Geophys.
    Res. Lett.
    , 34, L16603, DOI: 10.1029/2007GL030126. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Boyer, T. P., S. Levitus, J. I. Antonov, R. A. Locarnini, H. E. Garcia, 2005: Linear trends in salinity for the
    World Ocean, 1955–1998, Geophys. Res. Lett., 32, L01604,
    DOI: 10.1029/2004GL021791. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Cabanes, C., A. Cazenave, C. Le Provost, 2001: Sea Level Rise During Past 40 Years Determined from Satellite and in Situ Observations, Science, 294, 840-842, DOI: 10.1126/science.1063556. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Cabanes, C., T. Huck, A. Colin de Verdière, 2006: Contributions of Wind Forcing and Surface Heating to Interannual Sea Level Variations in the Atlantic Ocean, Journal of Physical Oceanography, 36, 1739-1750, DOI: 10.1175/JPO2935.1. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Chambers, D. P., B. D. Tapley, R. H. Stewart, 1997: Long-period ocean heat storage rates and basin-scale heat
    fluxes from TOPEX, J. Geophys. Res., 102, 10,525–10,534,
    DOI: 10.1029/1997/96JC03644.
  • Chambers, D. P., 2006: Observing seasonal steric sea level variations with GRACE and satellite altimetry, J.
    Geophys. Res.
    , 111, C03010, DOI: 10.1029/2005JC002914.
  • Church, J. A., J. S. Godfrey, D. R. Jackett, T. J. McDougall, 1991: A Model of Sea Level Rise Caused by Ocean Thermal Expansion, Journal of Climate, 4, 438-456,DOI: 10.1175/1520-0442(1991)004%3C0438:AMOSLR%3E2.0.CO;2. [gravity=25+, Woodward=0, TEOS-10=n/a]
  • Gille, S. T., 2004: How nonlinearities in the equation of state of seawater can confound estimates of steric sea level change, J. Geophys. Res., 109, C03005, DOI: 10.1029/2003JC002012.
  • Gille, S. T., 2002: Warming of the Southern Ocean since the 1950s, Science, 295, 1275-1277, DOI: 10.1126/science.1065863. [gravity=1, Woodward=0, TEOS-10=n/a]
  • Gouretski, V., K. P. Koltermann, 2007: How much is the ocean really warming?, Geophys. Res. Lett.,34, L01610, DOI: 10.1029/2006GL027834. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Harrison, D. E., M. Carson, 2007: Is the World Ocean Warming? Upper-Ocean Temperature Trends: 1950–2000, Journal of Physical Oceanography, 37, 174-187, DOI: 10.1175/JPO3005.1. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Ishii, M., M. Kimoto, K. Sakamoto, S.-I. Iwasaki, 2006: Steric sea level changes estimated from historical ocean subsurface temperature and salinity analyses, Journal of Oceanography, 62, 155-170, DOI: 10.1007/s10872-006-0041-y. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Ishii, M., A. Shouji, S. Sugimoto, T. Matsumoto, 2005: Objective analyses of sea-surface temperature and marine meteorological variables for the 20th century using ICOADS and the Kobe Collection, International Journal of Climatology, 25, 865-879, DOI: 10.1002/joc.1169. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Jayne, S. R., J. M. Wahr, F. O. Bryan, 2003: Observing ocean heat content using satellite gravity and altimetry, J. Geophys. Res., 108, 3031, DOI: 10.1029/2002JC001619. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Levitus, S., J. Antonov, T. Boyer, 2005: Warming of the world ocean, 1955–2003, Geophys. Res. Lett., 32, L02604, DOI: 10.1029/2004GL021592. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Levitus, S., J. I. Antonov, T. P. Boyer, 1994: Interannual Variability of Temperature at a Depth of 125 Meters in the North-Atlantic Ocean, Science, 266, 96-99, DOI: 10.1126/science.266.5182.96. