Sea Levels!!! A Validation of Beenstock et. al.


A Validation of Beenstock et. al.

Guest post by Hank

In recent science news there was a very interesting study by Beenstock et. al. titled “Tide Gauge Location and the Measurement of Sea Level Rise” [1] where the authors offer evidence that the current Satellite record of Sea Level Rise (SLR) is grossly overestimated. What I find interesting relative to this study is the satellites are calibrated to the GPS buoy and tidal gauge network. You would think they would all agree on SLR. They don’t.

I wanted to apply some of the tools I’ve used in the past to clean up the raw tidal gauge datasets then perform my own reanalysis and compare it to the author’s finding.

The tidal gauge network has experienced quite a number of random data gaps – more so in years before 1950. Thus, segments of some tidal gauge records must be infilled. Tidal gauge records have a strong seasonal component. If the data gap is too wide, there is a tendency to infill with a seasonal bias when averaging adjacent data points. The number of data points being infilled multiplies the seasonal component. My approach, which avoids this issue, was as follows:

For single random missing samples:

For random missing single samples, I averaged the lower and upper adjacent samples as they were close enough that the seasonal component would be negligible.

For blocks of two or more contiguous missing samples with sufficient adjacent ranges:

For blocks of missing samples where there was at least three years before and three years after with complete samples I calculated a “best fit” polynomial trend across the same month for the three years preceding and for the same month in the three years following. From that I calculated the missing value based on where the missing point was in the polynomial trend.

For blocks of two or more contiguous missing samples with missing samples in adjacent ranges:

I used an algorithm very similar to that described above. However, I allowed the function to walk a wider span of adjacent samples in a way that it balanced the temporal distance of the samples selected so as to not bias towards either direction which could result in an overestimation or underestimation of the missing sample point.

For blocks of two or more contiguous missing samples with insufficient samples preceding or following the block:

For missing blocks where there wasn’t sufficient samples behind or ahead, I infilled using a differencing algorithm that analyzed the same month for up to five preceding or five following years. It estimates the mean for the missing sample, taking into account the trend (difference between samples) of the selected good samples. Typically these missing samples were near the beginning or end of the dataset.

For blocks spanning greater than two years with dropout.

For large missing blocks of data, I simply scanned the file to find any good segments lasting 10 years or more. I then treated them as individual datasets using the above methods. I had considered a spatial infill but after noting the sometimes opposite SLR trends between adjacent gauges, I concluded the authors made the right call. I used their method in this scenario.

To be clear, I don’t intend to suggest the authors made a wrong call in the other scenarios. My choosing a different method in some scenarios was more a matter of having the ability to write my own tailored to task tests and functions in R, SAS, SPSS, or C#. I like to blaze my own trails in independent analyses because in following the author’s exact methods, I’d be repeating the same mistakes if they made any. If their methods are sound my results should be fairly close.

I chose to work with the monthly datasets as opposed to the yearly because I like working with larger samples and I don’t trust that the aggregation methods used by PSMSL were adequate. That’s the skeptic in me.

My results

The data from before 1950 was too discontinuous to be useful. Additionally, there weren’t enough tidal gauges with global representation. Here is a graph of the number of tidal gauges that went into my reconstruction:


Figure 1 (High Resolution Image)

This is the big picture from 1866 to 2010:


Figure 2 (High Resolution Image)

The green line denotes the cut off between unusable and usable tidal gauge data. While the tidal gauge to the left of the green line is interesting, it is not robust. The blue line represents where satellite era sea level measurements began. Satellite measurements were not used in my analysis. There are two black linear trend lines which break at 1980. Rest assured I’m not cherry picking. There’s a statistical reason why 1980 was chosen which I’ll discuss in a bit.

Lets zoom into 1950 through 2010:


Figure 3 (High Resolution Image)

I added a third order polynomial fitted trend line to give a better visual feel for changes in the rates of the SLR trends. The R2 (coefficient of determination) indicates that the fit is quite good and therefore reliable for estimating the average trend across the timespan. The average trend for SLR from 1950 to 2010 is 1.69 mm / year.

I call your attention to the satellite era in the graph. It clearly shows an increasing trend if all you’re looking at is satellite data. However, if you compare the trend historically to the 1950’s it’s not unprecedented.

