Accelerating The Acceleration

Visitor Put up by Willis Eschenbach

I see that the retailers of hype are at it once more. The scary headline says “Report: Sea-level rise ‘accelerating’ alongside U.S. coasts, together with within the Bay Space“. And within the textual content, it says “The Bay Space was house to 2 of these stations: one in Alameda and one in San Francisco, which each recorded a year-over-year rise.” In fact, they blamed the same old suspect, international warming.

I see that and I say … whaaa? I stay an hour and a half north of San Franciso, and I’ve been following sea ranges round right here for some time. I knew nothing of any sea-level acceleration. 

The media article references one thing known as the “US Sea Stage Report Card“, which certainly lists San Francisco and Alameda. So I went to the NOAA Tides and Currents website to get the information. Let me begin with the shorter of the 2 datasets, Alameda. It’s an island, albeit simply barely, in San Francisco Bay close to Oakland. It’s pretty, I lived there on the waterfront for a bit simply after I received married.

Initially it was a part of the Oakland mainland, however within the 1890s the canal on the decrease proper was lower by way of. This allowed flowing water to forestall the continued downside with siltation in that estuary. As a consequence, the land throughout from the island turned the primary location for the Port of Oakland. The channel between Alameda and the mainland is a beautiful a part of the world. Right here’s a photograph I took the final time I sailed these waters, displaying the enormous land horses of the Port.

So what’s the story of the Alameda sea ranges? Right here you go:

Determine 1. Sea stage in Alameda, California. The purple line is an Eight-year centered Gaussian common, the blue line is the linear pattern

Hmm … not seeing a complete lot of acceleration in that report. It would present as acceleration, nevertheless, as a result of it each begins and ends at a excessive level.

The oddity of this sea-level report is that it’s not removed from San Francisco, however the sea stage rise is lower than half that of SF … say what? Should be some vertical motion of the land itself, go determine. It might’t be an precise actual distinction in sea stage, in any other case in comparison with 1939, after 80 years the ocean stage in Alameda would completely be some 4 inches (100 mm) decrease than the extent ten miles (16 km) throughout the bay. Not potential.

Primarily based on that impossiblity, I’d advise not placing any weight on the Alameda report … however I digress.

How about San Francisco? It has a for much longer report, so any acceleration needs to be extra seen. Right here’s that graph:

Determine 2. Sea stage in San Francisco, California. The purple line is an Eight-year centered Gaussian common, the blue line is the linear pattern

Man, that’s about as straight a line as anybody might need.

Mystified by the claims of acceleration, I went to see how the “Sea Stage Report Card” examine accelerated the acceleration. Seems the reply is easy. 

1) Throw away the entire information earlier than 1969.

2) Calculate a quadratic (accelerating) match to the information.

three) Topic it to bootstrap and Monte Carlo checks to see if it’s vital.

four) Prolong the quadratic match out to the yr 2050

5) Declare success.

Severely, that’s what they’ve accomplished. Right here’s their “Sea Stage Report Card” for Alameda, beginning in 1969:

Determine three. Alameda graph from the examine. Projection of unverified acceleration out to 2050. 

And right here is identical factor for San Francisco:

Determine four. San Francisco graph from the examine. Projection of unverified acceleration out to 2050. 

As you may see from the graphs, in each instances the quadratic (accelerating) pattern is just trivially totally different within the interval coated by the precise information. The 2 traces overlap virtually fully throughout that interval. Occams Razor says don’t unnecessarily multiply causes. And by that maxim, a straight line is the higher selection. However Occam has been flawed greater than as soon as …

So to keep away from getting a nasty shave from Occam, I ran my regular evaluation on each datasets. Utilizing the full-length datasets in each instances, I began by wanting on the Hurst Exponent of the datasets. The Hurst Exponent varies from zero to 1, with random datasets measuring zero.5. It measures how “autocorrelated” the information is, which means how a lot this month is like final month, this yr is like final yr, this decade is like final decade. 

And the issue is that when the Hurst Exponent is excessive, it means the information is of course fashionable, so that enormous swings up and down aren’t unusual. See right here for a dialogue of the problems.

In each instances, the Hurst Exponent is excessive — zero.77 for Alameda and zero.73 for SFO. That is loads giant sufficient to invalidate regular statistical checks.

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And talking of checks, the conventional statistical take a look at (ANOVA) reveals that for San Francisco, the accelerating “Quadratic Development” seen in Determine 1 is not statistically higher than only a straight line.

