Guest Essay by Dr. Alan Welch FBIS FRAS, Ledbury, UK — 3 May 2023
The release of the Sea Level Data up to Jan 2023 marks 30 years of satellite measurements using the quartet of satellites Topex and Jason 1, 2 and 3. It also marks 5 years of my interest in sea level rises, not as a climate scientist, but as a chartered engineer with nearly 40 years’ experience in engineering analysis. This interest was stimulated by the 2018 paper by Nerem et al (1) in which they introduced the concept of dangerously high sea level accelerations.
A year ago, I produced 2 essays. The first essay (2) showed the “accelerations” derived were probably the outcome of the methodology used. The second essay (3) showed that 30 years is too short a period to derive a meaningful acceleration.
The important graph in this update is Figure 3 which shows the change in “accelerations” using the Nerem approach when applied to the NASA data set and also to a sinusoidal data set. When accelerations are embedded in “ “ it implies these are based on 2 times the quadratic coefficient of a curve fit and may not necessarily be considered as a physical acceleration per se.
Every 1, 2 or 3 months the sea level data is released on the https://climate.nasa.gov/vital-signs/sea-level/ web site and these data have been analysed continuously since Feb 2018. The latest readings were downloaded via the April 2023 NASA Climate Change Newsletter. Figure 1 shows the NASA Data together with linear and quadratic best fit curves.
It is much easier to see trends when just the “Residuals”, the differences between actual values and the straight line, these being plotted in Figure 2.
For most of the analyses since 2018 a sinusoidal curve with a period of 22 years and an amplitude of +/- 3.5 mm was used. In reference 2 this was judged as needing updating and the period and amplitude were increased by about 20% and a small change in phase shift applied. The standard deviation of the residuals is 4.12mm whilst the standard deviations of the actual results about the quadratic and sinusoidal curves are 3.06 and 3.01 mm respectively implying that the sinusoidal may be a slightly better fit. (The use of an amplitude of +/- 4.2 mm is slightly embarrassing as it implies a degree of exactitude that many “climate scientists” would be proud of!).
In reference 2 the process of calculating “accelerations” for each successive batch of readings was applied to the sinusoidal curve and the resulting “acceleration” using the modified sinusoidal curve plotted in Figure 3 together with the actual derived “accelerations”. The sinusoidal curve has been (rightly or wrongly) extended to the year 2026. If extended much further the curve would approach zero in an oscillatory manner as shown in Note 2 of Reference 2 but this should not be considered a definite long-term prediction. The main danger in all climate change work is Extrapolation – a few years may be justified but many graphs are produced with eye watering amounts of extrapolation. Note the curve labelled “Sinusoidal” is not sinusoidal in shape but relates to the fact that it is based on the sinusoidal data. (In the comments in reference 2 the way the original sinusoidal curve was handled was justifiably criticised as not being mathematically precise, but a pragmatic engineering approach (aka gut feeling) led to the idea presented in figure 3. With the previous sinusoidal equation, the 2 curves were separated by 3 years but displayed sufficient similarity as to point to a promising line of enquiry).
The calculated “accelerations” have been reducing with every set of data since peaking in Jan 2020 and Figure 4 plots the % reduction in perceived “accelerations” since Jan 2020. This works out at about 4.5% reduction per year. On the NASA Web Site reference is made to the recent La Niña event having reduced the “acceleration” so it will be interesting to see what the next year or two will bring.
Figure 5 combines the Linear Fit with the Sinusoidal Variation.
Main Findings
1 The perceived “accelerations” have been reducing month on month since peaking in Jan 2020.
2 The Quadratic and Sinusoidal curves fit equally well. Remember they are products of the data available and great restraint must be used if extrapolation is contemplated.
3 Should the reduction in “accelerations” follow that shown by the sinusoidal curve as shown in figure 3 in 5 years’ time or so the “acceleration” should be down to nearly half the 2020 peak. (In 5 years, I’ll be over 90 so hopefully someone else will pick up the batten if I shuffle off this mortal coil!)