Lets look closer at 1950 through 1979:


Figure 4 (High Resolution Image)

The black line is the linear trend for the period. I calculated the trend to be 2.06 mm. per year. And now, lets zoom into 1980 through 2010:


Figure 5 (High Resolution Image)

In this current timespan, the trend dropped to a mere 1.39 mm. per year. To put into perspective how fast that rate is, a dime is very close to being 1.39 mm thick. There’s 87 years left in the 21st century. If you were to stack one dime every year on a stack of dimes, representing the rise in sea level, in 2100 your stack of dimes will be 4.6 inches tall. The actual SLR would be 4.7 inches, holding all things constant.

You’ll notice that SLR in the period of 1950 through 1979 was greater than present. I’ll caution you to not get too excited about that. Prior to 1980, the southern hemisphere and certain oceans and coastlines were underrepresented. Most tidal gauges were located in more densely populated areas that were more prone to glacial isostatic changes to the land where the land was sinking. These issues introduce a positive bias for this time period. It was finally in 1980 that there was a more representative distribution of tidal gauges. That’s why I chose 1980 as the dividing line.

Conclusion and Discussion

Much has been made of sea level and its rate of rise since global warming became a concern. The fact is sea level is a local and relative thing. It’s local because not all coastal locations are experiencing increasing sea levels. Quoting from Beenstock et. al.,

“Although mean sea levels are rising by 1mm/year, sea level rise is local rather than global, and is concentrated in the Baltic and Adriatic seas, South East Asia and the Atlantic coast of the United States. In these locations, covering 35 percent of tide gauges, sea levels rose on average by 3.8mm/year. Sea levels were stable in locations covered by 61 percent of tide gauges, and sea levels fell in locations covered by 4 percent of tide gauges. In these locations sea levels fell on average by almost 6mm/year.” [1]

It’s relative because coastal lands are undergoing a constant process of lift and subsidence, changing the sea level relative to the shoreline. The Earth Observatory gives a good example.

“The new map shows how the UK and Ireland are responding to the ice sheet compression of the earth’s core and the current rate of land tilt across the UK. In Northumberland, researchers found sediments from 7,000 years ago five metres below, and others from 4,000 years ago at 1 metre above the present sea level. This indicates that the sea level rose above present levels from around 7,500 years ago to 4,500 years ago, and then dropped and is continuing to fall.” [2]

Based on my analysis of the tidal gauge records, using my preferred methods of infilling, I came fairly close to the results of the authors and conclude that the study has strong statistical merit. A reasonable explanation for why my trend was slightly higher than the authors is because Beenstalk et. al. adjusted for area GDP following the finding that tidal gauges located close to coastal cities experienced a higher rate of subsidence as compared to unimproved coastal areas. I made no such adjustments.

What becomes readily apparent is there is a significant disparity between tidal gauge records and the current satellite record. Presently, satellites show a SLR trend of 3.0 to 3.1mm per year. The tidal gauge network shows a more modest 1 to 1.4mm per year trend.


1. “Tide Gauge Location and the Measurement of Global Sea Level Rise”; Michael Beenstock, Daniel Felsenstein, Eyal FrankYaniv Reingewertz.; Department of Economics, Hebrew University of Jerusalem, Jerusalem 91905 

Web ref:

2. “New Coastland Map Could Help Strengthen Sea Defences”; October 7, 2009, Carl Stlansen, Durham University

Web ref:

Source Data:  The complete PSMSL RLR Monthly dataset can be downloaded from here:


Note from Suyts: 

Hank!  Excellent work, once again!  More than it being a validation of just Beenstock et. al., I see it as also a validation of many skeptics who have been saying the satellites are overstating the SLR.  My thanks.

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69 Responses to Sea Levels!!! A Validation of Beenstock et. al.

  1. suyts says:

    So, does this mean that the Antarctic probably hasn’t slid into the ocean?

    • HankH says:

      They say chunks of it keep breaking off so it’s prolly teetering now. 😉

    • Latitude says:


      Hank, here’s my argument for no sea level rise at all….as you know, satellites were tuned to tide gauges in the first place and the Envisat working papers are still online…they are a hoot if you haven’t read them…they kept tuning it to show sea level rise…and it kept showing sea levels falling!!

      61% of their sample showed no sea level rise at all….over the entire period
      only 35% showed sea levels rising avg 3.8mm/yr
      and 4% showed sea levels falling 6mm/yr

      65% showed no sea level rise at all…..

      This is heavily weighted to show sea level rise….
      which is impossible, when the majority of gauges show none at all

      • HankH says:

        Very true, Lat. As I said, it’s a relative thing. I’m fairly confident that a lot of what we’re looking at is the aggregate differences of glacial isostatic changes in coastlines relative to the sea. Contrary to what warmists claim, it works both ways.

