Watts Up With That?

By Dr. Alan Welch FBIS FRAS

General Summary

This study consists of two parts: –

Part 1 – Variation of NOAA Sea Levels globally and for the 24 sub-areas.

Part 2 – Variation of NOAA Sea Level data based on individual satellites.

Most of the figures can be found in 2 Google Drive files details of which can be found in the appropriate Parts.

Part 1 – NOAA Sea Levels – Variation of each sub-area

Having studied the sea level data released on https://climate.nasa.gov/vital-signs/sea-level/ over the last 7 years in became opportune to apply the same methods and procedures to the NOAA data released on https://www.star.nesdis.noaa.gov/socd/lsa/SeaLevelRise/LSA_SLR_timeseries.php.

These datasets were published at irregular intervals and listed the sea level readings from the 5 individual satellites both globally and for 24 sub-areas of the Oceans, Seas and Gulfs.  As each sub-area has generated at least 5 graphs there are well in excess of 130 graphs produced, too much for a paper, but they can all be found on a Google Drive link https://drive.google.com/file/d/1KCYo7iYmVxbEoTubeP7YB06jEVQo82k5/view?usp=sharing.

This paper will not go into much discussion but will act as a depository for the graphs for others to have access to.  The following notes describe the study.

1. Both the individual satellite results and the combined results for each sub-sea have been studied but this paper only concerns the latter.  Graphs for all sub-seas have been produced.  Some aspects of the individual satellite results will be reported in Part 2.

2. The order of the presentation will be different from the NOAA order as follows:-

     First the Global results

     Next 22 sub-seas listed in increasing value of Easting.  The Easting for each area is defined as the number of degrees E an approximate centre of the sub-sea is East of the 180-degree longitude.  The reason for doing this is in the off chance that one or more derived parameters varies in a systematic way in the longitudinal direction which would be informative.

   Finally, the 2 circum-global areas, namely the Southern Oceans and the Tropics.

3. When analysing the combined results if two satellites have the same date/time then their values are averaged.

4. The data are from Sept 2024.  The latest available data are for about the end Feb 2025.  At the time of writing no updates have taken place since Feb 2025.

5. The graphs produced for each area are as follows with the graphs for the Yellow Sea being used to illustrate:-

• A graph, Figure 1, of all the satellite readings colour coded for each satellite.

•  A graph, Figure 2, of the full combined data with the linear and quadratic best fit lines shown together with their equations.  It may seem rather excessive precision has been used but better to be safe than sorry.  Sometimes actual year dates, like 1993, may have been used and when powers of these appear in equations extra precision must be used to guarantee accuracy.

• A graph, Figure 3, of residuals defined as the actual value minus the equivalent value on the linear best fit line.  Added is a best fit sinusoidal curve calculated via an iterative process along with the parameters of that curve.

• In Figure 4 is a spectral analysis of the data indicating any peaks generally between about periods of 10 and 40 years.  Usually, peaks with about a 10-year period or less are due to irradiance variation or El Niño events.

• A plot, Figure 5, of how the derived “acceleration” changes with the year of determination.  In previous papers it was suggested that this plot for analyses of the Global Sea Level was important in the way it changed with time.  It seemed that the shape was like a slightly underdamped sinusoidal oscillation, but events change so slowly that repeating it for several other sea areas may prove informative.

At this stage a short thought on the term global sea level.  Both Tidal Gauges and Satellite readings are not global.  The former cover only a very limited portion of the sea but the length of monitoring can be useful as some stretch back over 200 years.  Conversely the satellite coverage is just over 30 years and covers 95% of the seas.  In previous work I have suggested that this missing 5% is the cause of the sinusoidal oscillation in the global variation.  Also, that the missing 5% may mainly be found in the North Atlantic, North Sea and Arctic Ocean areas.  A preliminary investigation some years ago of several Tidal Gauge records of ports in these areas showed promise but a further study making more use of spectral analysis has been carried out that is more comprehensive and will be reported on at a later date.

The results of the various analyses have been collated in several tables.  A first preliminary look at the satellite and residual plots was made to ascertain if any data were suspicious. Having calculated all the residuals a histogram was produced for each sea and the standard deviation derived.  The table of statistics is shown below, Table 1.

The South China Sea and the Tropics each contained a suspicious reading.  Calculating the ratio of the maximum absolute value of any residual to the standard deviation showed values of 13.3σ and 11.8σ respectively, which are very large hence they were replaced by the average of the 2 adjacent values.  The analyses then proceeded with Table 2 giving the slopes and “accelerations” for each sea.  Results for the South China Sea and the Tropics are presented but only using the modified data.

The next stage was fitting a sinusoidal curve via an iterative process.  The equation is shown in Excel Format.