4 A question (hypothetical?) that could be asked is if there is a small sinusoidal content in the variations where does it come from? Possibly it is not within the data as measured but comes about by what is not measured. The satellite readings only cover about 95% of the oceans. If there are decadal ocean oscillations across the +/- 65 degree latitudes this could show up as a sinusoidal variation. Figure 6, from the NOAA site (https://www.star.nesdis.noaa.gov/socd/lsa/SeaLevelRise/LSA_SLR_timeseries.php) shows the extent of the ignored polar regions in relation to the polar seas.
5 The variation considered is only +/- 4.2 mm – that’s just over 0.16 inches in old money – which is next to nothing in comparison with some of the ocean variation given in the NOAA site over the last 30 years. Examples worth inspecting are the northerly seas such as the Bering Sea and the North Sea. Figure 7, taken from the University of Colorado site, https://sealevel.colorado.edu/data, showing variations of 20cm or more over the last 30 years. A change of 4.2 mm would only be as big as the “o” in Colorado!
References
1. Nerem, R. S., Beckley, B. D., Fasullo, J. T., Hamlington, B. D., Masters, D., & Mitchum, G. T. (2018). Climate-change-driven accelerated sea-level rise detected in the altimeter era. (full text .pdf) Proceedings of the National Academy of Sciences of the United States of America, 115(9). First published February 12, 2018
2. https://wattsupwiththat.com/2022/05/14/sea-level-rise-acceleration-an-alternative-hypothesis/
3. https://wattsupwiththat.com/2022/06/28/sea-level-rise-acceleration-an-alternative-hypothesis-part-2/
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Comment from Kip Hansen:
Dr. Welch has been working on these analyses for years and has put his findings for the now-30-year climatic-period length of satellite era sea level measurements together in this essay. This and his two previous essays on the topic (linked in the essay and in the references) are offered here by Dr. Welch as an alternative hypothesis to Nerem (2018) ( .pdf ) and Nerem (2022). [ In a practical sense, Nerem (2022) did not change anything substantial from the 2018 paper previously discussed by Welch.]
On a personal note: This is not my hypothesis. I do not generally support curve fitting and an alternate curve fitting would not be my approach to sea level rise. I stand by my most recent opinions expressed in “Sea Level: Rise and Fall – Slowing Down to Speed Up”. Overall, my views have been more than adequately aired in my many previous essays on sea levels and their rise or fall here at WUWT.
I find Dr. Welch’s analyses interesting and feel strongly that Dr. Welch’s analyses deserve to be seen and discussed. I have encouraged him to present his findings here at WUWT.
Dr. Welch lives in the U.K. and his responses to comments on this essay will be occurring on British Summer Time : UTC +1.
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OK, good report on an aspect of global climate health. But remember, to a geologist 30 years is only a popcorn fart. Unless Mikey Mann can torture that linear trend into something, never mind.
When discussing the rate of sea level rise, I think it is instructive to note how it compares to other geological processes. Th US Geological Survey says that the average (mode?) rate of movement of tectonic plates is about 25mm/year, with the East Pacific Rise being greater than 150mm per year. And, climatologists are getting their panties in a knot over 2.5mm versus 3.5mm/yr. Figure 7 suggests that over the last 30 years, the maximum average SL rise has been about 6.6mm/yr. Actually, the lateral movement of tectonic plates may be higher than 25mm/yr because that is the continuous creep rate, and when a large earthquake occurs, the horizontal displacement can be nearly 8,000mm/event (San Andreas Fault, 1906). Vertical displacements along the shoreline have been as much as about 2,500mm/event. Assuming an occurrence average interval of 500 years for major earthquakes such as the 1906 San Andreas, that is an average of about 16mm/yr lateral, and 5mm/yr vertical, on top of the creep rate.
https://pubs.usgs.gov/gip/dynamic/understanding.html
Again and again, I note the fraught assumption that the rock walls and floors that are the ocean basins should not be assumed to contain a constant volume, because we have ample evidence of some movement while we look. It follows that sea level change should never be stated without a mention of ocean basin volume change. The latter has never been measured to adequate accuracy, but it cannot simply be assumed to be zero.
Therefore, all of these sea level maps have a BIG question mark ??? over them. Geoff S
Geoff Sherrington ==> It all depends on what one is trying to show — what one is really measuring.
