On 20/02/2018 15:08, Alastair wrote:
On Tuesday, 20 February 2018 12:43:52 UTC, N_Cook wrote:
My Jason1 + Jason2 + Jason3 concattenated graphical plot
http://diverse.4mg.com/jason1+2+3r.jpg
2003 to Nov 2017
retaining as much as possible of the 3 separate images, 2mm
discontinuities, linear "fit" segments etc.

Other such long-term plots

http://www.kpress.info/images/Jan_20...level_rise.jpg

https://www.aviso.altimetry.fr/filea... rence_sm.png

Anyone doubt a curve is a better fit than linear, then just a matter of
what sort of curve is the optimal fit.

There is another plot he
https://cires.colorado.edu/council-f...r-steven-nerem
but I am doubtful since parts of the plot show sea level falling.


Especially as he's not stated the source, or even if a composite of
sources, a bit chalk and cheese as the Saral sytem is calibrated against
tide-gauges rather than inland lakes and transponders.
The ends of any of those plots is problematic, until the filters pass
through and the curve can be fixed firmly into the record.
It looks as though that curve has not had the seasonality removed,
unlike the "black" curve on the Aviso/Jason plots I've used, so could
well be showing negative.
Plotting out the 4/3 power curve, I see its highly inflexive , where the
2017 hickup is, so perhaps not valid for later projections, any more
than a quintic curve or summation of sines or whatever.
So the quadratic curve may be the more representative
although a worse fit, but at least the exponential is no longer in first
place.

STOP PRESS
The Aviso site has added another 6 weeks of Jason3 data, starkly upward,
reminiscent of what went on a year ago (a year ago plus 3 months delay
in data output to the public).
Enough to elevate the linear trend from 1.65mm/year to 2.41mm/year.
Unfortunately its a matter of revisiting at least 6 months of
datapoints, due to the way seasonality works forwards and backwards, at
the ends of these plots.
A job for tomorrow.

Updated set of Jason-3 curve-fit results
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 = 1.433052 + 0.333468*x
R^2= 0.977762
RMS Error = 0.247845
projecting into the future
year 2030, 11.437cm SL rise
2050, 18.11cm
2100, 34.78cm

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 = 1.974884 -6.192150*(1-Exp(0.035713*x))
R^2 = 0.981796
RMS Error = 0.226836
projections
2030 , 13.860 cm
2050 , 32.709cm
2100, 2.156 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 = 2.055140 + 0.196003*x + 0.006093*x^2
R^2 = 0.981960
RMS Error = 0.225811
projections
2030, 13.419cm
2050, 27.088cm
2100, 82.585cm

Fractional Indicial, approx 4/3 fractional indicial power
Best fit on R^2 and RMS, and same ranking of Lin,Exp,Quad,Indicial
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)
Update
Still best fit on R^2 and RMS
Y = 2.283709 + 0.097257*x^1.380886
R^2 = 0.982094
RMS Error = 0.224969
2030 , 12.941cm
2050, 23.861cm
2100 , 58.478 cm (23.7cm more than linear , the official standpoint)

I'll update the graphic, with the new fitted curves, same URL

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

later today. With the new scaling of the J-3 output, the superimposed
legends around the J-3 component might be a bit clearer .
Also I'll revisit the Jason2 data from what it was in 2016, when the
previous serious upshoot/overshoot occured. Add the J-1 data and run the
curve-fits for the then data, and also the now fixed data for that
period. Because of the 2 steps forward , one step back and vice-versa
business, to better gauge what the effect of the "recent" data becomes
in a years time, especially for the exponential century-projected situation.
Also I'll revisit the ENSO compensator and GRAVE weighing Greenland from
space data, to see how the end of 2017 situation compares with 2016
situation.

On 20/02/2018 12:43, N_Cook wrote:
My Jason1 +Â* Jason2 + Jason3 concattenated graphical plot
http://diverse.4mg.com/jason1+2+3r.jpg
2003 to Nov 2017
retaining as much as possible of the 3 separate images, 2mm
discontinuities, linear "fit" segments etc.

Other such long-term plots

http://www.kpress.info/images/Jan_20...level_rise.jpg

https://www.aviso.altimetry.fr/filea... rence_sm.png

Anyone doubt a curve is a better fit than linear, then just a matter of
what sort of curve is the optimal fit.

A curve might well be a (slightly) better fit, but I am not convinced
the data are strong enough to merit fitting an extra free parameter.

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

I am curious as to why Jason1 data is smooth but Jason2 has a distinct
sinusoidal variation with a 3 year period. There is some weak evidence
for a change in slope but it is just within the noise. More recent data
seeming to have quite a lot more of it than earlier in the decade.

--
Regards,
Martin Brown

On 21/02/2018 09:15, Martin Brown wrote:
On 20/02/2018 12:43, N_Cook wrote:
My Jason1 + Jason2 + Jason3 concattenated graphical plot
http://diverse.4mg.com/jason1+2+3r.jpg
2003 to Nov 2017
retaining as much as possible of the 3 separate images, 2mm
discontinuities, linear "fit" segments etc.

