Guest Post by Willis Eschenbach [See update at the end]
Since publishing my last two posts here and here on the Church and White (“C&W”) 2011 sea level dataset, some folks have queried why I didn’t use the Church and White 2013 dataset instead. The answer is simple. It’s because of the hockeystick.
What hockeystick, you might ask? Why, the C&W hockeystick … the figure below shows the difference between the C&W 2013 and the C&W 2011 data.
Figure 1. Red line shows the difference between the sea levels of the two C&W datasets. Larger values show where the 2013 dataset has higher sea levels than the 2011 dataset.
Now, I can understand the slight, ~ ± 1 mm differences between the two datasets in most of the record. They’ve recalculated with a slightly different algorithm, or maybe used a somewhat different mix of tide gauges and weights, with resulting small differences.
And I can understand the offset in most of the record, where the 2013 data is generally about 2 mm less than the 2011 data. It’s an anomaly so the zero point doesn’t matter.
What I don’t understand is the blade of the hockeystick from about 1992, the start of the satellite sea level era, to 2009 when the C&W 2011 record ended.
It looks to me like they’ve munged the data in order to make the data take up a smooth transition from the smaller acceleration of the tidal gauge record to the larger acceleration of the satellite record. That way, they could claim that the tide gauges and the satellite data agree … and if that is the case, I can only say bad scientists, no cookies …
Anyhow, that’s the only explanation I can think for this hockeystick … suggestions gladly accepted.
[UPDATE] I thought I might point out the biggest problem we have with sea level estimates, which is the lack of data. Here’s a graph showing how many tide gauges we have by the number of years of data that they have:
So for example, there are only 35 tide gauges which have 120 years or more of data … and that only gets us back to about the year 1900.
Not only that, but because the tide gauges are on land, the world’s oceans are only sampled around the edges and on a few islands …
Here’s another look, this time at how many gauges we have going at any given time:
Note that at the maximum, only half of the tide gauges in the historical record were in operation.
I bring this up to point out that we simply cannot place much faith in the tidal gauge data to provide any “global” average sea level rise.
Here, amazingly, we’ve had rain again. It hardly ever rains this late in the spring in Northern California, and the redwood forest around our house is redolent with the earthy odors of new growth and old decay … I blame global warming. After all, global warming has been blamed for a host of bad things from low birth rates to volcanic eruptions, so why not balance the scales by blaming it for a lovely gentle late spring rain?
Best of this wonderful wet world to you and yours,
w.
MY USUAL REQUEST: When you comment, I ask, beg, implore, request, and importune you to QUOTE THE EXACT WORDS THAT YOU ARE DISCUSSING so we can all understand who and what you are talking about.
DATA: The C&W data is here, h/t to Nick Stokes for finding it.
Hmmmm….
Hiding a decline?
Hmmm… same problem as the thermometers – a set on instruments each individually sited with a local focus and never intended as part of a global network with a view to determining global trends etc.
On the upside it is a perfect data set to do dodgy alarmist science with, generate SCARY HEADLINES for the msm and SUPPORT FUNDING APPLICATIONS etc
Surface stations actually report less than 0.000006% of the land surface temperature, so trying to say that the globe is the hottest it has been by .01 deg is B.S. (A sensor accurately reports only the temperature w/in 6′ of that sensor-a total area of all the sensors of the world adding up to 0.02 sq mi. When I was in Navy forecasting school our instructors, in demonstrating the criticality of correct siting, described one case where moving the sensor 20′ made a 6 deg F difference on the low temperature on clear cool winter nights.) Satellite readings are much much more accurate, even though they only get about 20% of the surface per day due to clouds.
What they are trying to hide….is the fact that they just proved SLR is decoupled from temps
Latitude
May 26, 2018 at 9:21 am
What they are trying to hide….is the fact that they just proved SLR is decoupled from temps
————————-
Maybe also they just proved that SLR acceleration is invalid in the data these guys using, zero flat, as otherwise there wold not be a “hockey stick” signature in the output data, which to my understanding is the result signature of the over amplification of noise….where in this case noise is higher than the signal…..small noise – flat or non existing signal…no acceleration signal.
Some thing like in the case of Mann’s hockey stick, where the outcome holds a hockey stick signature and it it invalidates the acceleration of warming in the data that Mann was using;
and a warming without acceleration when both CO2 concentrations and human CO2 emissions still going up invalidates the AGW.
Adjustments and even over amplifications are not wrong, what is wrong is misinterpretation of the result, where the proof of invalidation is deceptively served as proof or even indisputable proof of validation and confirmation of something that actually does not even exist in the data as a signal.
Maybe got this wrong, but just saying….
cheers
“Hiding a decline?” and my comment disappeared into the ether, not even an ‘awaiting moderation’ message.
See https://wattsupwiththat.com/2018/05/22/dumbing-down-extinction/comment-page-1/#comment-2824022
(TL;DR: just be patient)
It’s the utter lack of notification that is annoying. Saying it’s in moderation is fine, but just ignoring it altogether is not user friendly. I’m assuming it’s WordPress, ofc.
Please tell the readers why that has happened with two years gap? Otherwise it gives an impression that you have chosen the data that —!!!
Dr. S. Jeevananda Reddy
Dr. Reddy, I have no clue what you mean by the “two years gap”. What am I missing?
w.
He might mean 1999 and 2000, when the 2013 dataset was lower than the 2011 dataset ?
The difference — 2013 – 2011 = 2 years, then why that difference in data?
Jeevananda writes
Those are dates of the papers. The underlying dates on the data show the “2013 paper” seems to have 4 more years of data because it uses data to 2013 but the 2011 paper used data to 2009. But that has little to do with the “differences” which is what Willis is questioning himself…
“There are Lies, damn lies, statistics, and then there are climate hockey sticks.”
– Samuel Clements, climate realist.
Note: The CC community is an orthodoxy with no shame, no ethics. Just an agenda where the end justifies the means.
That was Ben Disraeli, not Mark Twain, Joel, old fruit.
Twain popularized it and credited Diraeli. But historians have found *no* evidence that ever wrote or said it. So to Twain the credit goes. Modesty? Mr Clements did like invoking mischief.
Samuel Langhorne Clemens (November 30, 1835 – April 21, 1910)
Mark Twain’s real name was Clemens, not Clements. Just saying…
By “real” I presume you mean the name on his birth certificate. To millions of fans over a hundred years his “real” name is Mark Twain.
