Guest Post by Willis Eschenbach (NOTE UPDATE AT END)
There’s a recent and good post here at WUWT by Larry Kummer about sea level rise. However, I disagree with a couple of his comments, viz:
(b) There are some tentative signs that the rate of increase is already accelerating, rather than just fluctuating. But the data is noisy (lots of natural variation) and the (tentative) acceleration is small — near the resolving power of these systems (hence the significance of the frequent revisions).
(c) Graph E in paper (5) is the key. As the world continues to warm, the rate of sea level rise will accelerate (probably slowly).
This question all revolves around whether the rate of sea level rise is relatively steady, or whether it is accelerating … so how do we tell the difference?
Well, how I do it is to fit two models to the data and see which one works better. The first is a straight-line model (a linear fit), and the other is an accelerating model (a “quadratic” fit). Figure 1 shows an example of some pseudo-tidal data which in fact has an accelerating rate of sea level rise. I’ve created it by simply adding an accelerating trend to an actual tidal record.
Figure 1. Artificial pseudodata of a tidal gauge recording an accelerating rate of sea level rise.
As you can see, the blue line showing an accelerating (quadratic) fit matches the data much better than the linear fit (red). How much better? Well, that’s measured by something called “R-squared” (R^2). This is a value between zero and one which measures how well the given line explains the dataset.
The R^2 for the blue line (0.88 ± 0.02) is much larger than the R^2 for the red line (0.77 ± 0.02). And since the difference between the two values is greater than the sum of the standard errors of the two values, we can say that the difference between them is statistically significant. In other words, in the Figure 1 case, we can say that there is a statistically significant acceleration in the dataset.
So that is what I planned to look at—whether the difference between the R^2 for the linear and the quadratic fits is greater than the sum of their standard errors.
With that as prologue, let me discuss my methods. I took the full tidal dataset from the Permanent Service for Mean Sea Level. It has 1,505 tide station records in it. However, as with most historical datasets, there are lots of gaps and stations with short or spotty records.
So I had to use a subset of the data. Because the long lunar tidal cycle is just over fifty years, you need at least that much data to get a serious estimate of the rate of sea level rise. And we are interested in any recent acceleration. So I limited my analysis to tidal stations with data starting before 1950 and ending after 2015. This cuts the list down to 171 stations which cover the period of interest.
However, some of these are missing a lot of data, some with over half of the data gone. I wanted enough data to have faith in the analysis, so I further limited the dataset to those stations having 95% or more of the data during 1950-2015. This further reduced the number of tidal stations to 63. Figure 2 shows a sample of 10 of these.
Figure 2. Typical records which fit the criteria of the ex-ante data selection process (95% data coverage from 1950-2017)
Now, my Mark 1 Eyeball says that if there is acceleration there, it is minor … but let’s look at the numbers. Here is a scatterplot of the R^2 values of the linear fit versus the R^2 values of the quadratic fit:
Figure 3. Scatterplot, R^2 of the linear fit vs. the R^2 of the accelerating (quadratic) fit. Dots above the diagonal line are stations where the R^2 of the accelerating (quadratic) fit is larger than the R^2 of the linear fit.
As you can see, in almost all cases the gain in the goodness of fit when we go from linear to quadratic fits is trivially small, invisible at this scale. And when I examined the gain in R^2 versus the standard errors for each of the 63 stations, in every single case the accelerating fit was NOT statistically better than the linear fit.
In other words, not one of these datasets shows statistically significant acceleration.
And that is why at the top I said that I disagree with the following statement from the other post, viz:
There are some tentative signs that the rate of increase is already accelerating …
Simply not true. Figure 3 shows clearly that the tidal gauges contain no such “tentative signs”. NOT ONE of these 63 full tidal datasets shows statistically significant acceleration, and more to the point, most of them show only a trivially small difference between acceleration and a simple linear fit.
