Guest Essay by Alan Welch – facilitated by Kip Hansen –14 May 2022

__Nerem et al Paper, 2018, 4 Years on__

by Dr Alan Welch FBIS FRAS, Ledbury, UK — May 2022

(Note: One new image has been added at the end of the essay.)

** Abstract** Having analysed the NASA Sea Level readings over the last 4 years it has been concluded that the accelerations derived by Nerem et al. are a consequence of the methodology used and are not inherent in the data. The analyses further predict that the perceived accelerations will drop to near zero levels in 10 to 20 years.

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It is now 4 years since the paper by Nerem et al. (2018) ** ^{1}** was released. It spawned many disaster pictures, such as the Statue of Liberty with the sea lapping around her waist, and a proliferation in the use of Climate Crisis or Climate Catastrophe in place of Climate Change by the likes of the BBC and the Guardian.

It also kick-started my interest in Climate Change, not by what it presented, but by the unacceptable methodology used in determining an “acceleration”. I have inserted acceleration in quotes as care must be used in interpreting the physical meaning behind the coefficients derived in fitting a quadratic equation. In the paper by Nerem et al. there were 3 stages.

Mathematical – Coefficients are calculated for a quadratic equation that fits the data set.

Physical – Attaching a label – ”acceleration” – to 2 times the quadratic coefficient.

Unbelievable – Extrapolating to the year 2100.

The first is straightforward and acceptable. The second is very dependent on the quality of the data and the length of period involved. The third is fraught with danger as the quadratic term dominates the process when used outside the range of data. The last point is illustrated in Figure 1. This appeared in https://edition.cnn.com/2018/02/12/world/sea-level-rise-accelerating/index.html with the caption “Nerem provided this chart showing sea level projections to 2100 using the newly calculated acceleration rate”.

Figure 1

As a retired Civil Engineer with 40 years’ experience in engineering analysis I appreciate that curve fitting can, with care, be used to help understand a set of data. But to extrapolate 25 years’ worth of data for more than 80 years into the future is in my mind totally unacceptable. But it is this “acceleration” that generated the alarmist press following publication.

I will now discuss several aspects concerning the sea level data, including what could have been done differently in 2018, what the current situation is and what can be learnt from studying the last 10 years’ worth of data. Prior to 2012 the data, and any related analysis, were more erratic, but with time a steadier picture is emerging.

The Feb 2018 data were the first data analysed. The data used were derived from the NASA site https://climate.nasa.gov/vital-signs/sea-level/. These data do not include any of the adjustments introduced by Nerem et al. but calculated values for slope and “acceleration” are not too dissimilar. In discussing “acceleration” the process can be made simpler by taking the values of the straight-line fit, i.e., the slope, away from the actual readings and working with what are called the “residuals”. Using residuals or the full data results in the same “acceleration” but it is easier to see the trends using the residuals.

Figure 2 below shows quadratic and sinusoidal fits starting in Jan 1993 up to the Feb 2018 using the latest values of sea levels. (See Note 1 below)

Figure 2

__Situation in 2021.__

A later set of results refer the period from Jan 1993 up to Aug 2021. The above graph has been updated in Figure 3 to show that the x^{2 }coefficient is now 0.0441.

Figure 3

This update shows that the sinusoidal form curve is still a reasonable alternative to the quadratic curve although the period could be extended to 24 or 25 years and the amplitude increased slightly. The 22-year period and the amplitude have been retained for the sake of continuity although the quadratic curve is reassessed at each update, which has the effect of slightly modifying the slope and residuals.

__Study of the last 10 years set of data.__

The NASA data were analysed over the last 10 years on a quarterly basis using the full Aug 2021 set of data. The “acceleration” was calculated for each time step using the data from 1993 up to each date. In tandem with this a second set of “accelerations” were derived by assuming the data followed the pure sinusoidal curve listed on the figures above. In the long-term these “accelerations” will approach near zero but when the wavelength and period being analysed are similar unrepresentative “accelerations” will be derived. Note 2 gives more detail for the sinusoidal curve to explain the process and results and illustrate the curve fitting process.

