Guest Essay by Dr. Alan Welch FBIS FRAS — 5 April 2024 — 1900 words/8 minutes
Abstract In part 1, it was proposed that the sea level rise was basically linear with a small sinusoidal variation added. Part 2 investigates whether this variation is caused because the satellites orbit at 66 degrees inclination and a decadal oscillation in the seas spanning this latitude creates a lack of some data. Tidal gauge readings at locations around the Greenland and Norwegian Seas and the Arctic Ocean are analysed to see if there is any evidence of a decadal oscillation.
The main premise of part one in studying the 2023 satellite sea level data (Ref 1) was that the increase generally followed a linear line of about 3.3mm/year on which is superimposed a sinusoidal variation of about +/-4.2mm over a 26-year cycle. In reality the linear trend could be a small acceleration commensurate with those found in the longer-term Tidal Gauge data sets. This difference is sufficiently small as not to affect any conclusions. Figure 1 is reproduced from Part 1 to show this behaviour as of November 2023.
Figure 1
The differences between the actual reading and the linear line are called residuals and Figures 2 and 3 show these together with a quadratic fit and the sinusoidal curve as of December 2023. The latter was fitted by eye and has no mathematical basis for its parameters. Also shown are the standard deviations for the two curves which are 3.15 and 3.01 respectively compared with the standard deviation of the actual residuals of 4.20.
Figure 2
Figure 3
In the comments to Part 1 questions were rightly asked about this sinusoidal component and to why it may be occurring. A suggested answer was that as the satellites were at an inclination of 66 degrees areas of the Earth around each pole were not being monitored. It may therefore be what was not measured that creates the sinusoidal variation. So, what might that be? One suggestion is that there may be Ocean Decadal Oscillation that spans the latitude at which the satellites stop measuring. Sea level changes one side of that latitude will be measured but the related variations on the other side will be missed resulting in a sinusoidal variation.
This process is very similar to the sinusoidal variation that is evident in the long-term Tidal Gauge measurements. This was shown in the paper “Sea Level Rise Acceleration – An Alternative Hypothesis – Part 2” (Ref 2) and Figure 4 shows this behaviour. The underlying trend in this case is a low acceleration of 0.0126mm/year2. On top of this is superimposed a sinusoidal variation of +/- 6mm over a 57-year cycle.
Figure 4
A small diversion at this stage is to refer to a 2012 paper by Chambers, Merrifield and Nerem (Ref 3) in which they propose a 60-year Global Ocean Decadal Oscillation. It is worth quoting their final sentences.
“Until we understand whether the multi decadal variations in sea level reflect distinct inflexion points or a 60-year oscillation and whether there is a GMSL signature, one should be cautious about computations of acceleration in sea level records unless they are longer than two cycles of the oscillation or at least account for the possibility of a 60-year oscillation in their model. This especially applies to interpretation of acceleration in GMSL using only the 20-year record of from satellite altimetry and to evaluations of short records of mean sea level from individual gauges.”
How quickly the thinking process changed when in only 6 years the paper by Nerem et al appeared advocating the use of a quadratic interpretation in the calculation of accelerations as high as 0.1 mm/year2. Soon extrapolations up to 2100 followed with alarming graphs that caused fear amongst the population. If Moses could add an eleventh commandment he could add “Thou shalt not extrapolate polynomial regression curves”.
In the Chambers et al paper they show that there might be a Global Ocean Decadal Oscillation with a period of 60 years. Figure 5 below shows plots of sea level variation and how a 60-year curve may be envisaged. It is not an exact science and there are much shorter periods of behaviour that complicates the process, but it points to what difficulties may lie ahead in trying this with the satellite data.
Figure 5
Back to the satellite readings. A look at the coverage of the satellites may help. Figure 6 shows the limits to the satellite coverage. It is very difficult to visualise the polar regions from full global projections but it can be seen that there is less ocean below the Antarctic Circle than above the Arctic Circle and what there is in the Antarctic are parts of very large portions of the Earth’s oceans and so probably part of longer decadal Oscillations.
Figure 6
Views from above and below, Figure 7, are more informative and whilst the Arctic Sea is fully contained within the Arctic Circle there is a sizeable amount of sea between it and the North Atlantic Ocean, formed in main by the Greenland and Norwegian Seas, which will be subject to possible decadal oscillations.
Figure 7
To investigate several Tidal Gauge locations around the Arctic Ocean, the Greenland Sea and Norwegian Sea will be investigated. They were all processed in a common manner starting with the NOAA graph of sea levels then Excel graphs of sea levels with a quadratic fitting curve, of the sea levels with 100 month moving average of residuals from quadratic curve and of the 100-month moving average of the residuals.
The chosen locations have a reasonably long period of measurement with none or only short breaks in readings. Figure 8 shows the chosen locations. These are listed below in order of increasing longitude East. Hence the first few are more associated with the Greenland Sea/Norwegian Sea/ Arctic Ocean combined area.
