ig |

Fig. 1 |

**I. Introduction**The "Golden 23 Zones" are actually fifteen WOD zones (

__Fig. 2__) which contain the PSMSL "23 golden tide gauge station locations" (

__Fig. 1__) which scientists selected years ago as a valid local-group that is representative of global sea level change (SLC).

The Golden 23 Group's "fingerprints" are also representative of which ice sheets are melting during a given span of time.

The analysis of SLC has been problematic because of, among other things, oversimplification ("

*Everything should be made as simple as possible, but no simpler*." Albert Einstein). and failure to consider or attribute seminal scientific papers (On the robustness of predictions of sea level fingerprints).

Fig. 2 |

Regular readers know that I was convinced of the use of the golden 23 and have posted about that subject (Golden 23 Zones Revisited).

**II. TEOS-10**Since the current dogma concerning SLC is enamored of the notion that SLC is mostly due to thermal expansion, anyone who is seriously looking into that hypothesis, in addition to studying SLC measurement practices, must also take on some of the precepts of oceanography and thermodynamics.

Since I do a lot of research using software modules I construct with C++, I eventually ran across the TEOS-10 toolkit.

It is a special-case toolkit that has the blessings of scientific communities:

The Intergovernmental Oceanographic(TEOS-10 Flyer, PDF). ThatCommission (IOC), with the

endorsement of the Scientific Committee on Oceanic Research (SCOR) and the International Association for the Physical Sciences of the Oceans (IAPSO), has adopted the International Thermodynamic Equation Of Seawater - 2010 (TEOS-10) as the official description of seawater and ice properties in marine science. All oceanographers are now urged to use the new TEOS-10 algorithms and variables to report their work.

Fig. 3

Notable differences of TEOS-10 compared with EOS-80 are :

(1) the use ofAbsolute Salinity[S] to describe the salinity of_{A}

seawater; Absolute Salinity takes into account the spatially varying composition of seawater. In the open ocean, the use of this new salinity has a non-trivial effect on the horizontal density gradient, and thereby on the ocean velocities calculated via the “thermal wind” relation.

Fig. 4

(2) the use ofConservative Temperature[CT] to replace

potential temperature q. Both of these temperatures are calculated quantities that result from an artificial thought experiment (namely, adiabatic and isohaline change in pressure to the sea surface). Conservative Temperature has the advantage that it better represents the “heat content” of seawater by two orders of magnitude.

Fig. 5

(3) the TEOS-10 properties of seawater are all derived from a

Gibbs function (by mathematical processes such as differentiation) and so are totally consistent with each other (in contrast to the now obsolete EOS-80 approach where separate polynomials were provided for each thermodynamic variable and they were not mutually consistent).

Fig. 6

*EOS-80*usage had led to many an innocent conflicting result over the past 40 years of use.

This has led to further improvement as an adjunct to my use of WOD and PSMSL data sets in terms of analyzing SLC, especially as that analysis involves the hypothesis of thermal expansion induced SLC.

**III. The Procedure**Remembering Einstein's guidance about making things as simple as possible, but no more

Fig. 7 |

I query the SQL server for all WOD data from that zone, order it by year, and I also query the SQL server for all PSMSL data from that zone, and also order it by year.

I then pass the WOD data through some TEOS-10 functions to derive the absolute salinity and conservative temperature (the relevant TEOS-10 functions begin with "gsw_").Golden 23 Zones

First derive sea pressure from the depth (in meters) the measurement was taken at (now called "height"): p = gsw_p_from_z (depth, latitude); then derive absolute salinity: S

_{A}= gsw_sa_from_sp (sp, p, longitude, latitude); and finally derive conservative temperature: ct = gsw_ct_from_t (sa,t,p), where "sp" is the

*in situ*measured salinity that has been recorded in the WOD data, "t" is the

*in situ*measured sea water temperature that has been recorded in the WOD data, and "p" is the sea pressure (dbar) calculated from the measured

*depth*and latitude where the measurements were taken.

Fig. 8 |

A critical function, in terms of thermal expansion analysis, comes next (the thermal expansion coefficient): tec = gsw_alpha(sa,ct,p), which is required for the final formula, thermal volume change (thermal expansion or contraction).

We start with the existing volume of the WOD zone in question.

A bit more reaching is required to determine the quantity of sea water (volume or mass) for the ultimate function:

**ΔV = V0 β ΔT**or

**V**, where V = volume, T = temperature (CT), and β = thermal expansion coefficient.

_{1}= V_{0}* β * (T_{0}- T_{1})That is because: 1) the zones are not the same size (as the may seem in

__Fig. 2__); 2) they do not have the same depth; 3) they do not have the same amount of land mass (compare zone 7215 with zone 7308 @

__Fig. 2__); and 4) not to mention temperature and salinity.

I use latitude and longitude calculus to determine the length and width of the four (unequal) sides of each golden 23 zone, then multiple all of them by the same depth value (median depth of the ocean), then subtract from that volume the percentages of the zone that is land, not water.

So, now we can write the TEOS-10 version: zoneV

_{1}= zoneV

_{0}* tec * (CT

_{0}- CT

_{1}), where CT

_{0}is last (previous) year and CT

_{1}is this current year, zoneV

_{0}is the zone's beginning volume (prior to the temperature changes in that zone over the year being calculated), and zoneV

_{1}is the new volume after the thermal change calculation.

The resulting zoneV

_{1}volume can be more (expansion), or less (contraction), than the beginning zoneV

_{0}volume.

**IV. The Graphs**I use synchronization checks to make sure that the change-patterns match the actual-value-pattern of the entity that is changing in value.

For examples,

__Fig. 3__checks volume patterns,

__Fig. 4__checks absolute salinity patterns,

__Fig. 5__checks conservative temperature patterns,

__Fig. 6__checks sub-surface water pressure patterns, and

__Fig. 8__checks SLC patterns.

Those match, so we can now discuss the main feature, the graph at

__Fig. 7__.

**V.**

**Calculation**The

__Fig. 7__ending value for SLC during 1967-2015 is 78.1 mm, and the

__Fig. 7__ending value for thermosteric change is -284.773

**.**

How much of the 78.1 mm sea level rise in the

*Golden 23 Zones*is to be attributed to thermal expansion?

**VI.**

**Thermal Expansion in The Golden 23 Zones**

**VII. Conclusion**(being updated)