Accelerating The Acceleration

Guest Post by Willis Eschenbach

I see that the merchants of hype are at it again. The scary headline says Report: Sea-level rise ‘accelerating’ along U.S. coasts, including in the Bay Area. And in the text, it says “The Bay Area was home to two of those stations: one in Alameda and one in San Francisco, which both recorded a year-over-year rise.” Of course, they blamed the usual suspect, global warming.

I see that and I say … whaaa? I live an hour and a half north of San Franciso, and I’ve been following sea levels around here for a while. I knew nothing of any sea-level acceleration. 

The media article references something called theUS Sea Level Report Card“, which indeed lists San Francisco and Alameda. So I went to the NOAA Tides and Currents site to get the data. Let me start with the shorter of the two datasets, Alameda. It’s an island, albeit just barely, in San Francisco Bay near Oakland. It’s lovely, I lived there on the waterfront for a bit just after I got married.

Originally it was part of the Oakland mainland, but in the 1890s the canal at the lower right was cut through. This allowed flowing water to prevent the ongoing problem with siltation in that estuary. As a consequence, the land across from the island became the main location for the Port of Oakland. The channel between Alameda and the mainland is a gorgeous part of the world. Here’s a photo I took the last time I sailed those waters, showing the giant land horses of the Port.

So what is the story of the Alameda sea levels? Here you go:

Figure 1. Sea level in Alameda, California. The red line is an 8-year centered Gaussian average, the blue line is the linear trend

Hmm … not seeing a whole lot of acceleration in that record. It might show as acceleration, however, because it both starts and ends at a high point.

The oddity of this sea-level record is that it’s not far from San Francisco, but the sea level rise is less than half that of SF … say what? Must be some vertical movement of the land itself, go figure. It can’t be an actual real difference in sea level, otherwise compared to 1939, after 80 years the sea level in Alameda would permanently be some four inches (100 mm) lower than the level ten miles (16 km) across the bay. Not possible.

Based on that impossiblity, I’d advise not putting any weight on the Alameda record … but I digress.

How about San Francisco? It has a much longer record, so any acceleration should be more visible. Here’s that graph:

Figure 2. Sea level in San Francisco, California. The red line is an 8-year centered Gaussian average, the blue line is the linear trend

Man, that is about as straight a line as anyone could want.

Mystified by the claims of acceleration, I went to see how the “Sea Level Report Card” study accelerated the acceleration. Turns out the answer is simple. 

1) Throw away all of the data before 1969.

2) Calculate a quadratic (accelerating) fit to the data.

3) Subject it to bootstrap and Monte Carlo tests to see if it’s significant.

4) Extend the quadratic fit out to the year 2050

5) Declare success.

Seriously, that’s what they’ve done. Here’s theirSea Level Report Cardfor Alameda, starting in 1969:

Figure 3. Alameda graph from the study. Projection of unverified acceleration out to 2050. 

And here is the same thing for San Francisco:

Figure 4. San Francisco graph from the study. Projection of unverified acceleration out to 2050. 

As you can see from the graphs, in both cases the quadratic (accelerating) trend is only trivially different in the period covered by the actual data. The two lines overlap almost entirely during that period. Occams Razor says don’t unnecessarily multiply causes. And by that maxim, a straight line is the better choice. But Occam has been wrong more than once …

So to avoid getting a bad shave from Occam, I ran my usual analysis on both datasets. Using the full-length datasets in both cases, I started by looking at the Hurst Exponent of the datasets. The Hurst Exponent varies from 0 to 1, with random datasets measuring 0.5. It measures how “autocorrelated” the data is, meaning how much this month is like last month, this year is like last year, this decade is like last decade. 

And the problem is that when the Hurst Exponent is high, it means the data is naturally trendy, so that large swings up and down are not uncommon. See here for a discussion of the issues.

In both cases, the Hurst Exponent is high — 0.77 for Alameda and 0.73 for SFO. This is plenty large enough to invalidate normal statistical tests.

And speaking of tests, the normal statistical test (ANOVA) shows that for San Francisco, the accelerating “Quadratic Trend” seen in Figure 1 is not statistically better than just a straight line.

However, the situation is different for Alameda. The ANOVA test shows that the Quadratic Trend does a significantly better job than a straight line in explaining the data.

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

The number of months or other data points in a dataset is usually represented by “N”. For San Francisco, there are 1,896 months of data, so N = 1,896. That’s lots of data points, which is good. It makes any conclusions that we draw more solid. It reduces the uncertainty in trends and the like. The more data points we have, the better.

The normal way to deal with a high Hurst Exponent dataset is to calculate an “effective N” which reflects the number of normal random data points that the dataset will act like. I use the method of Koutsoyiannis to calculate effective N, as I described in the link above. And I discussed the question of sea levels and effective N here.

For the San Francisco data, instead of the N of 1,896 months of data (data points), the effective N turns out to be only 57 data points.