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Levitus, S., J. I. Antonov, T. P. Boyer, H. E. Garcia, R. A. Locarnini, 2005: Linear trends of zonally averaged thermosteric, halosteric, and total steric sea level for individual ocean basins and the world ocean, (1955–1959)–(1994–1998), Geophys. Res. Lett., 32, L16601, DOI: 10.1029/2005GL023761. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Levitus, S., J. I. Antonov, T. P. Boyer, H. E. Garcia, R. A. Locarnini, 2005: EOF analysis of upper ocean heat content, 1956–2003, Geophys. Res. Lett., 32, L18607, DOI: 10.1029/2005GL023606. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Levitus, S., J. I. Antonov, T. P. Boyer, C. Stephens, 2000: Warming of the World Ocean, Science, 287, 2225-2229, DOI: 10.1126/science.287.5461.2225. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Levitus, S. et al., 2001: Anthropogenic Warming of Earth's Climate System, Science, 292, 267-270, DOI: 10.1126/science.1058154.
  • Lombard, A., A. Cazenave, P. Y. Le Traon, M. Ishii, 2005: Contribution of thermal expansion to present-day
    sea-level change revisited, Global and Planetary Change, 47, 1-16, DOI: 10.1016/j.gloplacha.2004.11.016. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Lombard, A. et al., 2007: Estimation of steric sea level variations from combined GRACE and Jason-1 data, Earth and Planetary Science Letters, 254, 194-202, DOI: 10.1016/j.epsl.2006.11.035. [gravity=1, Woodward=0, TEOS-10=n/a]
  • Lyman, J. M., J. K. Willis, G. C. Johnson, 2006: Recent cooling of the upper ocean, Geophys. Res. Lett., 33, L18604, DOI: 10.1029/2006GL027033. [gravity=10+, Woodward=0, TEOS-10=n/a]
  • Miller, L., B. C. Douglas, 2004: Mass and volume contributions to twentieth-century global sea level rise, Nature, 428, 406–409, DOI: 10.1038/nature02309. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Miller, L., B. C. Douglas, 2006: On the rate and causes of twentieth century sea-level rise, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 364, 805-820, DOI: 10.1098/rsta.2006.1738. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Munk, W., 2003: Ocean freshening, sea level rising, Science, 300, 2041-2043, DOI: 10.1126/science.1085534. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Wadhams, P., W. Munk, 2004: Ocean freshening, sea level rising, sea ice melting, Geophys. Res. Lett., 31, L11311, DOI: 10.1029/2004GL020039. [gravity=3, Woodward=0, TEOS-10=n/a]
  • Willis, J. K., J. M. Lyman, G. C. Johnson, J. Gilson, 2007: Correction to “Recent cooling of the upper ocean”, Geophys. Res. Lett., 34, L16601, DOI: 10.1029/2007GL030323.
  • Willis, J. K., D. Roemmich, B. Cornuelle, 2003: Combining altimetric height with broadscale profile data to estimate steric height, heat storage, subsurface temperature, and sea-surface temperature variability, J. Geophys. Res., 108, 3292, DOI: 10.1029/2002JC001755. [gravity=0, Woodward=0, TEOS-10=n/a]
  • Willis, J. K., D. Roemmich, B. Cornuelle, 2004: Interannual variability in upper ocean heat content, temperature, and thermosteric expansion on global scales, J. Geophys. Res., 109, C12036, DOI: 10.1029/2003JC002260. [gravity=0, Woodward=0, TEOS-10=n/a]
(NOAA). A substantial array indeed ... but let's look behind the curtain pointed out by my [gravity=0, Woodward=0, TEOS-10=n/a] insertions above.

