Wandering Thru The Tides

Guest Post by Willis Eschenbach

I got to thinking about the records of the sea level height taken at tidal stations all over the planet. The main problem with these tide stations is that they measure the height of the sea surface versus the height of some object attached to the land … but the land isn’t sitting still. In most places around the planet the land surface is actually rising or falling, and in some places, it’s doing so at a surprising rate, millimeters per year.

The places that are the most affected, unfortunately, are the places where we have some of the longest tidal records, the northern extra-tropics and northern sub-polar regions. In those sub-polar regions, during the most recent ice age, there were trillions of tonnes of ice on the land. This squashed the land underneath the ice down towards the center of the earth … and as result of that, just like when you squeeze a balloon it bulges out elsewhere, the extra-tropical areas further from the North Pole bulged upwards in response to the northern areas being pushed down.

Now, of course, other than scattered glaciers all of that ice is gone. With that weight removed the land is now experiencing the reverse effect. This is called “post-glacial rebound”, or PGR. The effect of the PGR is the reverse of that of the ice—northern areas are rising and mid-latitude areas are sinking. So when we look at long-term records from northern Europe, for example, the land is actually rising faster than the sea level … and as a result, the tide gauges there are recording a sea level fall rather than a sea level rise.

The issue comes up when we want to know how fast the sea level is rising, both now and in the past. Unfortunately, most tide gauges around the planet don’t have co-located GPS units capable of measuring the altitude to the nearest millimeter…

Me, I’m not that interested in exactly how fast the sea level is rising. I’m much more interested in whether that rate of sea level rise is speeding up. For three decades now climate alarmists have been predicting an imminent acceleration in the rate of sea level rise that is supposed to drown whole cities by 2100, the usual Chicken Little scenario. However, I’ve not seen any convincing evidence for that claimed acceleration.

My thought about how to investigate the purported acceleration was simple. I’d get every one of the tide records, the most recent I could find. These are kept at the Permanent Service for the Mean Sea Level, or PSMSL. They are obtainable individually here or in bulk here. As the curators recommend, I used the RLR version.

Then I’d detrend them all. That would remove any post-glacial rebound. The PGR, whether slow or fast, doesn’t change much in a couple centuries. So detrending would set the PGR to zero. This would allow me to look at the average shorter term multidecadal variations in sea level. I would average the records, and see what kind of acceleration I might find in the results.

I thought about this while reading GLOBAL SEA RISE: A REDETERMINATION, by Bruce C. Douglas, available here. In it, he averages a subset of the 1509 stations after adjusting them for post-glacial rebound (PGR). However, he’s picked a tiny subset, only twenty-four stations … out of the more than 1500 tide stations available worldwide. Hmm … seemed like a very small sample.

So I thought I’d take a look at some other subsets of the tide station data. I decided to filter based on a couple of criteria. One was that I wanted to have long records. So I started with a hundred years minimum. No particular reason, it just seemed like a good place to start.

The other criterion was that I wanted them to be mostly complete, with little missing data. I started with the requirement that they be ninety percent complete. I expected that I’d find only five or ten such stations around the globe, but to my surprise, I found that there are no less than 61 tide station records that meet those criteria.

Following the usual method, I took the “first differences” of these individual sea level records. This is the change in the data over time. Since we have monthly data, the “first differences” in this instance are the month-to-month changes in the sea level for each tide station.

Then I averaged those first differences, month by month. Finally, the cumulative sum of that average of the first differences reconstructs (in theory) the average change in sea level height.

Figure 1 shows the result of that procedure. Remember that this is detrended data. I’m not looking at the trend. I’m looking at the decadal and multidecadal variations within the overall record, to see where the trend changes.

Figure 1. Averaged sea level. The average was taken as the cumulative sum of the month-by-month average of the individual station first differences. No standardization of standard deviation was performed. The yellow line is a six-year centered Gaussian smooth. I put the ocean in the background because … well, because I got bored with plain white, plus … it’s the ocean …

OK, nothing much surprising there. Yes, I know I haven’t made any effort to do a gridded or other geospatial average … but I find that for first-cut investigations the differences aren’t worth the programming time. That can come later to refine the results. First I want to take a broad view and come to an overall understanding of the oddities and the outliers and the overall style and substance of the dataset.

Now, in Figure 1, sixty-one records is not a whole lot. So my next thought was to reduce the completeness threshold a bit. I decided to look at all the hundred-year-long records which contain at least eighty percent data, instead of ninety percent. That increased the station count from sixty-one to seventy-one. And the result was what I love the most about science … a big surprise.

Figure 2. As in Figure 1, except only requiring 80% data instead of 90% data.

Dang-a-lang, sez I, say wut?!? … and I went off to find the fault in my computer program that extracts the data and draws the plots.

However, when I couldn’t find anything wrong with my program, I realized that the answer had to be somewhere in the ten additional stations that were added in between Figure 1 and Figure 2. Here are those ten stations:

Figure 3. The ten stations which were added to the subset between Figure 1 and Figure 2.

You can see the problem, I’m sure. What is going on with the tide record from the Manila South Harbor? So I pulled Manila South Harbor out of the mix … which led to big surprise number two.