The other statement I disagreed with was:
As the world continues to warm, the rate of sea level rise will accelerate (probably slowly) …
Look, this is just the same nonsense that the alarmists have been peddling for the last thirty years, that in the future the sea level rise will accelerate, that New York will be underwater, and the like … but it has been thirty years since the first bogus prognostication was made, and there is still no evidence that the sea level rise is accelerating.
Look, I’m all in favor of taking care about the future … however, call me crazy but I need EVIDENCE before I start hyperventilating about Miami sinking into the ocean.
5 PM, the dreaded global warming has cooled down now. Me, I’m going to post this and then go outside to lay some pavers in the new level space I just made with my own sweat. Plus a rented backhoe. I could have hired someone, but why should illegal immigrants have all the fun? I like living in the hills … but this is the first and only flat spot on my land, so I’m making it nice.
What a universe!
Best to everyone,
w.
PS—The Usual: When you comment, please QUOTE THE EXACT WORDS YOU ARE DISCUSSING, so that we can all be clear about your precise subject.
DATA—I’ve put the 63-station data here, as a CSV file so that anyone can use it in Excel or any other program.
[UPDATE] Over at Tamino’s website, where since about 2009 I’m barred from commenting because I was asking inconvenient questions, he points out that there is a simpler and more accurate method for finding out if a dataset contains acceleration. This is to see if the squared term in the quadratic equation is statistically significant after correction for autocorrelation, duh … he is correct.
My thanks to him for pointing this out, although I do have to deduct points for his repeated ad hominem attacks on me in his post … haters gonna hate, I guess.
Using his method I identified seven of the sixty-three stations as having statistically significant acceleration and three stations with statistically significant deceleration. However, the average value of their acceleration is 0.015 ± 0.012 mm/yr2 … which is not statistically different from zero. Here are the stations and their accelerations:
VLISSINGEN BALTIMORE SMOGEN KEY WEST KETCHIKAN
0.0605 0.0542 0.0676 0.0477 -0.0543
WEST-TERSCHELLING SANDY HOOK JUNEAU SITKA KWAJALEIN
0.0979 0.0510 -0.1052 -0.0573 0.1258
I note that one station he says has significant acceleration doesn’t appear in this list (Boston). I find that the p-value of the acceleration term for Boston is 0.08, not significant. I suspect the difference is in how we account for autocorrelation. I use the method of Koutsoyiannis, detailed here. I don’t know how Tamino does it.
I would also note that the average acceleration of the entire 63-station dataset is 0.014 ± 0.008, still not statistically significant. And if this turns out to be the long-term acceleration, currently the rate of rise is on the order of a couple of mm/yr, or 166 mm (about 7 inches) by the year 2100. IF this increases at 0.014 mm/yr2, this will make a difference of 48 mm (under two inches) this century.
Curiously, in the previous fifty-year period 1900-1950 there are only three sites with significant acceleration out of 38 datasets covering the period, and none are in the first list:
NEW YORK (THE BATTERY) HARLINGEN SEATTLE
0.0976 -0.1182 0.0959
Whatever any future sea level acceleration turns out to be, it is very unlikely to put the Statue of Liberty underwater anytime soon …
Man, I love writing for the web. All my errors get exposed in the burning glare of the public marketplace of ideas, I get to learn new things, what’s not to like?
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Willis quotes
I dont understand how they come to this conclusion as it simply doesn’t follow. Increased rate of sea level rise is dependent on the energy flow increasing but the temperature is dependent on the energy accumulating. Totally different and one doesn’t imply the other.
Sailing from San Diego to Auckland New Zealand, anyone telling me that sea levels are increasing 1.3mm a year needs a head Doctor !
(water, water everywhere and all the boards did shrink )
Willis
The aspect that i find difficult is that the sea level rise shows an abrupt change in 1850 and then a linear increase. The oceans are a large body of water. I cannot envisage a forcing that would generate such a response. I would expect the forcing to be sinusoidal. That would not generate such a response.
A (stupid?) question: Have your data been corrected for ‘uplift/subsidence’ (where the gauges stand) ??