You want volume of water in all the world’s oceans? or do you want where the sea hits the land in Miami Beach, Florida USA? The first is only of academic and scientific interest. The second is the only thing about sea level that is important to the people of Miami Beach.
In my opinion, like “global temperature”, there is no single “sea level”.
To your point Jeff:
The Thingvellir Valley in Iceland is running rampant compared to sea level rise.
”…fairly constant, about two centimetres a year.”
Do you smell popcorn?
It’s difficult to gauge what the satellite data says when every time it’s updated, all of the
existing historical data up to that point has been changed. Besides that, the recent claim
is still the 0.084 mm/yr² which doesn’t agree with the tide gauges that say it’s 0.01 mm/yr²
over the long histories of stations with 100 years of data. Here’s how CU’s data has been
changed from 2004 to 2016. Each plotted plotted point represents the rate of sea level
rise since the start in 1992 for the release dates as shown.
Sorry about the formatting that got screwed up )-:
“sensors slowly fail” yup
Nick Stokes will probably tell you its too expensive to keep giving you the old data. I await his clever argument to explain the appearance of those new numbers, though…
(In reference to Nicks verrry convoluted arguments yesterday around the cost of allowing you access to records you will probably just find fault with …:-)
Steve,
Interesting graph.
A first impression is that a change in thinking happened between 2005 and 2006 when the left axis start point changed a lot in one jump. Any idea what it was?
Geoff S
Colorado University (CU) began to include the Glacial Isostatic Adjustment (GIA) in their somewhat irregular regular releases of satellite sea level data in 2011. You can read their publication about that here. In a nutshell they wrote:
“In essence, we would like our GMSL [Global Mean Sea Level] time series to be a proxy for ocean water volume changes.
…
Prior to release 2011_rel1, we did not account for GIA in estimates of the global mean sea level rate,”
Why they didn’t start an Ocean Volume page is anyone’s guess.
When they first started the GIA nonsense, they included a note on their graph that said GIA corrected, but they dropped that starting with the 2016 releases. At the time I posted that interesting factoid here at WUWT and to my surprise nobody said boo about it.
Well that didn’t address the 2005-06 change or did it? Anyway it’s obvious as the north end of a south bound goat that CU changes data to fit the narrative.
Thanks for your inquisitive comment (-:
Steve ==> CU wants to support the Climate Crisis viewpoint. They want to show BIG sea level rise and ACCELERATING SLR.
It all depends on what one is trying to show — what one is really measuring.You want volume of water in all the world’s oceans? or do you want where the sea hits the land in Miami Beach, Florida USA? The first is only of academic and scientific interest. The second is the only thing about sea level that is important to the people of Miami Beach.
And don’t forget the instrument accuracy of 33MM
leefor:
Exactly! Would someone please explain to me why they even try to record mm when the uncertainty is in centimeters?!
IIRC after a recent earthquake in California there was some article gushing about how accurately satellites could measure the ground movement: “to within 4 cm”. This was over land.
Now for the ocean you must include waves, tides, wind, orbital fluctuations, and oh, the equatorial bulge (in kilometers!). Sea level change is a local issue and unless there is correspondence with local tide gauges satellite data should be ignored.
“Exactly! Would someone please explain to me why they even try to record mm when the uncertainty is in centimeters?!”
Good question.
So they don’t really know how much the sea level has risen using satellites.
…plus you must prove that your tide gauges are absolutely stationary within the reference frame. Or do we suppose the land level around tide gauges follow different rules than every other bit of geology on earth?
I think they are mostly measuring the weight of angels.
“I think they are mostly measuring the weight of angels.”
Which, the anorexic angels or the morbidly obese angels ???
Lizzo angels.
To that point, not criticizing Dr. Welch, but where are the error bars in these graphs? (I don’t know if they are available in his source data or not)
Steve ==> As for me, it is always presented as “Errorless Sea Level”
We keep worrying about sea level relative to continental land level, but really we should be studying both relative to the center of the Earth. Land level goes up and down about a foot a day due primarily to the Moon’s gravity.
70% of the planet is under water, and there is nothing equivalent to satellite data about what sea bottom level is doing relative to the center of the Earth. Continents going down a little, pushing sea floor up a little, looks the same as more sea level rise to a satellite whose distance from the Earth is calibrated by microwave soundings from land stations.