        • Latitude says:

          this is where we get into trouble with numbers….

          of 90% show none…
          …but 10% shows 100

          the average is not realistic

          If there were really sea level rise, the majority of tide gauges would reflect it is, the opposite…

          ..and they wouldn’t have to add a fudge factor for the sea floor sinking…which just happens to be exactly what the sea level rise is

        • HankH says:

          They do hyperventilate over the numbers. Sea level rise is not what they think. As I understand it, the satellites are measuring the sea level by comparing it to the land mass. The land is uplifting and subsiding too. As you well point out, the ocean basins are sinking. Heck, the earth wobbles and the atmospheric expands and contracts relative to the satellites, causing propagational changes in the altimetry signals. I doubt the satellites are in a perfect orbit. They’re measuring all sorts of changing stuff and distortions and think their numbers speak only to sea level.

          Maybe I should have been more direct in my wording but I don’t think the tide gauge network speaks to sea level as much as it speaks to relative changes to coastal land. Otherwise, as you say, they would all agree.

        • HankH says:

          Another thing I think needs mentioning is the satellites re-calibrate on specific land based calibration points – relatively few of them. If those calibration points are moving, and they are, the satellite translates that movement into a global thing when it’s not.

        • HankH says:

          I forgot… one of the calibration points NASA uses for JASON II is an oil rig off the California coast. So all this sea level rise might be partly explained by a sinking oil platform.

        • Latitude says:

          Don’t forget, the only reason satellites are constantly re-tuned…is because the orbit they are in is not fixed….they are constantly falling out of orbit…
          ….which shows sea level rise
          That’s all in the Envisat working papers….if you haven’t read them…do….they are really a hoot
          ..and, after you read them, you’ll have absolutely no faith in satellite sea level measurements
          When Jason’s and Envisat refused to show sea levels rising…they kept bumping them up to show it rising (tuning it to tide gauges)…..when 65% of tide gauges show no sea level rise at all

          …so where did they find tide gauges showing sea level rise? and why did they only use them?

        • Latitude says:

          the biggest mistake they made with these satellites is not having anyway onboard to keep them in a constant orbit….

        • kim2ooo says:

          I don’t think the tide gauge network speaks to sea level as much as it speaks to relative changes to coastal land.

          Is there a stable land mass to use as scale?

          Why isn’t it [ SLR ] measured by laser with an Altimeter as base?

          Great Read! 🙂 Thank you.

        • cdquarles says:

          Exactly. We are trying to ground truth a dynamic system within the system and are lacking a fixed frame of reference. Even using laser altimetry using both Earth and lunar locations will still have drift issues.

        • HankH says:

          Kim, cdquarles pretty much nailed it. We’re lacking a fixed frame of reference that is stable and has sufficiently low error range.

        • suyts says:

          @ Kim, Cd, et al…… but, isn’t the point of “Sea Level” measurements is how it relates to land, anyway?

        • philjourdan says:

          But that begs the question then. Why are they inflating the rise to account for the land bounce? If the land is rising as well as the sea, then the sea is not rising in relation to the land.

        • HankH says:

          Yes… how it relates to land. A good analogy would be there’s this lake called Tequesquitengo down in central Mexico. I’ve visited it many times. It didn’t used to be there. One day the land started sinking and filling up with water. There’s a church at the bottom of the lake that used to be on dry ground but it sank with the land.

          From a purely practical point of view, the water didn’t rise as the water table didn’t change. The land sank below the water table. You can no longer visit that church without diving gear. This is how I view sea level. It doesn’t matter if, in reality, it is lowering, rising, or staying the same. What matters is what’s happening on the coastal land at the water’s edge.

        • kim2ooo says:

          suyts says:

          October 22, 2013 at 12:27 pm

          @ Kim, Cd, et al…… but, isn’t the point of “Sea Level” measurements is how it relates to land, anyway?

          Ummm call my logic – fuzzy…but if you have two dynamic objects that could at anytime be at direct opposites [ one rising – one sinking – or any combination of ]… And you can’t measure either , precisely ,….. what “relation” is there?

          We can throw out conjecture………… but other than physical properties [ one wet – one dry ] ….??

        • kim2ooo says:

          cdquarles says:

          October 22, 2013 at 10:13 am

          Exactly. We are trying to ground truth a dynamic system within the system and are lacking a fixed frame of reference. Even using laser altimetry using both Earth and lunar locations will still have drift issues.