In Denmark, where I live, such vertical movements are substantial – see example here:
http://www.fotoagent.dk/single_picture/10852/25/mega/Figur_4.JPG
(scale in mm per year)
I suppose there are similar movements where ‘your’ (63) gauges are located(?).
Good question, Hans. It’s the reason I used the method I did. You see, the uplift/subsidence is slow and steady, only changing slowly. That means that the in the comparison I used between linear and quadratic for each site, the uplift/subsidence cancels out.
w.
Juneau is rising at ~14mm/yr due to isostatic rebound.
On the site of the Dutch Government local sealevel rise is depicted linear at a rate of 1,9 mm/year(1890-2014) and includes a statement of no acceleration. A footnote on global sealevel mentioned acceleration.
Willis – thank you for your interesting post. I work in coastal engineering based in the UK, obliged to apply SLR scenarios that reflect the accelerating SLR hypothesis to scheme design. Compliant but sceptical, I point colleagues to the UC global mean SL satellite data record (’93 – ) which eyeballs no acceleration trend. Is this dataset too short to apply your statistical approach to, or did you simply go for the longest dataset(s) available?
Thanks, Prolefed. I just went for the longest available. However, there’s only 24 years * 12 months = 288 data points in the satellite dataset. This means that the errors will be correspondingly larger than in the datasets I used, by about 50% …
It’s 2 AM here, I’ll look at it tomorrow, but I’d be stunned if there is any statically significant acceleration.
w.
Thank you Willis – I wasn’t expecting a reply so soon – get some rest!
And here’s me thinking I was the only one that had problems with that post and by the sound of it probably the least schooled .
Thank you for your work Willis and stellar job on the retaining wall , hope you put drainage in for the forthcoming Armageddon.
I must say I find fitting relatively simple matehematical formulae to long term data of what is implicitly a very, very complex mechanism’s outcome is a bit reckless. In the example given we have the quadratic fit used to postulate that the trend for sea level rise on the out years ahead is ‘accelerating’ whereas a quick glance says that in about 1963 it had just stopped falling. Longer period data tells as this is nonsense so on what basis is the quadratic a meaningful ‘model’.
The worst, the dumbest, the most moronic example of this sort of frogshite ‘science’ was in apeper on sea evel rise where that tracked the western Pacific MSL over a reasonable time and loa and behold there was a periodic variation they attributed ( quite logically and correctly it seems) to the Pacific DEcadal Oscillation. Then the wheels fell off. They fitted a line to the data and got an uptrend! DOOM, we’ll all be droended etc. The trouble was the oscilating pattern clearly started on a trough and finished (after several cycles) on a peak so the ‘uptrend’ was just a conbstruct of that bit of idiocy. They would have got the same result if the data conformed to a pure sine wave which must have zero uptrend by definition.
Anyway whenever I see linear fits I just turn the page these days. Now a Fourier series I can come at but even that is dependent on getting a long enough data set.
Units and terminology please?
……………..
Sea level rise is a distance. A distance between a measured point and a reference point. A convenient unit is millimeters, mm.
This distance is not constant over time. The first derivative of distance with respect to time is velocity. Convenient units might be mm per year.
This velocity is not constant over time. The first derivative of velocity, being the second derivative of distance, with respect to time is acceleration. Units here are mm per year per year.
(Please excuse the lack of formal scientific notation for the units, a bit complicated for Word Press).
……………
There is no reason to mention the word “rate” because its use is confusing. I wonder what Larry Kummer really means by “the rate of sea level rise will accelerate”. Likewise with you Willis, “an accelerating rate of sea level rise”. Are we moving to the third derivative of distance? Heavens, no, do not go there. It is named the “jerk”.
I am being more than pedantic. For example, “rate” by itself has to be qualified to have meaning, like rate with respect to time, rate with respect to weight, rate w.r.t wavelength and so on through the physics library.
………………
The full meaning of sea level changes can be captured by the proper, basic, scientific variables of distance, velocity and acceleration, so why not use them and only them?
…………..
