There seems to be some interest in global sea level as estimated by tide gauges. In particular, we have recently been directed to a graph of the data from Church & White, which is the most reputable of the available choices. Alas, the graph we were directed to only shows their data up to the end of 1992. What, you may wonder, happens after that?
The data extend for another 21 years, to the end of 2013. And here it is:
How, you may ponder, does this compare to what the satellites report after 1993? Like this:
How fast, you may ask, is the estimated trend since 1993 according to these tide-gauge-based data? It’s 3.56 mm/yr, even larger than the estimated rate from satellite data:
Do bear in mind that the difference (from the satellite-based estimate) isn’t statistically significant. Essentially, they agree (certainly within their uncertainty limits).
The original graph easily gives the visual impression of following a straight line since 1930. But, as I’ve cautioned so often, “looks like” isn’t a realiable way to determine results from data. It’s a great way to get ideas and clues, but history is littered with the carcasses of ideas that are wrong but were believed because of “looks like.”
One way to improve the “look” is to fit a straight line (by least squares or other methods), then subtract that fit from the data to see what’s left over. These are called “residuals,” and show a clearer picture of what the data are doing besides that straight-line increase. Here they are:
The pattern of acceleration and deceleration is now evident. Especially prominent is the recent upswing, a sign of the acceleration that has happened recently.
If we smooth the data, a lot depends on the time scale for smoothing. Too short a time scale will tell us about the ubiquitous wiggles, which is not what we’re interested in. We want to know about the persistent trends. In my opinion, a good choice for these data result in this smoothed estimate:
This also produces an estimate of the rate of sea level rise:
It’s rather apparent that the rate has gone both up and down (both acceleration and deceleration of sea level), but that recently we’ve seen a sizeable increase in how fast the ocean is rising.
To some, it may seem puzzling that those in denial of the danger of sea level rise focus so strongly on denying the existence of acceleration. Claims of its absence are sometimes based on fitting a quadratic curve when such is not an appropriate choice and falling back on the simpleton’s approach, but are more often based on linking to a graph from NOAA and saying “See!”
But even without acceleration, the present rate is real trouble. Miami is already spending about half a billion dollars to deal with the flooding they’re already getting from sea level rise. Another foot will bring yet more damage, and threatens the economic viability of somewhere in the neighborhood of a trillion dollars of prime real estate development.
We expect to see considerably more acceleration this century. This is suggested by empirical models (such as those of Vermeer and Rahmstorf), on “process models” (which emulate the physical process), and on something we like to call “laws of physics.”
Of this we can be certain: deniers will continue to declare “no acceleration” based on shoddy analysis or, more often, none at all. Meanwhile, the sea will continue to rise.
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Open Mind 
Great stuff. Looks like a small typo, though: “The data extend for another 11 years, to the end of 2013.” should be “The data extend for another 21 years, to the end of 2013.”
[Response: Thanks, fixed.]
One important point is that given the spatial and temporal variability in individual tide gauge records, and the scale of local sea level changes, the acceleration in sea level rise becomes evident in the *global* record decades before it’s consistently clear in *individual* records. To put it another way, acceleration shows up in the global record much earlier because “global sea level has an order of magnitude smaller internal variability than sea level at
individual sites” (Haigh et al 2014, DOI: 10.1038/ncomms4635). Mr. Wakefield argues that because we can’t yet see clear acceleration in every local record, the acceleration in global sea level must be bogus (or at least unproven). I think this argument is clearly invalid.
This, BTW, is precisely what we see in tobacco. Studying individual records made showing the tobacco-cancer causal connection very difficult to see. Studying aggregated records of thousands upon thousands of cases made the process much easier.
Of course that did not keep tobacco denialists from saying that since no particular case could be 100% quantified to be caused by tobacco and tobacco alone that any regulation of tobacco on public health grounds was unwarranted.
OP: “certainly within their uncertainty limits”. You meant to do that, didn’t you 8^D?
[Response: Yes. I rather liked it.]
What happens if you do the same analysis with Jevrejeva 2014?
[Response: Why do you ask?]
Because I know you would get the opposite results.
[Response: You think you know — but you ask anyway? Is this a lame attempt to start an argument, or just your version of “Dance for me, monkey boy”? Sorry, we’ve already filled our quota for the month.]
Uhmm, just how do you know that, plazaeme? When are you publishing?
Tamino: Let’s consider the acceleration of SLR shown in your last graph. SLR increased from about 2 mm/yr to 4 mm/yr (cm/decade) over about the last 4 decades. That gives an acceleration of about 0.5 cm/decade/decade or 0.2 inch/decade/decade. I find the use of the unconventional units of inch/decade/decade useful because SLR in the satellite era (latest revision) averaged 1 inch/decade (2.5 cm/decade) and we need an acceleration of 1 inch/decade/decade to get in the vicinity of 1 m of SLR by 2100. These round numbers are easy to remember and inches of SLR per decade are tangible changes non-scientists can understand. (For 1 inch/decade/decade, starting in the 2010’s = 44 inches of SLR; starting in the 2020s = 35 inches of SLR). So, IF a quadratic model is appropriate (a debatable assumption), the acceleration we have experienced over the last four decades is only about 1/5 that needed to produce 1 m of SLR this century.
If we use 4 mm/yr (1.6 inch/decade) as the current rate and accelerate at 0.2 inch/decade/decade, SLR will be 3 inch/decade after 8 decades and total SLR will be 20 inches for the century (about double the 20th century). Therefore, the current level of acceleration (if it is statistically significant) produces the IPCCs central estimate for SLR.
There are a large number of caveats associated with this extrapolation, beginning with the fact that acceleration has been highly variable was almost as high during the 1925-1945 period as it was over the last four decades (:)). However, using the simplest model (quadratic), acceleration is still far below that needed to produce 1 m of SLR by the end of the century.
[Response: Extrapolating either a linear or *quadratic* trend to the end of the century is downright foolish. Just dumb.
Bot process models and empirical models suggest that 1m or 2 is within the realm of possibility. The extrapolation arguments only draw attention away from the proper range of possibilities we need to prepare for.]
Part of the problem with extrapolation is that SLR consists of both thermal expansion and ice melt. The latter contribution is accelerating *easily* fast enough to imply metres of global sea level rise by the end of the century, if it were to continue.
Steady now!! Talk of an “easily accelerating ice melt contribution” is a bit out of date these days. (See Figure 30 in Hansen et al 2016) Data from Grace shows the acceleration from Greenland that yielded melt equivalent to 1¼mm/yr SLR by 2012 has been wobbled away in the years since. And the wobbly acceleration still evident from Antarctica has been up to now the junior partner in SLR creation.
I see two problems with the lines extrapolating the Greenland & Antarctic melt rates in that Figure 30. Firstly, the extrapolation of these melting rates is a bit too adventurous for me. They depend on mundane factors like snow fall, ice melt, ice flow, SAT & SST, none of which should be lightly extrapolated individually. So collectively it would be ill-advised even to start extrapolating.
The second problem concerns the possibility of multi-metre SLR this century. In my understanding, with one exception, the science is providing no credibility for multi-metre SLR this century (although it will be a sure thing in the following century under strong AGW). The worrying exception is Hansen’s hypothesis set out in Hansen et al (2016) which requires massive heat transport to the poles to allow massive ice melt and SLR. To achieve this SLR, the global warming bit of AGW stalls in a very obvious way. While deluded denialists may jump for joy at the prospect of a grand hiatus in the rise of global average temperatures this century, it is what Hansen’s hypothesis requires and that is a future which no sane person would want to wish on humanity.