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).
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 mass-unit of the ocean slice (e.g. 100m - 200m depth level) must be computed (for total ocean volume see Live Science).
Once the total ocean mass-unit (i.e. mass) is known, a "section" or "slice" of that total ocean mass 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 mass down into slices based on the 33 standard WOD manual depth levels in Appendix 11 as mentioned above.
The mass-units of those depth level slices are not all the same, because the height or span of the levels change.
That is, the mass of the 0-10 m slice is not the same as the mass 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 mass-unit of the sea water at issue before attempting to compute its thermal expansion / contraction volume 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);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):
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);
tec = gsw_alpha (sa, ct, p)In the following formula, let vc = volume change, mu = mass-unit quantity 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 = mu * (1 + (tec * ct - prev_ct))Since vc , like mu ("mass-unit", a.k.a. "eustatic"), 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
in Thermosteric Computations
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:(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 ").
"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 unit compared to steric / spatial volume is that mass is how many atoms/molecules the water column contains, but steric / spatial volume refers to how far apart from one another those atoms/molecules are.
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.
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:(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).
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.
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).
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.