Also, a minor disagreement about choice of a quadratic to fit a non-linear response curve. Some recent papers have proposed that the global sea level curve is sigmoidal, with a velocity v1 from say 1900-60, a lower or even negative velocity v2 1960-90 or whenever, followed by a return to the original velocity v1 1990-today. There is no “one curve fits all different hypotheses”, but the quadratic is one of the worst fits for such a sigmoid.
………….
Never mind, Willis makes the point that no acceleration is seen in tide gauge data from goodness of fit studies over multi-decade terms like these. That is what is important.
Geoff
Geoff, I don’t understand your point. You say:
Geoff, the word “rate” here is used as a common synonym for “velocity”. It is, as you point out, the first derivative of the sea level with respect to time, and has units typically of mm/year.
So I can never say “I was doing a hundred around the corner when the car came unstuck”? In many applications the units are obvious from the context. If you think that the rate of the sea level rise is with respect to weight … well, I don’t know what to say.
Now, as to whether the rate is “accelerating”, it would likely be more accurate to say that the rate of sea level rise is “increasing over time” … but do you truly think anyone misundersands what is being said? If so, they haven’t mentioned it.
Why not? Because words become “terms of art”. “Terms of art” are words that have a special meaning in a certain context. For sea level rise, people use “rate” for “velocity”. Is this exact? No … but that’s the way she is spoken.
For data on that, Google finds 410,000 examples for the exact term “rate of sea level rise”. But when you search for “velocity of sea level rise” Google only finds …
… four measly examples. Four.
You can rail against that all night long, but that’s how she is spoken. We say “Things were going along at a rate of knots” because in common parlance, “rate” is a substitute for “velocity”. That’s why we don’t say “the velocity of inflation” … the English language, even in science, is far from logical. You have two choices about that fact … dig it or complain about it. Because you sure aren’t going to change it.
While that may be true for the globe, let’s start from our start, the data we’re using. Here’s Figure 2 again, sample data.
Those look like sigmoids to you?
Thanks, Geoff.
w.
“Never mind, Willis makes the point that no acceleration is seen in tide gauge data from goodness of fit studies over multi-decade terms like these. That is what is important.
Geoff”
This thread and umpteen more like it demonstrate very well the principle that it takes far longer to debunk a load of BS than it does to spew it.
The ocean is right where it has always been, and although it acts up occasionally, it always goes back into it holding pen eventually.
The average position varies slightly over time, but it changes every day by far more than the average has changed over the lifetime of me, you, our parents, grandparents, great grandparents, and who knows who else.
But people who are good at making crap up and convincing others it is true, can run circles around dry facts like “Where is the ocean”?
Same as it ever was.
https://youtu.be/I1wg1DNHbNU
a comprehensive analysis of selection bias in tide gauge measurements between 1807-2010 indicated that (a) sea levels are only rising at a rate of about 1 mm/yr (as of 2010), and (b) a total of 65% of the world’s tide gauges have recorded stable to falling sea levels.
http://notrickszone.com/2017/06/05/sea-levels-are-stable-to-falling-at-about-half-of-the-worlds-tide-gauges/#sthash.ZzzcusEg.dpbs
Another long term view:
http://climate.mr-int.ch/images/graphs/sea_level.png
Note the steep rise-rate around 1800, and the multi-decadal rise-rate oscillations (over an increasing trend).
Willis, what do you think what is the reason that the recent years are a bit warmer, say less than a degree C than what the temps were when our great-grandparents were born, but that the seas rise so linearly as they do?
I think it is odd to see how linear the sea level change is. Freaking odd! I don’t see any good reason behind it.
I come up with two explanations. The land-based temps have little to do with ocean heat uptake and glacier melt. And of course, the linearity can be accidental, since it will not be linear forever. But assuming land-based air temp at 2m has been risen, is that just something that does not correlate with sea level rise?
Great analysis, but a pity that it seems to be episodic. By that I mean that it takes significant human work to do and isn’t likely to be done on an ongoing basis in an affordable manner. Isn’t this something that would better be done every month automatically with summaries for the general population that could be absorbed within a few seconds at most and ideally in the sub-second time frame?