That is some diamond level pedantry there. I’m impressed.
“real” and “name” don’t belong together. Names are just names, not a real thing. “Dolphin” isn’t more real, nor less, than “Tursiops truncatus”
Unless you mistake the map for the territory
After all, global warming has been blamed for a host of bad things from low birth rates to volcanic eruptions, …
Willis, you can’t do anything about volcanic eruptions.
Lies you can throw all the climate den@ers in along with any left over virgins.
Probably every school with a bell tower has the legend that a brick falls out every time a virgin graduates. Well Stetson University (Deland) did finally have to demolish their tower but it was after a hurricane damaged it structurally. Supposedly now a secret society meets secretly beneath what remains. So this has nothing to do with climate but my assumption there’s no great plethora of “left over” virgins.
They do blame climate change for causing an increase in volcanoes. link
Post-glacial rebound is still happening.
The thing is that the glaciers were so big that the water they contained meant that the oceans were around 400 feet lower than they are now. Given that the tectonic plates float on molten rock it’s reasonable that huge changes in mass (from the glaciers melting and the oceans re-filling) would cause the plates to flex and result in volcanoes. Some alarmists predict that CAGW could cause increased volcanoes. link They really do blame CAGW for everything.
commieBob,
I’m still waiting for someone to blame the “heartbreak of psoriasis” on CO2.
If sea level rise from ice cap melt flexes tectonic plates for an increase in volcanic activity, then the increased volcanic activity will cause global cooling, so no need to worry about run-away heat death for Gaia.
I wonder if anyone has considered that feedback loop yet?
don’t wait anymore, Clyde
https://www.everydayhealth.com/columns/howard-chang-the-itch-to-beat-psoriasis/does-climate-change-affect-psoriasis/
How about geothermal fracking next to a volcano?
Holocene era rising sea levels, adding as that did, 120 tons per sq metre, does in fact increase infiltration and no doubt provoke earthquakes and volcanic activity.
There are about two entire oceans’ worth of water in the Earth’s mantle. If everything settled and squeezed it up, there would be no dry land at all. It would be covered with about 8 km of water. And we would all be eating seaweed and riding dolphins to work on ships anchored above the Everest Sea Mount.
think they did something of that nature in Hawaii, but had to close the plant due to a lava intrusion.
It’s definitely a theorist versus empiricist approach. Even a scientist versus an engineer situation. One is accountable and the other isn’t hence the slip into hypothetical.
The lovely scientific method allows you to add assumptions and to have a mix of real data and made up data as long as your conclusions are limited to the reach of your assumptions. That’s the reason why in something like Physical Review Letters you can have a theoretical paper right beside a measurement of a Bose Einstein condensate.
Sadly though the physical world works on results and repeatability and transparency because you can be audited. This type of Hockey Stick would ring alarm bells immediately. There is probably an innocent reason (no malice) but still some quality control would be going on.
If you graph CO2 say for June each year of the early paper MSL data that was tabulated, there is a very tight, direct correlation of CO2-June and MSL. The slope is 0.761. The author in review complained there was an adjustment to a slope of 0.78, which given I just picked June, looks like a correlation match. The data just matches or was manipulated to match CO2. I don’t know how to get pics posted. I don’t see the function to do that. I have the data graphed with the trend. The correlation coefficient is an astounding 0.9701. Generally, natural systems are noisy with correlation of 0.6 or so. 0.97 is a law of physics in a constrained system, or the MSL data was made up or carefully adjusted.
Willis,
I think the explanation from the authors is here.
“potential instrumental drifts” are invoked to justify wholesale alterations into the GPS era of the GMSL data.
Just more truncation and appending adjustments when the previous data set didn’t give the needed story.
It very much like the Mann hockey stick “hide the decline” Nature trick. All that pre-GPS data, yeah it’s good since we can’t use GPS to adjust it. But this GPS-era data, let’s adjust it. Lots of places here to make code adjustments. Just like tree rings telling the truth “as needed” before the instrumental record. Just truncate and append adjusted data to any inconvenient data in the instrumental era where we can make “informed” adjustments.
Yeah that’s the trick. It’s all good now.
Excuse me if I’m not skeptical of their adjustments. An all too common phenomenon.
Excuse if I’m highly skeptical of their GPS era aided adjustments.
That creates two wholly different data sets that should not be appended, unless one has an agenda.
Yep the instrumental drift took off from a nice and steady background because someone noticed a problem.
https://trs.jpl.nasa.gov/bitstream/handle/2014/43312/12-4412_A1b.pdf
What gets left because this is climate science and you have to appear confident is it still isn’t solved properly and won’t be until 2021 at the earliest.
So C&W and all the data will need to be done again at that point.
“because this is climate science”
In fact, it is oceanography.
Nick Do you still believe in CAGW?
I watch the Bloomberg clock almost every day. These days Im disappointed cause the CO2 level is on its yearly downward photosynthesis trend. It will reverse though by summer and i will be happy again. We need more CO2 NOT less
Just shows how powerful photosynthesis is when despite mankinds dumping billions of co2 in air, the co2 actually goes down during photosynthesis.
Nick, if this really was oceanography we wouldn’t even be talking about because we would just let it play out over time like much in science. However John Church is in, on and around the IPCC and there you have why this becomes important. If it wasn’t for climate change then sea level rise would get the attention it did for the previous 150 years, which is a faint entry in the columns of science.
LdB,
That’s an very interesting paper. Thanks for posting it. It gives an idea of all the potential for bias in the data, and how they identify and fix it. It should alleviate the concerns some people have about the number of times the data are adjusted to know why and how they do it.
I don’t understand your remark about 2021 or “still isn’t solved properly.” If you are asking for perfectly accurate and highly precise data, you’ve got the wrong science. Global parameters like mean sea level can only be estimated, and corrections are made over time. This is nothing new, nor is it hidden. If you have an issue with the way it’s done as described in the paper, that might be reason to say it’s not solved properly, but you haven’t identified one.
@Kristi Silber
Surely you can read so go to section 6, I mean read it and understand it.
They state one of the error sources in absolute terms, here lets help you out
Now there are two other sources which haven’t been given as a number because they don’t know them, lets see if you can identify them yourself. The is still another known issue with the adjusted data they are currently producing it is covered in section 4.
Now the funny part that does need some explaining look at the systematic error sea level rise is quoted with in C&W.