Pulling out the Manila record made no particular change. The result still had the big drop seen in Figure 2.

After much faffing about, I finally determined that the miscreant was actually Trois-Rivieres, which is certainly not obviously different from its compatriots. It’s second from the bottom left in Figure 3 above, looks like the rest … except in size. I’d made the mistake of not paying attention to the different scales. Here’re the same ten stations, but this time all to the same scale.

Figure 4. As in Figure 3, but with all stations shown at the same scale.

In this view the problem is evident. We’re doing a “first differences” analysis. But that weights the data in some sense proportional to the stations’ standard deviation, how much it swings from month to month.

Setting that question aside, however, the surprising part to me was the large effect of one single record among 71 others. One bad actor in the lot totally changed the whole average … and it brings up a question for which there is no “right” answer.

How do we deal, not just with this instance of Trois-Rivieres, but with the more general underlying problem that the month-to-month variations in sea level are of very different sizes at different tidal stations around the globe?

Do we scale them all to the same standard deviation, to give them all equal weight? Or as in this case, is it valid to just heave Trois-Rivieres overboard and continue the cruise? Hang on, let me get a histogram of the standard deviations so we have some information. The standard deviation is a measure of how wide the swings in the data are … I’m writing this up as I work my way through the issues, so you can see how I go about understanding the dataset. Here’s the histogram of the standard deviations:

Figure 5. Histogram of the standard deviations of 1,509 tide stations.

OK, that’s a problem for this kind of analysis. This shows a bunch of stations with standard deviations over say 150 mm … and as we saw above, to my surprise, just one wide-swinging station can poison seventy other stations. So any analysis will be dominated by the widest-swinging datasets. Oooogh. No bueno.

As I said above, there’s no “right” answer to this question. About all that I can see to do is to set them all to the median standard deviation, which is about ninety mm. This gives them all equal weight and also makes them comparable to the raw data. Figure 6 shows the same 71 hundred year plus stations as in Figure 2, but this time after they’ve been set to the same standard deviation. Note that Trois-Rivieres is no longer dominating the results.

Figure 6. Averaged sea level. The average was taken as the cumulative sum of the month-by-month average of the individual station first differences. All first difference station data was set to a standard deviation of 88 mm before averaging the first differences. 

I think that’s about the best I can do. I say that because I’m interested in decadal and multi-decadal changes … and there’s no reason to assume that tide stations with large month-to-month swings are more representative of those multidecadal changes than any other stations. With no theoretical reason to prefer one group of stations over another, I can only give them all the same weight.

(Upon reflection while writing up my investigations, I just now realized we might also find interesting results by using a yearly average of the data. At least this would get rid of the month-to-month variations … but at the cost of throwing away some data. So many possible analyses, so little time … I return to the current analysis).

Now, I mentioned that I was led to look at this by the Douglas re-examination of sea level changes. So I thought I’d take a look at the twenty-four stations he used. Here’s that result. All the stations have similar standard deviations, so I’ve not made any adjustments. Unlike my own analysis these are not detrended. In addition, the trends have been adjusted for post-glacial rebound using the data from the Douglas paper.

Figure 7. Stations from Douglas GLOBAL SEA RISE paper. These stations have been adjusted for PGR using the data in the cited paper. Note that these have not been detrended.

Hmmm … I’m not seeing any reason to prefer that Douglas subset to any of the others. It is different from any of the others that we’ve seen in that there is a clear acceleration in the rate of rise around 1970. This has not been visible in any of the other datasets. However, my main objection is the tiny size of the sample, only 24 stations.

According to the cited Douglas paper, among other requirements, to be usable the individual tide station records should “be at least 60 years in length” and be at least “80% complete”. Here’s the subset of the 1,509 records, the 235 stations  that fit those two criteria.

Figure 8. Averaged of detrended sea levels, sixty year + datasets with eighty percent data. All datasets have been standardized to a standard deviation of 88 mm. This is the median standard deviation of the full 1,509-station dataset.

That’s not much different from the hundred-year-plus dataset shown in Figure 6. Let’s see what happens when we reduce Douglas’s required length of sixty years down to say forty years …

Figure 9. Averaged sea level, forty year + datasets with eighty percent data. All datasets have been standardized to a standard deviation of 88 mm.

As you can see, once there’s very little difference from adding the additional shorter-length station records. Figure 6 shows hundred-year-plus records, only 71 stations. It differs only in the smallest details from Figure 9, which shows forty year plus records and averages 500 stations.

However, there is a final perplexitude. So far, we’ve been looking at records with 80% of the data … but what if we make the requirement stricter? How about if we require that ninety percent of the data be present? It turns out that, just as with the eighty percent criterion, the results at ninety percent look quite similar at records lengths from forty to a hundred years … but the oddity is that they do not look like the eighty percent records.

Here are all the sixty year plus records with ninety percent data, 193 stations:

Figure 10. Averaged sea level, sixty year + datasets with ninety percent data. All datasets have been standardized to a standard deviation of 88 mm.