And yes, I’m actually interested in setting up something like that. Contact me if you’re interested.
Yes, we need month to month updates for something which has not changed appreciably in a hundred and fifty years.
Yes, you do, because if you do that in an automated way, when somebody claims otherwise *as alarmists are claiming right now* they won’t be taken seriously.
The cheaper computing power gets, the more these sorts of calculations need to be done. Anything done once when it’s expensive should be done regularly when the task becomes trivially cheap because of reduced computing costs.
Church & White along with other studies show a rapid acceleration of the rate of sea level rise.
The tide gauges have gone from approx 1mm per year circa 1880’s to 2.0mm circa today. While the satelite measurements have gone from 3.0mm to approx 3.2-3.3mm circa today. Both the tide gauges and the satelite measures show a doubling of the rate of approx 100-150 years.
The acceleration is cited in the numberous studies appears to be mostly from the switch from tide gauges to satelite measurements. The remaining acceleration appears to be from the short term cyclical changes.
Actually they don’t. The two Church and White papers I have studied used bith different time frames and different subsets of tide gauges. Apples to oranges. See my recent guest post on SLR and closure for more details.
Houston, J. R. and Dean, R. G., “Sea Level Acceleration Based of U.S. Tide Gauges and Extensions of previous global-gauge analyses,” J. of Coastal Research, Vol. 27, No. 3, pp 409 – 417 (May, 2011).
They used 57 U.S. tide gauge records from PSMSL with lengths of 60 – 156 years. They found a small deceleration from 1930 – 2010.
For global extent, they extended Douglas (1992) by 25 years, and analyzed revised data of Church and White (2006) from 1930 – 2007 and obtained small decelerations similar to the U.S. records.
Acceleration: -0.012 mm/yr^2 for U.S. or Global.
the notion of accurately measuring millimetres of sea level rise never mind thousandths of millimetres no matter what equipment is used is to me a nonsense.as usual a great expose of the numbers by willis ,but i fear the numbers at the outset bear no relation to reality,a consistent trend in climate science i believe.
bitchilly July 21, 2017 at 4:50 pm Edit
Depends on your equipment. The Australian SEAFRAME tide stations combine a stilling well and a sonic measuring apparatus. It measures the sea level every six minutes, accurate to 1mm …
w.
How many tide gages and for how long use such a method?
The scatter plot is interesting, but I think it would be more definitive to plot linear vs linear+quadratic. N’est Pas?
Most interestingly, they have just found the missing sea level acceleration
https://www.scientificamerican.com/article/satellite-snafu-masked-true-sea-level-rise-for-decades/?utm_source=pdb&utm_medium=email&utm_campaign=07202017&variable=a553eadb90dd3b52fbf8d01481e04811
obviously if the data don’t match your dogma, you torture them, until they confess.
Hi Willis. I think this analysis shows that your analysis is incorrect. Can you comment?
http://tamino.wordpress.com/2017/07/21/sea-level-rise-is-accelerating/#more-9358
Tamino throws in a red herring by declaring acceleration in Boston and deceleration in Juneau is evidence that Willis’s analysis is incorrect. But the claimed deceleration at Juneau is claimed to be caused by the reduced glacier mass attracting less ocean water. This case has been presented a number of times, always without reference. However, if you calculate from Newton’s law F=Gm1m2/r^2 for an estimate of the glacier melt and it’s average distance from shore, and apply some hydrostatics, you will find this claim to be highly exaggerated. Like most warmunist stuff, a small investment in truth yields a major return in catastrophic predictions, plus a major return in donations to the website.
Doug: Gravitational effects of melting ice on local sea levels now is well established. An easy way to enter the literature is to search for peer reviewed papers by Jerry Mitrovica. Here is a brief lay explanation: http://nautil.us/issue/33/attraction/why-our-intuition-about-sea_level-rise-is-wrong
Tom Dayton, that was some painful reading. I always hurt mentally when I read a journalist’s interpretation of a discussion with a scientist. That was a lot of generalization and not a lot of detail and it, as usual, raises more questions than it answers.