Nonetheless, the scenario is totally different for Alameda. The ANOVA take a look at reveals that the Quadratic Development does a considerably higher job than a straight line in explaining the information.

Ah, however the Hurst Exponent … let me take a small digression. 

The variety of months or different information factors in a dataset is normally represented by “N”. For San Francisco, there are 1,896 months of information, so N = 1,896. That’s numerous information factors, which is nice. It makes any conclusions that we draw extra stable. It reduces the uncertainty in developments and the like. The extra information factors we’ve, the higher.

The conventional option to cope with a excessive Hurst Exponent dataset is to calculate an “efficient N” which displays the variety of regular random information factors that the dataset will act like. I take advantage of the strategy of Koutsoyiannis to calculate efficient N, as I described within the hyperlink above. And I mentioned the query of sea ranges and efficient N right here.

For the San Francisco information, as an alternative of the N of 1,896 months of information (information factors), the efficient N seems to be solely 57 information factors.

And since we couldn’t say that the Quadratic Development is a greater match with 1,896 information factors … there isn’t a likelihood of it being statistically vital with solely 57.

Concerning Alameda, it has an N of 969 months. However once we calculate the efficient N, it’s solely 24. And whereas (in contrast to San Francisco) the ANOVA take a look at confirmed the Alameda accelerating Quadratic Development was considerably higher with out adjusting for autocorrelation, as soon as we take the Hurst Exponent into consideration, the acceleration is now not vital.

In fact, after they chop off the early a part of each data earlier than 1969, it simply will get worse. Each datasets now have solely 612 information factors … and the efficient N is just 12 for Alameda and 14 for San Francisco. And with that small an N, all bets are off—it’s far, far too little information to come back to any conclusions of any type about small ranges of acceleration.

Now me, along with wanting on the statistical calculations, I take advantage of one other technique. Just lately I noticed that we will make use of an uncommon utility of Full Ensemble Empirical Mode Decomposition evaluation, often known as “CEEMD”, to the ocean stage query. CEEMD breaks down (“decomposes”) any sign into its part cycles by frequency bands. It removes these bands of cycles (often called “empirical modes”), separately, from the sign. On the finish of the method, what’s left behind is the half with out cycles, known as the “residual”. My perception was that we will take a look at that residual to know probably the most fundamental swings within the tidal dataset after all of the pure tidal cycles are eliminated.

The CEEMD technique is classed as a “noise-assisted” technique of information evaluation, which looks like a contradiction in phrases. For these unfamiliar with the strategy, I wrote about it right here.

So let’s see how the CEEMD works out in follow. Right here is the Full Ensemble Empirical Mode Decomposition (CEEMD) of the San Francisco dataset.

Determine three. CEEMD decomposition of the San Francisco tide ranges. The highest panel reveals the uncooked annual sea stage information. Empirical Modes C1 to C5 present the part cycles beginning with the best frequency (shortest interval) cycles and dealing all the way down to the bottom frequency (longest interval). The underside panel reveals the residual that’s left as soon as C1 by way of C5 are subtracted from the uncooked information. The person Empirical Modes even have totally different amplitudes, however I’ve set all of them to the identical dimension for straightforward comparability. Items are Normal Deviations.

We are able to take one other take a look at this identical decomposition in a “periodogram” that reveals the lengths and strengths of the cycles.

Determine four. This reveals the durations of the assorted Empirical Modes C1 by way of C5. As you may see, there are robust cycles at about 13 years (Mode C4), and 27 and 36 years, with smaller cycles centered at 50 and 80 years (Mode C5).

As I mentioned, the related graph for our functions is the “Residual” proven as the underside panel in Determine three. That is what’s left in spite of everything tidal cycles are eliminated. As we’ve seen, there are vital cycles within the San Francisco information out to round fifty years and extra. This typically agrees with Mitchell’s conclusion in “Sea Stage Rise in Australia and the Pacific” who famous (see p. 15) that even after 50 years, sea-level rise accuracy continues to be solely ± a few mm. It is because the tides have lengthy, gradual oscillations, and if we use shorter information, we could be taking a look at a tidal cycle somewhat than a real sea-level change.

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So right here’s how I plot up the CEEMD residual. I overlay it on the linear pattern of the residual so I can see simply how the residual modifications over time. Right here’s that graph.

Determine 5. The “residual” of the CEEMD evaluation of the San Francisco sea stage information, what stays in spite of everything cycles have been faraway from the information.

As you may see, as soon as we take away the tidal cycles from the information there isn’t a acceleration. Nonetheless, I believe that the authors of the examine have mistaken the slight improve in pattern from the comparatively stage interval 1975-2000 for acceleration. Go determine.

