Golden 23 Zones Revisited

Fig. 1 Golden Stations

I. Background

The "golden 23" (more or less) began as an effort associated with "the European problem."

Fig. 2

That problem was the result, among other things, of researchers not knowing about a seminal paper explaining the earliest scientific awareness of the dynamics of ice sheet gravity and its impact on sea level change (On the robustness of predictions of sea level fingerprints).

That problem was also perpetuated by a lack of the knowledge of sea level change "fingerprints" which could be used to determine what ice sheet melt was causing observed sea level fall and rise (Calling All Cars: The Case of the "Missing Six" - 5).

Fig. 3

Researchers were perplexed by the hundred year old tide gauge station records that recorded both sea level rise and sea level fall at different tide gauge stations (Proof of Concept , 2, 3, 4, 5, 6, 7, 8).

II. Some Light Shines Through

Fig. 4

Professor Mitrovica (see video below) and his team helped to clarify and improve upon the scientific work that had been done by Woodward a century earlier.

Fig. 5

Mitrovica also explained that previous scientific papers, as well as his own work, made it possible to use the records of certain tide gauge stations in order to derive an understanding of global sea level trends.

Fig. 6

Dr. Mitrovica likes to use many tide gauge station records, as I do, to balance things out.

Fig. 7

So, instead of 23 golden tide gauge stations, I use 23 golden zones that contain a grand total of about 300 tide gauge stations within them.

For a complete list, links, and other details of the zones and tide gauge stations, see "IV. The Data Sources" in the Dredd Blog post Calling All Cars: The Case of the "Missing Six" - 5.

III. The New Approach

Then I "went and did it", i.e, I stirred up some controversy about aspects of thermal expansion caused sea level change in a Dredd Blog series (On Thermal Expansion & Thermal Contraction, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18).

Among the arguments presented in that series is one that points out the dearth of evidence to support the assertion that "thermal expansion is the major cause of sea level rise in the 19th and 20th centuries."

During the discussion I had not used the golden 23 zones approach.

Instead, I tended to used the layered approach (see e.g. On Thermal Expansion & Thermal Contraction - 18).

So, the new approach today is to get back to the golden 23 realm, while keeping and using some of the tools and techniques developed during the use of the layered approach.

IV. One Useful Tool

One useful tool is the steric volume calculation algorithms that use the latitudes and longitudes of a WOD zone, along with average world ocean average depth,  to calculate the volume of ocean water in that zone.

Fig. 8

By also using temperature and sality change with the volume calculation, we can calculate the amount of volume increase and decrease of the ocean in that zone.

Comparing that and the pattern of the volume changes with sea level change patterns, we can see just how related or unrelated the steric (thermal expansion and contraction) changes are to the sea level changes.

V. Today's Graphs

In that light, I have used the golden 23 zones data from the World Ocean Database (WOD) in combination with the data from the Permanent Service For Mean Sea Level (PSMSL) tide gauge station records to generate some graphs.

The graphs at Fig. 3 - Fig. 7 are pattern tests.

The graphs at Fig. 2 and Fig. 8 are of the same data, however, the graph at Fig. 8 is a graph of the values from year to year, while the graph at Fig. 2 is a graph of the changes in that data from year to year.

Fig. 9  Trend Change

The pattern tests compare the mean averages (Fig. 8) with the calculated changes (Fig. 2), to see if the change patterns exactly match the mean average values.

If the patterns do not exactly match, then there is a problem with the software.

Since they do match, the software is ok, so I generated a golden 23 graph that compares values so as to consider the thermal expansion hypothesis mentioned earlier in Section III.

VI. Conclusion

As you can see in the graph at Fig. 2, the sea level pattern in the first pane (upper left pane) does not match the steric, thermal expansion pattern in the fourth pane (lower right pane).

Interestingly, the graph at Fig. 9 shows that a trend change in global air temperatures also took place during that time frame.