As you can see, Figure 10 is similar to the eighty percent data shown in Figure 9 in that it has the high point at the start. It’s also similar in the range from about 1875 to about 1920.

From 1920 to the present, however, the eighty percent complete records go up in a pretty straight line … and the ninety percent complete records go down, again linearly. Who knew?

So, after that voyage through the 1,509 records, what can we say? Well, we can’t say anything about the trend, because we’ve been using detrended records. Heck, we can’t even say whether there was a change around 1920, because the records with eighty percent data say yes, the rate of rise increased around 1920 … but the ninety percent records say no, there was no change in the rate around 1920.

However, something that we can say is that the one and only subset I’ve found that shows any recent 20th-century acceleration is the extremely small 24-station subset used by Douglas. It claims that there was an acceleration in the rate around 1970 or so.

All the other subsets we’ve looked at agree, eighty and ninety percent data alike, at all lengths from forty years plus to a hundred years plus. They all say that there has been a uniform gradual sea level change since around 1920, a change which has varied little over that time. In detrended terms, some subsets say it went up since 1920, some say it went down since then.

But not one of them show any recent acceleration in the rate of sea level rise.

In other words, despite thirty years of alarmists telling us that the seas are going to start rising at some accelerating rate any day now … there is no sign of that predicted acceleration in any of these subsets of the detrended tide station records. Of course, this doesn’t prove anything, you can’t prove a negative. However, it joins all the other evidence out there showing no recent acceleration in sea level rise.

My final thought out of all of this is that the sea level data from the tide gauges around the world is very sensitive to the exact selection of the subset of stations used in any analysis. There are differences even what I would have thought would be a trivial change in cr, say between eighty and ninety percent data for all stations over sixty years in length, which only went from 193 stations at ninety percent data to 235 stations at eighty percent data. And despite the fact that both groups contain datasets with what we would call good coverage, and despite the two datasets having over 80% of the stations in common … despite all of that, changing the requirement from eighty percent complete to ninety percent changes the overall change in trend since 1920 from rising to falling …

So I’d say the takeaway message is, be cautious in claims regarding the sea level rise speeding up. I’ve looked a lot of places for acceleration without finding any sign of such an increase in the rate of sea level rise, and this latest peregrination through the tidal data has only strengthened my skepticism about any claims made about the global sea level. It’s just too dependent on the methods used and the choices made to give me any sense of solidity.

Here, I’m very happy to be back from my Solomon Islands adventure. Before I left I had just finished building a large patio here by our hillside home. I rented a backhoe, bought a few pallets of blocks and bricks, and started digging and filling. Then when the rough backhoe work was done … shoveling. And more shoveling. What in a less politically correct time we called “Playing the Swedish banjo”. Here’s a shot halfway through the process with the downhill retaining wall in but not the uphill wall, featuring my weapons of mass construction, a McCloud and a couple shovels, plus my hand grader (a board attached to a rake) at the far right …

Once the level spot was made I had to decide how to treat the flat surface. I decided to brick it in. My artistic vision was to make what would look like a river of bricks running out from under our house to a pool, of brick of course, and then flowing out from that brick pool over the rapids at the far end of the patio where the retaining wall stops.

And here’s how it looked shortly before I left, with my gorgeous ex-fiancee tending her beloved plants …

And finally, here it is this lovely warm December morning upon my return, with verdant, insistent nature starting to push up through the spaces just like I’d hoped … I plan to let it grow and periodically mow it short.

So, propped up against the south wall of our house, enjoying the physical realization of my vision of a river of bricks, and smiling like an idiot up at the sun, I remain,

Yr. Obt. Svt.,

w.

PS—Please, folks, when you comment I ask you politely to QUOTE THE EXACT WORDS YOU ARE DISCUSSING. I can defend my own words. I cannot defend your understanding of those same words. Without the quotation, I often have no idea what you are referring to. I know it’s perfectly clear to you … but on this side of the screen, it is often a total mystery just what it was that I said that someone thinks they are referring to. So do yourself and all of us a favor and quote before replying, so we can follow your logic and comprehend your argument.

Finally, no, generally I don’t remember what I said in some discussion with you six months, six years, or often even six days ago. I’ve written over six hundred posts for the web, many of which have engendered long and complex discussions with a huge number of people, with most of the people using fake names. I make no attempt to remember who said what, or what I said. Instead, I simply do my utmost to tell the truth as best I understand it at all times so I don’t have to remember all the trivia—if I need it I’ll look it up.

So please, if you’re going to say anything resembling “But Willis, you were wrong last time when you said that …” to me or anyone, please follow that with a quotation of the exact words that were said. NOT what you remember about those words. NOT what you’ve understood those words to mean. THOSE EXACT WORDS!

Thanks,

w.

DATA: The data in the PSMSL archive is in a horrible format, with a separate file for each station with individual start and end dates. I’ve combined them into the normal data block, stations in columns, times in rows, as a  zipped CSV file here. So … if you have questions about the results or you think I should have done some other kind of analysis … the ball’s in your court. Drop the CSV sea level data file into Excel or your favorite program, do the analysis you think I missed or messed up on, and let us know what you find out.