On 20/01/2019 21:49, Martin Brown wrote:
It should *always* converge - which numerical package are you using to
solve it? Matlab and Excel are certainly not up to the task (although
the chart fitting routine probably will be at least for a cubic).

At one point during the Excel 2007 roll out Mickeysoft wrecked the
previously good polynomial chart fitting routine by making it agree with
the broken but generally accepted as OK in engineering circles Matlab.
It was fixed although I haven't tested the latest versions.

You can improve the condition number of the matrix problem for
polynomial fits enormously by rescaling your time axis so that the
entire x axis runs from -1 to 1. After that you need to fit Chebeshev
polynomials which are virtually orthogonal on equally spaced data.

The www curve fit site must remain undisclosed as a minor site, at the
moment, free-access, allows 70 datapoints, 6 dependent and 4
independent variables and no apparent iteration limit and apparently no
over-use lockout. If more contention, who knows.
It did not like 4 parameters and that function, it was ok with 4
previously, so trying c=1 and 3 parameters, converged on
(1.835379+ 0.233802*x)/(1 -0.106677*x)
and R^2 goodness better than linear but worse than exponential.

year Sea Level Rise (cm)
2030 13.014
2040 19.514
2050 28.986
2060 44.073
2070 71.869
2080 140.124
2090 573.325
2100 -377.624

swapping out parameters c and d and redoing as 3 parameters made no
significant improvement. I'd previously tried balancing out the x-axis
for cubic and quartic functions, but either no convergence or badly
behaved like this recent one , when going beyond the 2003 to 2019 input
range,out to 2100.

On Friday, 18 January 2019 19:43:09 UTC, N_Cook wrote:
On 18/01/2019 19:01, JGD wrote:
On 18/01/2019 17:05, N_Cook wrote:

Oceanographers seem to be comfortable with quoting IPCC projections for
SLR to 2100 but at the same time will only fit a straight line to the
Jason data.

I'm afraid that there's a reason for that, which is that they are
scientists. And a good scientist should never (and usually will never)
try to fit an arbitrary curve to a set of data, especially so when very
considerable extrapolation is involved (which is inevitably the case
when trying to forecast 80 years into the future).

The only pragmatic answer available is to use the most conservative of
assumptions or tools, which in this case is limited to a linear trend.

Obviously this creates a major headache for climate change predictions,
but the only way out is to base the curve-fitting on some sort of
defined model, which will take account of parameters like thermal
expansion of the oceans, estimated melting of land ice (insofar as it
can even be estimated roughly), and so on. I presume that there are
interdiscplinary teams that can try to put this sort of model together
and I'd guess that there this must have been happening already for a few
years. So the embryonic models must be out there somewhere in the
oceanographic literature.

But please, please, please let's not fit arbitrary functions,
exponential or otherwise, to a set of data and pretend that
extrapolation of such curves way into the future means anything at all.


Have you seen the IPCC predictions?
Well above the linear "fit" of 3.34mm per year.
I hope you can admit , that to reach such IPCC predictions, there must
be some sort of up-curve at some point.
Where is the evidence this deviation from the current "scientific"
straight line would be as late as 2080 or 2060 say , it has to happen
sometime, what is wrong in putting it where there is some evidence of
curving upwards, ie before 2020.

Nick,

There is a paper here that you might find interesting: Evolution of 21st Century Sea-level Rise Projections

https://www.researchgate.net/publica...se_Projections

If the link does not work let me know.

Nick,

There is a paper here that you might find interesting: Evolution of 21st Century Sea-level Rise Projections

https://www.researchgate.net/publica...se_Projections

If the link does not work let me know.



