Between a Rock and a Wet Place - The USGS Creates a Hockey-stick

The journal Nature Climate Change published a paper (pdf here, supplemental information & figures here) by US Geological Survey authors a few days ago. Titled "Hotspot of accelerated sea-level rise on the Atlantic coast of North America", it seeks to show that a "hot-spot" of higher (than global, and elsewhere in the US) sea-level rise exists on the north-eastern seaboard of the US. In their introduction, they say

Here, we present evidence of recently accelerated SLR in a unique 1,000-km-long hotspot on the highly populated North American Atlantic coast north of Cape Hatteras and show that it is consistent with a modelled fingerprint of dynamic SLR. Between 1950–1979 and 1980–2009, SLR rate increases in this northeast hotspot were ~ 3–4 times higher than the global average.

Wow - 3–4 times higher than the global average? That merits critical examination. The authors used what they termed "windows" of 60, 50, and 40 years ending in 2009, calculating trends for two halves of each window. While between 40 and 60 years would seem adequately long for trend calculations, bear in mind they split each window into two. This means that for the 40-year window they used two periods of 20 years, and they used annual data, so they produced trends using just 20 data-points for each period. in the supplement linked above, they used New York (headline-grabbing? - perish the thought) to illustrate their technique.

Notice that their quadratic trend (dashed) curve plots a convincing trail through the scattered (annual  average) data points. Note also, that neither trend line is a tangent to the convincing quadratic trend. Notice that the trend lines don't abut one another. Notice that the green 1980-2009 trend line represents a period with three low data points (1980-1982) at the start. These observations convince me that the linear trend differences are statistical artefacts, don't represent a true picture, and don't support the assertion of a large trend increase. Lets look at a few real graphs, with some real, long-term trends.

The trend for the 1950-2009 "window" used in this study is almost identical to the long-term 1856-2011 trend. Since the authors chose to use low-resolution annual averages, a peek at the 1950-2009 annual averages wouldn't go amiss.

It's immediately obvious that the 1980 "break point" is in a dip in the plot, as is the 1990 "break point". Both are flanked by higher data points. The claimed large increase in trend is an artefact of the start points for the second-half of each "window". There is a slight acceleration, but it's a fraction of that claimed. All the gauges used in the study show this feature, as do gauges well outside the claimed "hot spot".

There's a statistically robust method of analysing changes in trend for time series, called "asymptotic analysis". I've used it previously to demonstrate how variation in long-term trends evolve, can be analysed, and conclusions drawn. I've plotted the trend for new York from 1893 (after the big gap) to end points from 1950 (the start of the 60-year "window") to 2009 (the end of the "window"), using annual averages.

If there was a true "breakpoint" in the trend around 1980 marking a significant increase, I'd expect to see a distinct break in slope of this plot. Instead, the rate continues to drop, stabilising in 1990. That's where the breakpoint is, though it's not of any great significance compared with what's claimed. There's a slight rise to 1998 associated with the 1997/8 El Niño, after that the trend is almost constant to 2009. Peak trend was reached in 1973, dropping through 1980 and for a few years later. The pre/post 1980 "break" in trend is an artefact of the dip in sea level around that point. The paper contains a rather strange statement:

South of Cape Hatteras, SLRDs are not statistically different from zero (mean SLRDs=0.11±0.92 mm yr−1), whereas north of Boston, SLRDs are either negative or not different from zero (mean=−0.94±0.88 mm yr−1). The 40-yr window (1970–2009) exhibits the largest mean NEH SLRD (3.80±1.06 mm yr−1), and positive differences continue north of Massachusetts and into Canada

If SLRDs (sea-level rate differences) north of Boston (Massachusetts) are either negative or not different from zero, how is it that positive differences continue north of Massachusetts and into Canada? The two sentences are mutually exclusive. This will bear further investigation, which I intend to continue.

There's no analysis of vertical land movement (measured using GPS) in this paper, somewhat surprising for the US Geological Survey? If such movement contributes significantly to local sea-level rise, and recent short-term data indicates that it does, then extrapolating a 30-year trend forward to 2100 is unsafe and unjustified, as there's no way of predicting such movement over that period.

There's no sign of a break in trend around 1980 which would confirm the claims in this USGS paper, and the post-1990 increase is moderate. No "hockey-stick", no "blade", just a handle, and a lot of (to my mind) superfluous maths.