# Misleading Trends: Sea Level Version

Here’s some data, and the question is: what’s the trend rate at present (in the year 2016)?

Here, for your edification, is the rate over time:

The rate during 2016 is +3 mm/yr.

So no, it’s not a trick question. The trick is what the unaware do innocently, and deniers often do not-so-innocently, to make you think the present trend isn’t what it is. They’ll compute the “30-year trend” (or whatever) by fitting a straight line to 30 years’ data, giving this:

Then they’ll tell you that the trend rate in the year 2016 is zero.

That is a reasonable way to estimate the average trend rate over the 30-year period from 1987 through 2016, possibly not the best way but at least reasonable. The average time of that span is 2001.5. Hence that’s an estimate of the trend rate at 2001.5. I’ll plot that estimate as a red dot, along with the actual trend over time as a black line, here:

In this case it turns out the estimate is even correct — at 2001.5.

Now I’ll plot that trend estimate as a blue dot, along with the actual trend over time as a black line, in the way deniers often want you to believe:

That estimate of the trend at 2016 is not correct. They’re plotting the estimated rate from 15 years ago as though it were the estimated rate today.

They do it most often to claim that there’s “no acceleration” of sea level rise. If you fit straight lines over sliding time windows, you’ll get estimated rates at the centers of the time windows — but they’ll plot them at the ends of the time windows to make it seem the final estimate is current. They also generally don’t mention that the methodology doesn’t even give an estimate for the current rate.

Perhaps a more realistic example will help. Let’s take three stations from Florida: Fernandina Beach, Key West, and Pensacola. Here are their data series (with the annual cycle removed) from the Permanent Service for Mean Sea Level:

Data for these three station records are used to compute sea level rise rates shown in a graph by Steve Case in a comment to a post at WUWT:

There are a lot of things wrong with Steve Case’s graph, but most important is that he’s plotted the linear trend estimates for 30-year time spans at the end time, not the mean time, giving the false impression that the final estimate is “current.” It’s not.

There are other problems too. For instance, his estimates start at 1951. To get a 30-year trend estimate ending at 1951, you’d need data starting no later than 1922. But the data for Pensacola don’t start until May of 1923. Then there’s Fernandina Beach, with no data from July 1925 through October of 1938, a 13-year period of missing data. That hardly makes for an optimal estimate of the “30-year trend,” but he makes no mention of the missing data, just refers to the three stations as “three long running Florida tide gauges.” But all told, those are minor quibbles compared to plotting rate estimates 15 years later than they apply.

We can ameliorate the missing data problem by combining the stations to form a single composite, if they’re properly aligned. I get this:

Now we have a continuous record for Florida from June 1897 through December 2015. We can also smooth the data (using a lowess smooth) thus:

We can compute the linear trend rate for overlapping 30-year time spans, and if we plot it as Steve Case did (at the end times) it’s here:

Of course, he only shows the results from 1951 onward, which I’ve enclosed in the red box.

Plotting the estimates at their correct times, we can see that the most recent estimate is really for 2001, not 2016:

There are mathematical methods for estimating the trend rate all the way to the limit of the data, and here’s the result of one of them shown as a red line atop the moving-30-year-windows estimates:

Now we can see two important things. First, there has indeed been acceleration of sea level rise (and deceleration too, although acceleration is most recent). Second, the most recent trend estimate is the highest.

That rather undermines Steve Case’s support for one of the central themes of the original post: that an LA Times article (about Donald Trump’s climate denial and Florida’s sea level rise problem) is invalid because there’s been no acceleration of sea level rise.

But the bizarre thing about the whole post is that it doesn’t really depend on acceleration of sea level rise. Sea level rise, with or without acceleration, is already a serious problem in south Florida, and Donald Trump’s denial of the human origin of sea level rise is a slap in the face to the people who are already paying a huge price for the problems it brings.

But, deniers seem to fall back on the “no acceleration” argument every time sea level is discussed. Never mind that they focus on a tiny region of the globe to increase the noise level, never mind that the issue at hand may be a huge problem even in the absence of acceleration, never mind that they’re simply wrong about “no acceleration.” It’s a talking point, the choir they preach to lap it up, and that’s good enough for them.

As for the main post, there are many, very serious, problems with it, but that’s a topic for another blog post. Soon.

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### 20 responses to “Misleading Trends: Sea Level Version”

1. Jacques

Typo after 3rd plot: 1987 (not 1997).

[Response: Thanks. Fixed.]

2. “Now we can see two important things.” Surely three important things: the first is that sea-level has been rising since 1920.

3. Characteristically clear. Thanks.

4. Cugel

At some point we’ll start hearing there’s no acceleration in the acceleration so everything’s tickety-boo.

I would like to see estimates of the rate of sea level rise in future years alongside the increases. We hear estimates of a few meters by 2100, which may make people think that rise slows by then, rather than increasing. Adaptation to rise is made much harder as the rate increases. E.g. How far inland does a port have to relocate, and how short is its useful life at that point.

6. Thomas P

I think it would help if when you write “There are mathematical methods for estimating the trend rate all the way to the limit of the data, and hereâ€™s the result of one of them” you actually mentioned what method you use. Possibly even the error bars, which I imagine are very significant towards the end.