After much work and calculations ITRF has determined that the volume of the planet is consistent within average diameter of .2 mm per year. Of course, they have had a couple of big kerfuffles of as much as 6 cm. error as new satellites are “calibrated”.
https://agupubs.onlinelibrary.wiley.com/doi/full/10.1029/2011GL047450
DMakKenzie: If you look into it in detail, you’ll find that the satellites (attempt to) measure sea surface level relative to the satellite’s orbit using radar. Their measurements can (conceptually) be easily converted to distance from the Earth center. There are all sorts of problems starting off with the satellite’s orbit being near circular whereas the sea surface is a sort of lumpy ellipse. And the fact that the volume of the oceans is constantly changing because water expands when warmed. And water evaporated from the sea often condenses and falls on land and may take months or years or more to find its way back to the sea. Which is to say that there is a seasonal component to overall sea level and it’s not quite the same from year to year. And, of course, radar is less than perfect at measuring distance from the satellite to an ocean surface that is in hardly ever flat and waves often aren’t simple sinusoids. … And a bunch of other things like somewhat uncertain ionospheric delays that alias into range estimate errors.
To their credit, the folks who designed the systems have done really extensive system and error analyses. Page after page after page of them. If you’re curious there are satellite “handbooks” that provide a lot of detail about the systems, available data products, and the required processing. Here’s a link to the handbook for the Jason-3 satellite. https://www.ospo.noaa.gov/Products/documents/hdbk_j3.pdf You might want to skim through it. Studying it in detail would take months. More likely years. And that’s just one satellite.
So, are satellites and tide gauges measuring the same thing? They are trying to. But there are all sorts of problems with both sets of measurements. Bottom line. We don’t really know exactly how much sea level is changing over time. There is very good geological evidence that sea level can and does change by quite a lot over long periods of time — millenia. But the tide gauges and satellites do agree that the current annual change is quite small. Substantially less than a meter per century. And the data contains so much noise of various sorts that I don’t think any reasonable person would try to extract an acceleration from it. IMO, if you can’t see a pronounced curve in the raw data (and you really can’t) there’s no hope of extracting a meaningful acceleration.
“We don’t really know exactly how much sea level is changing over time.”
and I bet 99% of the human race doesn’t give this “problem” ever a thought- not counting the crazies out there- people have endless things to worry about and this issue isn’t on their top 1,000 list
Joseph Zorzin ==> I have a friend who lives in the “mountains” of New York state (really, they are only hills, less than a thousand feet). She hears NPR warn her about Sea Level Rise and is terrified that the world is in great danger…worries about her kids and grandkids living in the Carolinas who, in reality, are all quite safely far above even hugely exaggerated sea level rise, but she doesn’t understand that.
She must be listening to the NPR station in Albany. It’s very far left. To this day, it spends much of its political discussions on hatred of Trump. I emailed the honcho there (Alan Chartock) about wasting energy on that subject. He wrote back that I should apologize to him. I then blasted him- which I won’t repeat here. Chartock has a PhD in political science so he thinks he can pontificate on all politics. It’s my understand his income for running this station is almost 200K/yr.
If she’s in the Adirondacks, the mountains there up to 4,200′- though she might be in the Catskills which are much lower.
“Bottom line. We don’t really know exactly how much sea level is changing over time.”
That is the bottom line.
Yes, I have pointed out at WUWT a couple of times that the JASON accuracy is only about an inch. See Section 2.3.1 of the manual, says 2.5 cm. Everyone seems to think the table is in mm when it is in cm. Target drift is 1mm per year…how close they achieve to target is not stated. As to the Earth tides I referred to, they use the Cartwright and Taylor tidal potential method. It’s just not accurate enough for what they are attempting. NOAA needs to get over their accuracy hubris.
DMacKenzie ==> You underestimate the error bars. 2.5 cm is the specified accuracy for any one individual measuremennt, assuming a perfectly flat stable sea. Add to that (really, they should be multiplied) are tens of other factors with error estimates orders of magnitude larger.
DMacKenzie ==> What do you want to know? How much water is in the seas?
