I’m not asking how fast it *was* rising. I looked at that in the last post, using three different reconstructions of sea level since 1900 based on tide gauge data. And my goal wasn’t really to estimate the rate of sea level rise, as much as it was to show that the rate has not been steady, it has changed over time; in fact it has gotten faster (acceleration).

For that purpose, I used “slow” smoothing, meaning I used a long “time scale” for both methods (lowess smooth, and piece-wise linear fit) to estimate how the rate changes over time. Essentially, the estimated rate of sea level rise at a given moment was based on data covering about 30 years of time; in fact for the piece-wise linear fits it is nothing more nor less than the average rate over each 30-year segment.

Thus each momentary estimate is based on enough data to give a precise enough answer to the question: does the rate remain constant? The longer time scale gives us less uncertainty in the estimates, but it also mutes the changes which are faster than the time scale of the smooth. You just won’t see fast changes with a slow smooth.

Now I’m asking how fast sea level *is* rising, so I’ll use a “fast” smooth to get more *detail*. After all, a 30-year time span (the length of time spans used in the previous piece-wise linear fit) gives the most precise estimate of the *average* rate during the 30 years, but if the rate changes *during* that interval, such a slow fit won’t detect it. We especially want the most recent rate — so I’ll make the smooths faster, sacrificing precision for more time detail.

With both the lowess smooth and the piece-wise linear fit set to a time scale of 10 years, when we apply them to estimate the rate using the data from Church & White, we get this:

The red line shows the rate estimated by the lowess smooth (pink shading its uncertainty), the blue line the rate according to PLF (piece-wise linear fit, dashed blue lines above and below its confidence interval).

I note two thing I think are important. First, we see *multi-decadal fluctuation*, with the *rate* of sea level rise itself changing on multidecadal time scales on top of its overall rise (rise of rate = acceleration of sea level). Until about 1990, the multi-decadal fluctuation was bigger than the long-term slow increase.

Second, since 1990 things have changed. The multi-decadal fluctuation may or may not be still present (I’d be surprised if it weren’t there), but the rate has increased way beyond the pre-existing pattern of slow rise with large fluctuation. It has soared to levels high enough to establish: things are different now, and that means the future is harder to predict.

We see essentially the same thing using the data from Dangendorf et al., in fact the acceleration of sea level (increase in the *rate*) is even clearer:

We see it yet again using the data from my own sea level reconstruction:

The overall pattern is the same. Throughout most of the 20th century, there was multi-decadal fluctuation on top of a slow increase in the rate (slow acceleration of sea level). But since about 1990, the rate has increased dramatically (fast acceleration of sea level). We also have numbers for the rate of sea level rise now. For the Church & White data, lowess says 4.7 mm/yr, PLF says 4.1. For the Dangendorf data, lowess says 3.5 mm/yr, PLF says 3.7. For my own data, lowess says 5.0, PLF says 4.8.

We have yet more data to study: that from *satellites*. I’ll look at three different versions of satellite-derived sea level: from the University of Colorado (U.Colo), the Copernicus group in Europe (Copernicus), and CSIRO in Australia (CSIRO). The data don’t start until about 1993, but that’s fine; we have nearly 30 years of satellite altimetry to deduce how the sea surface height has changed in that time.

And here they are (notes: I’ve shifted them by different amounts so they don’t plot on top of each other, and I’ve removed the annual cycle):

Again I’ll apply both models, lowess smooth and PLF, with the “knots” for PLF set at 2002 and 2012 to divide the available time span into three segments of about 10 years each. When I do that to the U.Colo data I get this:

For the Copernicus data it’s this:

Finally, the data from CSIRO say this:

All three satellite data sets confirm what the tide-gauge data sets say, that the most recent decade has seen by far the fastest sea level rise. As for how fast it’s going up now, U.Colo data say 4.8 or 4.6 mm/yr (from lowess or PLF), Copernicus data say 4.2 (both models), and CSIRO data give 5.1 mm/yr.

My bottom line: based on global sea level estimated by tide gauges and by satellite altimetry, the current rate of sea level rise is about 4.5 mm/yr, probably not less than 3.5 or more than 5.5. This is relevant to sea level rise around the world, including the coast of New Jersey …

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What about acceleration of sea level rise?

As tamino notes above in the paragraph starting “The overall pattern is…” any change in *rate* of rise *is* an acceleration (or deceleration) of sea level rise. Remember your Calc 101 here.

Or, am I missing something in your question?

I took the mean rise of the s l rise rate – 13 mm/dec² (dec = decade) eyeballed out of the plots between 1990 and 2020, and wrote the rise rate function

r(t) = 50 mm/dec + a t with a = 13 mm/dec²

and integrated it to get the 2100 s l r , which yielded

h(2100) = [50 mm/dec * t + 6,5 mm/dec² * t²] (t=8dec) = 816 mm

This is the s l r got by just extrapolating the accelerating rise.

Kinimod, Thanks,