And since we couldn’t say that the Quadratic Trend is a better fit with 1,896 data points … there is no chance of it being statistically significant with only 57.

Regarding Alameda, it has an N of 969 months. But when we calculate the effective N, it’s only 24. And while (unlike San Francisco) the ANOVA test showed the Alameda accelerating Quadratic Trend was significantly better without adjusting for autocorrelation, once we take the Hurst Exponent into account, the acceleration is no longer significant.

Of course, when they chop off the early part of both records before 1969, it just gets worse. Both datasets now have only 612 data points … and the effective N is only 12 for Alameda and 14 for San Francisco. And with that small an N, all bets are off—it’s far, far too little data to come to any conclusions of any kind about small levels of acceleration.

Now me, in addition to looking at the statistical calculations, I use another method. Recently I realized that we can employ an unusual application of Complete Ensemble Empirical Mode Decomposition analysis, also known as “CEEMD”, to the sea level question. CEEMD breaks down (“decomposes”) any signal into its component cycles by frequency bands. It removes these bands of cycles (known as “empirical modes”), one at a time, from the signal. At the end of the process, what’s left behind is the part without cycles, called the “residual”. My insight was that we can look at that residual to understand the most basic swings in the tidal dataset after all the natural tidal cycles are removed.

The CEEMD method is classed as a “noise-assisted” method of data analysis, which seems like a contradiction in terms. For those unfamiliar with the method, I wrote about it here.

So let’s see how the CEEMD works out in practice. Here is the Complete Ensemble Empirical Mode Decomposition (CEEMD) of the San Francisco dataset.

Figure 3. CEEMD decomposition of the San Francisco tide levels. The top panel shows the raw annual sea level data. Empirical Modes C1 to C5 show the component cycles starting with the highest frequency (shortest period) cycles and working down to the lowest frequency (longest period). The bottom panel shows the residual that’s left once C1 through C5 are subtracted from the raw data. The individual Empirical Modes actually have different amplitudes, but I’ve set them all to the same size for easy comparison. Units are Standard Deviations.

We can take another look at this same decomposition in a “periodogram” that shows the lengths and strengths of the cycles.

Figure 4. This shows the periods of the various Empirical Modes C1 through C5. As you can see, there are strong 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 said, the relevant graph for our purposes is the “Residual” shown as the bottom panel in Figure 3. This is what’s left after all tidal cycles are removed. As we’ve seen, there are significant cycles in the San Francisco data out to around fifty years and more. This generally agrees with Mitchell’s conclusion in “Sea Level Rise in Australia and the Pacific” who noted (see p. 15) that even after 50 years, sea-level rise accuracy is still only ± a couple of mm. This is because the tides have long, slow oscillations, and if we use shorter data, we may just be looking at a tidal cycle rather than a true sea-level change.

So here’s how I plot up the CEEMD residual. I overlay it on the linear trend of the residual so I can see just how the residual changes over time. Here’s that graph.

Figure 5. The “residual” of the CEEMD analysis of the San Francisco sea level data, what remains after all cycles have been removed from the data.

As you can see, once we remove the tidal cycles from the data there is no acceleration. However, I suspect that the authors of the study have mistaken the slight increase in trend from the relatively level period 1975-2000 for acceleration. Go figure.

How about Alameda? Here’s the CEEMD data:

Figure 6. As in Figure 4, for the Alameda data.

And here are the periodograms of the Alameda Empirical Modes:

Figure 7. This shows the periods of the various Empirical Modes C1 through C5. As you can see, there are strong cycles in the range from 10 to 15 years, and around 30 years.

Here we can see the problem with even a 60-year dataset. There’s still energy in cycle lengths all the way out to 60 years, so we’re unable to truly disentangle the trend from the cycles. However, given that, here’s the residual.

Figure 8. CEEMD residual, as in Figure 5, but for Alameda Island

YIKES! You can see what I meant about problems with the Alameda data. I suspect it has to do with the groundwater levels. I find the following:

From the 1850’s, Alameda Island had been known for its abundant, pure water supply. Early wells varied in depth from a few feet to hundreds of feet deep. Even in the early days, it was common knowledge that artesian waters would be found along the southwestern side of the island at a depth of 100 feet or so. The water would rise in the bore holes to about high tide level. SOURCE

So obviously, there is trapped water a hundred feet under the island exerting significant upward pressure. Since then, these wells have been pumped, and then shut down, and new wells drilled, and pumped, and then shut down. In addition, the island was a Naval Air Base during the war, and the population and the water use varied greatly before and after. My guess is that what we are seeing in the Alameda sea-level record are changes in land level resulting from changes in groundwater pressure.

Intrigued, I thought I’d look further. Here’s the sea-level record for San Diego, California.

Figure 9. Title says it all. SOURCE

To my surprise, a standard analysis shows a very slight acceleration over the period. The rate of sea-level rise is increasing by a hundredth of a millimetre (0.01 mm) per year … be still, my beating heart. Almost too small to measure. 