I like the final line,

" As awareness grows that other aspects of the climate system
may be characterized by deep uncertainty as well (e.g., Lenton
et al., 2008), examples of how the SLR and coastal risk
communities have integrated different types of information and
projection approaches over time may prove instructive. "

I'd not found that paper using "meta study" (term for medical multiple
comparison papers only?) as they seemed to have used the
odd term "evolution". Interesting to get a wider handle to my analysis ,
assuming it has some validity.
From their assessed papers of 2016/17/18 only, of Table S1, and taking
my best fit , so far, middle projected SLR of +0.55m on 2000 global
level to 2100.
2016
RCP4.5
4.5
4.5
4.5
2deg C above pre-industrial warming
2017
2.6
2
RCP8.5
between RCP 4.5 and 6.0
2.6
8.5
between 6.0 and 8.5
between 2.6 and 4.5
intermediate low emission
450ppm stabilisation
2.6
2018
1.5 deg APIW
unquantifiable
2 deg


Averaging the quantifiable ones of that lot , giving about 0.55m as
their central estimate , something like 3.9 deg C.

As gov.usa still kaput and no NOAA ENSO update on
https://origin.cpc.ncep.noaa.gov/pro...uff/ONI_v5.php
El Nino defined there as 3 consecutive rolling 3 month means, above +0.5
deg C anomaly of SST
for declared El Nino 3.4 sector/sea area 120 to 165 deg ,+/-5 deg
latitude, processed from the twice weekly NOAA global image , by colour
binned pixel counting, a few spot values
NOAA ENSO , last full SepOctNov Quarter, +0.7
2018 Julian day 358, ENSO value +0.8
361, +0.8
365, +0.75

2019
JD 14, +0.75
17, +0.63
21, +0.41
Despite the tail-off in January, the running 3 month mean for NDJ
quarter will probably above the qualifying value of 0.5

On 23/01/2019 19:21, N_Cook wrote:
From their assessed papers of 2016/17/18 only, of Table S1, and taking
my best fit , so far, middle projected SLR of +0.55m on 2000 global
level to 2100.
2016
RCP4.5
4.5
4.5
4.5
2deg C above pre-industrial warming
2017
2.6
2
RCP8.5
between RCP 4.5 and 6.0
2.6
8.5
between 6.0 and 8.5
between 2.6 and 4.5
intermediate low emission
450ppm stabilisation
2.6
2018
1.5 deg APIW
unquantifiable
2 deg


Averaging the quantifiable ones of that lot , giving about 0.55m as
their central estimate , something like 3.9 deg C.

I'd overlooked their conversion table S2, so a correction, simple mean
of the latest 18 papers, comes out at 2.3 deg C above pre-industrial
warming.

Latest projection for global sea level rise , from Jason 3 data
to 29 Nov 2018, public output 02 Feb 2019 on

https://www.aviso.altimetry.fr/en/da...ts-images.html

via best (RMS optimisation) curve-types and curve-fit of 73 datapoints
concattenated to Jason2 and Jason3 data back to 2003.

I suspect the Aviso reference rise of 3.34mm per year has not been
updated (3.34 previous value) as I make the linear slope 0.3377 cm /yr
or 3.37 mm per year and previous
update calculations have come out near enough the same to +/-0.01 mm per
year, nothing like 0.03/0.04 mm . Considering the Jason-3 filtered
(dotted line) output plot is above 8cm for the first time.

Linear
y= 1.394804 + 0.337655 * x
R^2 = 0.983013
year Sea Level Rise (cm)
2020 8.147
2050 18.277
2100 35.16

Exponential
y= 1.925352 -7.599908*(1-e^(0.030612 * x))
R^2 = 0.986048
year Sea Level Rise (cm)
2020 8.343
2050 29.444
2100 156.607

Quadratic
y= 1.996267 + 0.211446*x + 0.005277*x^2
R^2 = 0.986157
year Sea Level Rise (cm)
2020 8.335
2050 25.761
2100 75.91

Indicial
y=2.238733 + 0.108241*x^1.344403
R^2 = 0.986287
year Sea Level Rise (cm)
2020 8.313
2050 23.059
2100 55.107


Upward trend still, for the best curve-fit by R*R goodness factor, by
only a whisker from the quadratic fit.

