Hotspot Data

In the last post we discussed the “Northeast hotspot.” It’s a region of the Atlantic coast of North America where sea level rise has accelerated in recent decades, identified by Sallenger et al.


They analyzed tide gauge data over time “windows” of various sizes, comparing the rate of sea level rise (SLR) in the first half of the window to that in the second half. They chiefly used windows of 60 years, 50 years, and 40 years, ending with 2009. They refer to the difference as “sea level rate difference,” or SLRD, and positive values mean sea level rise was faster over the most recent two to three decades than over the previous two to three decades. Hence their analysis mainly (but not exclusively!) focused on the last 60 years, i.e., the data since 1950. What’s interesting is that during this time span, the region from about Cape Hatteras to Boston shows more increase in the rate of sea level rise than other parts of the North American coast.

They identified 20 tide gauge stations within the area of the Northeast hotspot (or “NEH”). One which shows the recent acceleration most clearly is Boston. Let’s take the data from PSMSL (monthly mean sea level from the Permanent Service for Mean Sea Level) for that location, remove the annual cycle to compute anomaly data, then smooth the result to reduce the noise and enable us to see what the trend is actually doing. Let’s also fit a straight line to the data (by least-squares regression) so we can compare the smoothed trend to what would have happened if the rate of sea level rise had been constant since 1950:

The data itself is quite noisy, but the smoothed curve shows an upward curvature near the end, indicating the increased rate of sea level rise. We can even take the smoothed curve and subtract from it the straight-line fit, to show how the trend has departed from a constant rate of sea level rise:

We see that relative to the average rate of increase over the time since 1950, sea level at Boston rose more slowly until about 1987, more quickly since then. Station data records which show this behavior will exhibit a faster linear trend over the 2nd half of the time window than over the 1st half, and Sallenger et al.’s analysis is designed to detect exactly that. By smoothing the data, and comparing the smooth to the straight-line fit, we get the added benefit of finding out approximately when the rate of sea level rise changed (Sallenger et al. also determined that, but by a different method).

Sallenger et al. demonstrate the behavior of their method by applying it to artificial data. They did so for two kinds of acceleration. In one case, sea level rises at one constant rate for a while then switches to another constant rate. In another case, the acceleration is steady (so that sea level roughly follows a parabola). They took a window of the artificial data and compared 1st-half trends to 2nd-half trends, then let the window slide through time to see how the comparison changed over time:

In both cases their method detects the acceleration, since in both cases it shows positive values of SLRD (sea level rate difference). But for a sudden change in rate, the SLRD is only positive when the window includes the change point, and peaks when the window is centered on the change. For a steady rate of acceleration, the SLRD is positive, but constant throughout. In either case, when sea level really does accelerate their method will detect, and even quantify, the change.

There is one danger with their method, a circumstance which can lead to false detection of sea level acceleration. Suppose sea level changes at a constant rate for a while, then makes a brief dip, then recovers to its previous level and resumes its steady change at the same rate as before.

In that case sea level hasn’t really accelerated, but the linear trend over the 2nd half of the window will be more than that over the 1st half, giving a positive value of SLRD. I’ve examined all the station records in the hotspot used by Sallenger et al., and although many of them do show a dip, they all also show a genuine acceleration — so the results of Sallenger et al. are correct.

I took the data since 1950 for all 20 stations in the hotspot, computed anomalies, smoothed them, then subtracted the linear trend line from them to show the departure from a linear trend. Here are all of them, plotted on the same graph:

Most of them do indeed show a dip in the mid-1980s. But they also show genuine accleration, rising faster since about 1990 than they did before that. It’s abundantly clear that yes, sea level rise really did accelerate recently at these stations, so there really is a “hotspot” of sea level rise on the Atlantic coast.

We can also combine the 20 station records into a composite. To that end, I aligned the data using the “Berkeley method,” smoothed the result, and computed a straight-line trend as well. That gives this:

We can also, as before, subtract the linear trend from the smoothed change:

The combined record shows the same essential behavior as the individual records (surprise!), namely, a dip in the mid-1980s and faster rise since about 1990 than before.

We can even take the aligned data and fit a quadratic polynomial, which also illustrates the presence of acceleration. It’s more clearly visible when plotted against annual averages rather than monthly:

This analysis illustrates the behavior of sea level changes in the hotspot, and confirms the results of Sallenger et al. The one thing I haven’t done in this post is any statistical significance testing of the results. But I really don’t need to — Sallenger et al. already did that.

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14 responses to “Hotspot Data

  1. John Brookes

    What confuses me is why Tisdale wouldn’t like Sallenger et al. Its a nice analysis and I can’t see why it would offend the sensibilities of a fake skeptic.

    • my guess, based on Tamino’s last post: because John Droz has said that sea level rise isn’t accelerating, and therefore any papers suggesting otherwise must be attacked.

    • Ahh. Its obvious, isn’t it? You just challenge any serious climate work. It doesn’t really matter what its about, or what conclusions it reaches. All you are trying to do is make people doubt all science, and distrust all scientists.

  2. Martin Smith

    The links to diagrams are all broken for me.

  3. @ Martin – All graphs are visible here on my side of the Internet.
    @ Tamino – Again, beautiful clarity of graphs. I don’t know statistical, but I do know clarity.