Or do you want to know if the sea will come up and cover your dockside lawn or flood your house?
ONLY Relative Local Sea Level is of any real concern to real people. The owner of a marina in Florida does not care how much sea level rise is reported in Manila. He wants to know if he needs to build a sea wall to protect his restaurant.
When the Climate Alarmists get into sea level rise, suggesting that is going to be an increasing issue at time goes by, I remind them of historic sea level height changes.
Then to ensure the anxious dears are not left without a modern day fix, if one were ever required. I point out there are huge areas of the earth that are below sea level which we could back fill if needed (which we don’t need to do).
The Caspian sea is 27 meters below sea level and has an area bigger than the British isles.
The dead sea is so low it would require a canal running from the Red sea to the Dead sea to back fill it over flowing for 100 years. Well that depends on the size of the canal of course. I was thinking the Birmingham Manchester size canal here.
Areas of North Africa and of course Death Valley USA are all way to low, so a bit of back fill would be helpful.
Alternatively, we could let nature do its thing and stop worrying about natural variation.
The Salton Sea is below the sea level of the Gulf of California. There is talk about building a canal from there to save it from evaporating.
It will be interesting to see if the Alarmists allow backfill to happen.
They will be aware doing such would reduce one of their pet anxieties. 🙂
As the Author I will have less time to respond as I have the builders in (putting the house on stilts to counteract Nerem’s sea level – we are only 219 feet above sea level!!). It’s an extension actually.
Seriously my reason for doing this work was to negate the methodology in calculating “accelerations” in sea level rise by Nerem et al. Their findings were then picked up by the likes of the BBC and the Guardian and caused Swedish school girls to play truant. It is the fear that has been instilled into the general public, and especially the youngsters, that is so frightening.
My Figure 3 was a way of capturing the trend in a single simple graph, meaningful or not, which is worth keeping an eye on. Unfortunately Nature changes slowly as far as Climate is concerned (not weather) so watch this graph.
Alan, are you related to Dr Geof Welch? I worked with him in Wolverhampton back in the 1980s a great guy to know and work with.
No sorry.
“As the Author I will have less time to respond as I have the builders in (putting the house on stilts to counteract Nerem’s sea level – we are only 219 feet above sea level!!)”
Oh dear! I’m at about 220′! Should I be worried??
/s
Now THAT’s some scale right there! Always resfreshing to read people who live in the real world. A bit of wit helps, of course.
The period required to detect acceleration depends on the size of the acceleration.
If 30 years is too short, acceleration is too small, i.e., non-different from zero.
What I showed in reference 3 was that the shorter the period analyzed the higher the perceived acceleration. Half the period and the acceleration might result in a 2, 3 or 4 times increase and will at times be high deceleration. Nerem’s value of nearly 0.1mm/year2 could easily drop to 0.01mm/year2 after 100 years more in keeping with Tidal Gauges. After a very very long time it’s going to approach zero.
As I implied in reference 2 you can calculate a quadratic coefficient, you can call it acceleration but what is wrong is to extrapolate and frighten everyone that that is what is going to happen.
Sea level presents multidecadal oscillations, like the rest of the climate variables.
Jevrejeva, S., Moore, J.C., Grinsted, A. and Woodworth, P.L., 2008. Recent global sea level acceleration started over 200 years ago?. Geophysical Research Letters, 35(8).
The Pacific and Atlantic Oceans present two multidecadal oscillations, one of a 50-70 year period (AMO & PDO) and another one shorter, of about 20 years and with different causes (not a harmonic).
The long-period oscillation in sea level was included in Marcia Wyatt’s “stadium wave hypothesis.”
With 30 years of data, you can start to detect the short-period oscillation.
To this old, retired, experimental physicist, the data in the Figure 1 should only ever be fitted with a linear function. Especially as the error bars are not shown. Second, everyone seems to be concerned with sea level rise acceleration. Isn’t the acceleration of a time dependent parameter given by d2x/dt2; ie the second derivative? Obviously the linear fit yields exactly a zero second derivtive. The less likely quadratic fit yields a very low 0.0818mm/yr2. Either way, there appears to be no sea level rise acceleration since 1993. Why bother with all this additional analysis??