Steric, thermal expansion is not the major cause of sea level rise in the golden 23 zones (the zones to watch for global sea level change trends), even though it may be more closely related to other climate factors.

Review the excellent presentation in the video below, by Dr. Mitrovica, if you like.

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Steric β, Mass, and Volume In Sea Level Calculations

Mass, volume, and density

Let's begin with the reason for today's post: "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" (Jorda & Gomis, Journal. of Geophysical Research: Oceans, Vol. 118, 953–963,p. 953, 2013).

And, let's refine it down to the nitty gritty: "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. This is for instance the case of thermal expansions/contractions due to surface heat fluxes" (ibid).

Immediately, then, we must consider what changes "the mass of the considered water body," and how significant that change is.

In yesterday's post I wrote "Think of mass as how many molecules of seawater there are in a layer or zone, and think of volume as how far apart from one another those molecules are at a given temperature and salinity" (On Thermal Expansion & Thermal Contraction - 18).

What primarily changes ocean mass is melt water and ice bergs flowing into it from Greenland, Antarctica, and land glaciers around the globe.

Evaporation of seawater changes the ocean's mass, as does rain falling back onto the ocean surface.

By the way, that change of mass also changes the volume, but it is not steric volume change.

So, assume that after the ocean mass has been changed then becomes stable and constant for a time, only the volume can be changed by thermal factors ("the steric component only represents actual volume changes when the mass of the considered water body remains constant").

Thus, this is "... the case of thermal expansions/contractions due to ... heat fluxes."

In other words, sunlight impacting the surface of the ocean or heat radiating from the ocean does not change its mass (the number of ocean water molecules), even though any resulting change in temperature / salinity can change the ocean's volume.

The formula for that volume change (V₁ = V₀(1 + β ΔT) was also discussed in yesterday's post.

As a final thought, note that Jorda & Gomis, 2013 (link up-thread) did not mention gravity (The Gravity of Sea Level Change, 2, 3, 4) or ghost-water (The Ghost-Water Constant, 2, 3, 4, 5, 6, 7, 8).

Those two dynamics can change the mass and sea level on a regional basis because relocation of ocean water takes place.

Later.

On Thermal Expansion & Thermal Contraction - 18

Fig. 1  World Ocean Database layers

I. Background

The major cause of sea level change, at the most basic level, is global warming induced climate change.

Fig. 2 Layer Zero

The next level after that is the dynamics that change the mass and/or volume of the oceans.

Fig. 3 Layer One

It is important to know what these dynamics are, because the security of civilization as we know it is at stake (Climate Central).

Fig. 4 Layer Two

In the previous post I presented graphs that compared ocean water temperature and salinity change to sea level change (SLC).

Fig. 5 Layer Three

In today's graphs I have added another factor, steric volume change.

Fig. 6 Layer Four

The ocean areas in today's post are identical to those in the previous post.

That is, both feature Layer Zero - Sixteen (compare Fig. 1 with Fig. 1 On Thermal Expansion & Thermal Contraction - 17).

Fig. 7 Layer Five

The fourth pane (lower right pane), in each graph today, depicts the change in volume of each layer of the ocean.

Fig. 8 Layer Six

Those panes and the data are totally unrelated to the PSMSL data utilized to make the SLC graph in pane one (upper left pane) of each graph.

Fig. 9 Layer Seven

I mention that because generating the data in pane four is orders of magnitude more difficult than any of the other panes in each graph.

Fig. 10 Layer Eight

II. Let Me Explain

Fig. 11 Layer Nine

Layer Nine First, let's consider the difficulty of calculating the volume of a layer.

Fig. 12 Layer Ten

When one views the map at Fig. 1, at first blush it looks like a simple volume formula for a square will do (v = l * w * h).

Fig. 13 Layer Eleven

But the equal-sided looking latitude, longitude "squares" are not squares because they are on a globe, a sphere.

Fig. 14 Layer Twelve

The four sides are no longer equal, nor flat anymore (since librul scientists changed the flat earth into a globe: Once Upon A Time In The West - 2).