I can only assume they made the brave assumption the bias offset will be uniform which was probably ok in the 2011 paper but in the 2013 as per Willis graph above it would be stupid.
Nick, all I see there are discussions of the satellite data, not the tide gauge data. And if that were the explanation, why the large jumps plus and minus in the blade of the hockeystick? There’s nothing like that in the satellite data to my knowledge.
Next, they say:
What they are saying is that reducing satellite sea level rise in the first part of the sea level data makes it agree better with their new 2013 hockeystick C&W data …
And because they’ve reduced the first six years of the satellite data more than the rest, guess what?
In other words, sea level acceleration in the satellite era is Worse Than We Thought™!
This is my shocked face …
So unless I’m missing something, this doesn’t explain the hockeystick in the slightest … all it does is show that whenever C&W start messing with the sea level data, it always moves in a more alarmist direction and the acceleration increases.
Best to you,
w.
“…whenever C&W start messing with the sea level data, it always moves in a more alarmist direction and the acceleration increases.”
BINGO!
The problem Nick is if you search hard enough, you can always find justification to tweak the data to fit your expectations. Any data set which is so tweaked is (and ought to be) very suspect. This is a real problem in much of science, not just climate science and oceanography. Paraphrasing Lindzen: it is not plausible that every real ‘error’ in the data goes in the same direction, nor is it plausible every data adjustment fulfills our expectations. Willis is right to be skeptical of the recent sea level adjustments, both satellite ‘corrections’ and ‘adjusted’ vertical land movement for tide gauges, which lead to the expected (hoped for?) “acceleration” in the rate of sea level rise.
From their supplementary information
https://media.nature.com/original/nature-assets/nclimate/journal/v5/n6/extref/nclimate2635-s1.pdf
What systemic drifts one might ask?
From the supplementary data
And the whole endeavor has no basis in reality other than the measured values not corresponding to modeled values unless the model is changed to a fitted one and the measured values are all adjusted. They have no physical reason to do this. They’re not correcting drift. Or sensor degradation. Or anything specific…just a “what we think it should be” correction.
TimTheToolMan,
My take is that they are examining and correcting for variance in readings from Topex side A, which are larger than other readings and therefore suspect (Fig. 3). They find biases not by looking for them directly, but using algorithms that include tide gauge data. I admit, though, that I didn’t read all the supplementary material; it’s frankly beyond me.
I’m just guessing, but reading the article itself might illuminate some of the things done in the supplementary material. And personally, not understanding the statistics they use, I’d be hesitant to judge them. Based on your comment, I’m not sure you have a thorough understanding of the proper identification and treatment of satellite bias, either, but I could be wrong.
It’s one thing to take something on authority, and quite another to assume something is wrong and corrupt when one doesn’t understand it.
Kristi writes
You mean we need to redo the math to understand it? I dont think so…
There are things we can look at with regards the methodology and how the results look without re-doing the work.
Check out Supplementary Table 1
For example, how is it that using the piece wise linear model, the variance is reducing over the life of the readings for TOPEX Side A? One might expect the sensors to get worse and worse until they finally failed in 1999, not more and more consistent. TOPEX Side A variance cant be due to satellite drift or diurnal issues because its shadowed by the second redundant sensor TOPEX Side B on the same satellite.
But in general, I have a real issue if a correction is made to data without a physical cause being stated and tested for. Its not enough to say something looks wrong and that’s enough justification to change it.
TimTheToolMan you are correct it’s a modelled response and it has a number of unresolved issues. First up just between the satelitte data they aren’t uniform they seem to have different cold night response, wave response and another yet to be identified other problem. The result is your sort have to munge the data together with some blending.
Then there is a significant orbital frame issue when you try to relate the data to the tide gauges. It comes up in another paper apparently they are using the volume centre of earth not the gravitational centre of earth. So the centre they are using oscilates around the gravitational centre of earth which they call a reduced-dynamic technique and was first used on TOPEX/Poseidon back in 1994
https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/94GL00010
There have been refinements in the process to currently bring the error down to 1mm/year.
Now there are two more interesting errors. One of the proposed solutions to reconciling Jason 1 & 2 is a currently unaccounted spatial error. There is a satellite called SWOT proposed for launch in 2021 and you can look it up and read it’s aims.
There is also an orbital error which I am still trying to find details on.
Pulling a Mikey Mann and grafting two data sets derived from different methods together is what happened here. What, pray tell, was the actual tide gauge records showing as far as SLR?
To be fair to Church and White they just added the adjustments from the NASA team/products they didn’t create them. The deception is probably in not talking about the adjustments in enough detail and the fact the numbers are far from settled.
“However, satellite-based GMSL estimates do not include an allowance for potential instrumental drifts (bias drift4,5)”
Really?
After a couple of decades they now claim no allowance for drift? How strange is that because they’ve been using that excuse to correct the temp records for at least a decade, as they tried to torture satellite records into matching their fiddled ground data.
And shouldn’t it be ACTUAL drifts and not ‘potential?
“Here, we report improved bias drift estimates for individual altimeter missions from a refined estimation approach that incorporates new Global Positioning System (GPS) estimates of vertical land movement (VLM)”
Yep, sounds like the priests of AGW – “We have fiddled the GPS ‘estimates’ so we have an excuse to invent a new ‘estimates’ system that lets us alter the satellite ‘estimates’ so we can reverse the decline in SLR rates.
I’m pretty sure my maths teacher in year 9 would have failed me for cascading estimates like that and pretending the results mean anything at all.
The first estimate may be an estimate. All subsequent estimates based on the original are guesses, pure and simple.
Incdentally is there a net ice loss from Greenland large enough to justify their conclusions when taking into account the growth of the ice cap? I’m only asking ‘cos I don’t know.
I’ve suggested to Neil White [of C & W} to simply take a look outside and see for himself how virtually nothing has happened WRT sea levels in his own back yard for the last century but he doesn’t want to know about the real world.
A GPS chip is showing the couple of inches of recorded rise in that time is about the same as a the sinking of the tide gauge.
~ Zero SLR at Fort Denison.
Fort Denison (Sydney) is an instructive case. It is actually one of the few locations in the world which seem, at first glance, to show evidence a significant acceleration in sea-level rise.
Since the 1920s the long-term trend there has been only 1.2 ±0.2 mm/yr (i.e., less than 6 inches per century).
