On The More Robust Sea Level Computation Techniques - 2

Fig. 1a

I. Background

I have been surprised by the outcome of using the TEOS-10 thermodynamics toolkit.

Fig. 1b

As regular readers know, for the longest time I calculated thermal expansion caused volume change as a percentage of sea level change.

Fig. 1c

That percentage was 5.1% calculated from actual sea level change minus the ghost water percentage.

Even that 5.1% was lower than current establishment science calculates, which was said to be more than sea level change caused by the melting of the Cryosphere.

II. Along Comes TEOS-10

Looking for possibly a more accurate way to calculate the percentages that thermal expansion and contraction (thermosteric) contribute to sea level change, I ran across the TEOS-10 Toolkit (TEOS-10 Website).

I made various experimental attempts to calculate thermal expansion values with the TEOS-10 toolkit, partnering it up with the traditional formula for such calculations and WOD, PSMSL, and GISS data.

Fig. 2a

Then I came across a bombshell paper which narrowed down the remaining techniques to two.

Fig. 2b

That bombshell paper pointed out the following:

Fig. 2c

"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."

(On The More Robust Sea Level Computation Techniques, quoting from 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). That certainly can change things.

III. Along Comes New Graphs

And so, today's graphs are presented to show the stark difference between the results of those two techniques mentioned in the paper.

Fig. 3a

The graphs are numbered in Fig. 1, Fig. 2, and Fig. 3 groups, each group having an 'a', a 'b', and a 'c' member graph.

Fig. 3b

The 'a' member of each graph group is in compliance with the paper quoted above, which sternly points out:
"The crucial point to be noted is that the steric component [thermosteric] 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." (ibid, emphasis added).

Fig. 3c

In other words, one must calculate the ocean volume from the 1st year a calculation of sea level change commences.

Then one must use that same quantity throughout all the other years of that span of time being calculated and graphed.

That is, the increasing and decreasing sea levels (ocean mass and volume changes) over a span of time are not to be used if one seeks to present an accurate estimation / calculation of thermosteric volume change over that span of time.

IV. The Tide Gauge Station Selections

In these graphs I present the two techniques using three lists of tide gauge stations: Fig. 1 group) 491 stations used by Church & White (2011), Fig. 2 group) all stations (1,484), and Fig. 3 group) "the Golden 23".

The 'a' member in each of those three groups shows the calculation mandated by the paper quoted in Section II.

As you can see, the thermal expansion calculations show significantly less sea level change caused by thermosteric dynamics than the old Dredd Blog 5.1% method shows.

Yikes !

Can "thermal expansion as the main cause of sea level rise in the 19th and 20th centuries" be that much of a myth?

V. How I Process The Data

I won't go through the arduous task of building a billion rows of SQL based data after downloading that data from PSMSL, WOD, and GISSTEMP.

I won't go through the software architectural work of designing software modules to analyze that data.

Today, let's just look at how the completed modules handle that data, beginning with TEOS-10 functions.

First we acquire in situ (at a specific latitude, longitude location) temperature along with in situ salinity ("practical salinity") readings from a specific ocean depth at that location.

Let's call them 'T' (temperature) 'SP' (practical salinity) and 'Z' (a depth or 'height' in TEOS parlance).

First we convert those in situ values into TEOS values:

1) Z into P (pressure) using the TEOS function P = "gsw_p_from_z(double z, double lat)";

2) S_A using  S_A = "gsw_sa_from_sp(double sp, double p, double lon, double lat)";

3) T into "conservative temperature" CT = "gsw_ct_from_t(double sa, double t, double p)";

Now, we can calculate the all important "thermal expansion coefficient"
(symbol 'β') β = "gsw_alpha(double sa, double ct, double p)".

Last but not least, we use a traditional formula for calculating thermal expansion / contraction volume change: V₁ = V₀(1 + β ΔT) as I noted early on in the struggle:

The one I settled on is: V₁ = V₀(1 + β ΔT), where: V₁ means new volume, V₀ means original volume, β means temperature coefficient, and ΔT means change in temperature (T₁ - T₀), which is another way of "saying" dV = V₀ β (t₁ - t₀), a formula in widespread use (Engineering Toolbox, cf here).

(On Thermal Expansion & Thermal Contraction - 18). When calculating a long span of years, the "ΔT" becomes the previous years temperature minus the current year's temperature (change in temperature), or vice versa depending on the direction (backwards in time, or forward in time) in which you are calculating.

VI. Discussion Of The Graphs

The 'a' member of each graph group features what happens when the mass-volume (V₀) remains constant as conservative temperature (CT), absolute salinity (SA), and pressure change over time.

The 'b' member graphs the temperature and salinity changes.

The 'c' member shows what happens when the volume (V₀) changes along with the temperature and salinity.

The difference in the thermal expansion / contraction is dramatic between the two usages (constant volume, variable volume).

VII. Conclusion

There is more work to do to figure out just how the oceanographers calculate thermosteric volume.

Any suggestions?

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