How does this specifically have to do with Juneau? Is there an exceptionally large glacier nearby? Is it melting fast enough to show a true gravitational effect? Is the shape of the land nearby sufficient to justify this explanation? If this was all due to gravitational effects from local glaciers does that mean that only gauges near a glacier are showing this phenomenon? Are there any gauges in the tropics showing this downward slope? What’s the excuse for those?
Andrew, my suggestion was for you to search for the peer reviewed literature, which has details. Instead of complaining about the lack of detail in the brief lay explanation I was nice enough to point you to, why don’t you read the actual literature?
Tom, you make my exact point…referring to articles with no calcs….maybe you should study Mitrovica’s calcs yourself before you start sending me “lay information”. I did similar calcs for university physics assignments 40 years ago. And gravity, despite being “real physics” doesn’t explain the amount of Juneau deceleration. Try again.
Thanks, Martin. I’m including an update on this in the head post. Short answer is that I had slightly overestimated the error. By Tamino’s method, there are seven stations with significant acceleration and three stations with significant deceleration. My thanks to Tamino.
w.
Thanks Willis. Are you sure you used Tamino’s method? He doesn’t include it in his post. What method did you use to correct for autocorrelation?
Thanks.
Sorry, I didn’t see your update. Thanks.
i am sure willis can/has commented,though i fear it would be a waste of time with the individual concerned.
Willis is mistaken—sea level rise is accelerating. See this post from Tamino: https://tamino.wordpress.com/2017/07/21/sea-level-rise-is-accelerating/
I decided to follow the click bait, although I try to not do that very often. What followed was an interesting bit of “Willis is ‘insert insult here’ ” followed up with a discussion in statistical analysis. The p- value is then trotted out along with comments about how that is used to determine that sea level rise is accelerating.
How about this. Why don’t you show your full design of experiments. If you are going to trot out the p-value, you need to make sure you define the H0 and H1. Why? Because the p-value only is important if it allows us to reject the H0 or Null Hypothesis. I may be wrong but Willis’ H0 appears to be that it is a linear fit only. That means that the H1 would be that it is either statistically the same or the quadratic fits. That means the very low p-value would support the H1, which might be why Willis used the R^2 instead of the p-value.
Of course I could be wrong……..but if I am it is because no one has taken the time to express what their H0 or H1 might be. Don’t play around with p-values unless you plainly express your H0 and H1 values.
Tamino is a mistake himself.
Global Absolute Sea Level can not be determined from uncorrected Tide Gauge data. Tide Gauge data relates only and exclusively to Local Relative Sea Level. The relationship between each local Relative Sea Level and Global Absolute Sea Level is unknown without a great deal of additional data.
All Tide Gauge data, to be used outside of its proper place — determining local Relative Sea Level — must be first corrected with reliable precise information on the vertical movement (up and down) of the land to which the gauge is attached. The only truly reliable data on this comes from the NOAA CORS system.
Even when corrected, Tide Gauge data only speaks to the question of what the sea level is doing locally. Global Eustatic Average Sea Level ( “eustatic” refers to global changes in sea level relative to a fixed point, such as the centre of the earth) can not be determined from Tide Gauge data — nor can rates or rise or fall of global sea level.
Tide Gauge measurements are in effect measuring from a moving platform — the land — which moves up and down on its own, independent of the sea surface. The sea surface also moves up and down on short term cycles (tides) and long-term changes. The local long term changes are not linearly connected to Global Sea Level rise or fall. Local sea level may fall while global levels rise, and vice versa.
That said, all human related sea level problems are LOCAL. It only matters where the sea touches the land. New York cares not what the sea level is doing in Hong Kong, no NY subway is flooded by sea level rising in Hong Kong. If local sea levels are rising and it is a problem for that locality then whether or not Global Sea level is going up or down is irrelevant.
“That said, all human related sea level problems are LOCAL.”
Which is why all of the forecasts concerning sea level that have come out of decades of climate research have thus far have been of nearly zero practical use.