However, sea-level “sloshed down” sharply at Fort Denison in the 1990s. Over the period 1988-1997 the trend was sharply negative. So if you do a regression analysis for Sydney “over the satellite era” (i.e., starting in 1993) you’ll find that sea-level has been rising since then at an average rate of nearly 4 mm/year! That would come to nearly 13 inches by 2100, if it continued.
Of course it does not represent a true increase of that magnitude in the sea-level trend. The apparently-accelerated rate is really mostly an artifact of the particular starting point.
Interesting Dave, that your graph shows twice the rate of SLR as this one:
https://tidesandcurrents.noaa.gov/sltrends/sltrends_global_station.shtml?stnid=680-140
But that’s the way it is with the theory whereas if you go and check at the top of the highest astronomical tide you will see that the old sea walls that were built to king tide data 60-70 years ago are still up to a foot above HAT today [depending on BP], beaches are wider and healthier than ever and homes that were being washed away 60 years ago are currently selling for multi-millions.
I realise that’s only local data but it is the most believable data you can find.
There are a few things going on there, drongo.
1. Part of the NOAA Tidesandcurrents site is down at the moment. They have some sort of fallback scheme which causes their site to display the old static web pages when that happens. If you’re seeing 0.65 mm/year for Fort Denison then that’s what you’re seeing. You’ll notice that the end date is 2010 (seven years ago).
Sea-level has “sloshed up” a bit at Ft. Denison over the last eight years, Their out-of-date page lacks that newest data.
In a few hours (or perhaps days, since this is a holiday weekend in the USA), it will be back to normal.
2. They started their regression with the beginning of the data (1886). But there was a slight acceleration evident in the first forty years or so. (Quite a few locations saw a slight acceleration in the late 19th century or first few decades of the 20th century.) I started my regression in 1930, to avoid that, so I got a slightly higher trend.
If you use my site’s tool to regress over that same interval they used, you’ll get the same result:
https://www.sealevel.info/MSL_graph.php?id=Sydney&c_date=1880/1-2010/12
But, really, 0.65 mm/yr and 1.20 mm/yr are almost the same. It’s a difference of just 55 mm (2.2 inches) per century, which is utterly inconsequential.
daveburton May 26, 2018 at 1:37 am
Yes, I like spangled drongo am a bit puzzled by the difference between the 0.65 and 1.20mm/year for Fort Denison.
It’s a big difference (but I take your point that basically there’s nothing serious happening) but what is meant when the “NOAA’s Tides and Currents” site states under its graph that: ” the “Data for 1886-May 1914 are based on high and low waters and on monthly mean tide levels plus a1.7mm corrections”? Could this be part of the reason for the difference?
I don’t think so, Alastair. It’s just that for the very early data they only had high & low tide readings, and to approximate mean sea level they averaged the high and low values and added a tiny correction. After 1914 they apparently just read mean sea-level directly, on a schedule according to the tide tables.
Even two hundred years ago a careful observer with a stilling well, a tide pole, an accurate clock, tide tables, and a notebook, could to a very good job of measuring sea-level — better, I suspect, than the $360 million state-of-the-art Jason-3 satellite does.
CORRECTION
I was wrong, drongo. The NOAA TidesAndCurrents site isn’t down. It’s just that they’ve changed their web site, and we were using the wrong URL:
This is the old URL, which takes you to the old web page:
https://tidesandcurrents.noaa.gov/sltrends/sltrends_global_station.shtml?stnid=680-140
This is the new URL:
https://tidesandcurrents.noaa.gov/sltrends/sltrends_station.shtml?id=680-140
I don’t know why they have data for Sydney only through 2010, even on the new page. PSMSL has data through the end of 2016, and that’s what my site uses:
http://www.sealevel.info/MSL_graph.php?id=680-140
Dave, tide gauges tell us many things more than satellite altimetry, but the most important thing they tell us is the height of the normal barometric pressure king tides and these, in my area around Brisbane/Moreton Bay/Gold Coast, an area acknowledged as vertically stable, are lower now than they were 60-70 years ago by up to a foot.
Between 1946 and 1953 Moreton Bay [normal BP] king tides would cover our lawn and trickle into our well if we didn’t keep a levy around it.
This is in an area close to a main shipping channel and that hydrology hasn’t changed.
These days they are consistently below that height.
I just opened the altimeter app, which I believe is GPS operarated, installed on my smartphone, and it says the altitude it shows me is “+/- 13.21 ft”. A couple inches SLR or SLF in that is meaningless. You can’t even get the sign right.
What altimeter app do you use?
“It looks to me like they’ve munged the data in order to make the data take up a smooth transition from the smaller acceleration of the tidal gauge record to the larger acceleration of the satellite record. ”
This reminds me of my original reaction to seeing the drop of stations in GHCN.
stations drop, temperature goes up. BINGO. I and many other jumped to a conclusion.
Turns out the great thermometer drop off did not result in warming
some of that is addressed here
https://wattsupwiththat.com/2010/08/19/the-big-valley-altitude-bias-in-ghcn/
Well, whats the point? The point is folks, including me, had a theory. The temperature goes up because
of sampling diferences. That’s theory. Gotta test it. We did. Theory busted.
But for years skeptics thought the answer was simple. Drop off correlated with temps going up.
easy peasy. No one questioned this because it fit the skeptical story. Same with UHI.
Now comes your thoughts on Church 2103. Hmm. not very compelling. you need to do two two things
A) show, not assert, that they munged the data in the way you claim.
B) demonstrate that if they “munged”, that it is actually “munging”
I could claim that UHI munges together multiple disparate data sets. They do Homogenize various sensors.
It’s tricky business, but it is the business of observational science. And in the business, you have to actually engage the data. Which you normally do. So I will assume that this essay is a one off random gripe
Mosher writes
What would you consider “munging”? If the observations are changed to better agree with modeled data, is that munging? Or in your mind is munging, only the very far end of the spectrum where say a random adjustment was applied?
Steve,
You keep repeating your self while ignoring the doctoring of the evidence that is well documented.
Doing that does not make your point more credible.
Steven Mosher May 26, 2018 at 1:18 am
Mosh, always good to hear from you.
But nope. It’s not a gripe of any kind. It is a request and an explanation.
First, it’s an explanation of why I didn’t use the 2013 data … because I don’t understand why there is a hockeystick in it, particularly one that only affects the post-1992 data.
