Acceleration in the rate of sea level rise

Some people are looking at sea level data and trying to fit a quadratic time curve to find the alleged acceleration in the rate of rise of sea level.   This doesn't work, and so they are very skeptical that the rate of rise of sea level has accelerated over the last century.

IMO, really they should be looking for piecewise linear fits, and a change in slope of the line segments. The point is that acceleration is simply a change in a rate; and nobody has claimed a constant acceleration in the rate of sea level rise. The rate of sea level rise has changed.

E.g., using data and the graphing utility at sealevel.info, here are three graphs.

Here is sea level data at Delfiziji, Netherlands from January1865 to December 2015.  The fitted line has a slope of 1.72 +/- 0.14 mm/year.

1/1865 - 12/2015 - 1.72 +/- 0.14 mm/yr

The web page also gives this:

Regressions 
Linear:
  y = B + M·x
  y = 6797.353 + 1.716·x mm 
Quadratic:
  y = B' + M·x + A·x²
  y = 6784.346 + 1.716·x + 0.00685·x² mm 
where:
  Date range = 1865/1 to 2015/12
  x = (date - 1940.46)  (i.e., 1940/6)
  slope = M = 1.716 ±0.141 mm/yr
  acceleration = 2·A = 2×0.00685 = 0.01369 ±0.00722 mm/yr²

The posited constant acceleration is there, but extremely tiny and buried in the noise.

We now break the time series into two periods of about 75 years each, from January 1865 to December 1940; and January 1941 to December 2015.
The first period has the sea level rising at 1.31 +/- 0.37 mm/year.
The second period has the sea level rising at 2.25 +/- 0.43 mm/year.

Note that the confidence intervals don't overlap (i.e., 1.31 + 0.37 = 1.68; 2.25 - 0.43 = 1.82).
The rate of sea level rise has increased, ergo, accelerated.

1/1865-12/1940 - 1.31 +/- 0.37 mm/yr

1/1941 - 12/2015 - 2.25 +/- 0.43 mm/yr