Why are so many of your R^2s in Figure 3 less than 0.5? Doesn’t this analysis similarly indicate that the linear trends are not statistically better than pure intercept models?
Good point !
Forrest Gardener July 21, 2017 at 2:48 am
You misunderstand my purpose in fitting the model. It is NOT to provide an accurate model for the last two hundred years of data. Instead, it is simply to determine whether a given short section of the data is better fitted by a straight line or an accelerating curve of some type.
So you are right that “There is nothing about sea level rises which suggests a quadratic relationship with time” … but I’m not trying to show that. Heck, you propose using an exponential function … are you claiming that that suggests sea level has an exponential relationship with time? I see nothing to suggest that either.
I don’t see that at all, nor did I say it. How do you get that result? Remember, Figure 1 is pseudodata …
Hey, you were the one heading for the door after I asked you to fit an exponential curve to the Juneau record shown in Figure 2, not me. Whether you’ve “run out of answers” or not, I still don’t have an answer to that question …
If you don’t want to put your money where your mouth is, that’s up to you. However, the proposal YOU make to use e.g. some exponential function or other is YOUR proposed analysis, not mine.
You don’t get to wave your hands and say it’s better to do it some other way and then expect me to prove or disprove YOUR claim for you. If you think it’s better to do it some other way then please show us.
I gave up doing that kind of snipe hunt long ago. I used to go and, for example, use some exponential analysis or other. Then I’d return and tell the person my results, and they’d say “Oh, that’s not the kind of exponential analysis I was referring to …”
You see the problem. After doing that a few times, I just gave it up. If you think it can be done better, I invite you to show us how. I say this because I’m not a mind reader, so I DON’T KNOW HOW YOU PLAN TO DO IT and I’m damned if I’m gonna guess just so you can tell me I’m wrong.
The same to you, and thanks for your willingness to continue the discussion
w.
Sea level is still lower than it was during the Medieval, Roman and Minoan Warm Periods and Holocene Climate Optimum.
Eemian interglacial sea level in the continental US, without benefit of a Neanderthal industrial age in Eurasia:
http://www.tobiasbuckell.com/wordpress/images/2013/01/NewImage3.png
Don’t know where that image came from, but it is mistaken. Maximum sea levels were 5 to 7 meters above those of today. Image shows all of Florida submerged. But look at an elevation map of Florida: http://ete.cet.edu/gcc/style/images/uploads/Sea%20level%20risk-FL.png
More than half the state is higher than 10 meters above sea level, and some 40-50 meters above sea level. Florida was not all under water during the Eemian.
That map shows a tongue of water extending up almost all the way to Illinois, past places that are 300 feet above sea level.
Although it also shows Philadelphia, at about 40 feet, not under water.
I guess one thing I have never heard people talk about is how we are draining ground water, that used to never be used. We pull millions of acre feet of water out of the ground every year that finds its way to the oceans. This water used to not be on the surface! I have a well from an aquifer that is essentially not refilling and has enough water for our little area for about 50-100 years.
The effects of ground water irrigation on sea level has been discussed on this blog fairly often.
Hmm. You seem to be unaware that simply comparing R^2 values is no way to compare how well two models characterize the process that generates a set of data. That should be pretty obvious from just LOOKING at your Figure 1.
Patrick wrote
in response to Willis’ article where Willis wrote
So Willis wasn’t even trying to characterize the process generating the data. That wasn’t even his aim. He even said he was fitting the data.
Willis: I think the “standard method” for detecting acceleration in SLR is to perform a fit to
h = at^2 + bt + c
and then look at the confidence interval for a. And that requires correcting for autocorrelation (in the residuals). I’ve tried this with the satellite altimetry record (before the recent correction) and found a small acceleration with zero barely within in the 95% ci. In that case, the R2 for the linear and quadratic fits were essentially the same (0.97 and 0.98).
More importantly, currently SLR is about 1″/decade and we need to experience an acceleration of 1 inch/decade/decade to reach about 1 m of SLR by the end of the century. Even the high end of the 95% ci was well below this value.