Resume of these projections from the Aviso Jason3 updates concattenated
to the Jason 1 and Jason 2 data,
for the best-fit of indicial power curves and global sea level rise for
the rest of the century, based purely on the Jason altimetry data .

to year 2100 using Dec 2017 data , 56.15 cm
data to 05 Feb 2018 to 2100 , 60.7 cm
data to 25 May 2018 to 2100 , 52.1 cm
data to 02 Aug 2018 to 2100 , 49.1 cm
Update to 01 Sep 2018, public output 07 Dec 2018
to year 2100 , 50.7 cm
Update to 01 Oct 2018, public output 18 Jan 2019
to year 2100 , 50.9 cm
Update to 29 Nov 2018, public output 02 Feb 2019
to year 2100 , 55.1 cm

So between 49.1cm and 60.7cm SLR to 2100. Well above the 35.2cm of
linear "fit".

Also evidence of the emergence in the Pacific (and so upward global sea
level) of the next
El Nino. Anomaly in degrees C for Nino 3.4 sector/sea area 120 to 165
deg ,+/-5 deg latitude, processed from the NOAA global SST anomaly image.
https://www.ospo.noaa.gov/data/sst/a....1.31.2019.gif
A few spot values in Jan 2019
Day ; SST anomaly
14 ; +0.75
17 ; +0.63
21; +0.41
24; +0.34
28; +0.36
31; +0.69
Despite the dip late January, the running 3 month mean for NDJ quarter
is probably above the qualifying value of 0.5 , NOAA processed for SON
quarter +0.7 , and OND quarter +0.9 .
https://origin.cpc.ncep.noaa.gov/pro...uff/ONI_v5.php

On 02/02/2019 14:19, N_Cook wrote:
Latest projection for global sea level rise , from Jason 3 data
to 29 Nov 2018, public output 02 Feb 2019 on

https://www.aviso.altimetry.fr/en/da...ts-images.html


via best (RMS optimisation) curve-types and curve-fit of 73 datapoints
concattenated to Jason2 and Jason3 data back to 2003.

I suspect the Aviso reference rise of 3.34mm per year has not been
updated (3.34 previous value) as I make the linear slope 0.3377 cm /yr
or 3.37 mm per year and previous
update calculations have come out near enough the same to +/-0.01 mm per
year, nothing like 0.03/0.04 mm . Considering the Jason-3 filtered
(dotted line) output plot is above 8cm for the first time.

Linear
y= 1.394804 + 0.337655 * x
R^2 = 0.983013
year Sea Level Rise (cm)
2020 8.147
2050 18.277
2100 35.16

Exponential
y= 1.925352 -7.599908*(1-e^(0.030612 * x))
R^2 = 0.986048
year Sea Level Rise (cm)
2020 8.343
2050 29.444
2100 156.607

Quadratic
y= 1.996267 + 0.211446*x + 0.005277*x^2
R^2 = 0.986157
year Sea Level Rise (cm)
2020 8.335
2050 25.761
2100 75.91

Indicial
y=2.238733 + 0.108241*x^1.344403
R^2 = 0.986287
year Sea Level Rise (cm)
2020 8.313
2050 23.059
2100 55.107


Upward trend still, for the best curve-fit by R*R goodness factor, by
only a whisker from the quadratic fit.

Resume of these projections from the Aviso Jason3 updates concattenated
to the Jason 1 and Jason 2 data,
for the best-fit of indicial power curves and global sea level rise for
the rest of the century, based purely on the Jason altimetry data .

to year 2100 using Dec 2017 data , 56.15 cm
data to 05 Feb 2018 to 2100 , 60.7 cm
data to 25 May 2018 to 2100 , 52.1 cm
data to 02 Aug 2018 to 2100 , 49.1 cm
Update to 01 Sep 2018, public output 07 Dec 2018
to year 2100 , 50.7 cm
Update to 01 Oct 2018, public output 18 Jan 2019
to year 2100 , 50.9 cm
Update to 29 Nov 2018, public output 02 Feb 2019
to year 2100 , 55.1 cm

So between 49.1cm and 60.7cm SLR to 2100. Well above the 35.2cm of
linear "fit".

