# 30 Years of Measuring and Analysing Sea Levels using Satellites

Guest Essay by Dr. Alan Welch FBIS FRAS, Ledbury, UK — 3 May 2023

The release of the Sea Level Data up to Jan 2023 marks 30 years of satellite measurements using the quartet of satellites Topex and Jason 1, 2 and 3.  It also marks 5 years of my interest in sea level rises, not as a climate scientist, but as a chartered engineer with nearly 40 years’ experience in engineering analysis.  This interest was stimulated by the 2018 paper by Nerem et al (1) in which they introduced the concept of dangerously high sea level accelerations.

A year ago, I produced 2 essays.  The first essay (2) showed the “accelerations” derived were probably the outcome of the methodology used.  The second essay (3) showed that 30 years is too short a period to derive a meaningful acceleration.

The important graph in this update is Figure 3 which shows the change in “accelerations” using the Nerem approach when applied to the NASA data set and also to a sinusoidal data set.  When accelerations are embedded in “ “ it implies these are based on 2 times the quadratic coefficient of a curve fit and may not necessarily be considered as a physical acceleration per se.

Every 1, 2 or 3 months the sea level data is released on the https://climate.nasa.gov/vital-signs/sea-level/ web site and these data have been analysed continuously since Feb 2018.  The latest readings were downloaded via the April 2023 NASA Climate Change Newsletter.  Figure 1 shows the NASA Data together with linear and quadratic best fit curves.

It is much easier to see trends when just the “Residuals”, the differences between actual values and the straight line, these being plotted in Figure 2.

For most of the analyses since 2018 a sinusoidal curve with a period of 22 years and an amplitude of +/- 3.5 mm was used.  In reference 2 this was judged as needing updating and the period and amplitude were increased by about 20% and a small change in phase shift applied.  The standard deviation of the residuals is 4.12mm whilst the standard deviations of the actual results about the quadratic and sinusoidal curves are 3.06 and 3.01 mm respectively implying  that the sinusoidal may be a slightly better fit.  (The use of an amplitude of +/- 4.2 mm is slightly embarrassing as it implies a degree of exactitude that many “climate scientists” would be proud of!).

In reference 2 the process of calculating “accelerations” for each successive batch of readings was applied to the sinusoidal curve and the resulting “acceleration” using the modified sinusoidal curve plotted in Figure 3 together with the actual derived “accelerations”.  The sinusoidal curve has been (rightly or wrongly) extended to the year 2026.  If extended much further the curve would approach zero in an oscillatory manner as shown in Note 2 of Reference 2 but this should not be considered a definite long-term prediction.  The main danger in all climate change work is Extrapolation – a few years may be justified but many graphs are produced with eye watering amounts of extrapolation.  Note the curve labelled “Sinusoidal” is not sinusoidal in shape but relates to the fact that it is based on the sinusoidal data.  (In the comments in reference 2 the way the original sinusoidal curve was handled was justifiably criticised as not being mathematically precise, but a pragmatic engineering approach (aka gut feeling) led to the idea presented in figure 3.  With the previous sinusoidal equation, the 2 curves were separated by 3 years but displayed sufficient similarity as to point to a promising line of enquiry).

The calculated “accelerations” have been reducing with every set of data since peaking in Jan 2020 and Figure 4 plots the % reduction in perceived “accelerations” since Jan 2020.  This works out at about 4.5% reduction per year.  On the NASA Web Site reference is made to the recent La Niña event having reduced the “acceleration” so it will be interesting to see what the next year or two will bring.

Figure 5 combines the Linear Fit with the Sinusoidal Variation.

Main Findings

1 The perceived “accelerations” have been reducing month on month since peaking in Jan 2020.

2 The Quadratic and Sinusoidal curves fit equally well.  Remember they are products of the data available and great restraint must be used if extrapolation is contemplated.

3 Should the reduction in “accelerations” follow that shown by the sinusoidal curve as shown in figure 3 in 5 years’ time or so the “acceleration” should be down to nearly half the 2020 peak.  (In 5 years, I’ll be over 90 so hopefully someone else will pick up the batten if I shuffle off this mortal coil!)

4 A question (hypothetical?) that could be asked is if there is a small sinusoidal content in the variations where does it come from?   Possibly it is not within the data as measured but comes about by what is not measured.   The satellite readings only cover about 95% of the oceans.  If there are decadal ocean oscillations across the +/- 65 degree latitudes this could show up as a sinusoidal variation.  Figure 6, from the NOAA site (https://www.star.nesdis.noaa.gov/socd/lsa/SeaLevelRise/LSA_SLR_timeseries.php) shows the extent of the ignored polar regions in relation to the polar seas.

5 The variation considered is only +/- 4.2 mm – that’s just over 0.16 inches in old money – which is next to nothing in comparison with some of the ocean variation given in the NOAA site over the last 30 years.  Examples worth inspecting are the northerly seas such as the Bering Sea and the North Sea.  Figure 7, taken from the University of Colorado site, https://sealevel.colorado.edu/data, showing variations of 20cm or more over the last 30 years.  A change of 4.2 mm would only be as big as the “o” in Colorado!

References

1.      Nerem, R. S., Beckley, B. D., Fasullo, J. T., Hamlington, B. D., Masters, D., & Mitchum, G. T. (2018). Climate-change-driven accelerated sea-level rise detected in the altimeter era. (full text .pdf)  Proceedings of the National Academy of Sciences of the United States of America, 115(9).  First published February 12, 2018

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Comment from Kip Hansen:

Dr. Welch has been working on these analyses for years and has put his findings for the now-30-year climatic-period length of satellite era sea level measurements together in this essay.  This and his two previous essays on the topic (linked in the essay and in the references) are offered here by Dr. Welch as an alternative hypothesis to Nerem (2018) ( .pdf ) and Nerem (2022). [ In a practical sense, Nerem (2022) did not change anything substantial from the 2018 paper previously discussed by Welch.]

On a personal note:  This is not my hypothesis.  I do not generally support curve fitting and an alternate curve fitting would not be my approach to sea level rise. I stand by my most recent opinions expressed in  “Sea Level: Rise and Fall – Slowing Down to Speed Up”. Overall, my views have been more than adequately aired in my many previous essays on sea levels and their rise or fall here at WUWT.

I find Dr. Welch’s analyses interesting and feel strongly that Dr. Welch’s analyses deserve to be seen and discussed.  I have encouraged him to present his findings here at WUWT.

Dr. Welch lives in the U.K. and his responses to comments on this essay will be occurring on British Summer Time : UTC +1.