Replicating Climate Papers on Sea Level Rise

Frequently I'm told that climate-related papers are fraudulent, usually because the person revaluating the paper is 1) predisposed to deny any data they don't like and 2) completely illiterate about what they're reading. In discussing these papers, I often find that wading through the details of the analysis can go so far over their heads that they don't even bother reading either the paper they're complaining about or my corrections to their reading of the paper. Brandolini's Law can get the for two reasons: it takes an order of magnitude more time to refute nonsense than it does to create it and those those who create the nonsense frequently lack the literacy to read the rebuttal (a point I make here).

Occasionally there's a congruence of two conditions that can allow rational discussion to proceed: 1) the paper is simple enough to be replicated with a spreadsheet (reducing the time it takes to refute nonsense) and 2) the individual is at least attempting to understand the paper. In my experience, the first condition is met with far greater frequency than the second, but a congruence of both occurred just today that I thought would be fun to share as an illustration that, even with the advantage afforded contrarians by Brandolini's Law, with patience nonsense can be refuted. I think this might be a good object lesson on how to debate papers with the (now seemingly rare) contrarian that is actually interested in the climate discussion.

The discussion had to do with Hamlington et al 2024,[1] a paper that determined that SLR rates have doubled between 1993 and 2024. The person on social media had this (among other things) to say about the paper:

As explained in the paper, the authors took the satellite altimetry data, which is ACTUAL measured sea level rise, then “corrected” it for Global Isostatic Adjustment (GIA). GIA is an estimate, mostly pulled out of thin air, for the deformation of the sea bed/ocean floor. But we don’t care what the deformation of the sea floor is. We care about the actual measured rate of sea level rise. By adding a GIA, which they don’t bother to explain how much adjustment they made to the actual data, they are able to adjust the data to fit a desired profile.

From this (and other largely inconsequential things), he concludes, "Clearly, their claim that the rate of sea level rise doubled from 1993 to 2023/2024 is a fraud. A fraud that many folks continue to regurgitate." Now a few initial corrections should be immediately obvious before getting into the details of the paper:

1. The GIA correction in the paper stands for "glacial isostatic adjustment" not "global." This reader hasn't even read the paper well enough to know what GIA stands for.
2. The GIA correction is not "pulled out of thin air." It's a bias correction that is both small and strictly linear at ~0.3 mm/yr (it's so small it's roughly equal to the uncertainty in the trend for 1993-2023) that accounts for the fact that the ocean basin is enlarging. And Hamlington links to another paper with altimetry data without GIA applied.
3. Because GIA is strictly linear, it has zero impact on calculated acceleration; it doesn't affect how curved the GMSL graph is. This is also explained in the paper: "The procedure is the same for the acceleration, except that GIA can be neglected since there is no acceleration associated with GIA."
4. We do care that the ocean basin is getting larger; we can only expect the sea level rise budget to close if we account for all the significant factors that affect SLR. And the authors also indicated why its applied here: "The GIA correction ensures that the observed sea level changes are reflective of actual water volume and mass changes, and to allow for direct comparisons to the projections from the IPCC AR6."
5. The authors did bother to explain that they added GIA, which is a well-known correction, and the paper contains citations so that readers can discover what isn't explicitly stated in the paper.

Already we're seeing that this person has not read the paper carefully, and the conclusion that the paper's claim is fraudulent doesn't follow from the argument in his post. His reasoning here is that the GIA applied to the data is an arbitrary guess, pulled out of thin air, and so the 2-fold increase in SLR rates could be the product of the applied GIA and not the measured data. This logic is obviously flawed because GIA is a linear adjustment, so it doesn't affect the calculated acceleration value of 0.08 ± 0.06 mm/yr^2. It only affects the overall trend of 3.3 ± 0.3 mm/yr (1993-2023). 

And the fact that Hamlington applied the GIA correction actually reduces the ratio of 2024:1993. This is easy to demonstrate. Here are the reported acceleration values from the above graph in the paper:

With GIA

1992     2.1 ± 1 mm/yr

2024     4.5 ± 1 mm/yr

Ratio: 2.14 ± 1.1 x

Without GIA (reduce each by 0.3 mm/yr)

1992     1.8 ± 1 mm/yr

2024     4.2 ± 1 mm/yr

Ratio: 2.33 ± 1.4 x

By applying GIA, Hamlington essentially reduced the ratio from 2.33x to 2.14x, so the adjustment works exactly in the opposite direction of what this person considers fraudulent. Now you may be unsurprised that this response by itself was not convincing for this person, so I downloaded the satellite data and plotted the best fit quadratic through the data. Here's my plot with the equation for the best fit quadratic.

As expected, I got similar results. The acceleration value is 2x the quadratic coefficient, so 0.0752 mm/yr^2. The difference between this and Hamlington's calculation is likely because of the ~19 months of data I downloaded after this paper was published. But now that I have constructed this graph and found the best fit quadratic, I can replicate the findings of Hamlington's paper. The best fit curve can be written with its first derivative as:

f(t) = 0.0376t^2 -148t +144906.

f'(t) = 0.0752t-148

If we plug in 1993 and 2024 into the second equation, we get:

f'(1992) = 1.80 mm/yr

f'(2024) = 4.20 mm/yr

Ratio = 2.34x

Now we can add 0.3 mm/yr to each to apply GIA to these values. We get a new equation, which we'll call g'(t):

g'(t) = 0.0752x-147.7

Notice the slope (acceleration value) is the same; what changes is the y-intercept value (it's reduced from 148 to 1.47.7). Here we get rates that essentially replicate Hamlington's paper:

 

g'(1992) = 2.10 mm/yr

g'(2024) = 4.50 mm/yr

Ratio = 2.15x

So we can conclusively rule out any reasonable possibility of fraud in this paper. Hamlington has described his methods and data used sufficiently for anyone with a spreadsheet and a little patience to come up with the same conclusion as Hamlington. Using the GIA correction has no effect on acceleration, but does reduce the size of the ratio by a small amount, meaning that the person I was responding to was complaining about a feature of the study that worked in the opposite direction of his conspiracy theory. But here's the rub. I spent at least 2 hours doing this work. I doubt very seriously that it took this person more than 10-15 minutes to write his post questioning this paper. And this is where Brandolini's Law favors contrarians. It takes almost no time at all to make up nonsense about a paper you don't understand. It takes an order of magnitude more time to prove that this person's claims are just nonsense. But thankfully, it can be done.

Reference:

Hamlington, B.D., Bellas-Manley, A., Willis, J.K. et al. The rate of global sea level rise doubled during the past three decades. Commun Earth Environ 5, 601 (2024). https://doi.org/10.1038/s43247-024-01761-5