That reminds me I must get back to
https://www.aviso.altimetry.fr/en/da...sea-level.html

unfortunately the Jason-2 satellite had to have its orbit shifted
outwards and public outputting of data has still not recommenced, but it
looks as though Jason-3 output now has enough output to concattenate to
the previous Jason2 data, seemingly compatible.
As it stood before abandoning that curve-fitting.
For Aviso/Jason-2 data as of 20 Dec 2016, public access 13 March 2017,
from a suite of a few hundred curve types to try, the best R^20.998
fit was for exponential curve type (soon gets alarming not so far into
this century)
Aviso plot (y cm as in Aviso plots and scaling, and years where x=0 for
year 2000)
y=2.1465 - (2.00209)*(1 - e^(+0.07779*x))

The situation has apparently improved since end of 2016, all those nasty
El-Nino effects etc producing a very bumpy plot, ie not so steeply
exponential.

Tide gauges also problematic as they may as well be mounted on a
water-bed , as the ground is not fixed. Currents and gyres , salinity
etc change in the oceans , also , upsetting local land-bordering
mean-sea levels.
From BODC data for Lerwick , between 1957 and 1999 mean sea level has
only risen 30 mm relative to their rising land , isostatic rebound
there. But for Portsmouth between 1962 and 2002 , sea level relative to
sinking Portsmouth then 170mm a rise (contra-rebound to compensate for
rising Scotland).

May as well add a link, as relevant.
An expert on this stuff , next month Southampton, giving a talk in the
open-to-public series of science talks I run
http://www.diverse.ip3.co.uk/scicaf.htm

Ignoring the first and last six months of Jason 1,2 and 3 plots,
scaling, hovering transparent at the joins. The central parts of the
overlap curves agree, but with a vertical displacement of about 2mm .
Seems odd querying 2mm when dealing with the slippery commodity that is
sea level. From one of the team on the Jason project, they use
land-locked lakes like Windermere in Cumbria, other such lakes around
the world and also active transponders they can place anywhere before
overpasses, for calibrating and therefore cross-calibrating different
satellite outputs. So I assume the end result is that there is smooth
transition in the outputted results from J1 to J3 and the jumps have
some technical justification. Anyway concattenating the 3 plots from
the Aviso site , ignoring the transistion steps , continous from 2003 to
end 2017 and 46 datapoints for curve-fitting .
At least exponential is no longer the best fit in the rankings from
Linear, Exponential, Quadratic and Fractional Indicial, any other
curve-type suggestions?
Linear
Y= cm of sea-level as per Aviso output and x=0 for year 2000
Y = 1.446098 + 0.331877*x
R^2= 0.978086
RMS Error = 0.244821
projecting into the future
year 2030 11.402 cm SL rise
2050 18.04 cm
2100 34.63cm

Exponential
Y = 1.948854 -6.880730*(1-Exp(0.033013*x))

R^2 = 0.981571
RMS Error = 0.227110
projections
2030 13.593 cm
2050 30.919 cm

Quadratic
Y = 2.023609 + 0.204265*x + 0.005656*x^2
R^2 = 0.981740
RMS Error = 0.226064
projections
2030 13.242cm
2050 26.377cm

Indicial, approx 4/3 fractional indicial power
Best fit on R^2 and RMS
Y = 2.252107 + 0.104773*x^1.355666

R^2 = 0.981919
RMS Error = 0.224954
2030 13.058cm
2050 23.313 cm
2100 , 56.15 cm (21.5cm more than linear , the official standpoint)

Then staying with indicial curve type , chopping off later data and
curve-fitting for an idea of trend over time.
The fractional index to near end of 2017 ,1.355666
to mid 2017 , 1.378523
to 2017.0 , 1.571937
to 2016.0 , 1.730158
to 2015.0, 1.449256
to 2014.0, 1.428276
so knocked back from the year 2016, when things looked to be going fully
exponential.