Obviously to most of us it is not worth all the effort but it is the way a quadratic term in the second order fit over 30 years is judged to be an acceleration then extrapolated up to 2100. Then all hell breaks out as pictures appear of New York under water etc. I’ve been showing that the long term acceleration is probably much lower, although only time will tell, but my figure 3 is worth pursuing. I’ll keep analyzing and hope to be around in another 5 years to see the trend.
Ahh… so basically you are trying to counter a specious argument based on the quadratic fit. From my own personal experience with these people before retirement, any such attempt at rational, or even mathematical argument is fruitless. They believe what they believe, and nothing will dissuade them. It’s a religion. You can’t make a scientific argument and convince a religious believer.
Kip,
Why is satellite measured sea level rise roughly twice that of tide gauge measured rise, when the tide gauge is corrected for isostasy?
Denis ==> You have the right question. I (Kip Hansen, not the author of this essay) have given my view many times here at WUWT. Tide gauge data are not corrected for Vertical Land Movement (VLM) of the structure to which they are attached. There has been some effort along those lines, but usually it is not adjusting for the movement of the Tide Gauge itself. ONLY those sites with “Continuously Operating GPS units attached to the same structure” (GPS@TG/ss) can reliably distinguish between the movement of the tide gauge itself (up and down) and the movement of the surface of the water it is measuring. With Sea Level Rise being on the scale of mm/yr, the tiny movement of the tide gauge (and the structure it is attached to) are of the same magnitude, In some areas, the VLM of the Tide Gauge is greater than the change in mean sea level at that location.
This paper is worth reading: “Relative sea-level rise and land subsidence in Oceania from tide gauge and satellite GPS”The author used the datas of 5 GPS corrected tide gauges in the Pacific area.
Relative sea-level rise and land subsidence in Oceania from tide gauge and satellite GPS (degruyter.com)
Not Kip, but simple answer. The satellite accuracy is about 3.5cm. They claim mm, which is impossible. The proof of gross satellite error is also simple. The satellite measurements do not close, while dGPS vertical land motion long record tide gauges do. For details, see my long ago guest post here ‘Sea level rise, acceleration, and closure.’.
Let me reformulate the 3.5 cm accuracy: It is an accuracy of a satellite measurement of a waveless, perfectly smooth, sea surface. Abundant everywhere.
Denis ==> See mine here.
Denis,
A partial answer to your valid question is this:
The IPCC asserts that 40% of the (satellite data) SLR is due to thermal expansion. The bad news for the IPCC is that there is no measurable thermal expansion at the coast because there is no significant depth of water. It is effectively zero at a beach.
Removing the thermal expansion factor would reduce the SLR from, say 3.5 mm/yr to 2.1 mm/yr, much more in tune – but not completely – with tide gauges.
Having said that, the point made elsewhere on this thread that any suggestion that climate scientists can make confident statements on accurate SLR projections is just silly.
Arfur
Sorry, the last paragraph should begin with: “Having said that, the point has already been made elsewhere on this thread…”.
One needs to remember that satellites that measure sea levels get their drift corrections and are calibrated by tidal gage references. Satellite readings are thereby of secondary quality and accuracy.
How much of the sharp rise off of Japan is do to the huge tsunami creating earth quake?
good lord … this is trying to measure angels dancing on the head of a pin at a distance with unfocused binoculars… trying to measure down to .1 mm the height of a body of water in constant vertical motion is a fools errand … must be a good mental exercise because that is the only reason to bother with this sort of math …
One thing that makes a sinusoid fit a bit tricky compared to a quadratiic one is that you also have to estimate the period of the sinusoid. With detrended data, a quadratic fit just needs one parameter. Anyway, as I illustrated earlier on WUWT, there’s plenty of variations in acceleration over the past century or so based on tide gauge data. I used a 25 yr window, A sliding quadratic window is a cool way to measure acceleration and if you make the window smaller than about half the period of the expected sinusoid, it should do quite well.
Meanwhile, we have tidal gages around the world that show no evidence of acceleration; those located in tectonically stable locations such as Slipshavn, Denmark show a smidge over 1 mm/yr. of constant sea level rise