On 23/02/2018 12:27, Martin Brown wrote:
On 21/02/2018 21:39, N_Cook wrote:
Updated corrected set of Jason-3 curve-fit results including the
latest data from 17 December 2017, previous data outputed up to 2017.911,
associated plot

http://diverse.4mg.com/jason1+2+3r.jpg

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
Update for extra 6 weeks of data, to 17 Dec 2017
Y = 1.414689 + 0.335684*x
R^2= 0.976966
RMS Error = 0.254395
gradient gives the linear MSL rise of 3.357 mm / year
projecting into the future
year 2030, 11.485cm SL rise
2050, 18.199 cm
2100, 34.983cm

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
2100, 1.819 metres
update
Y = 2.002894 -5.56543*(1-Exp(0.038595*x))
R^2 = 0.981615
RMS Error = 0.229845
projections
2030 , 14.153cm
2050 , 34.771cm
2100, 2.605 metres

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
2100, 79.010cm
Update
Y = 2.088926 + 0.187200*x + 0.006555*x^2
R^2 = 0.981759
RMS Error = 0.228941
projections
2030, 13.604cm
2050, 27.836cm
2100, 86.359cm


It is worth noting on physical grounds that since the coefficient of
expansion of water is not a constant but varies almost linearly with
temperature you would expect there to be some second order polynomial
like behaviour in the ocean expansion and sea level rise.

Temperature Density (0-100°C at 1 atm, 100 °C at saturation pressure)
Specific weight Thermal expansion coefficient of liquid water

[°C] [g/cm3] [*10- 4 K-1]
0.1 0.9998495 -0.68
1 0.9999017 -0.50
4 0.9999749 0.003
10 0.9997000 0.88
15 0.9991026 1.51
20 0.9982067 2.07
25 0.9970470 2.57
30 0.9956488 3.03
35 0.9940326 3.45
40 0.9922152 3.84
45 0.99021 4.20
50 0.98804 4.54
55 0.98569 4.86
60 0.98320 5.16

Taken from https:
//www.engineeringtoolbox.com/water-density-specific-weight-d_595.html

I get the best fit to its properties as a cubic (almost exact)

-0.671+0.17114*T-0.00192*T^2+0.0001*T^3



I decided to limit to 20 deg C tops, using your figures and got very similar
-0.691901 +0.186743*T -0.003414*T^2 +0.000049*T^3
(R^2= 0.999978 RMS Err= 0.008323)

So I'll try a cubic curve-fit on the J1+2+3 data