Also evidence of the emergence in the Pacific (and so upward global sea
level) of the next
El Nino. Anomaly in degrees C for Nino 3.4 sector/sea area 120 to 165
deg ,+/-5 deg latitude, processed from the NOAA global SST anomaly image.
https://www.ospo.noaa.gov/data/sst/a....1.31.2019.gif
A few spot values in Jan 2019
Day ; SST anomaly
14 ; +0.75
17 ; +0.63
21; +0.41
24; +0.34
28; +0.36
31; +0.69
Despite the dip late January, the running 3 month mean for NDJ quarter
is probably above the qualifying value of 0.5 , NOAA processed for SON
quarter +0.7 , and OND quarter +0.9 .
https://origin.cpc.ncep.noaa.gov/pro...uff/ONI_v5.php






An updated image of Jason 1 +2 +3 data and image masques to the same
scale , showing linear "fit" and best fit curve, even to the eye a
better fit, visualising balancing of the excursions either side of the
curve.

http://diverse.4mg.com/jason1+2+3_29nov2018.jpg

shame about to the disjunctures between them, but the x,y axes are the
Jason 1 image ones extended on to 8cm and 2020.
For the disjunctures, with no other info about the filters, a matter of
avoiding the last or first 6 months of a mission, compare with the Aviso
Reference image and check the slope of a linear "fit" near enough agrees
with the reference slope , being aware that theirs also includes the
early T/P mission , which I've not included in all this.
Not included the exponential or quadratic curves as only 3 pixels
different at 2010. The original blue gradient lines retained of the 3
images.

On 04/02/2019 14:16, N_Cook wrote:
On 02/02/2019 14:19, N_Cook wrote:
Latest projection for global sea level rise , from Jason 3 data
to 29 Nov 2018, public output 02 Feb 2019 on

https://www.aviso.altimetry.fr/en/da...ts-images.html



via best (RMS optimisation) curve-types and curve-fit of 73 datapoints
concattenated to Jason2 and Jason3 data back to 2003.

I suspect the Aviso reference rise of 3.34mm per year has not been
updated (3.34 previous value) as I make the linear slope 0.3377 cm /yr
or 3.37 mm per year and previous
update calculations have come out near enough the same to +/-0.01 mm per
year, nothing like 0.03/0.04 mm . Considering the Jason-3 filtered
(dotted line) output plot is above 8cm for the first time.

Linear
y= 1.394804 + 0.337655 * x
R^2 = 0.983013
year Sea Level Rise (cm)
2020 8.147
2050 18.277
2100 35.16

Exponential
y= 1.925352 -7.599908*(1-e^(0.030612 * x))
R^2 = 0.986048
year Sea Level Rise (cm)
2020 8.343
2050 29.444
2100 156.607

Quadratic
y= 1.996267 + 0.211446*x + 0.005277*x^2
R^2 = 0.986157
year Sea Level Rise (cm)
2020 8.335
2050 25.761
2100 75.91

Indicial
y=2.238733 + 0.108241*x^1.344403
R^2 = 0.986287
year Sea Level Rise (cm)
2020 8.313
2050 23.059
2100 55.107


Upward trend still, for the best curve-fit by R*R goodness factor, by
only a whisker from the quadratic fit.

Resume of these projections from the Aviso Jason3 updates concattenated
to the Jason 1 and Jason 2 data,
for the best-fit of indicial power curves and global sea level rise for
the rest of the century, based purely on the Jason altimetry data .

to year 2100 using Dec 2017 data , 56.15 cm
data to 05 Feb 2018 to 2100 , 60.7 cm
data to 25 May 2018 to 2100 , 52.1 cm
data to 02 Aug 2018 to 2100 , 49.1 cm
Update to 01 Sep 2018, public output 07 Dec 2018
to year 2100 , 50.7 cm
Update to 01 Oct 2018, public output 18 Jan 2019
to year 2100 , 50.9 cm
Update to 29 Nov 2018, public output 02 Feb 2019
to year 2100 , 55.1 cm

So between 49.1cm and 60.7cm SLR to 2100. Well above the 35.2cm of
linear "fit".