Next, it’s a request for someone to educate me about why the hockeystick was added. I said that IF, and it was a big if, viz:
It appears that you don’t have an explanation for it either … which is OK, but that’s no reason to accuse me of unspecified malfeasance …
Nick Stokes thought he’d found the explanation, but his citation just made things worse—they’ve not only adjusted the last few years of their data upwards, they’ve adjusted the first few years of the satellite data downwards … and guess what? In both cases, it increases the putative acceleration.
It bears remembering that C&W were the first scientists to claim they’d found an acceleration in the sea level data, so they most definitely have an axe to grind here …
My best to you,
w.
They make it definitely worse and as per my answer to a rather stupid exchange with Kristi above I am fascinated by the quoted systemic error when you consider that paper.
Surely tagging satellite measurements to tidal gauge data is wrong? Did C & W run a period of running the two methods of collecting sea level data in parallel before publishing their results?
(Also was this done when weather measurement went to electronic methods?)
You don’t graph in parallel. You graph on in X and one in Y and get a least squares trend. Then you check the slope of the line to see if it is close to one. The trend needs to have a high correlation coefficient. Overlays proves nothing and is not statistics.
“one in X”
Run the data collection together (i.e. in parallel) and then plot X against Y.
The graph is an annealing of two sets of data that have no correlation.
I’ve posted the following update to the head post …
============
[UPDATE] I thought I might point out the biggest problem we have with sea level estimates, which is the lack of data. Here’s a graph showing how many tide gauges we have by the number of years of data that they have:
So for example, there are only 35 tide gauges which have 120 years or more of data … and that only gets us back to about the year 1900.
Not only that, but because the tide gauges are on land, the world’s oceans are only sampled around the edges and on a few islands …
I bring this up to point out that we simply cannot place much faith in the tidal gauge data to provide any “global” average sea level rise.
Willis, probably a stupid question, but we are in the final preparations for Alberto which is expected to be a fair to middlin’ tropical storm, maybe a weak hurricane, and I’m wondering how gauge data handle storm surge? For example, Ivan gave us roughly 16 ft of surge and Camille gave MS about 26 ft as I recall. Would the recent active period in the Atlantic since 1995 have any impact on trends during that period? As you indicated, the data are really sparse in terms of geography and history. Idle questions, I know
The current forecast calls for Alberto to make landfall just to our west, which is normally bad for a cyclone with a well-defined traditional structure. Tropical storms, and unwinding hurricanes, can be different however and the strongest quadrant can be non-traditional. Alberto will not be an Opal, Ivan, Dennis or even an Erin but it will be a nuisance for someone!
JRF in Pensacola May 26, 2018 at 3:29 am
JRF, the only stupid questions on my planet are the ones you don’t ask … they’re guaranteed to come back some day and bite you on the okole …
The best answer is to read this description of how sea level trends are determined. In particular see the section called “asymptotic trend evaluation” starting on page 5.
Best regards,
w.
Thanks, Willis, that paper was certainly worthwhile and another example of time conquering all.
Willis, the graph of the number of tide gauges was my biggest take away. 35 gauges, which I bet are not “evenly” distributed to determine the entire earth’s sea level change the past 120 years is a bit of a stretch. Then to combine such limited tide gauge data with satellite data, which is actually measuring sea level is a totally different way and then claiming much of anything for the past 100 years goes beyond being a stretch. Well it appears to me the authors had a goal in mind that really had little to do with the impacts of sea level rise but a lot to do with press release and feeding the true believers.
It’s even worse because of those 35 sites 20 are around the Baltic which is about 0.12 % of the World Ocean.
There really isn’t a lack of sea level data as far as the actual study of global sea level is concerned. It is recorded on thousands of coastlines all over the world. The conclusion, the Earth’s sea level has been at standstill since the Laurentide ice sheet finished melting ca. 12,000 years ago.
Source of your bar graph data, Willis?
Kristi, the bar graph data is from PSMSL, the Permanent Service for Mean Sea Level.
You also say:
Kristi Silber May 26, 2018 at 7:25 pm
Your guess is correct. Not sure what you are calling “the TG record”. If you mean “tide gauge”, it says a lot. It says that we have precious few long-term records …
However, you’ve inspired me to look at this in a different way:
Best regards,
w.
Just taking a wild guess, in the absence of the source data or anything about it, that some of the gauges were recording data at previous times (i.e., the 10 year gauges were not all installed in 2008). They might even be replacements for other gauges at the same site. This graph doesn’t say much of anything about the TG record.
“Not only that, but because the tide gauges are on land, the world’s oceans are only sampled around the edges and on a few islands …”
The only place where sea level matters is around the edges and on the islands. Otherwise, who cares how high or fast or whatever it does in the middle of the ocean. And if they do, they need to say why.
“ And if they do, they need to say why.”
Because it would be a very important data point(s).
“Matthew W May 26, 2018 at 4:28 am
Because it would be a very important data point(s).”
Of academic importance only. But our wonderful left wing scare mongering media takes that middle of the ocean figure and applies it to places like the California coast to make ridiculous claims for sea level rise in the coming decades.
Here’s a story from this morning
http://www.marinij.com/article/NO/20180525/NEWS/180529836
that says:
That comes to an average rate of 9 mm/yr for the next 100 years. The obvious question that the news media fails to ask is, when will this jump to three times the current rate shown by the Point Reyes
http://www.psmsl.org/data/obtaining/stations/1394.php
and San Francisco
http://www.psmsl.org/data/obtaining/stations/10.php
tide gauges begin to happen?
The San Francisco Bay Conservation and Development Commission is dishing out B.S. pure and simple. They’re doing it in broad daylight, and they’re getting away with it.
Have you ever tried sailing up-hill? Do you know how much more evil bunker oil will be consumed by all those freighters having to plow up a mountain of water in the middle of the ocean? It’s Worse Than We Thought!
Depuis des millions d’années il y a des milliards de km³ d’eaux douces (venus des pluies, des fleuves & des rivières) qui se sont déversés dans les mers & océans… SANS QU’ELLES OU ILS NE MONTENT !!! Çà alors ! Tout simplement parce que l’eau s’infiltre continuellement dans les planchers océaniques et maritimes vers le magma où cette soupe toxique (les poissons chient dans la mer !) y est chauffée/bouillie et remonte donc (comme dans une cafetière électrique) vers les sources (chaudes ou froides suivant l’altitude) et vers les nappes phréatique qu’elle remplit.