          HankH says:

          October 22, 2013 at 12:10 pm

          Kim, cdquarles pretty much nailed it. We’re lacking a fixed frame of reference that is stable and has sufficiently low error range.

          I agree with both of you.


          If I can see this flaw – ??????????????

        • cdquarles says:

          Sea level indeed matters to those at that interface, but I think it is sloppy to call land subsidence sea level rise if the water level isn’t rising (and there is some evidence that it isn’t really rising over much of the world). To know if the sea level is rising we have to know what’s happened/happening to the land level, too. If both are rising (True positive) at the same rate, the margin remains the same. If one is sinking and the other isn’t (False positive) then the rise in the water is apparent (not real, for it is the land that’s sinking, not the water rising).

  2. tom0mason says:

    Fine work. It is always good to have work validated by other methods, that keeps real scientists and researcher honest. Not the Mann-made way 🙂

    • HankH says:

      Thanks Tom. There’s usually more than one method to arrive at a statistical result. In my research work, I will often run several methods as an internal check. We call it “validation” – a process climatology would do well to appreciate more.

      • tom0mason says:

        ““validation” – a process climatology would do well to appreciate more.” What and all the extra work of ‘normalizing’ the new methods. No it’s so much easier the way Hansen, Mann, Cook…etc


  3. Latitude says:

    ok, I’m being distracted too much at home right now!
    ..and forgot my head and manners

    Excellent work Hank!!!
    and well written too!

  4. HankH says:

    Thanks Lat!

  5. copernicus34 says:

    excellent!!! The key to this whole thing is pre Jason, Jason, and post shutdown Jason. Excuse my language Mr Suyts, but this is all fuckin’ ruse. The satellite data is messed up, they know it is. I believe they have done it intentionally.

    • HankH says:

      Forgetting the huge number of variables that add error to the satellite measurements, I could never quite fathom how you can achieve an accuracy down to the millimeter from 8,500 miles away (up).

    • suyts says:

      Cop, it’s “James”, or if you prefer the formal, Mr. Sexton. But, that’s what they used to call my dad. And, yes, it’s a lie. I don’t believe they’re as stupid as they come across.

      Given the nature of water, and given the length of time, there’s no way all of the people examining the tidal gauges are wrong.

      Hank could have easily made this into a publishable work to stand on it’s own. I’d encourage him to do so, but, he’s other axes to grind beyond the sophistry of perceived sea level madness.

  6. philjourdan says:

    Thanks Hank. I Heard of the Beenstock, but had not chased it down yet.

    • HankH says:

      There’s a few warmists who aren’t happy with his paper. In fact, the reason why I did this validation is because his results were so different from the satellites that I wanted to understand why. I don’t think I can take a satellite based SLR graph seriously (not that I ever did).

      • David A says:

        Hank, just for insight into satellite accuracy, try goggling the “Palmdale bulge.” This is a desert in Calif, and they, geologist, have been arguing about what the satellites really say for decades. Mind you, this desert has very little wave action or lunar cycles, etc, but they argue about 100s of mm of movement.

        • HankH says:

          David, I googled on the Palmdale bulge. I never heard of it before but it’s a fascinating read. It looks like the earth does a lot of flexing.

        • philjourdan says:

          Actually, while a fad in the late 70s, there is great debate over whether the bulge existed at all. Apparently people forgot about siting across temperature gradients.

          It was a very interesting read.

        • David A says:

          On reflection they may have been using surveys, but no matter, they debated that for well over a decade. We, the human mind, appear quit capable of reasoning ourselves into or out of most anything.

        • HankH says:

          True that. 😉

        • HankH says:

          From what I was reading, the debate still isn’t settled.

        • suyts says:

          David, it’s a hard thing to understand. Most never will. People like and want to believe things are and should be static. They never were. And so goes our sea level. Indeed, the satellites incorporated the geoid. Which, they assumed to be nearly static. It isn’t. And, being charitable, this is why we see SLR with satellites but nothing beyond the norm from the tidal gauges.

          The stupidity of the lunatics is that if we extrapolate their stupidity is that we’ll end up as a cylinder, all the while having SLR. They add 0.4mm/yr for the GIA. But, that assumes the earth doesn’t also concave. If it emerges in one place, then it digresses in another. Or, maybe we’re shrinking or expanding?

  7. copernicus34 says:

    little OT, but not much….check out Goddard’s latest post on downwelling LW in the tropics. these alarmists are quacks i tell ya’

  8. copernicus34 says:

    Geoid is still WGS1984 correct? Hasn’t been done in some time. Updated in 2004.