The results of these 2 sets of analyses are plotted in Figure 4 as “accelerations” against date NASA data set was released and analysed. For example, the two “accelerations” for 2018 would be those derived using a quadratic fit for both the NASA data and the pure sinusoidal curves over the period Jan 1993 to Jan 2018 respectively. The graph on the left shows the “acceleration” for the NASA data and the sinusoidal curve. Their shapes are very similar but offset by about 3 years. Shifting the sinusoidal curve over 3 years shows how closely the 2 curves follow each other. This close fit is of interest. The NASA “acceleration” peaked in about Jan 2020 and is reducing from then onwards dropping by about 8% over 2 years. Working backwards from the peak the “accelerations” keep reducing until at about Oct 2012 they were negative, i.e., deacceleration. The close fit with the shifted sinusoidal curve may be coincidental but there seems to be a clear message there, that is the high “acceleration” quoted by Nerem et al. is more an outcome of the method used and not inherent in the basic data.

Figure 4

The next few years will be telling as to whether the sinusoidal approach is more representative to the actual behaviour and if the NASA data continues to produce a reducing “acceleration”. If the actual “acceleration” curve follows the trend of the sinusoidal curve the perceived “acceleration” will have halved in about 6 years and reached near zero values in about 15 years.

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

**Note 1.** The NASA data changes from month to month. Usually this is confined to the last month or two of data due to the method used in smoothing the readings. In July 2020 there was a major change to all the data by up to 2.5 mm which had little effect on the slope, but the “acceleration” was reduced by about 0.005 mm/yr^{2}. I have been unable to ascertain the reason behind these adjustments, but they have little effect on the overall findings.

**Note 2.** The Sinusoidal Curve shown in figure 5 will be analysed.

Figure 5

The “accelerations” derived from analysing this sinusoidal curve over a range of periods from 2.5 years to 70 years are shown in figure 6.

Figure 6

The next 5 figures illustrate the curve fitting process for various time periods.

Figure 7 uses a short 5-year period and the fitted quadratic curve is very close to the actual sinusoidal curve and in this instant gives an “acceleration” of -0.2716 mm/yr^{2} very close to the curve’s maximum acceleration of 0.285 mm/yr^{2} obtained by differentiating the equation twice.

Figure 7

Figure 8 uses a 15-year period and the “acceleration” drops to -0.0566 mm/yr^{2}.

Figure 8

Figure 9 is very close to the period used by Nerem et al. in that it uses 25 years. The resulting “acceleration” is 0.0904 mm/yr2 similar to that paraded by Nerem.

Figure 9

Figure 10 covers 35 years and results in a rapid reduction in “acceleration” to 0.0118 mm/yr^{2}. (typo corrected with thanks to Steve Case)

Figure 10

Finally extending the period to 65 years, which is nearly 3 periods of 22 years, results in a near zero “acceleration” as shown in Figure 11.

Figure 11

The following image has been added at the request of Dr. Welch (15 May 2022, 9:00 am EST):

Fig 2 from Nerem 2022 with prediction by Welch

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__About Dr. Alan Welch:__

Dr. Welch received a B.Sc.(Hons 2A) Civil Eng. From the University of Birmingham and his PhD from the University of Southampton. He is a Chartered Civil Engineer (U.K.), a member of the Institution of Civil Engineers (U.K.) (retired), a fellow of the British Interplanetary Society, and a fellow of the Royal Astronomical Society.

Currently retired, he has over thirty years’ professional experience across many fields of engineering analysis. Complete CV here.

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__Comment from Kip Hansen:__

Dr. Welch has been working on this analysis for years and has put his findings together at my suggestion as an essay here. The above is the result of many edited versions and is offered here 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 discussed by Welch

On a personal note: *This is not my hypothesis*. I do not support curve fitting in general 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 previous essay on sea levels here at WUWT.

I do feel that Dr. Welch’s analysis deserves to be seen and discussed.

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

Praise for his work in comments should be generous and criticism gentle.

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