For millions of years there are billions of km³ of fresh water (from rains, rivers & rivers) that have poured into the seas & oceans … WITHOUT WHERE THEY DO NOT UP !! ! That’s it! Quite simply because water continuously seeps into the ocean and sea floors to the magma where this poisonous soup (the fish shit in the sea!) Is heated / boiled and goes up (as in a coffee maker) to the sources (hot or cold depending on the altitude) and towards the water tables it fills.
Willis (& anyone else who values rational thought and science absent shenanigans): are you aware of Gregory et al. (2013, I think), wherein the authors conclude that no acceleration, or only a minuscule one, if evident from the data?
I believe Church or White was a co-author.
Gregory, White, Church, et al (2013). Twentieth-Century Global-Mean Sea Level Rise: Is the Whole Greater than the Sum of the Parts? Journal of Climate, Volume 26 Issue 13 (July 2013), AMS. (See abstract: “…a relationship between global climate change and the rate of [Global Mean Sea Level Rise]… is weak or absent during the twentieth century.”) doi:10.1175/JCLI-D-12-00319.1.
This whole sea level rise threat is such a farce anyway. Even if all 200000 glaciers in the world melted the sea level rise would only be 400mm. That is less than 16 inches. Antarctica will never melt even if global average temperatures go up 4C because almost all of the continent is way below freezing even in the antarctic summer. Since the Arctic ice sits on the ocean sea level will not rise even if the whole Arctic melted. What is left to melt? OOOOOOOOOOOh Greenland. Okay Consider this. In the medieval warming period sea level rose 1.6 metres at the high end. The temperatures were 2C warmer. So even if the CAGW alarmists are right and the temp rises to 4C over today, How much of Greenland would melt? Well in the vast interior of Greenland only the very top of the ice melts in the summertime. Even the IPCC has stated that a 3C rise in temp over the next 80 years would result in a 1 metre rise in sea level. I dispute that because the vast majority of Greenlands ice sheet never even comes close to reaching 0C. It would take a much larger increase of temperature to melt it. Everybody just seems to take the alarmist view on this without looking at the actual size of ice that would have to melt. Recently an engineer on this site calculated that it would take 105000 years to melt the Antarctica even if you had all the energy of the world running blowtorches melting the ice. Greenland is not nearly as big but I challenge Michael Mann to try and melt even a thousandth of Greenland even if he had access to industrial melters on every last inch of the Greenland interior. Greenland has 2,850,000 km3 of ice.
All of it would have to melt to raise sea level by 7 metres. This is just not going to happen especially even with a 4C average global temperature rise which is at the high catastrophic range of IPCC predictions. You just cannot melt that large a block of ice with air temperatures 4C higher . This is because you are dealing with averages here. Even in the summertime inland Greenland is a very cold place. The global alarmist position is a farce on every level.
Alan Tomalty,
Additionally, what isn’t commonly appreciated is that the weight of the Greenland ice has depressed the interior of the continent and disrupted any drainage that existed prior to being covered in ice. If the ice should be completely melted, a significant fraction of the water won’t make it to the oceans until isostatic rebound removes the ‘bowl.’ The bottom line is that theoretical calculations converting the ice volume of Greenland to an increase in ocean level overstates the immediate effect.
I would also like to draw your attention to this graph
https://www.climate.gov/news-features/event-tracker/new-record-temperature-southwest-greenland
It shows the alltime record summer temp for Summit station in inland Greenland. Notice that it barely got above 0C. Since summers are only 2 months long here how in the hell is Greenland supposed to melt any appreciable amount even if global temps went up 4C. The summit is 2 miles high and the mean thickness of the ice in all of Greenland is 2135 metres or 7000 ft. Since this total of ice is 2850000 km3 , how would this melt in 2 months? It wouldn’t. fall and winter would come and the ice would refreeze. Spring would come again and as you see on the graph there wouldn’t be any melting in the spring even if global world temperatures soared above an increase of 4C. sure Greenland has been losing ice mass over last 20 years but thus has happened thousands of times in the past. There was less ice in the 1920s in Greenland than there is today. Global warming is a farce. We need more CO2 NOT less.
Remember a global average temperature (if there really is such a thing) doesn’t tell you what regional temp’s will do. Greenland’s temp may not be affected at all! Heck it may get colder.
To further cement this hypothesis of Greenland ice sheet not melting from of top, there have been studies that the melting is happening from underneath because of a volcanic ridge extending from Iceland right to the Arctic. Even the alarmist scientists are admitting that the top of Greenlands interior ice sheet is not melting and that the upper surface every year gets fresh snow/ice and the reason that there is a net loss of ice is the amount of icebergs calving off on the shore line. These icebergs have calved off for millions of years and the volcanic activity has come and gone for millions of years.
Willis. I for one have had enough. Stop trying to confuse us with facts. everyone knows it isn’t what the data says. It is what we believe it says that matters.
Eleventy One is much better
I once counted to Eleventy seven. I was about five when I achieved that feat of numeracy.
If you plot C&W 2011 as two series – 1870 to 1969, and 1970 onwards – and get a quadratic best fit for the first series, the second series falls below the extrapolation. This suggests there is no recent acceleration.
Andrew Chantrill,
Polynomial extrapolations are notoriously ill-behaved!
No matter what the real measurements might be, even if we suddenly saw a dramatic rise (or fall) in sea level, the automatic assignment of cause-effect is typical of an egocentric attitude. In much the same way, earthquakes, dry spells, floods, etc were attributed to human behavior by witch doctors of the past—people were clearly upsetting the spirits . . . or they were in league with the devil, requiring a that a witch be found and burned.
No one seems to bother with science any longer. We’ve gone backwards
“The world’s oceans are only sampled around the edges and on a few islands” with tide gauges. And that’s exactly what matters. Satellites measure mostly areas far away from lands. I don’t believe that they can do it with a proclaimed accuracy – have you ever seen a sea surface as smooth as a mirror? – but let’s take their claims at a face value. Bottom-dwelling creatures probably don’t care much whether there are 2,000 meters of water above them, or 2,000.6 meters. And those who cared probably went extinct during a 130 m sea level rise in the last 13,000 years.
Everyone, see the forest through the trees!!!! What about the CO2 molecule and the GHG effect could ever cause a dog-leg in such a data set? More importantly, those dog-legs don’t line up with the dog-legs in the Hockeystick. Lastly, the oceans are warming, how would LWIR warm the oceans and cause thermal expansion. Nothing about the CO2 molecule can cause a dog-leg, in fact, its absorption of LWIR has a log decay. The linear charts don’t support the log decay of CO2’s absorption. Lastly, look at MODTRAN, CO2 has no impact on the lower atmosphere, even if you double CO2. H2O dominates the lower atmosphere.
