"Hotspot of accelerated sea-level rise on the Atlantic coast of North America" - final reality check

Last year I shredded the Sallenger et al. paper "Hotspot of accelerated sea-level rise on the Atlantic coast of North America" here. Now, with updated CGPS data from SONEL, I can finally place the headstone on its grave. South of Boston, the coast is subsiding, and subsiding at a generally increasing rate all the way south to Florida. Sandy Hook, a rather inconsequential spot, which all boat traffic in and out of New York harbour pass with barely a glance, had the honour of being one of the few sites along the NW coast with published GPS data. I say had, because SONEL has carried out a massive update of sites worldwide, adding fairly up-to-date data to many. Sandy Hook now has a downloadable record from 1995 to 2013. The record shows that the downward rate has been increasing from less than 2 mm/year in the late 1990s to over 3 mm/year in the three years 2011-2013. I've used the entire record for station SHK5, 2007-2013, which plots at -2.57 mm/year. The SONEL analysis shows -2.65 mm/year, but I've taken account of a few short-term gaps in the data; I assume they didn't. Here's the SONEL plot:

And mine:

Sandy Hook 1993-2015 (Sea-level satellite era):

The relative rate (relative to the tide-gauge/land) is 5.36 mm/year. Absolute rate (relative to the Earth/Geoid) is 2.79 mm/year. The subsidence rate is almost half the relative rate.

The SONEL plot for New York Battery Park, where both tide-gauge and GPS pillar are located:

The rate during the late 1990s was around -1 mm/year. My analysis:

The chart for New York (Battery Park) 1993-2015:

Relative rate is 3.92 mm/year; absolute rate, allowing for subsidence of 1.93 mm/year is 1.99. The "Hotspot" isn't one of sea-level rise, but one of subsidence. Sallenger et al. were also being somewhat disingenuous when they claimed that the rates of subsidence along the coast "were almost constant", and therefore didn't affect their complex analysis or results. They weren't constant when the paper was written, and the rates are generally increasing over the last 20 years; some very little, some like New York and Sandy Hook, significantly increasing. The "Hotspot" was an artefact of questionable and almost impenetrable analysis, ignoring the inconvenient past, and coastal subsidence.

Note also the obvious cycles which appeared in the record after 1970 - large and small alternating. Sallenger et al. used PSMSL annual average data, and so they wouldn't have been obvious. Take some data and torture it using complex and (to me, impenetrable) statistical techniques I imagine most sea-level experts and authors couldn't fathom, and get the answer you want. What I do know is that those techniques aren't suited to relatively small datasets, which is what you have if you use annual average data. Also PSMSL omit years from annual data, even if just one month is missing. The annual data Sallenger et al. used had quite a few years missing, shrinking their database even further.

Something else Sallenger et al. failed to mention is that a comparable rate of rise occurred before the mid-1950s. Somehow their "long-term" analysis wasn't quite that long:

Trend, in mm/year for 30-year sliding window, end year on x-axis.

The red circle marks 2009, the end year for the "Hot-spot" analysis. It's easy to see the rate of increase was much higher prior to 1953. If the whole record shows an inconvenient truth, just analyse part of it.