[Response: I often do, but there’s a trade-off between getting into technical details and getting to the point. In this case, I used a modified lowess smooth, which I’ve programmed to include the estimated rate as well as the estimated value. It gives results nearly identical to other methods, such as MC-SSA (Monte Carlo Singular Spectrum Analysis) which has been used by other researchers. And yes, the error bars get larger as one approaches the endpoints of the time range.]

7. scottdenning156684402

Thanks to Tamino as always for pointing out the glaring problems with Case’s statistics. My own take is that the whole “no acceleration” tempest in a teapot because the more important issue is that when we add boatloads of heat and water to the oceans (which is “Plan A”), sea levels *will* rise much faster than they *have risen* up to now.

There’s a false narrative out there that first, we noticed SLR, then we noticed acceleration, then we attributed it to global warming, and therefore we need energy policy. The truth is that we’ve known for a long time that warming melts land ice and also causes seawater to expand.

We need energy policy to prevent the emission of heat-trapping gases, not in response to recent SLR acceleration.

8. Stephen Spencer

I am a lurker on this site. I have learned a lot from Tamino’s posts and the comments. Apologies for this off topic request, but I can’t think of anywhere else to ask my question.
The anthropogenic nature of CO2 increase is clear – C13/C12 ratio changes, O/N ratio changes, carbon cycle mass balance and many more.
I have came across a climate “skeptic” who claims that CO2 change and temperature change do not correlate closely. I checked myself and got a correlation coefficient of 0.55 for Giss and Mauna Loa CO2.
My inexpert guess is that the natural variability imposed on the rising temperature trend means that a close correlation is not likely.
I would be delighted if our host would discuss this in a post, and would welcome assistance from the many expert commentators on this site.

• I think that temperature should increase with the logarithm of CO2 concentration, at least in the simplest model. So a doubling of CO2 will lead to a 2 – 4 degrees C temperature increase. And another doubling will lead to the same increase again.

• My take would be that you’d see closer correlation over longer time scales. IIRC, there’s a very good correlation over millennial scales in the ice core record, though I don’t have a number on that off the top of my head.

• Stephen,
Regress T vs. ln[CO2]. Your correlation will improve substantially. Now just for shits and grins, Do it a decade at a time. Your R-squared will be all over the place. Now try it vs. 5 and 10 year averages. Much better.

• Bob Loblaw

Stephen: was your correlation using monthly or annual data? It will make a difference. There is an annual cycle on CO2, which would reduce correlation with a gradual temperature rise, Plus, monthly temperature data will be more variable due to other causes (El Nino/La Nina, volcanic activity, etc.) which will also reduce the correlation. You only expect a “perfect” correlation when no other variable affects either CO2 or temperature, other than the CO2–>temperature relationship.
The other possibility is that the “skeptic” is talking about CO2 and temperature through the glacial/interglacial cycles, from ice cores. That is yet another kettle of fish.

9. Mr. Spencer,

I routinely get r ~ 0.8-0.9 when correlating GISTEMP and CO2 over 1880-present, or for that matter, Hadley Centre CRUTEM4 and CO2 over 1850-present.

In any case, the theory of Anthropogenic Global Warming did not come from someone finding a correlation. It was predicted as a matter of radiation physics (by Arrhenius in 1896). The correlation only confirms it.

• Stephen Spencer

Thank you, Barton Paul Levenson, for your pointer to CO2 from 1880. I found the data on a Giss page, and got a correlation of 0.9 . I expect the response of the “Skeptic” who made the lack of correlation comment will be to reject the CO2 data.
You might wonder why I bother to engage with this person. Most climate “skeptics” write such obvious nonsense that there is no value engaging. This particular one has a science background (mineralogy) and is an example of an educated climate “skeptic” who can work out more sophisticated arguments. Although I find his arguments untrue, researching his claims has helped me to learn more of the science.

• Stephen Spencer

One more question (I hope it is my last). I got a 0.95 correlation from a Lowess smooth of the temperature data. I wasn’t surprised that the correlation improved, but is that a statistically legitimate thing to do?

• JCH

I’ve never seen it done. Is there any reason you cannot make the calculation with the Ocean Heat Content Anomaly data?

10. barry

Is acceleration in the sea level data statistically significant? How would one ascertain this?

11. angech

Both of you appear to be indulging in a bit of mathematical juggling.
I think I get your point that a trend over a time period where the previous point is at the same level as the last point will give a trend of zero for that time period.
Whereas a shorter or longer time interval, in this particular case, will show a different and increasing trend.
If, as you assert, this leads to him making an erroneous assumption in the long term trend you can call him out but you will have to stop making assertions about short term trends.
And most of the patterns that people are talking about are short term trends.
For instance, in your example there is a decreasing acceleration from 1999 to 2002 just as there is a an increasing acceleration from 2002 to 2015.
Why?
Since sea level was lower in the past there will always be a positive trend on any slightly longer time span you choose. How can one talk about acceleration or deceleration in the short term without using short term time spans which bring up the problem you mention.
Good that you use a skeptics chosen graphs to illustrate your point but when talking about Florida tidal levels and south Florida already being a serious problem are we ignoring other issues relevant to sea levels there?
Would we have the same problem all over America or are there tidal gauges showing falling levels elsewhere.
Are there current related erosion problems.
Is there more rebound occurring.
Should you mention caveats or do they get in the way of the maths.

• JCH

All of this is researched and in the number. You’ve got almost nothing, and you just keep puffing it. It’s like you actually believe Jerry Mitrovica is unaware of geology.