Steven Mosher wins the KewPie Doll for best quote so far! “It’s tricky business…..”
Yes, indeed! All of the side shows associated with the business of AGW claims are indeed tricky!
Nice graph showing the adjustments W. I can’t imagine taking raw data and claiming because that the data needs adjusting and then proceeding to adjust the final product be exactly what I desired to find. It’s basically science in reverse. I think climastrologists need to start by being honest with themselves first. That’s where their dishonesty starts.
Do the satelites used for sea level measurement just measure the sea? Do they run 24/7 and capture a large portion of the globe? If so, then there should be many control points(dry land) to see if the satelite data is drifing, and by how much. Just compare several sections of land in each data set and use that to help zero out any drift.
I suspect we have tide gauges everywhere it actually matters what the sea level is. While it’s technically interesting to measure sea level globally, what does it actually matter what the level is in the middle of the ocean? The fish don’t care and I suspect even they can’t notice if it goes up or down by a few meters or even a few tens of meters.
In terms of consequences of sea level rise that justify spending any money, the only thing that matters is level relative to significant human structures and navigable waterways. Which I strongly suspect is exactly where the tide gauges are. Funny about that.
Everything that everybody said, ………. OR
8 mm
Getting WordPress to post that is a better trick then their sea level graft
Did anyone happen to see this:
“We are currently attempting to more thoroughly evaluate the methodology and to improve the reconstruction so that it better represents the variability (Legresy et al., Workshop on Global and Regional Sea Level variability and change, Mallorca, Spain, June 2015).”
It’s right under the link to the 2013 data
http://www.cmar.csiro.au/sealevel/sl_data_cmar.html
Seems like they would have been done with it by now, but who knows? Forgot to update the site? I don’t presume to know. Maybe if there are doubts, one should ask one of the researchers, or use a different dataset. Of course, that means passing up a chance to imply wrongdoing. This thread is chock full of guesses and assertions about the ways the scientists have committed fraud. If there’s a perfectly good explanation, who cares? As long as it looks like corruption, that’s all that counts – it’s worth posting. Find enough examples of things you don’t understand, and you can build a case to make it seem like the whole dam* industry is full of low-life scumbags. It doesn’t matter if the examples later turn out to have valid explanations – the goal is to instill the idea of misconduct, corruption and falsity, not to reveal the truth.
These days the ends justify the means, apparently. Saving conservatives from having to compromise on energy policy is worth destroying the public trust in science. Saving liberals from having to question their values and admit their arrogance is worth alienating half of Americans and dividing the nation.
It’s politics. The Swamp is not confined to D.C., it’s in us all. It’s power, entitlement, hypocrisy and tribalism. It’s ideology triumphing over pragmatism, bias over reason. It’s the human characteristics that must be acknowledged and tamed in order to live productively together in today’s world. We did not evolve in the environment we’ve created, and we need to put effort and thought into making it work socially as well as logistically. If it means anything to call ourselves Americans, it necessarily means recognizing that we are ALL part of this group called Americans, and as wonderfully diverse as we are, we all have something to contribute. It’s up to us whether we want to contribute destructively or constructively.
Oh, dear! Rambling again. Sorry.
(P.S. I know there are many who post here who aren’t American. I don’t mean to exclude you, and I’m not in favor of American exceptionalism, but I love my country.)
I find it mildly amusing that warmists like satellite sea level measurements because they show acceleration when grafted onto the tide gauge data. But they really don’t like satellite measurements of mid-troposphere temperature because they support the post-1998 “hiatus”.
It’s reminiscent of the way we skeptics like satellite temperatures but find good reasons to not trust satellite sea level measurements.
The difference, of course, is that we are right and they are wrong. How could it be otherwise?
Somehow the /sarc tag fell off.
Smart Rock: You are vastly overgeneralizing by treating all satellite measurements alike. Satellites are mere platforms. It is crucial to distinguish which instruments they are carrying, what those instruments are trying to measure, what the capabilities of the satellite platforms are relevant to the needs of the instruments and the intended measurements. And unlike you, I actually have years of experience designing and managing all the above–at NASA.
Thanks, Tom. I’m always amazed at the experience of the various people that read this blog.
The problem that I have is that the satellites are at an altitude of ~ 500 km, and they are trying to measure the ocean surface to an accuracy on the order of ± a half of a millimetre or so, in order to give answers to the nearest mm …
This means that it is attempting to measure the distance to a constantly moving surface to one part per billion (1E+9). This type of accuracy, one part per billion, is difficult to maintain over time in a laboratory, much less in space … not impossible, you understand, but very difficult. Instrument drift, orbital drift, exact position measurement, thermal expansion, ocean wave heights, there are lots of things that have to be known to extreme accuracy for it all to work. That sucker is doing one complete orbit of the earth every 56 minutes, which means if the timing is off by one second there’s an 11 km error in the location. And of course the orbit is not perfectly circular, so you have to constantly know the instantaneous altitude of the satellite at all times to something like a tenth of a mm or so …
Not impossible to do, as I said … just very, very difficult.
As a result, I trust the satellite data as to precision much more than I trust it as to accuracy … which means that e.g. the 10-day snapshots of the entire globe do show the relative heights in different parts of the planet, but the longer-term data that makes up the decadal and longer trends are much less trustworthy.
Best regards, any comments gladly accepted,
w.
Willis: Your arguments from ignorance and incredulity fail against knowledge. I suggest you take an inferential statistics class, paying special attention to the topics of populations versus samples. Read and really try to understand Nick Stokes’s comments here and on his blog. Read the actual academic papers before you criticize. Read spacecraft, space mission, and engineering and scientific project official proposals and reports. When you do not understand something in any of those, read the references on that thing, and if you still don’t understand, read a relevant textbook. Yes, doing all that will take you full days, weeks, months, or years for some topics. That’s how the people who actually do that work you criticize, actually plan and do their work. Space is hard. Science is hard.
Tom Dayton, you need to be more specific for your criticism to be valid. Make your argument otherwise your comment is meaningless.
Tom Dayton May 27, 2018 at 9:27 am Edit
Tom, you do realize that your entire response to me is an argument from ignorance and incredulity, right?
