## Thursday, September 28, 2017

### On The More Robust Sea Level Computation Techniques - 4

 Fig. 1a
 Fig. 1b

I have injected the NASA Satellite Records into the Test Case modules described earlier in this series (On The More Robust Sea Level Computation Techniques, 2, 3).

How this satellite usage works in general has explained previously (Syncronizing Satellite Data With Tide Gauge Data).
 Fig. 1c

The graphs from the Test Case module (Fig. 1a thru Fig. 1c) are like the graphs in other modules.

II. Test Case Scenario

The three Test Case scenarios ('Golden 23', 'Church 491', and 'All Stations' were also discussed in previous posts of this series.

Basically, the three test cases are used to emphasize how important it is to select balanced world ocean areas when they are to be used as being representative of the whole of the oceans.

The satellite record (conformed to RLR concepts so as to match the PSMSL values) matches best with the Golden 23.

The graphs show that the Golden 23 evinces about twice the amount of sea level rise that the other two cases do.

How does "twice as much" set with the official record?

III. By The Numbers

 Fig. 2a
 Fig. 2b
 Fig. 2c
Some numbers from the CSV files, from which the graphs @ Fig. 2a thru Fig. 2c were constructed, will also help us to discern that reality:
all stations:
103.339 mm * 361.841 = 37,392 (37392.287099) cu km
103.339 mm ÷ 304.8 mm = .34 (0.339038714) ft.
total: 4.07 (4.068464567) in.

Church 491:
93.7412 mm * 361.841 = 33,919 (33919.4095492) cu km
93.7412 mm ÷ 304.8 mm = 0.31 (0.307549869) ft.
total: 3.7 (3.690598425) in.

Golden 23:
197.136 mm * 361.841 = 71,332 (71331.887376) cu km
197.136 mm ÷ 304.8 mm = 0.65 (0.646771654) ft.
total: 7.8 (7.761259843) in.

The Golden 23 numbers indicate about 197 mm (about 7.8 inches) of sea level rise during the graphed time frame.

That comports well with the NASA estimation that "sea level has risen about eight inches since the beginning of the 20th century" (NASA, emphasis added).

The other two test case scenarios indicate about half of that Golden 23 amount, so we can discount them because the test case indicates that they are not produced from a balanced group of tide gauge, weather, or WOD stations and zones.

To produce those numbers, I use "361.841" as the cubic kilometers of ocean water required to raise the global mean average of sea level one millimeter; I use "304.8" as the number of millimeters per foot.

The Golden 23 sea level, then, indicates that an increase of 71,332 cu. km. of ocean water was added by Cryosphere melting during the graph time frame.

Again, the other two indicate about half of that amount.

IV. Back To Ocean Water Temperatures

 Fig. 3a
 Fig. 3b
 Fig. 3c

This is the toughest case to solve.

For starters, it is not axiomatic that the zones where tide gauge stations have been installed and working for centuries in some cases, decades in other cases, will have the same warming of waters as sea level change.

There is no direct link at the latitude / longitude location between warming waters and sea level rise or fall.

That is because a lot of the water comes from far away when released by ice sheets as they lose their gravity (The Gravity of Sea Level Change, 2, 3, 4).

Likewise, the melt water also flows toward the equator (ibid).

Furthermore, the World Ocean Database is composed of uneven depth measurements as well as uneven latitude / longitude measurements.

The graphs at Fig. 3a thru Fig. 3c show that the in situ measurements (actual measurements at actual locations) vary based on measurement location, and are at odds with the expected Test Case temperatures.

V. UPDATED GRAPHS

After doing some more thinking about this, I am providing graphs Fig. 4a thru Fig. 4c as
 Fig. 4a
 Fig. 4b
 Fig. 4c
well as Fig. 5.

The problem was essentially comparing apples to oranges.

The long span-of-time "expected temperature" as well as the long span-of-time sea level graph lines should not be combined with shorter time frames because it squishes both into a less revealing contortion.

The graphs at Fig. 4a thru Fig. 4c show expected sea level change and in situ (measured) sea level change in the modern satellite measurements era.

The graph at Fig. 5 shows expected ocean temperatures compared with in situ (measured) ocean temperatures in the modern satellite measurements era.

The graph at Fig. 5 is also constructed using ALL temperature measurements in the WOD database in all WOD zones.

The previous graphs (Fig. 3a thru Fig. 3c) only included WOD zones that had relevant tide gauge stations in them (Golden 23, all tide gauge stations, and the Church 491 tide gauge stations).

They were also compared to ocean temperatures from only those limited numbers of WOD zones.

 Fig. 5
The solution, then, was to compare the expected ocean temperatures to all WOD zones whether they had tide gauge stations in them or not.

The solution also included using all WOD measurements in those zones.

The bottom line is that all of the examples (Golden 23 stations, All stations, and Church's 491 stations) are reasonably close and accurate in terms of the modern satellite measurements which only span the years 1993-2016.

That is fine, because as we go back in time the measurements of ocean temperatures are much more likely to be non-existent, unlike PSMSL tide gauge station records.

VI. Conclusion

[I originally said] "I am going to do some examination of my portion of the WOD database (~1 billion measurements) to see if there is a collection of WOD zones that are closer to the Test Case scenario (even if they are outside of the Golden 23)."

[As the updated graphs and discussion show, I did what I said I would, and we now have a better, working understanding of how to do this.]

[I also originally said] "Additionally, I intend to explore whether I should add some other datasets to the mix (I currently use only the CTD and PFL datasets)."

[Again, that will not be necessary.]

[Finally, I originally said] "I will inform readers of that progress in future posts."

[That will not be necessary now, since I did it in this post in the form of an update.]

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