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”  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.
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.” 
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.” 
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
2. “New Coastland Map Could Help Strengthen Sea Defences”; October 7, 2009, Carl Stlansen, Durham University
Source Data: The complete PSMSL RLR Monthly dataset can be downloaded from here: http://www.psmsl.org/data/obtaining/complete.php
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.