 And in fact, we can kinda see this very small acceleration in the CEEMD analysis.

Figure 10. CEEMD residual, as in Figure 5, but for San Diego

This shows why I like my CEEMD method of looking at sea levels. The residual, showing the underlying changes in the rate of sea-level rise, starts out above the trend line. For forty years, from 1920 to 1960, it is a straight line exactly on the trend. It then decreases slightly and slowly for about 20 years, when it starts to increase, once again slightly and slowly. And at the end of the period, it appears to be slowing down again.

Is this a true acceleration of the rate of sea-level rise in San Diego? Well … I’d say no. I’d say that we are seeing very slight increases and decreases in the rate, but that they are not statistically significant. And the analysis using the Hurst Exponent to calculate “effective N” says the same thing—with an effective N of only 19, there is no statistically significant acceleration in the San Diego sea-level record.


There is no significant acceleration of any kind in the San Francisco tide level data.

Due to changes in ground level, the Alameda tide station is completely unsuited for any kind of comparison to other sites or for projections into the future. However, I can understand why the authors of the “Sea Level Report Card” study might mistakenly think that it is accelerating …

The San Diego record shows a very slight acceleration, but it is not significant when corrected for autocorrelation. It also appears not to be a true acceleration, but instead a slight “porpoising” above and below the trend line.

Whatever method the authors are using to determine if there is significant acceleration seems to be giving false positives.

Despite being warned about upcoming dangerous sea-level acceleration by societies of very learned folks and by climate alarmists since the 1980s, and despite claims that major cities would be underwater by 2020 or 2050, there is still no sign of such threatening sea-level rise. In particular, the ocean around San Francisco has been rising both slowly and steadily with very little variation for over 160 years.

And here in our house up atop the first major ridge in from the coast, on this lovely sunny spring day I gaze out upon a small bit of the distant ocean visible between the hills, whose level keeps rising at its historical pace of about eight inches per century. 

My very best wishes to you all,


PS – Just for humor’s sake, here’s their “Sea Level Report Card” from Crescent City, at the northernmost end of the California Coast.

According to their report card, the rate of rise is accelerating … in the wrong direction. Looks like no drowned cities up there …

PPS: As is my wont, I politely request that when you comment, you quote the exact words you are discussing so we can all be clear on your subject. 


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February 9, 2020 6:06 am

Nick would have been proud of that effort in abuse of statistics 101, everything is defining the justification.

February 9, 2020 6:32 am

Thanks Willis for a wonderfully explained course on statistical trends. I’ve often wondered if the wakes of the huge container ships in a confined area such as the San Francisco Bay has any effect on the tide gauge readings?
You can get quite a bit of water pushed up into an area if traffic is heavy.

Reply to  Willis Eschenbach
February 9, 2020 11:58 am

Best ribs in the Bay Area: Great American BBQ in Alameda on High Street just west of the bridge. Always long-haul aircrews from nearby OAK loading up on takeout – a good indicator.

Reply to  brians356
February 9, 2020 12:04 pm

Bummer. “Permanently closed”. 🙁

February 9, 2020 6:39 am

I watched a video of the 56 floor porsche design building in Miami, its absolutely incredible, you can drive in to your apartment, the penthouse is 32 million dollars, it as has 11 car parking spaces, 10,000 sqft of outside space just for the penthouse, lifts Everywhere, Oh and it includes a pool for each apartment.

And yes, its right on the beach front, and the other million building around that area, seems nobody is bothered about the meters upon meters of supposed sea rise 😐

old white guy
Reply to  Sunny
February 9, 2020 11:06 am

Sunny, I have been staying at the same beach for a very long time now on the gulf side. The beach has been expanding not contracting and the water level is the same as it has been for fifty years. I am always amazed at how many people cannot see that which is right in front of them. It also bothers me that many people actually think that what is happening has never happened before, that their life span is all there ever was or is.

February 9, 2020 6:40 am

Just out of curiosity – and pardon if you’ve talked about this before – where did you gain your breadth of statistical exposure?
I read everything you post at WuWT and enjoy continually learning about the ways to deploy statistical methods and practices to deconstruct bad “science-y” reports.

Reply to  Willis Eschenbach
February 9, 2020 10:58 am

Willis, you’re a legend and an inspiration for inquiring minds of all ages.

Not your chosen field I know, but what I’d like to read is a study of why some people have absolutely no inclination for skepticism on any topic, just accept everything they’re told or taught, whereas other people go – “hang on a minute, I want to convince myself about this”?

See, that’s “diversity” right there!

February 9, 2020 6:42 am

Thanks-impressed of Your eager to show the lack of acceleration. Acceleration is the most wanted sign of climate change
There is a graph useful and available fore the acceleration.
The change in change using 50 years average:
San Francisco
Cresent City

I use them often so if they are wrong or misleading let me know!

February 9, 2020 6:51 am

The title: Accelerating the Acceleration

That means jerk.

