Sea Level Rise – Acceleration and Trends

This post examines tidal gauge data downloaded from the PSMSL website.  Over varying time periods the sea level rise (SLR) acceleration, linear trend, and 21st century SLR is estimated.  This analysis also adjusts the local reference data derived from the tidal gauges with vertical velocity data from nearby GPS stations to give trends in absolute (geocentric) sea level.

The PSMSL’s “Revised Local Reference” (RLR) Annual data was first imported into the R statistical package.  Next SONEL’s vertical velocity GPS data was used to convert the RLR data into absolute level measures.  It is assumed that the vertical velocity has been constant through out the period.  The GPS data was filtered to only retain the station nearest to the tidal gauge, remove velocities outside of the +/- 3 mm/yr range and remove uncertainties exceeding 1 mm/yr.

Given a date range, the program would select the stations which had at least one data point in each decade.  Stations which were found to have an acceleration outside of the two standard deviation range of the sample were filtered out.  For those stations remaining, an absolute sea level reconstruction was created as follows:

  • For each station, take the difference between the sea levels for adjacent years
  • For each year calculate the average difference
  • Cumulatively sum these differences to create the reconstruction

For each reconstruction, a quadratic regression was performed to estimate the acceleration coefficient and the 21st century SLR.  A separate regression was also performed to estimate the linear trend over the sample period.  Table 1 summarizes the results of this exercise.

Table 1.  Regressed attributes of SLR reconstructions

start year 1900 1900 1920 1993
end year 1999 2015 2015 2015
sample size (# stations) 22 21 37 94
acceleration (mm/yr^2) -0.003 0.002 0.007 0.009
standard error 0.002 0.001 0.002 0.050
linear trend (mm/yr) 1.9 2.1 1.8 2.4
standard error 0.1 0.1 0.1 0.3
est 21st century slr (mm) 120 250 310 320
est 21st century slr (in) 5 10 12 13

The 20th century reconstruction shows a linear trend of 1.9 mm/yr which works out to about 7.5 inches for the period.  This is close to the value reported by the IPCC.  The 1993-2015 trend of 2.4 mm/yr is quite a bit below the University of Colorado’s 3.4 mm/yr trend derived from satellite altimetry.  Perhaps this can be reconciled by my 0.3 mm/yr uncertainty, UoC’s 0.4 mm/yr uncertainty, and UoC’s 0.3 mm/yr GIA adjustment.  It is understood that UoC’s Map of Sea Level Trends shows that SLR is not homogeneous across the world’s oceans.  It is also understood that my reconstruction under samples the coastlines of less developed countries.

Using the data associated with UoC’s Map of Sea Level Trends, I chose the grid point closest to each station in the sample and averaged the trends.  This brought UoC’s trend to within 0.3 mm/yr of my reconstruction.  As the UoC’s data presumably includes 2016 data, I suspect that we might have been even closer if using a common period.  The bottom line is that we are within each other’s error margin.  Note that this UoC data did not include the GIA adjustment.

Below is my sea level reconstruction for the period 1920-2015 and the associated quadratic fit.

Figure 1.


Here are the residuals associated with Figure 1.

Figure 2.


The residuals show an apparent 60 year cycle.  Could this be an artifact from oversampling the Atlantic?  From 1920 to roughly 1980 the residuals have a concave orientation, so the acceleration was slower than the quadratic fit.  From roughly 1960 to 2015 the residual have a convex orientation, so the acceleration was faster than the fit.

I then generated this histogram of the SLR Acceleration.  87 stations were selected from the unadjusted RLR data.  Each station needed at least one data point in each decade and any outside the initial 2 standard deviation range were removed.  The mean acceleration of the sample was 0.007 mm/yr^2 with an s.d. of 0.011 mm/yr^2.  About 30% of the stations had a negative acceleration.

Figure 3.


A similar graph was generated for the period 1900-2015.  This time 47 stations were selected with a mean acceleration of 0.004 mm/yr^2 and an s.d. of 0.005 mm/yr^2.  About 21% of the stations had a negative acceleration.


In my non-expert opinion, the IPCC’s AR5 report was correct in their assessment that 20th century SLR was about 0.17 meters or 7 inches.  I also believe that there is evidence to support a modest acceleration in SLR over the 1900-2015 period.  This, however, can be argued as the 20th century acceleration appears to be a deceleration.  Sensitivity to start and end dates suggests no acceleration.

As for the 21st century, this analysis indicates that the business-as-usual scenario will see an SLR of about a foot, give or take a few inches.  This corresponds to the lower end of the IPCC’s RCP2.6 scenario of declining emissions, where SLR is estimated to be between one and two feet.  Where RCP2.6 is not business-as-usual, the projections are not in agreement.

This issue may be resolved when the apparent cyclical behavior in the residuals is determined to be either a real or a transient phenomenon.  If it is real, then the acceleration will continue to remain modest.  If transient, then a faster acceleration can be expected.  We should know within the next 20 years.


Permanent Service for Mean Sea Level (PSMSL), 2017, “Tide Gauge Data”

Retrieved 12 Jan 2017 from
Simon J. Holgate, Andrew Matthews, Philip L. Woodworth, Lesley J. Rickards, Mark E. Tamisiea, Elizabeth Bradshaw, Peter R. Foden, Kathleen M. Gordon, Svetlana Jevrejeva, and Jeff Pugh (2013) New Data Systems and Products at the Permanent Service for Mean Sea Level. Journal of Coastal Research: Volume 29, Issue 3: pp. 493 – 504. doi:10.2112/JCOASTRES-D-12-00175.1.

SONEL “Absolute (geocentric) Sea Level Trends”

Retrieved 11 Jan 2017 from

CU Sea Level Research Group – Map of Sea Level Trends
Retrieved 11 Jan 2017 from

Code and Data


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