Further Exploration of Historical Sea Level Rise Acceleration

by Chris Hall


This article builds on a previous posting of mine entitled “Sea Level Rise: Hockey Stick or Roller Coaster”. See:

In that article, I outlined an approach that I used to tease out signs of acceleration in the rate of rise of sea level in the historical tidal gauge provided by the Permanent Service for Mean Sea Level or PMSL (Holgate et al., 2013; PSMSL, 2022). The posting was inspired by the peer reviewed article Nerem et al. (2018), herein referred to as PNAS2018. In that article, the authors estimated the current rate of change of the rate of sea level rise (i.e., sea level acceleration) and they argued that the historical tidal gauge record was inadequate for measuring sea level acceleration of the past. I wanted to see what the tidal gauge record had to say about historical sea level rise acceleration.

Briefly, I explored many different avenues to calculate prior sea level rise acceleration to see if I could determine whether modern acceleration found in PNAS2018 was a novel and new phenomenon, or whether this sort of acceleration ebbed and flowed throughout the 20th century. I wound up picking a subset of data from the most complete tidal gauge records over the period from 1925 to 2015, a kind of top 100 sites on the “Tidal Gauge Hit Parade”. Using that subset, the best method that I found to combine acceleration signals, in a manner that did not produce artifacts caused by missing data points, was to first calculate an acceleration record for each site and then combine the acceleration data using an area-weighted average. See the previous post for details on the method used.

Since posting that article of WUWT, I realized that I could use a similar technique to cast a wider net and exploit data from a much larger subset of the 1548 sites recorded in the PMSL dataset. The results of that effort are outlined in this posting and it represents the maximal amount of historical sea level acceleration information that I can derive.

Where The Data Are

The PMSL dataset that I had downloaded had site information for a total of 1548 tidal gauge sites, but only 1537 sites had local sea level data. Records begin in 1807 for the tide gauge in Brest, France, and the information that I had finished at the end of 2021.

To get a measure of sea level rise acceleration, ideally I would use 25 years (plus 1 month) of data centered about a point in time and I fitted a quadratic polynomial to the data. Because of missing data, the raw information can resemble Swiss cheese at times, so I relaxed the rules a bit so that I required that, for a given month at a site, there had to be a minimum of 200 valid data points within the plus or minus 12.5 year time window surrounding that month. The choice of 200 as a cutoff was arbitrary, but reasonable given that it meant that there were sufficient data points to get some decent fitting statistics and that both the time preceding and after the chosen month are represented.

In Fig. 1, I show the number of sites that could contribute acceleration data points to the overall record as a function of time. Note the logarithmic scale. There are very few usable sites in the first part of the 19th century, but after about 1880, things pick up a bit. By about 1920, the density of available date becomes much more substantial.

Figure 1: Where the data are. Number of sites with valid sea level acceleration values for each month covered by the PMSL dataset.

I also would like to express a mea culpa about my earlier article. I had neglected to calculate error estimates for the sea level acceleration values, which is a bit embarrassing for me given that the late great Derek York was my PhD supervisor. Derek was the man who taught isotope geochemists how to properly fit straight lines through arrays of isotope ratio data points, and before you scoff at that and say it’s trivial, in fact it is a tricky bit of nonlinear inverse theory. So as penance, I have endeavored to provide error estimates for acceleration values in this article.

But first, I want to address an issue raised in the comments from my previous article. It deals with the issue raised that it is important to look at the details of each site’s local conditions and that such factors can significantly affect the apparent sea level rise acceleration. In the next section, I look at this question, which to a certain extent hinges on the philosophical distinction in scientific communities between “lumpers” and “splitters”. I was trained as an engineer and worked in both physics and geology departments. Physicists tend to be “lumpers”, i.e., they are delighted if they can mostly explain a phenomenon. “Splitters” delight in examining all of the exquisite details and are never happy until all of the different details of a phenomenon are categorized.  Geologists tend to be splitters. Because I am fundamentally a lazy person, I tend to fall into the lumper category, and I confess my sins happily.

The Acceleration Record is Mostly Global, Mostly

It was argued that local effects like the pumping of groundwater might cause an increase of local sea level rise. My original take was that this was an anthropological effect that should show up as positive, recent acceleration. However, it was also noted that if pumping stopped, that this could show up as a deceleration and be misconstrued as being a natural phenomenon. I decided to do a little test of this hypothesis and the results are shown in Fig. 2.

It was argued that local effects like the pumping of groundwater might cause an increase of local sea level rise. My original take was that this was an anthropological effect that should show up as positive, recent acceleration. However, it was also noted that if pumping stopped, that this could show up as a deceleration and be misconstrued as being a natural phenomenon. I decided to do a little test of this hypothesis and the results are shown in Fig. 2.

Figure 2: Results of a randomized trial with subsets of sites having strictly local sea level rise beginning 1950-1970 and ending 1970-1995. See text for details

For this thought experiment, a percentage of sites, varying from 5% to 25% had local enhancement of sea level rise, presumably caused by increased groundwater use beginning somewhere from 1950 to 1970 and ending some time between 1970 and 1995. Start and stop times were randomized as it was assumed that local effects would not be synchronized around the world. Similarly, the amount of subsidence cause by water pumping was allowed to uniformly vary up to 5 mm/yr. The results show that even if a full quarter of all sites had significant time varying local subsidence, one would expect that the overall effect on the complete local sea level acceleration record to be significantly less than the PNAS2018 acceleration value. So, yes, local effects can show up as oscillations in the global sea level rise, but the effect is likely to be small compared to the variations calculated by the complete PMSL dataset. To get the wiggles seen in Fig. 2 to compare with the PNAS2018 value, you need to squint and increase the rate of subsidence and/or increase the percentage of sites with manic pumping.