Reykjavik – Iceland
Torshavn – Faroe Islands
Aberdeen – Scotland
Lerwick – Scotland
Bergen – Norway
Barentsberg – Svalbard
Narvik – Norway
Murmansk – Russia
Tiksi – Russia
If any Decadal Oscillations occur with the required periods it is only half of the solution. There is no way of knowing the direction the oscillations follow but there might be a good chance that they occur in a more northerly direction looking at the topography of the areas involved which does extend into the North Atlantic.
Figure 8
[Some Excel warnings. When unloading the NOAA Data it uses a CSV file. If an Excel file is produced and work is done on this with pictures created it is necessary to save as a XLS file otherwise much of the additional work will be lost. Also, when plotting moving averages do not use the Excel to plot the Trend Line as this is displaced relevant to any plots of the original data. Always calculate the moving values within the spreadsheet.]
Reykjavik
The NOAA Tidal Gauge data were extracted and are shown in Figure 9. Note there is a small gap in data around 1984 but not large enough to affect any processing. In other locations there are larger gaps in data occur and so some data is ignored. Figure 10 processes this data and produces a quadratic fit. The acceleration is low at -0. 021 mm/year2. Figure 11 shows the residuals between the 100-month average and the quadratic curve superimposed on the data with Figure 12 plotting just the residuals. Superimposed on the latter is a Sinusoidal curve with a 26-year cycle. In judging this the amplitude and phase shift are irrelevant.
Figures 9 to 12 show the process followed but for subsequent locations only the first (NOAA Graph) and last (Residuals) will be presented.
Figure 9
Figure 10
Figure 11
Figure 12
The period covered is quite short and whilst the correlation is poor the actual readings show approximately 2 cycles covering about 60 years.
Torshavn
Figure 13
Figure 14
There is a high degree of correlation between the 2 curves with the actual readings having a slightly shorter period.
Aberdeen
Figure 15
Figure 16
This location has the longest period of readings at nearly 160 years. This allows sufficient time for longer periods of oscillation to occur and it can be seen that there might be larger 90-year period superimposed. There sems to be a number of shorter periods of about 20 years throughout the period and especially after 1900.
Lerwick
Figure 17
Figure 18
Again, there is a good correlation between the 2 curves.
Bergen
Figure 19
Figure 20
Some correlation exists between the 2 curves except for around 1970.
Barentsburg
Figure 21
Figure 22
No reasonable correlation exists but some 20-year oscillations can be perceived.
Narvik
Figure 23
Figure 24
Two good periods of correlation exist at each end with an extra dip in-between.
Murmansk
Figure 25
Figure 26
This graph of the actual readings is dominated by a much longer cycle of about 70 to 80 years, but this site is more on the fringes of the Arctic Ocean.
Tiksi
Figure 27
Figure 28
This site is also on the Arctic Ocean and not expected to show the periodicity of the others although there are about 3 20-year cycles.
It was stated above that the amplitude and phase shift were of lesser importance but for completeness these are listed below together with the acceleration derived from the quadratic curve. The phase shift is calculated relevant to the sinusoidal curve given in Part 1 of this paper.
| Location | Acceleration mm/year2 | Amplitude mm | Phase degrees |
| Reykjvik | -0.021 | 15 | -124 |
| Torshavn | 0.053 | 12 | -28 |
| Aberdeen | 0.013 | 12 | -28 |
| Lerwick | 0.114 | 12 | -124 |
| Bergen | 0.021 | 15 | 152 |
| Barentsburg | 0.007 | 15 | -97 |
| Narvik | 0.079 | 17 | 55 |
Notes
The accelerations, or so called accelerations, are high because of the relative short (less than 100 years) periods involved. Only Aberdeen (started 1862) and Bergen (started 1915) cover more than 100 years.
Interestingly all the amplitudes fall between 12 and 17 mm. Figure 29 shows all 7 locations plotted over the period 1990 to 2024.
Figure 29
The 7 sets of results were combined and averaged to produce Figure 30 which shows the averaged variation compared with the 26-year perceived variation. The averaged results peak at +/-5.3mm, not too different from the perceived value of +/-4.2mm. The phase shift between the 2 curves is approximately 120 degrees. If the perceived variation is due to a partial lack in measuring the more northerly levels, there would be a discrepancy in value of the phase shift.
Figure 30
What conclusions can be drawn?
All the graphs show some form of decadal oscillation. In the areas away from the Arctic Ocean there is evidence of cycles in the range of 20-to-30-year periods.
The averaged graph shows an amplitude close to that found when analysing the satellite data.
The 26 year cycle proposed is sufficient to generate “accelerations” when analysed over periods as small as 30 years.
The decadal oscillations envisaged are capable of creating a 26 year, +/-4.2mm variation about the linear sea level rise of about 3.3mm/year.
It all points to the fact that the Tidal Gauge and Satellite data is of a remarkable high quality with coherent patterns of behaviour being displayed when processing it.
References
2 https://wattsupwiththat.com/2022/06/28/sea-level-rise-acceleration-an-alternative-hypothesis-part-2/
3 Chambers, Merrifield and Nerem (2012). “Is there a 60-year oscillation in global mean sea level?” https://acp.copernicus.org/preprints/15/20059/2015/acpd-15-20059-2015.pdf
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