February 9, 2020 6:58 am

.Thank you Willis

Your review here is a perfect example of why skepticism is always warranted with any new alarmist claims. Easily debunked with a bit of math and science, not to mention common sense.

The study authors clearly tortured the data until it cried “uncle” and said what the authors wanted it to say.

That notion of tortured data brings to mind, with all due apology to musician John Prine, the climate alarmists’ new verse to his paean to”Paradise” should be:

Then the climate alarmists came with the world’s largest model
And they tortured the data and stripped all the science
Well, they ran their fake models till man’s end was a given
Then they wrote it all down as the progress of science.

S Geiger
February 9, 2020 7:01 am

Should the first two graphs be meters?

Reply to  S Geiger
February 9, 2020 8:11 am

Yes, either correct the units or the scale.

February 9, 2020 7:07 am

My first guess as to what’s happening at Crescent City would be stress building up from the Cascadia fault zone.

Reply to  MarkW
February 9, 2020 9:10 am

Indeed. California is filled with faults, so you cannot trust the land level to stay still any more than the sea level. A certain amount of urban land is landfill, but government geologists probably wouldn’t put their reference point there; pity people have built buildings there. Landfill slumps.

February 9, 2020 7:10 am

At San Diego sea-levels are are very strongly influenced by ENSO. During El Nino, the easterly equatorial trade winds diminish, and the Pacific ocean sloshes to the east, raising sea-levels at San Diego, and lowering sea-levels in the western Pacific. During La Nina, the opposite happens. Here’s graph showing the ENSO correlation:

comment image

Even so, the sea-level trend at San Diego is not significantly different from linear:

comment image
Linear trend = 2.176 ±0.184 mm/yr (9 inches / century)
Acceleration = 0.00879 ±0.01259 mm/yr² (positive, but statistically insignificant)
To see precise values, hover your mouse cursor over the graph traces (or touch the graph on a touch-screen).

AMO also influences sea-levels in some places, though generally not as much as ENSO. The AMO period is about 60-65 yrs. Using a sea-level measurement record significantly shorter than that is a good way to create the illusion of an acceleration or deceleration in sea-level trend.

    “It is well established that sea level trends obtained from tide gauge records shorter than about 50-60 years are corrupted by interdecadal sea level variation…”
    Douglas B 1997. Global Sea Rise: a Redetermination, Surveys in Geophysics, Vol. 18, No. 2-3, 279-292.

San Francisco is less influenced by ENSO than is San Diego, but San Francisco is also less tectonically stable. If you start your trend analysis after the 1906 earthquake, you get:
Linear trend = 2.006 ±0.200 mm/yr (8 inches per century)
Acceleration = -0.00292 ±0.01390 mm/yr² (negative, but statistically insignificant)

Honolulu is near the mid point longitude of the ENSO “teeter-totter,” so it is little affected by ENSO slosh. It also has the advantage of being on a tectonically stable “old” island, with little or no vertical land motion (though the whole chain of islands is moving to the NW at a rate of a few inches per year).

Honolulu has an extremely high-quality measurement record, extending back 115 years, without a single month missing. It has seen no acceleration in the rate of sea-level rise:

comment image
Linear trend = 1.485 ±0.208 mm/yr (six inches per century)
Acceleration = -0.00479 ±0.01403 mm/yr² (negative, but statistically insignificant)

Very, very few locations with long, high-quality sea-level measurement records have seen a significant acceleration or deceleration in the sea-level trend within the last ninety years.

February 9, 2020 7:23 am

As a former trial lawyer looking for simple ways to make a point, and to impeach an expert witness report, I wonder why your PS at the end showing the graph of sea level falling at a nearby city like Crescent City doesn’t effectively put in question itself their entire report of acceleration of acceleration of sea level rise. What would be their comeback to that?

Gordon Dressler
Reply to  Willis Eschenbach
February 9, 2020 11:12 am

“Geological changes along the East Coast are causing land to sink along the seaboard.

New research using GPS and prehistoric data has shown that nearly the entire coast is affected, from Massachusetts to Florida and parts of Maine.

The study, published this month in Geophysical Research Letters, outlines a hot spot from Delaware and Maryland into northern North Carolina where the effects of groundwater pumping are compounding the sinking effects of natural processes.”
—John Upton, “Sinking Atlantic Coastline Meets Rapidly Rising Seas”, Scientific American, 14 April 2016

Things are not always as they seem to be on the surface (pardon the pun). Land subsidence has NOT YET been asserted to be an effect of climate change.

Richard G.
Reply to  Willis Eschenbach
February 9, 2020 12:52 pm

The Hayward Fault just to the east of Alameda is well known to slowly creep.

February 9, 2020 7:26 am

Magisterial demolition of the sea level rise acceleration myth, thanks Willis!
When land level change is in the mix, interpretation of SLR must be very cautious, and extrapolation completely impossible. This malpractice must be exposed – and has been here.