Figure 3: Smoothed global sea level acceleration record from 1880 to the present. Light blue shading indicates 1 and 2 sigma error estimates. Effects of local variable subsidence and PNAS2018 estimate shown for reference.

The results of compiling all of the tide gauge record data are shown in Fig. 3. The sites were sorted into 5×5 degree latitude and longitude grid cells and for each month of the record, an error weighted average for every cell was calculated. To combine the information over the set of 321 grid cells that contributed to the record, a weighted average that included both error and grid cell area was calculated. The record plotted in Fig. 3 has been smoothed by removing the 3 highest frequency components from its CEEMD decomposition. The light blue shading in Fig. 3 shows both 1 and 2 sigma error bars and the results of the 25% local pumping study shown in Fig. 2 is shown for comparison. Note that as the number of sites contributing to the record increases with time (see Fig. 1), the width of the error bars shrinks. Note that my global historical sea level rise record agrees quite well with the PNAS2018 value.

To interpret what the record may mean, it’s important to note that whenever sea level acceleration equals zero, this corresponds to either a local maximum or a local minimum of the sea level rise relative to a constant linear trend. With that in mind, I estimate that there were local minima around the following years: 1883, 1902, 1922, 1958, and 1977. Local maxima occurred around 1893, 1915, 1940, and 1965. I’m trying to ignore minor excursions either plus or minus. We’ve been in a fairly protracted period of positive acceleration since 1977, but we flirted with deceleration around 2003. My estimate of the beginning of the positive acceleration is a tad later than that of Dangendorf et al. (2019). It’s certainly possible that some of the record is due to anthropogenic inputs, but is it “temperature” or “climate-change” driven? I try to address this question in Fig. 4.

Correlation or Causation?

Figure 4: Sea level acceleration compared to SST acceleration since 1880.

Fig. 4 shows the raw, unsmoothed sea level acceleration record, with annual variations included, compared to the HadCRUT4 sea surface temperature (SST) acceleration. Error estimates are included for the sea level record, but for clarity they are not included for SST. Typical SST errors are visually similar in size at this scale to sea level errors after about 1950. The overall correlation coefficient for the two functions since 1880 is 0.44 with a lag of zero months. As shown in my previous post, that’s not really a very high correlation coefficient for a function with this degree of autocorrelation. However, just by eye, it seems that there is some correlation, at least in the first half of the records. Something significant appears to have happened to both temperature and sea level at the end of the 19th and the beginning of the 20th century. Then sea level variations settle down a bit, but the two records still seem to be on the same dance card until about 1950 or so. However, after that, SST and sea level appear to become decoupled. See the large positive SST acceleration in the late 1960s, with nary a response from sea level. I think that sea level rise since about 1950 may have been significantly influenced by anthropogenic factors, but temperature is not likely to be the mechanism.

I’m just wildly speculating here, but I wonder if the variations seen in sea level acceleration since about 1950 might be caused by the building of large dam projects for decelerations, and mining of ancient groundwater for accelerations. The destruction of dams and/or the enhanced release of reservoir water, a so-called “snail darter” effect, could also lead to sea level rise acceleration. I don’t have the data on hand to say one way or the other, but it’s an interesting thought. A big caveat, however, is that the number of tidal gauge sites included in the record in its early part are measured in the dozens or scores, while near the end, they are measured in the hundreds. So it is quite possible that the correlation between sea level and SST in the late 19th and early 20th centuries is a coincidence.

In conclusion, I think that the sea level acceleration derived here from the entire tidal gauge record is close to the most you can squeeze out of the PMSL dataset. Of course, one could add in things like volcanic and ENSO effects, but to me those are just natural phenomena, the timing of which we neither fully understand nor can control. We may be affecting sea level rise acceleration, but it does not appear to be due to a rise in sea surface temperature. Could we then paraphrase Cassius by saying that the fault dear Brutus is not in our SUVs, but in our dams? 


Dangendorf, S., Hay, C., Calafat, F.M., Marcos, M., Piecuch, C.G., Berk, K. and Jensen, J., 2019. Persistent acceleration in global sea-level rise since the 1960s. Nature Climate Change, 9(9), pp.705-710.

Nerem, R.S., Beckley, B.D., Fasullo, J.T., Hamlington, B.D., Masters, D. and Mitchum, G.T., 2018. Climate-change–driven accelerated sea-level rise detected in the altimeter era. Proceedings of the national academy of sciences, 115(9), pp.2022-2025.

Permanent Service for Mean Sea Level (PSMSL), 2022, “Tide Gauge Data”, Retrieved 09 May 2022 from http://www.psmsl.org/data/obtaining/.

Simon J. Holgate, Andrew Matthews, Philip L. Woodworth, Lesley J. Rickards, Mark E. Tamisiea, Elizabeth Bradshaw, Peter R. Foden, Kathleen M. Gordon, Svetlana Jevrejeva, and Jeff Pugh (2013) New Data Systems and Products at the Permanent Service for Mean Sea Level. Journal of Coastal Research: Volume 29, Issue 3: pp. 493 – 504.  doi:10.2112/JCOASTRES-D-12-00175.1.

via Watts Up With That?


February 21, 2023 at 08:27AM

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