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 the “US 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 their “Sea Level Report Card” for 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.

CONCLUSIONS:

• 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.

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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,

w.

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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