February 9, 2020 7:33 am

Methinks the effort is under way to make sea levels to match climate models projections, such as those used by Union of Concerned Scientists to scare coastal dwellers and land owners. For example, here are their projections compared to a continued trend from the SF tidal guage. As the chart shows, reality is already diverging from imaginary sea levels since 2000.
comment image

Synopsis of their methodology is here:

Curious George
February 9, 2020 7:46 am

This travesty was put together by VIMS, Virginia Institute of Marine Sciences. I am almost sure that it is taxpayer’s money at work. Who else would pay these geniuses?

Brook HURD
February 9, 2020 7:56 am

Thank you, Willis, for another excellent analysis of of paper which used a flawed method for their projection. Once again, you have proven Mark Twain to have been correct.

M Courtney
February 9, 2020 7:57 am

In figures 5 and 8 what are the units for the y-axes, the empirical mode index?

Asking because I couldn’t follow what that is.

Thanks in advance.

M Courtney
Reply to  Willis Eschenbach
February 9, 2020 2:41 pm

Thanks again. That makes sense.
I was thinking wrong when I was looking for units. The SD are in the same units by definition and the scale is relevant for the same reason.
Also, I now can see that the residuals are not big compared to the variations that the real world experiences. (e.g. the non-tidal effects aren’t – practically – big).

February 9, 2020 8:10 am

Thanks, Willis, for the fun AND educational post.


February 9, 2020 8:15 am

A few more centuries before traffic on the Golden Gate is threatened…

February 9, 2020 8:40 am

You are not doing it correctly, instead take the last five years of figure 1, for example, and draw a straight line. Ergo acceleration for the acceleration.

February 9, 2020 9:16 am

Very interesting rebuttal of the claimed acceleration, Willis.

One thing that struck me was the 21.5y peak in figs 4 & 7. Also a 10.5 in strongly in fig 7 and much less strong but still present in fig 4. ( Alameda )

Fig4 also has a strong circa 13y peak , something which is found in many SST records but I have no idea what the cause of that is.

Reply to  Willis Eschenbach
February 22, 2020 5:11 am

One problem is that Fourier analysis works very well for detecting weak signals with unvarying periods, but poorly for detecting signals with varying periods. The “11 year” sunspot cycle is not really eleven years, it’s anywhere from 9-13 years.

What’s more, there’s a noticeable positive correlation between the length of one sunspot cycle and the length of the next. In other words, the rate of oscillation sometimes slows down or speeds up for an extended period of time. That behavior prevents Fourier decomposition from working well to detect a weak signal.

Johann Wundersamer
Reply to  Greg
February 21, 2020 10:25 pm
Ann in L.A.
February 9, 2020 9:16 am

As usual, no one puts error estimates on their data. I think it’s safe to say that 0.01 mm is well within the measurement error of the data.

Komrade Kuma
February 9, 2020 9:35 am

Oh what delicious incompetence by the goons who put that pile of scientific crap together! Fitting a quadratic with so little curvature that its almost linear but allows you to project ‘acceleration’ out in future fary land.

As it happens I used to use quadratic curves in my professional work as a naval architect to generate sheer lines for boat designs and also deck camber chapes. When working in a particular shipyard it was practice to use the arc of a circle for camber curve templates that could be used with greater flexibility and in many locations, not just the deck geometry, since you did not have to line up the centre mark. This was possible because for say a 150 mm in 5000 camber, a quadratic is within a mm or so of an arct with say 50000 radius (if I remember the numbers correctly – it was decades ago).

Taking that as a cue, these guys could have done a curve fit using a circle and guess what? The ‘acceleration would have disappear up it own ass eventually! I doubt if the goons in question would have twigged nor their review ‘pals’ and still published anyway. Oh well, one lives in hope they will find their true career end point eventually. Honestly, if you made this sort of folly up about someone they would have you cold for defamation.

Reply to  Komrade Kuma
February 10, 2020 5:17 am

Indeed. This paper is another demonstration of the fallacy that peer review provides some assurance of quality.

February 9, 2020 9:36 am

Most of the tide-gauge stations that provide the data used in our sea-level report cards began operation in the first few decades of the 1900s or even earlier. However, many stations—particularly along the U.S. East Coast—show evidence of a non-linear change or acceleration beginning in 1987, at the center of a 36-year sliding window beginning in 1969—thus setting the start date for our sea-level report cards. In short, we use post-1969 data because the linear sea-level trends of earlier decades do not accurately predict the sea-level changes that are most likely to occur given more recently observed acceleration in the rate of sea-level rise.

Amazing. So they openly admit they crop the data to get more “acceleration” . The more linear part of the data don’t count because they would give less acceleration… which they know is there “given” the fact they cropped the data to create it.

Seems like Occam must be using those new politically correct Gillette safety razors nowadays. You know, the ones free of “toxic masculinity”.

Steven Mosher
February 9, 2020 9:45 am

The hurst trick again.