What I said, in essence, was that measuring something like the ocean surface levels reliably and repeatably from 500 km away to one part per billion over decades is a very difficult technical problem. I listed a host of specific problems that need to be overcome. The difficulty has been proven and highlighted by the large number of revisions in the satellite sea level data over time. Heck, Church and White in the link Nick Stokes just gave are claiming that there are still significant errors in the results. And that doesn’t count the unknown unknowns.
I’m not arguing from ignorance. I’m arguing from knowledge as well as the actual experience of people trying to do the measurements and having a very difficult time doing it.
As to “paying special attention to the topics of populations versus samples”, I suspect that I understand them as well as most do, perhaps better. I know I understand them better than many professional scientists, because I’ve seen their laughable errors.
But since all you’ve done is handwave rather than making specific
objections, so far we don’t know … in that regard you might enjoy my post entitled Decimals of Precision.
M.W. Plia May 27, 2018 at 1:58 pm
What he said …
w.
Willis,
Now, I can understand the slight, ~ ± 1 mm differences between the two datasets in most of the record.
I can’t, because those differences don’t exist when comparing the real data. Between 1880 and 1989 the difference is exactly -1.6. Now, should I immediately accuse you of intentional dishonesty and fraud as you have? Or should I first propose a more likely reasonable explanation – that you’re still comparing with a digitisation rather than the real numbers, which is introducing errors but no real intentional bias. There is no change to the algorithm or in the mix of tide gauges, which is obvious because there’s actually no change at all over that time.
The reason why you get increasing differences (both positive and negative) closer to the present has already been explained to you: Additional tide gauge data made available after the 2011 paper was published. Church and White provide a list of tide gauges used in the paper in the link you already have. If you look down that list you’ll find that many of the locations do not have data up to 2009. In many cases this is not because no data had recorded at those locations, but because the recorded data had not yet been reported/logged to the PSMSL repository used by Church and White. And of course, the closer to the present the more likely it is not to have been reported yet, which is why no changes prior to 1990.
This can also be plainly seen by looking at how the uncertainty estimate increases for recent years in the original data, primarily due to coverage deficiencies. By the 2015 update, much of the deficiency had been filled in by those reports coming in, so that the 2009 annual uncertainty estimate substantially tightened. Whereas we can see that the 2013 annual estimate (the final year in the update reconstruction) has about the same uncertainty as 2009 in the original, because it too is affected by reporting lag.
Thanks, Paul. You’re right about the small ± 1 mm errors, they are indeed from the digitizing. Makes me happy to see that my digitizing is consistently that good.
Regarding the rest, it may just be that the few new tide gauges that they added are enough to change the trend of the other 750 gauges in the dataset by a very large amount in the direction of greater acceleration … but given that C&W have nailed their colors to the mast of the good ship “ACCELERATION!”, it may not be …
I’m also not seeing how adding even 10 or 20 new datasets could change the sea level by 8 mm in a decade.
You say they explain it “in the paper in the link [I] already have” … if you’d be kind enough to repost that link, I’ll look at it, because I haven’t been able to find the paper.
Your answer to the question of the small 1mm errors is appreciated,
w.
So, if you don’t understand it the way Tom understands it, then spend the rest of your life studying it the way Tom did, down to every last minute detail, EXACTLY the way he assimilated his perception, … which, oh by the way, will distract you for the rest of your life, from raising legitimate concerns.
Not saying Tom’s method is the wrong method. I’m saying that there might be a better way to point out that somebody has not considered relevant facts than to tell them to do another whole lifetime of studying to erase any questioning — a lifetime that a person does not have, of course.
Tom, might I suggest you take a couple of years of ballet, then some chef classes, then read a good text about how to mix alcoholic beverages, a class or two in how to set a table, how to use your eating utensils in a dignified, noble manner, how many times to chew your food for maximum digestion, in order to understand your body’s most elegant placement, and your best choices of food/drink and best way of eating/drinking them, … all BEFORE telling me that you don’t like the way I cook my broccoli and you don’t like the choice of wine I serve with it. (^_^)
The response just came across as a bit snobbish.
Regardless of the possibility of one’s great mastery of actually achieving (or believing that one can achieve) accuracy within a tiny fraction of a mm — LET ME REPEAT, <b<fraction of a mm
— the important fact seems to be that we are talking about MILLIMETERS. And we are talking about a FRACTION of a millimeter assessed GLOBALLY.
Admittedly, I speak from “ignorance and Incredulity” as to whether such accuracy is possible, but I’m pretty sure I have a feel for what a millimeter is and how the Earth has changed by far more than fractions of these or even multiples of the wholes of these very small units of measure.
Again:
8 mm</b<
… considering the ENTIRE surface of Earth, weighed against MILLIONS of years of sea level change, BEFORE humans ever set foot (precursor fin, tentacle, or proto-foot) on the planet.
Oops, coding flub.
8 mm
… and ANOTHER coding flub before that one, .. but, oh well, what the hell, I give up for now, you get the message.
Willis: “they are trying to measure the ocean surface to an accuracy on the order of ± a half of a millimetre or so, in order to give answers to the nearest mm”
According to NASA, “The primary instrument on Jason-3 is a radar altimeter. The altimeter will measure sea-level variations over the global ocean with very high accuracy (as 1.3 inches or 3.3 centimeters, with a goal of achieving 1 inch or 2.5 centimeters)”
According to Wikipedia, “From orbit 1,330 kilometers above Earth, TOPEX/Poseidon provided measurements of the surface height of 95 percent of the ice-free ocean to an accuracy of 3.3 centimeters.”
According to the IPCC, “The current accuracy of TOPEX/POSEIDON data allows global average sea level to be estimated to a precision of several millimetres every 10 days, with the absolute accuracy limited by systematic errors.”
So the trick here is to measure many times and take an average. But “Satellite altimeters measure the ocean’s surface height, passing over each point on the ocean’s surface every week or two.”, so can the IPCC be right?
Interesting aside: “In addition to mapping sea-surface height, the other primary mission for the altimeters is to provide maps of wave height and direction (Section 8.3.2 in Chapter 8). Mean wave-height estimates accurate to ±1 m or 25% of the actual wave height are possible from RADAR altimeter backscatter. This measurement is made possible by looking at the waveform returned to the satellite from the altimeter reflection. The slope with which it returns is a function of the significant wave height on the surface of the ocean. Many experiments have been carried out to verify this assertion.”
https://www.sciencedirect.com/science/book/9780750645522