Other such long-term plots

http://www.kpress.info/images/Jan_20...level_rise.jpg

https://www.aviso.altimetry.fr/filea... rence_sm.png

Anyone doubt a curve is a better fit than linear, then just a matter
of what sort of curve is the optimal fit.

A curve might well be a (slightly) better fit, but I am not convinced
the data are strong enough to merit fitting an extra free parameter.

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

I am curious as to why Jason1 data is smooth but Jason2 has a distinct
sinusoidal variation with a 3 year period. There is some weak evidence
for a change in slope but it is just within the noise. More recent data
seeming to have quite a lot more of it than earlier in the decade.


Part of the picture, beyond annual seasonality, may be
http://polarportal.dk/en/greenland/m...height-change/
and a conversion factor of 458 GigaTons Greenland ice loss equates to
1.45mm of global sea level rise

The other is ENSO which may be on
https://www.esrl.noaa.gov/psd/enso
but I cannot view it on this pc, and I've no idea how old the data is,
but basically invert and delay a few months, superimposed on the
altimetry plots.

Ignore the latest curve-fits and the new uploaded plot.
Only when looking at it, thought that does not look right.
I'd got the right input data for the curve-fitter but I'd typed the
wrong number of datapoints in , so it was running with an incomplete
data set, revisiting it all tomorrow.

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

Fractional Indicial,
Best fit on R^2 and RMS, ranking linear, exp, quad, indicial
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)
Updated best fit on
Y = 2.317755 + 0.089566*x^1.408787
R^2 = 0.981838
RMS Error = 0.228446
2030 , 13.106cm
2050, 24.481cm
2100 , 61.164cm (26.181cm more than linear , the official standpoint)

The second down image shows
http://diverse.4mg.com/jason2+enso_overlay2.jpg
the overshoot end of 2016, artifact of the filter or whatever, no longer
present in that period of the J3 plot.
Also a graphical interpretation of shifting and comparing the ENSO plot.

Jason2 , some spot data as outputted 24 Apr 2017, up to Jan 19, 2017, as
in that above image
2016.5, 7.32cm
2016.75, 7.17
2016.997, 7.61
2017.052, 7.71

Jason3, revisiting the same period
2016.5, 7.13cm, -0.19
2016.75, 6.97 , -0.2
2016.997, 6.95, -0.66
2017.052, 6.86, -0.85
note the 2mm long-term apparent offset betwen J2
and J3

So curvefitting on J3 adjusted downwards for end of 2017, the same same
degree as end of 2016, nullifying the "recent" sharp upswing
Y= 2.211603 + 0.114799*x^1.324879
2030, 12.609cm
2050, 22.669cm
2100, 54.462cm

compared with
as-is without reducing the perhaps overshoot end of 2017
Y = 2.317755 + 0.089566*x^1.408787
2030 , 13.106cm
2050, 24.481cm
2100 , 61.164cm

So best guess projection to 2100 is between 54cm and 61cm global
sea-level rise. So little difference in the fis of the different
curve-types, maybe the next J3 output, the indicial curve will be
surplanted.

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=Â* 0.978086
RMS Error =Â* 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=Â* 0.976966
RMS Error =Â* 0.254395
gradient gives the linear MSL rise of 3.357 mm / year
projecting into the future
year 2030,Â* 11.485cm SL rise
2050, 18.199 cm
2100, 34.983cm

Exponential
Y = 1.948854 -6.880730*(1-Exp(0.033013*x))
R^2 =Â* 0.981571
RMS Error =Â* 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 =Â* 0.981615
RMS Error =Â* 0.229845
projections
2030 ,Â*Â* 14.153cm
2050 ,Â* 34.771cm
2100,Â* 2.605 metres

Quadratic
Y = 2.023609 + 0.204265*x + 0.005656*x^2
R^2 =Â* 0.981740
RMS Error =Â* 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 =Â* 0.981759
RMS Error =Â* 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

But a workable engineering approximation would be

-0.6 +0.15*T -0.0009*T^2

--
Regards,
Martin Brown

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

But a workable engineering approximation would be

-0.6 +0.15*T -0.0009*T^2


I'd not considered that despite thermal expansion of ocean-water is the
priincipal component of MSL rise. Very small number differences but over
huge volumes of course. Just the other little known fact that melting
ice-shelves and ice-bergs , do have an effect on global sea-level rise.
Usually its considered, Archimedes fashion , to have no effect. Because
of the salinity/density variation, by memory its of the order of 1%, for
a given block of "berg", but with small country size bergs breaking off,
it is another minor constituent, along with ENSO and reducing "weight"
of Greenland.
I'm presently segmentally skewing the Jason1+2+3 plot , to flatten the
curve-fit consensus line in effect, to hover transparently when
recombined, over the latest ENSO multivariate curve.