    • suyts says:

      Well, yes. And no. GRACE are the satellites which defined the geoids for the sea level satellites. Not so much for our GPS navigation systems. Wonder why? Me too. And, yes, there are more current navigation plots. NAD something and a Euro something.

    • HankH says:

      Yes, you’re correct. WGS1984 has an accuracy of +/- ~2 cm relative to the center of the earth’s mass. I’m still amazed that satellites get it down to less than 1 mm. Well, not actually amazed… amused. 😉

      • David A says:

        Is the CG of the earth itself stationary within a few mm; especially relative to satellites in space and with consideration of the likelihood of changing mantel density. I am amazed that some consider Grace to be a means of telling if the polar glaciers are gaining or losing mass.

        • HankH says:

          I’m not sure but I highly doubt it. With changing mantel, underwater volcanos turning into islands (like the one Latitude and James called to our attention off the coast of Japan), and the internal dynamo of earth’s core, I would expect a margin of error magnitudes greater than < 1 mm claimed by satellite altimetry.

        • HankH says:

          Sorry, poor wording. The one off Japan didn’t turn into an island but it is huge and its growing.

        • suyts says:

          David, as far as I know, we still operate from triangulation rather than fixed points. It’s a hard thing to relate. Triangulation is more relative than a fixed point. If a fixed point was really “fixed”, then we’d have no problems. But, they’re not. So, we have no fixed points. We have fixed points relative to the points we know. And all points relate to the relative points we know.

          That’s the curse of expanded knowledge. It would be much easier with flat planes and assumptions of a flat solar system. A flat map works. We know it works because we worked off of it and grew from it. But, it isn’t so. It’s strange. We knew this back in the 1800s and we still can’t get it right.

        • cdquarles says:

          Keep in mind that the Earth is gaining mass while losing some of its atmospheric constituents and has been doing this for a very long time (if not since it reached its post moon creation by collision? state).

  9. daveburton says:

    1.39 mm per year is virtually identical to what you get from taking the median or calculating a geographically-weighted average of the rates of sea-level rise measured by the best GLOSS-LTT tide-gauge records.

    See (and scroll down to the bottom of any of the spreadsheets on the “data” page)

  10. Lars P. says:

    Well from satellite sea-level we have the direct info from Nils Axel Moerner about the adjustments to show a sea-level rise: ” we had to do it otherwise there would not be any trend” and some interesting graphs before and after:.
    here Jo has also a good post about it:

    • HankH says:

      It’s like everything else they touch. If they didn’t make any adjustments, there wouldn’t be anything to get all alarmed over.

      Thanks for the links. Joanne always puts up interesting articles.

      • Lars P. says:

        Now that you mention it – I just saw a temperature graph where the adjustment was removed in a recent comment on WUWT. A very pertinent comment, pity I have not kept the link…

  11. Jim Masterson says:

    I finally made time to read you post, Hank. Good job. Thanks for doing the analysis. The great John Daly did a satellite analysis years ago (, and found it wanting too.


    • HankH says:

      Thanks for the complement, Jim.

      John Daly’s paper was an excellent read. Thanks for linking to it. I was confident a satellite does not have the ability to measure to the accuracy of 1 mm, especially with radar altimetry.

  12. Pingback: Work At Suyts Confirmed Again!!!! | suyts space

  13. Pingback: Food For Thought —- NOAA’s Tidal Gauges — SLR Not Accelerating | suyts space

  14. daveburton says:

    If you want to understand why the satellite altimetry data is unreliable, I recommend that you watch this lecture by Physicist Willie Soon. Dr. Soon explains the problems with satellite measurement of sea level better than anyone I’ve ever seen, starting here:

    That segment of his lecture is 24 minutes long, starting at the 17:37 point. The link should take you directly to 17:37. But, actually, I recommend watching the whole 58 minute lecture at least once. I promise, you’ll learn a lot.

  15. talldave2 says:

    Thanks. Replication >> peer review.

    • suyts says:

      talldave, thanks, and welcome. I haven’t had many posts like this lately, but, we’ve done more than a few in the past, and will again, if and when the opportunity arises. Currently, I’m not posting as much or doing much work like this (the above is Hank’s work) because I’ve vision probs, but, hope for them to be corrected in a month or so. In the mean time, I throw out some topics to discuss and the commentators do the rest. They’re a really sharp group. Again, welcome.

  16. Pingback: LOL @ UCS And HuffPo!!!!! “New Reality Of Sea Level Rise”!!!!! | suyts space

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