Fig.3
Any more (post Newton, post Woodward 1888, and post TEOS-10). when I first load a peer-reviewed paper into my PDF editor, the first words I search for are "gravity," "Woodward," and "TEOS-10."

Concerning the above list of papers, if none of those words appear in a paper, or appear in ways that are properly related to sea level change (the papers are questionable in terms of supporting the myth that thermal expansion is the main cause of sea level rise) because gravity is the second most important factor after ice sheet melt (The Gravity of Sea Level Change, 2, 3, 4; The Ghost-Water Constant, 2, 3, 4, 5, 6, 7, 8, 9; NASA Busts The Ghost).

III. The Unfortunate Reality

As I have argued many times over the years, the literature does not uphold the hypothesis that thermal expansion is the main cause of sea level rise (see e.g.
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).

Fig. 4
None of the papers cited above in Section II  use the Gibbs thermodynamics formulas implemented by the current world standard for sea water thermodynamics.

They could not use TEOS-10 because it was not released until a year or so after the most recent of those papers was published.

The graphs at Fig. 2 - Fig. 4 show the comparisons of PSMSL tide gauge station data (hated by Oil-Qaeda) with TEOS-10 aware computations using the TEOS-10 library of sea water specific thermodynamics, which implements the powerful Gibbs functionality (The World According To Measurements - 12).

These graphs show that thermal expansion and contraction are not what the myth that thermal expansion is the main cause of sea level rise hypothesizes.

If thermal expansion is the main cause of sea level rise the graphs would be reversed, i.e. the tide gauge records would be the smaller amount (the red line).

IV. Conclusion

It is unfortunate that scientists, along with politicians, are coerced, intimidated, and influenced by fear of losing their jobs and the like, as pointed out by a well-known scientist:
"I suspect the existence of what I call the `John Mercer effect'. Mercer (1978) suggested that global warming from burning of fossil fuels could lead to disastrous disintegration of the West Antarctic ice sheet, with a sea level rise of several meters worldwide. This was during the era when global warming was beginning to get attention from the United States Department of Energy and other science agencies. I noticed that scientists who disputed Mercer, suggesting that his paper was alarmist, were treated as being more authoritative.

It was not obvious who was right on the science, but it seemed to me, and I believe to most scientists, that the scientists preaching caution and downplaying the dangers of climate change fared better in receipt of research funding. Drawing attention to the dangers of global warming may or may not have helped increase funding for relevant scientific areas, but it surely did not help individuals like Mercer who stuck their heads out. I could vouch for that from my own experience. After I published a paper (Hansen et al 1981) that described likely climate effects of fossil fuel use, the Department of Energy reversed a decision to fund our research, specifically highlighting and criticizing aspects of that paper at a workshop in Coolfont, West Virginia and in publication (MacCracken 1983).

I believe there is a pressure on scientists to be conservative. Papers are accepted for publication more readily if they do not push too far and are larded with caveats. Caveats are essential to science, being born in skepticism, which is essential to the process of investigation and verification. But there is a question of degree. A tendency for `gradualism' as new evidence comes to light may be ill-suited for communication, when an issue with a short time fuse is concerned."
(Scientific Reticence and Sea Level Rise, quoting Dr. James Hansen, emphasis added). So, it is time to stand up to the bully known as Oil-Qaeda.

A lot rests upon our standing up (Oil-Qaeda: The Indictment, 2, 3, 4, 5, 6).

The previous post in this series is here.

Back By Popular Request






















"Anybody have any questions .... ?"

Monday, June 11, 2018

Build Your Own Thermosteric Computational System

Fig. 1
I. Build Your Database

The place to begin is to download in situ measurements from the World Ocean Database (WOD).

The dataset selections which I download are "CTD" and "PFL" using both "observed depth level" and "standard depth level" categories.

That can mean two file downloads each for both CTD and for PFL, totaling as many as  four files per WOD Zone (yes, it is a lot of work to download over a billion rows of data as I have done).
Fig. 2

The depth level categories I use are the 33 depth levels in "APPENDIX 11. ACCEPTABLE RANGES OF OBSERVED VARIABLES AS A FUNCTION OF DEPTH, BY BASIN" in the WORLD OCEAN DATABASE 2013 USER’S MANUAL.

The reason I do that, instead of the 137 depth levels, is that the 33 depth levels in "Appendix 11" have standard maximum and minimum valid values posted for in situ temperature and salinity records (which applies at each of those 33 depth levels in all of the ocean basins of the global ocean).

In other words, that way it is easier to detect any out of bounds in situ measurements before they enter into and thereby contaminate the dataset.

I place both the "observed depth level" and the "standard depth level" values into the appropriate one-of-33 depth level categories.