             =  CONST + AMP * SIN(((SHIFT + 2 * A1)/PERIOD) * PI())

where CONST is a constant mean sea level (mm)

AMP is a +/- amplitude variation (mm)

SHIFT is a phase shift (years)

and PERIOD is a period of a complete oscillation (years)

Table 3 shows the results of the curve fitting, again in order of increasing Eastings.

Following the spectral analyses a comparison was made between the Period derived in the equation fitting and the main Period found in the spectral analysis.  All agreed within about 5% and most within 2% except for the result for the Persian Gulf which was 50% different.  The curve fitting gave a period of 12.2 years, but the spectral analysis showed 2 peaks of 12.3 and 24.5 years as shown in the Figure 6 below.  A best fit curve with a longer period is also shown in the file of graphs.

The Indian Ocean and the adjacent seas and gulfs show multiple peaks or short periods in the spectral analysis.  The Indonesian Sea has a single peak of 10.9 years, but this may be due to irradiance.  The Indonesian Sea is studded with 100’s of islands with its own particular flow pattern.  But what is of interest is the convergence plot that shows more clearly the damped oscillations pattern as is seen in Figure 7.

Finally, the Eastings order was used to see if there was any variation with longitude with any parameter.  No totally  clear evidence was found but below in Figure 8 is a plot of “acceleration” against Easting for the 24 areas which does not appear to be a random graph .

If there was a decadal oscillation around the Earth it would show up in the phase shifts which would affect the “acceleration” calculation.  This effect was investigated by repeating the Indian Ocean calculation but starting the data in 2000 instead of 1993.  Starting in 1993 it now registers an “acceleration” but starting in 2000 it registers a “deceleration”.  Both analyses are shown in the file of graphs.  The corresponding sinusoidal curves and spectral analyses are little changed.

At the start it was stated that this work was not a thorough analysis of all the NOAA sub-sea datasets but more a systematic presentation of a large amount of analysis and graphical presentation for others to comment upon.  It is hoped readers may find it informative.  I know many are sceptical of any curve fitting be it quadratic or sinusoidal.  Many reject the data totally,  but with such a large database of readings it seemed a waste not to carry out some investigations.  If you don’t look you don’t find.

Part 2 – NOAA Sea Levels – Variation based on individual satellites

Following on from Part 1 when the averaged sea levels were studied, Part 2 investigates the individual satellite readings.  Little has been produced studying the separate satellites although one example has been shown a number of times, namely the graph by Willis Eschenbach shown in Figure 9.

This has been used to help discredit the findings that an acceleration in sea level rises exists – a worthy use.  To a lesser extent the graph has been used to discredit the sinusoidal curve fitting but as part of this analysis the equivalent graph has been produced and is shown in Figure 10.

It can be seen that we are all singing from the same hymn sheet.  But Nature and NASA may have combined to mislead somewhat.  Figure 10 can be modified by subtracting the linear fit values from all the readings.  This results in Figure 11.  On this are marked 2 points of inflection where the curvature changes sign.  These are at a residual value of -0. 2 mm.

Each half of the sinusoidal curve is skew symmetric about an inflection point and in this case the 2 sets of satellite data are roughly skew symmetric about an inflection point.  If they had been exactly skew symmetric then each pair of satellites would have had the same slope.  Hence having 2 pairs of satellite data with almost the same slope is a sign that the data may follow approximately a sinusoidal curve.  Plots similar to Figure 11 are produced for all 24 sub sea areas and most are different from the Global graph as they have different phase shifts and/or different periods.  The only similar case is that of the Atlantic Ocean which hints that this has some input to why the Global variation has a sinusoidal variation.

Each region of sea will generally have 3 plots which are described by reference to the Yellow Sea again.

All the graphs can be found on the Google Drive file.

The first graph, Figure 12, shows the linear fit to all the data together with the linear line for each satellite.  All the lines for the Sentinel-6MF satellite are more erratic due to the short period involved and the domination of the latest El Niño during this period.

Figure 13 shows the 5 satellite linear lines superimposed on a best fit sinusoidal curve.

Finally, Figure 14, shows all the individual data with the best fit sinusoidal curve superimposed.

The 2 sets of graphs are arranged to have a similar outlay with each sub area occupying one page.  If possible, they can be viewed side by side on a split screen. Figure 15 shows a split screen presentation for the Indonesian Sea.  Some computers/systems may not be able to accomplish this. 

Comparing the first figure of each sub area with the “global” plot only the Atlantic plot is similar except for the 2 special areas namely the Southern Seas and the Tropics.  The North Atlantic and North Sea do not compare with the “global” so no definitive conclusion can be made.  Having said that the Atlantic Ocean, North Atlantic Ocean and North Sea all have a period in the range 24 to 27 years according to the fitted sinusoidal curves.   It is planned to revisit the question of why the “global” sea level has a variation by using later procedures, like spectral analysis, on the Tidal Gauges in the northern reaches of the Atlantic Ocean.

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