  4. Boston may be a particularly bad example. There may have been a station change in 1988, and there was the Big Dig between 1991 and 2007.

    • “Boston may be a particularly bad example. ”

      And yet it seems to follow the same trend as the other 19 sites. What’s your point?

      • My point is that if the Boston is contaminated, possibly others are as well. The east coast has seen a lot of development over the last 60 years, I note a number of gauges are (unsurprisingly) in larger coastal cities. Subsidence is certainly affecting these measurements. And the “hot spot” seems to be variable depending on the measurement and time range. 30 years of tide gauges put the spot mostly from NJ to VA. 20 years of satellite records puts the hottest spot as the CT coastline (get the PDF and zoom in). And the dip that Tamino warns of that affects the results, the AMO is an obvious suspect. If we’re comparing the downside of one cycle of the AMO against the upside of the next with some additional factors, while claims that the current trend is higher than an earlier trend may be correct, it seems premature to worry that this “acceleration” is going to continue.

      • “My point is that if the Boston is contaminated, possibly others are as well. ”

        What exactly do you mean by contamination? The authors appear to have accounted for subsidence (or at least tested possible effects) in the paper. If you are implying that massive urban development is a significant variable, then the 20 sites would vary amongst each other quite a bit, would they not?

      • Looking at Tamino’s graph, the starting departures were mostly 0-25mm with two outliers, and ended with all from 10-45, so the spread of the sites is increasing. Also, the subsidence tests from the paper showed that low subsidence risk sites have a higher mean sea level rise than high risk sites, a somwhat counter-intuitive result. But Boston in particular may be a bad choice since there have been two tunnels installed in Boston Harbor during the study period.
        However, another thing to look at is Figure 3 from the paper. The longest records have little to no sea level rate difference vs 2009, until calculations start from 1940 and later. (Since I had to track it down in the supplemental info, SLRD is the difference in the rate of the first and second half of the series) So it’s only shorter time series, which can be affected by endpoint noise, and are within a single 70yr AMO cycle that are showing the hotspot. Which may also negate my nonlinear subsidence idea.
        Figure 4 shows the hot spot, cold spot, hot spot series of the east coast. There’s nothing to suggest this recent hot spot will continue to exist.

  5. Doesn’t a quadratic fit refute the claim of an increase in the acceleration rate circa 1990? A quadratic trend analyzed using the SLRD method with a constant window size will give a constant SLRD, as shown in your third figure. SLRD will decrease with decreasing window size, though, and I don’t know if/how this is addressed in the paper.

    Your quadratic fit (using the NEH stations) should *also* show some discontinuity at 1990. However, 1989-1991 are well below the fit line rather than some faster-than-quadratic rate law kicking into effect at that point. The residuals appear to be distributed in a way (with data going above, below and above the trendline over time) that’s consistent with an increasing rate of acceleration (or jerk, as you’ve explained before), but probably not in any statistically significant way. This is a lot more consistent with trends of anthropomorphic carbon emissions as well as Northeastern coastal development that might impact tidal magnitude; neither experienced any sort of shift in 1990, but the pace of both has increased over time.

    I said this in the last thread but it’s worth repeating lest I come off as a climate skeptic: this data convincingly demonstrates a rate of sea level increase that guarantees a catastrophic rise within a century this rate is almost certainly increasing and disproportionately impacts areas where about a hundred million people live who should probably start caring about this.

    [Response: The claim made in Sallenger et al. is not “increase of acceleration” or “faster-than-quadratic” — it’s just that the rate in recent decades is faster than that in the preceding decades. The quadratic fit actually confirms that.

    As for the data being sometimes above, sometimes below that curve, that’s consistent with randomness, so I’d be extremely cautious drawing any conclusion without numerical analysis. The eye+brain is just too good at inventing patterns. If you want to draw conclusions from visual inspection, I’d suggest doing so from the other graphs, the ones of smoothed sea level and of smoothed sea level minus linear trend.]

    • “it’s just that the rate in recent decades is faster than that in the preceding decades”

      I didn’t read it that way. Positive SLRD is indicative of acceleration. Increased SLRD is indicative of greater acceleration. Fig. 3 plots how SLRD evolves over time. They see an abrupt increase in SLRD for time windows centered on ~1990, which they interpret as a shift to a regime of greater acceleration in the tidal anomaly time series (a minor point in the paper).

      Regarding residuals, there is an apparent trend going from positive to negative residuals (plot +1/-1 for points above/below trend; smooth a bit). That’s consistent with what you get if you fit, say, x^2.5 with a*x^2. This fails a runs test, but I think it’s more likely than not that the rate of acceleration is increasing. Fig. 3 is evidence of this; I just think it’s likely that the 3 points at end aren’t only harbingers of continued acceleration at that rate but are, to an extent, artifacts of the 1990 dip in tidal anomalies. It’s better evidence since using shorter time windows for more recent data would decrease SLRD if anomalies were increasing quadratically.

      I’m curious why they didn’t use the quadratic analysis in Fig. S4 instead. It gives qualitatively similar results without the midpoint bias introduced by SLRD.

  6. Could you provide a reference for your alignment method? By Berkeley method are your referring to BEST study?

    [Response: See this.]

  7. Why there? How does this info compare to ground water extraction rates?