Clyde Spencer
Reply to  Willis Eschenbach
February 9, 2020 10:43 am

Unlike you, Mosher either doesn’t realize, or at least doesn’t acknowledge, what you call “leopard knowledge.” Thus, while being bright, he doesn’t appreciate his limitations and behaves as though he thinks he has no peers here. As Dirty Harry was wont to say, “A man has to know his limitations.”

Reply to  Willis Eschenbach
February 9, 2020 6:00 pm


Consider this a vote of confidence from someone who spent most of a 40 year career looking at noisy highly autocorrelated process data. You are doing exactly what you need to do to make sense out of this.

Reply to  Steven Mosher
February 9, 2020 10:27 am

the strongest autocorrelation is probably AR1, remove that by differentiation and see what’s left.

Sweet Old Bob
February 9, 2020 9:54 am

Willis , do the tide cycles have any correlation to solar cycles ?
My old eyes see a 11 to 12ish year cycle in some ?
Can’t see an obvious reason for that .

Reply to  Willis Eschenbach
February 9, 2020 10:19 am

Maybe it would be more pertinent to look at the data you used here which seems to show strong 10.5y and 21.5y peaks. The seems to be what he was referring to .

Greg Goodman
Reply to  Greg
February 9, 2020 11:11 am

a quick spectral analysis of d/dt(MSL) at S.F. site (1898 on) shows a clear peak at 10.8y and 13.2y
longer periods are severely attentuated by diffing.

Reply to  Willis Eschenbach
February 9, 2020 12:21 pm

Sorry, I was misreading the log scale after 20, very careless. 28 indeed. That explains my not seeing in my spectrum using the derivative to remove AC.

In that spectrum the circa 11y peak is the same height as the 13y.

One problem with your CEEMD is that it applies band pass filters to separate C3,C4 etc. In this case 10-11y get attenuated in both those bands. I don’t know whether you can alter where the bands are centred but it may be worth experimenting.

I’m seeing poor resolution of those peaks. That is probably due the Kaiser-Besel windowing function, it is quite a heavy smoother. I’ll look into this some more.

Greg Goodman
Reply to  Willis Eschenbach
February 9, 2020 2:10 pm

I have not looked into the mechanics of how CEEMD splits the bands but to look at your fig 4 it sure looks like different bandpass filters. It may be a different technique which is doing something similar. Clearly is separating, ie filtering, the variability in some way.

Compare the circa 10.5 and 11.5 peaks in C3 and C4 , they are both present in each at about the same place but magnitudes are reversed.

Here is a (very) rough graph of the spectrum I get from a linear detrended SF sea level. The circa 11 and 13y peaks are comparable. I get similar results from using the first difference to remove AC.

It may be worth exploring how that CEEMD tool behaves with a known input. It will not remove an 11y cycle but it may be reducing it to a level which leads you to regard it as not significant.

Anyway, thanks for an interesting discussion. It’s always good to compare the output of different techniques.

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Reply to  Willis Eschenbach
February 10, 2020 3:43 am

I think you’ve put your finger on it. So the amplitude of the 10-11y year range is being split between C3 and C4 in some way. It’s similar but not the same as the filtering I thought was happening. (There’s no guarantee with bandpass filters that it all adds up. )

So you need to bear in mind that what looks rather small in both C3 and C4 needs to be added together mentally. Neither the C3 nor C4 amplitudes give an accurate comparison to the ( respectively ) lower and higher adjacent frequencies in their band.

If the height of the twin 10,11y peaks in C3 is added to their height in C4 ( to represent its contribution to the whole ) they would be less than but similar to the height of the 13y peak. That is consistent with my spectral analysis, which is reassuring from both ends.

February 9, 2020 10:08 am

Always ignored but constantly happening along the California coast is the uplifting of the Pacific plate on it’s endless northward journey. The 1989 Loma Preita earthquake lifted the coastal region by over one foot in 17 seconds as observed by mussels exposed on wharf pilings. No one ever talks about that as a component of sea level acceleration, but its there for all to see.

Reply to  Doonman
February 9, 2020 10:24 am

That would be a land level acceleration. It would lead to a drop in measured sea level. Land stays up in the air water doesn’t.

Clyde Spencer
Reply to  Greg
February 9, 2020 11:29 am

The Hayward fault, which is a splinter off the San Andreas, runs up the east side of the bay. I’m not sure that both faults are dancing to the same music. However, the SF Bay looks like it could be a graben, or down-dropped block. In which case, Alameda might be subsiding. However, the tide data don’t seem to support that. Without differential leveling to determine just what the land is doing and where it is doing it, using tide data, originally intended to keep ships from stranding, is speculation. The raw tide data are not fit for purpose of measuring sea level rise unless a tide station is demonstrated to be tectonically stable.

Reply to  Clyde Spencer
February 9, 2020 12:23 pm


Apparently they are fine for finding acceleration.