II. Convert To CSV

Once downloaded in the compressed WOD file format, I convert those files into the well known Comma Separated Values (CSV) file format.

The main reason I do that is because the SQL server can fast-load large CSV files, but it can't fast-load the WOD file format (because the WOD file format resembles a random slice of Pi).

Writing the conversion program to covert data from WOD file format to CSV file format is our punishment for being curious.

III. The Data and the TEOS-10 Process

No TEOS-10 or other calculations take place until the complete database of in situ measurements is tallied and averaged by Zone, year, temperature, and conductivity ("CTD" means conductivity, temperature, and depth) at each of the 33 depth levels (BTW, the advent of TEOS-10 changed "conductivity" to Absolute Salinity).

The bottom line is that only in situ measurements make up the database that is later used to calculate TEOS-10 values.

Once the database is built, we need software that uses the TEOS-10 library to compute other values from the WOD data, including Conservative Temperature, Absolute Salinity, and Pressure.

I wrote my conversion modules in C++, but several programming language libraries are available at no cost here, so you might want to write your conversion modules in one of those languages.

An additional factor (if you plan to compute thermosteric volume change), is that the volume of the ocean slice (e.g. 100m - 200m depth level) must be computed (for total ocean volume see Live Science).

Once the total ocean volume (i.e. mass) is known, a "section" or "slice" of that total ocean volume must be calculated for each of the 33 ocean depth levels (at least for the levels you are focusing on).

I break that total ocean volume down into slices based on the 33 standard WOD manual depth levels in Appendix 11 as mentioned above.

The volumes of those depth level slices are not all the same, because the height or span of the levels change.

That is, the volume of the 0-10 m slice is not the same as the volume of the 100-200 m slice (if v = lwh, then @ 0-10m h=10, while @ 100-200m h=100m).

So, it is important to consider the volume of the sea water at issue before attempting to compute its thermal expansion / contraction events over a period of time.

IV. Important TEOS-10 Functions

Once we load the in situ values (t=in situ sea water temperature in Celsius, sp = in situ conductivity ("salinity"), and depth) we can calculate some fundamental TEOS-10 values.
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);
ctmd = gsw_ct_maxdensity (sa, p);
Before we move on to calculate thermosteric volume changes (not mass changes) based on sea water temperature changes, we must calculate the thermal expansion coefficient (tec):
tec = gsw_alpha (sa, ct, p)
In the following formula, let vc = volume change, vol = mass-unit volume of depth layer ("ocean slice") mentioned in Section III above, prev_ct = last year's conservative temperature, ct = this year's conservative temperature.

Now we can calculate thermosteric volume change with this formula:
vc = vol * (1 + (tec * ct - prev_ct))
Since vc , like vol, is in cubic kilometers (km3), to convert vc into millimeters of sea level change (SLC), we divide vc by 361.841, which is the number of cubic kilometers per millimeter of SLC.

Now, all that is needed to move forward is to do this for large scale areas.

In street language, that means to "load a lot of measurements from the database and then send them through the process."

V. The Proper Use of Volume
in Thermosteric Computations

Fig. 3

Several Dredd Blog posts have emphasized the appropriate use of "volume" in thermal expansion / contraction calculations (e.g. On The More Robust Sea Level Computation Techniques).

In that post we quoted a peer-reviewed paper which pointed out something essential:
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.
(ibid). In other words, when you compute the thermal contraction / expansion of sea water over a period of years, you must use the same mass-unit value for the entire period (do not increase or decrease that mass-unit value because the issue is "volume changes per mass unit ").
Fig. 4

That means (since I use 33 depth levels) calculating the "mass unit" (number of atoms / molecules) in each depth level (which is in essence a slice of the total ocean mass-unit).

When the calculation involves one zone, or a few zones, the volume must be calculated based on the area of that zone or combined area of those zones.

For example, the value for the area of the entire ocean that I use is 361,841,000 km2, and the value for the mass-unit of the entire ocean that I use is 1,332,370,930.2 km3 (as of 2010, Live Science).

When I do the computation for only one zone, I must calculate the area of that zone.