Fig. 15 Layer Thirteen

So, to determine the lengths of each side of each zone, one must calculate using some trigonometric formulas. 

This involves sine, cosine, tangent, etc. values relating to the latitude and longitude lines that make up the four sides of each zone.

Fig. 16 Layer Fourteen

An interesting aside is that this also means is that the seawater volume of the zones touching the Equator is greater than the seawater volume of zones nearer to polar regions.

Fig. 17 Layer Fifteen

That is, the least seawater volume per zone is in Layer Zero and Layer Seventeen, while the most seawater per zone is in Layer Eight and Nine.

Fig. 18 Layer Sixteen

An additional complication is that not all zones are over water, instead some are over land.

Then, on top of all of that, there are zones where no WOD measurements have been recorded by researchers.

Thus, I had to have the actual number of valid zones per layer since I wanted to determine the volume of seawater per layer.

I wrote software to generate the following table:

{0,20} {9,33}
{1,26} {10,32}
{2,15} {11,31}
{3,20} {12,35}
{4,26} {13,36}
{5,27} {14,36}
{6,29} {15,36}
{7,32} {16,22}
{8,31} {17,0}

The first number (bold) is the layer, the second is the quantity of "valid" zones in that layer (valid means that there are measurements of temperature, salinity, and depth taken in that zone then recorded in the WOD database).

It also turns out that the ocean depth at each zone was "beyond reach."

That is not a show stopper in the sense that I am generating graphs for the purpose of comparing temperature and salinity induced volume change patterns.

Those steric patterns are used to compare with the PSMSL tide gauge station patterns in the same WOD zones and layers.

So I use the general average ocean depth value (3,688.08 m) for each zone and layer rather than the value of the deepest measurement taken in each zone (still, more complications arose).

III. The Steric Volume Changes

The ocean volume changes as the seawater temperature & salinity change.

The same goes for the volume of zones and layers for that matter.

So, next I had to find and use formulas for that calculation.

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).

The volume of seawater in a layer is V₀ which results in the new volume value V₁ after the rest of that formula is applied.

Thus, we derive a pattern of seawater volume ups and downs which we can then compare to the SLC pattern of ups and downs.

IV. The Nitty Gritty

If the SLC and steric volume change patterns match, in the sense of synchronized ups and downs, then we can say there is a relation between thermal expansion and sea level change.

The degree of that synchronization of ups and downs indicates whether thermal expansion is or is not "the major factor in sea level rise in the 19th and 20th centuries" (the current dogma).

V. One More Thing

Fig. 19 Thermal Coefficients

The lookup table shown in Fig. 19 defines the values of β in the formula shown above: V₁ = V₀(1 + β ΔT).

The leftmost column shows the Salinity values and the columns to the right of it progress from one degree C value to the next.

The coefficient β is derived by selecting a Salinity value matched to a temperature value.

The ΔT is derived by subtracting the current year's temperature from the previous year's temperature to derive the change in temperature, which is then multiplied by the β value, and finally 1 is added to it.

The result is the thermal coefficient by which the layer volume V₀ is multiplied to derive the value of V₁.

The change in that layer's volume for that year is then derived by: V₁ - V₀.

VI. Conclusion

So, look at the graphs for yourself to determine your take on this matter, remembering that "The steric component only represents actual volume changes when the mass of the considered water body remains constant" (Steric & Mass Components of Sea Level Variablilty, PDF).

(Think of mass as how many molecules of seawater there are in a layer or zone, and think of volume as how far apart from one another those molecules are at a given temperature and salinity.)

Anyway, this is a pattern observing operation today, so compare pane four (lower right pane) patterns with the SLC patterns (pane one, upper left) and see if the thermal expansion dogma needs to be tossed.

Does it need to be replaced with "Greenland, Antarctica, and other land based glacial melt and disintegration is the major cause of sea level rise in the 19th and 20th centuries" ???

UPDATE: The graphs at Fig. 4-18 were updated.

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