Reply to  Doonman
February 9, 2020 12:44 pm

Ignored — True. The California coast South of the Mendocino Triple point is a jumble of small crustal blocks moving around adjacent to major NS trending faults. Some of the little blocks are relatively stable. For example the San Francisco tidal gauge showed virtually no permanent vertical land motion during the 1906 earthquake. The San Diego gauge is on a block that seems relatively stable. But just to the West is an elevated block of countryside — Pt Loma and there’s another elevated block — the San Diego mesas — on the other side of the Rose Canyon Fault a couple of km NE of the gauge.

Crescent City is North of the triple point and thus is probably on the uplifting side of the Cascadia Fault Zone. Which would explain why sea level might appear to be dropping a bit there. Quite likely, the CC gauge will drop many tens of cm in about five minutes at some future time.

February 9, 2020 10:24 am

I understand that satilite readings of ocean elevations changes are not supporting sea level changes. One use for this data is to determine surface current flow for shipping purposes. Measures in the millimeter range. Shipping companies use this info to determine course and reduce fuel expenditures. Shouldn’t be too difficult to check out.

February 9, 2020 10:26 am

I understand that satellite readings of ocean elevations changes are not supporting sea level changes. One use for this data is to determine surface current flow for shipping purposes. Measures in the millimeter range. Shipping companies use this info to determine course and reduce fuel expenditures. Shouldn’t be too difficult to check out.

Michael Jankowski
February 9, 2020 10:41 am

Interesting how the SF linear trend is 0.10 vs Alameida 0.05 yet the quad trends are quite close and the quad hi 95s are almost identical (0.30 vs 0.29).

February 9, 2020 10:43 am

Fort Pulaski was build at the oceans edge with a sea water filled moat designed as a killing field. Today the fort is high and dry and the moat is empty.

Kevin McNeill
February 9, 2020 10:47 am

Well the Mosh made a typical appearance, but wait, no Stokes? Willis must be right then!

Reply to  Kevin McNeill
February 9, 2020 11:07 am

Nick is probably over at HotWhopper have a giggling gerty session with the inmates there about Willis’ latest expose.
Nothing of substance happening there of course, just the usual drive-by condemnation of the witches coven that for them is WUWT.
The last Enlightenment got rid of witches, the next one might get rid of climate alarmists.
We can only hope.

Clyde Spencer
February 9, 2020 11:06 am

I looked at the link you provided for the “Report Card.” I don’t see them providing the R^2 values for the trend lines. Have you calculated them independently during your analysis? If so, I’d be curious what they are.

Don K
February 9, 2020 11:24 am

Willis, I’m pretty sure that fitting quadratics to anything that isn’t likely to have an X-squared term is a bad idea. I think it’ll almost certainly show an acceleration or deceleration whether one is present or not. Here’s some support for that view from a possibly unexpected source

I think — could be wrong — that a quadratic amounts to the sum of a parabola and a straight line. If true, that’s something the smart kids figured out in High School, but many of us never noticed. If so, given enough data, quadratics might be great for predicting the trajectory of artillery shells, but likely rather poor at estimating sea level rise acceleration.

Don K
Reply to  Willis Eschenbach
February 9, 2020 2:15 pm

Apologies Willis. It wasn’t my intention to criticize your work — which seems fair and balanced. I was criticizing the Sea Level Report approach.

I would add however that I’m skeptical that quadratics can reliably detect SMALL accelerations in noisy data even after removing cyclical phenomena (Seems a good idea BTW). What can? I don’t know. I’ve done a little looking over the past year which is why I knew about the Real Climate and Tamino articles. I’ve found nothing much. Hopefully I just haven’t used the right search terms.

But maybe it’s just not possible.

Smart Rock
February 9, 2020 11:56 am

The only use of quadratic (or any other polynomial function) is to make a nice smooth curve through your data. Using a “nice fit” polynomial to extrapolate outside your data range (e.g. into the future) is very unscientific and should never be done for any reason. Its only role in this post is to make a sciencey-looking case for catastrophic SLR, and it is totally devoid of real-world meaning.

Unless you have a hypothesis that says the parameter you are studying is varying in response to physical processes that can be reasonably modeled by a quadratic or other polynomial equation. Which is not the case here. There is no hypothesis being tested, just a tenet of faith that says that global warming is accelerating (which it is not), ice cap melting must be accelerating, so SLR must also be accelerating and here’s a fabricated graph that purports to show it. Fake science.

On the other hand, looking for cyclicity, as Willis has done here, is a valid approach when there is good reason to expect your parameter (i.e. SLR) to be responding to cyclic or quasi-cyclic phenomena, such as PDO, AMO and Niño/Niña, that can be measured independently of SLR. It’s quite valid to extrapolate the linear trend that emerges after decomposition, but not too far into the unknown – what looks like a linear, secular trend could well be (and probably is in the case of SLR) a small part of a long cycle, e.g. the 1,000-year temperature cycle that can be seen in ice-core data.