Note that on the WOD map (Fig. 1) the zones look like even-sided rectangles, but due to the globe shape of the Earth, the zones are not the same size (area) everywhere.

So, you need to use some trigonometry and latitude / longitude considerations to get the real area value of any particular zone.

Fig. 5
Once that is accomplished, determine what percentage of the entire area of the ocean mass-unit any particular zone is, then determine the zone's mass-unit value by multiplying the entire ocean mass-unit by that zone's percentage of the global ocean's mass-unit value.

All that remains, before we then move into the deep waters, is to consider the ocean mass-unit slice value for the depth level in which you are calculating the thermal expansion / contraction events (e.g. On Thermal Expansion & Thermal Contraction - 34).

In other words the sum of all the areas (a1 area (l*w) + a2 area etc.) of the zones you are focusing on at any given time.

VI. Another Mass-Unit Concept

The mass-unit concept was also ignored in the analysis of the dynamics of the Cryosphere.

Those dynamics impact upon sea level change (SLC) in a significant way, and befuddled researchers who were unaware of the work of Woodward, including his paper published in 1888.

The research team led by Professor Mitrovica found Woodward's published paper (which other research teams had missed).

That paper described the way to detect when, where, and how much of the Cryosphere was melting into the oceans:
The science that is being ignored has been developing for well over a century:
To our knowledge, Woodward (1888) was the first to demonstrate that the rapid melting of an ice sheet would lead to a geographically variable sea level change. Woodward (1888) assumed a rigid, non-rotating Earth, and therefore self-gravitation of the surface load was the only contributor to the predicted departure from a geographically uniform (i.e. eustatic) sea level rise. This departure was large and counter-intuitive. Specifically, sea level was predicted to fall within ∼2000 km of a melting ice sheet, and to rise with progressively higher amplitude at greater distances. The physics governing this redistribution is straightforward.
(On the robustness of predictions of sea level fingerprints, emphasis added). This reminds me of the length of time between the discovery of "germs" and the acceptance of that fact by establishment medical professionals:
Semmelweis's observations conflicted with the established scientific and medical opinions of the time and his ideas were rejected by the medical community. Some doctors were offended at the suggestion that they should wash their hands and Semmelweis could offer no acceptable scientific explanation for his findings. Semmelweis's practice earned widespread acceptance only years after his death, when Louis Pasteur confirmed the germ theory. In 1865, Semmelweis was committed to an asylum, where he died of septicemia, at age 47.
(What Is Pseudo Science?). Doctors and other scientific professionals emphatically rejected the reality of "germs" back then.
(On the West Side of Zero). The proof of this concept was not difficult to locate and display, because the phenomena had been recorded for over a century (Proof of Concept, 2, 3, 4, 5, 6, 7, 8; NOTE especially episode 3).

The mythical bathtub model was a prime culprit (The Bathtub Model Doesn't Hold Water, 2, 3, 4); but NASA watched for it and finally busted the ghost with bottom pressure gauge records (NASA Busts The Ghost).

VII. Conclusion

The graphs at Fig. 3 - Fig. 5 show the variation in SLC when the mass-unit varies (I use the SOCCOM team's values for heat dynamics in the oceans, to wit: "The vast Southern Ocean, which surrounds Antarctica, plays a starring role in the future of climate change. The global oceans together absorb over 90 percent of the excess heat in the climate system and roughly three-quarters of that heat uptake occurs in the Southern Ocean", see The World According To Measurements - 13).

In other words, when calculating thermal expansion and contraction one must consider the volume change caused by in situ temperature changes only in relation to a static mass-unit.

In those three graphs, in order to emphasize the point, I used two individual mass-units on the exact same in situ conditions (T, SP, P) converted into modern TEOS values (CT,SA,P) as discussed in Section IV above.

Both mass-units were static (number of atoms / mass did not change) for the entire period graphed.

So, what is being detailed is that what is changing in those graphs is the thermosteric volume, not the mass.

When I get around to the next post in this series I am going to demonstrate the portion / percentage of thermal expansion and contraction in SLC measured in various tide gauge record scenarios.

The next post in this series is here.