How about Alameda? Right here’s the CEEMD information:

Determine 6. As in Determine four, for the Alameda information.

And listed here are the periodograms of the Alameda Empirical Modes:

Determine 7. This reveals the durations of the assorted Empirical Modes C1 by way of C5. As you may see, there are robust cycles within the vary from 10 to 15 years, and round 30 years.

Right here we will see the issue with even a 60-year dataset. There’s nonetheless vitality in cycle lengths all the best way out to 60 years, so we’re unable to actually disentangle the pattern from the cycles. Nonetheless, provided that, right here’s the residual.

Determine Eight. CEEMD residual, as in Determine 5, however for Alameda Island

YIKES! You may see what I meant about issues with the Alameda information. I believe it has to do with the groundwater ranges. I discover the next:

From the 1850’s, Alameda Island had been recognized for its plentiful, pure water provide. Early wells various in depth from just a few toes to lots of of toes deep. Even within the early days, it was widespread data that artesian waters could be discovered alongside the southwestern facet of the island at a depth of 100 toes or so. The water would rise within the bore holes to about excessive tide stage. SOURCE

So clearly, there’s trapped water 100 toes beneath the island exerting vital upward strain. Since then, these wells have been pumped, after which shut down, and new wells drilled, and pumped, after which shut down. As well as, the island was a Naval Air Base through the warfare, and the inhabitants and the water use various vastly earlier than and after. My guess is that what we’re seeing within the Alameda sea-level report are modifications in land stage ensuing from modifications in groundwater strain.

Intrigued, I assumed I’d look additional. Right here’s the sea-level report for San Diego, California.

Determine 9. Title says all of it. SOURCE

To my shock, a normal evaluation reveals a really slight acceleration over the interval. The speed of sea-level rise is growing by a hundredth of a millimetre (zero.01 mm) per yr … be nonetheless, my beating coronary heart. Virtually too small to measure. 

 And in reality, we will kinda see this very small acceleration within the CEEMD evaluation.

Determine 10. CEEMD residual, as in Determine 5, however for San Diego

This reveals why I like my CEEMD technique of taking a look at sea ranges. The residual, displaying the underlying modifications within the charge of sea-level rise, begins out above the pattern line. For forty years, from 1920 to 1960, it’s a straight line precisely on the pattern. It then decreases barely and slowly for about 20 years, when it begins to extend, as soon as once more barely and slowly. And on the finish of the interval, it seems to be slowing down once more.

Is that this a real acceleration of the speed of sea-level rise in San Diego? Properly … I’d say no. I’d say that we’re seeing very slight will increase and reduces within the charge, however that they don’t seem to be statistically vital. And the evaluation utilizing the Hurst Exponent to calculate “efficient N” says the identical factor—with an efficient N of solely 19, there isn’t a statistically vital acceleration within the San Diego sea-level report.


There isn’t a vital acceleration of any type within the San Francisco tide stage information.

On account of modifications in floor stage, the Alameda tide station is totally unsuited for any form of comparability to different websites or for projections into the longer term. Nonetheless, I can perceive why the authors of the “Sea Stage Report Card” examine may mistakenly assume that it’s accelerating …

The San Diego report reveals a really slight acceleration, however it’s not vital when corrected for autocorrelation. It additionally seems to not be a real acceleration, however as an alternative a slight “porpoising” above and under the pattern line.

No matter technique the authors are utilizing to find out if there’s vital acceleration appears to be giving false positives.

Regardless of being warned about upcoming harmful sea-level acceleration by societies of very realized of us and by local weather alarmists for the reason that 1980s, and regardless of claims that main cities could be underwater by 2020 or 2050, there’s nonetheless no signal of such threatening sea-level rise. Specifically, the ocean round San Francisco has been rising each slowly and steadily with little or no variation for over 160 years.

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And right here in our home up atop the primary main ridge in from the coast, on this pretty sunny spring day I gaze out upon a small little bit of the distant ocean seen between the hills, whose stage retains rising at its historic tempo of about eight inches per century. 

My easiest needs to you all,


PS – Only for humor’s sake, right here’s their “Sea Stage Report Card” from Crescent Metropolis, on the northernmost finish of the California Coast.

In response to their report card, the speed of rise is accelerating … within the flawed route. Seems like no drowned cities up there …

PPS: As is my wont, I politely request that while you remark, you quote the precise phrases you’re discussing so we will all be clear in your topic. 


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