Denis Rushworth
February 9, 2020 1:18 pm also provides NOAA sea level data and also includes where available GPS elevation and lateral movement data. At least since 1996, San Francisco has been moving vertically very little but is translating rapidly to the WNW at a little under 1 foot per decade. I hope there are lots of expansion joints in the bridge to Oakland.

February 9, 2020 1:29 pm

Thanks for this post Willis and even I can follow most of it.
Can you have a look at Andrew Bolt’s interview with Daniel Fitzhenry + data for Fort Denison Sydney a few months ago and tell us what you think about the claims?
A lot of people seem to dispute the claims made, thanks again for your interesting posts to WUWT over the years. Here’s the link.

Clyde Spencer
Reply to  Willis Eschenbach
February 9, 2020 8:36 pm

I believe the quote should be, “Just say ‘No’ to thugs, even if they are wearing jackboots!” 🙂

Reply to  Willis Eschenbach
February 10, 2020 4:02 am

“with a standard deviation of the difference about 5 mm …”

Kip reports in the new tide guage thread:

Note that the official NOAA specification for tide gauges states that the estimated accuracy for tide gauge monthly means is +/- 5 mm.

so getting that SD on a difference where you have two measurement errors is not bad.

Satellites get most of the signal form the reflection from the bottom of the swell.
Now if they think they can guess the height of the swell from 1300km to work out where mean sea level really is and to within 0.1mm , I’m sorry but I don’t believe their data fudging.

Never mind the sausage making that goes on to tack the various Topex/Jason etc records together to create a long term record. As always they have the flexibility to get whatever result fits their expectations/requirements and have a heave agenda to push. I stopped taking satellite altimetry seriously shortly after I looked at what they were doing and found the opacity of archiving old results which “changed”.

February 9, 2020 2:15 pm

What’s happening here is that we “deniers” have been throwing in their face that sea level rise has remained remarkably stable over the last century whenever they terrify us with tales of “accelerating” glacial melt. So they have to torture the data to get it to match their hyperbole.

Nicholas McGinley
February 9, 2020 8:12 pm

Awesomely complex analysis of what seems to be fairly evident from a glance at the long term tide charts.
In fact the tide graphs mostly seem to show sea level has been rising steadily all over the world, with a few notable exceptions.
Some of the graphs from Pacific atolls show almost zero sea level rise over many decades, even though those atolls sit atop sea mounts that are known to be steadily sinking into the crust of the Earth.
And some locations are obviously sinking due to ground water extraction, isostatic crustal movements due to unloading of the massive ice sheets that existed prior to about 12,000 years ago, and some other factors.
But a strange thing happens when we take a look at photographic evidence of seaside locations from around the world over more than 100 years.
In the photos we can find…all of them…there is zero evidence of any sea level rise whatsoever.
It does not matter if it is in Sydney Harbor in Australia, La Jolla Beach in California, Miami Beach in Florida…wherever.
Every place we can find photos of the sea with observable landmarks in them, from long ago, and compare them to recent pictures of the exact same places from the exact same perspective…there is no observable change at all!
I for one have a hard time ignoring my lying eyes, no matter how many people and charts give contrary information.

February 9, 2020 9:01 pm

Willis, great analysis. I tried another approach to determining acceleration in California sea level rise. Using data from six of the longest running tide gauge records–San Francisco, San Diego, Los Angeles, La Jolla, Crescent City, and Santa Monica (I avoided Alemeda due to it’s location in the interior of the bay)–I found the average annual six-guage relative sea levels. The change in the one year relative sea levels, in millimeters per year for the six, was calculated for each year beginning in 1856 (the second year of records for San Francisco). Then I calculated the difference with the rate thirty years later (chosen to represent climate change) and the first rate (the 1884 to1885 rate minus the 1855 to 1856 rate, for example) and divided this by the elapsed time of 30 years. This gives an average acceleration in millimeters per year squared as defined by those two data points 30 years apart. Plotting all the average accelerations up through the year ending in 2016 gives a sawtooth graph with accelerations ranging from 4mm/year^2 to -6mm/year^2, with the trend line almost perfectly flat at 0mm/year^2…showing no significant acceleration in sea level rise in the state. The graph can be found at my website: (scroll down). On the same graph I show the changes in atmospheric carbon dioxide using Law Dome and Mauna Loa data, and calculate the Pearson Correlation Coefficent between sea level acceleration and rising CO2, getting r = 0.0088, or effectively no correlation.
No evidence of sea level acceleration in California, nor of correlation with CO2.

February 10, 2020 8:16 am

California Geological Survey map of active faults

dozens in San Francisco region

under the sea – above the sea

February 10, 2020 9:54 am

Virginia Institute of Marine Science does discuss ENSO and some land changes in their paper from 2018 — Anthropocene Sea Level Change: A History of Recent Trends Observed in the U.S. East, Gulf, and West Coast Regions: (PDF)

Their definition of Anthropocine; ” a proposed new geologic epoch following the Holocene, the latest interglacial epoch that began nearly 12,000 years ago.”

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