Also evidence of the emergence in the Pacific (and so upward global sea
level) of the next
El Nino. Anomaly in degrees C for Nino 3.4 sector/sea area 120 to 165
deg ,+/-5 deg latitude, processed from the NOAA global SST anomaly
image.
https://www.ospo.noaa.gov/data/sst/a....1.31.2019.gif
A few spot values in Jan 2019
Day ; SST anomaly
14 ; +0.75
17 ; +0.63
21; +0.41
24; +0.34
28; +0.36
31; +0.69
Despite the dip late January, the running 3 month mean for NDJ quarter
is probably above the qualifying value of 0.5 , NOAA processed for SON
quarter +0.7 , and OND quarter +0.9 .
https://origin.cpc.ncep.noaa.gov/pro...uff/ONI_v5.php







An updated image of Jason 1 +2 +3 data and image masques to the same
scale , showing linear "fit" and best fit curve, even to the eye a
better fit, visualising balancing of the excursions either side of the
curve.

http://diverse.4mg.com/jason1+2+3_29nov2018.jpg

shame about to the disjunctures between them, but the x,y axes are the
Jason 1 image ones extended on to 8cm and 2020.
For the disjunctures, with no other info about the filters, a matter of
avoiding the last or first 6 months of a mission, compare with the Aviso
Reference image and check the slope of a linear "fit" near enough agrees
with the reference slope , being aware that theirs also includes the
early T/P mission , which I've not included in all this.
Not included the exponential or quadratic curves as only 3 pixels
different at 2010. The original blue gradient lines retained of the 3
images.

I'd not realised before , the Aviso reference curve includes 0.3mm per
year contribution of isostatic rebound correction or GIA glacial
isostatic adjustment. I'd thought there was too much disagreement over
the degree of GIA contribution to SLR, for anyone to use it for primary
reference purposes. Only the one paper by Peltier put a figure to it of
0.3mm/year, then the University of Colorado decided to include that
0.3mm /yr figure in their outputs. Despite loads of assumptions relating
to the known unknowns of the oceans sub-bottom geology. Anyway I'd
thought the answer lay in the term isostatic, ie all balanced out,
swings and roundabouts. For example , in a minor way and simplified (no
account of groundwater abstraction or change of current-streams etc)
for just the UK recovering from the last ice-age.
From BODC data for Lerwick tide gauge, between 1957 and 1999
mean sea level has risen 30 mm relative to the rising land there.
But for Portsmouth between 1962 and 2002, the sea level
relative to isostatic sinking Portsmouth ,had a 170mm rise.
Unfortunately no BODC long term tide gauge data for "middle " England ports.
But simply taking the average of 30 and 170mm and over about 40 years,
gives a ball-park figure of SLR around the UK over those decades to be
about 2.5mm per year, much like the global figure for those decades.
Anyway the Aviso reference data is simply the Jason data plus 0.3mm per
year added. I still have no explantion for the mismatch of curves on the
overlaps of J1 and J2, then J2 and J3 missions. But removing the yearly
pro-rata GIA amounts from the Aviso reference plots , for the periods of
overlap, is very much the lowest values, wheras previously I'd taken the
average, as I had no info on how to handle the transitions of missions.
This now exagerates the
knee of the concattenated J1+J2+J3 plots, revised image showing the
greater deviation from linear and more balanced passes through the plots,

http://diverse.4mg.com/jason1+2+3_29nov2018.jpg

, more of a curve and so higher projected global SLR to 2100.
Same ranking order via R^2 value , same J-3 data to 29 Nov 2018, but
higher projected SLR.
x= year minus 2000, y = Aviso global SLR
73 datapoints
linear
y=1.272075+ 0.343219*x
r*r = 0.976375
year Sea Level Rise (cm)
2020 8.136
2050 18.433
2100 35.593

Exponential
y=2.095669 -3.722926*(1-Exp(0.049906*x))
r*r = 0.984341
year Sea Level Rise (cm)
2020 8.473
2050 43.514
2100 545.734 = 5.46m
same r*r and SLR for this alternative manipulation of that expression
y= -1.630970 + 3.726249*1.051143^x
to sensible number of iterations for the curve-fit

quadratic
y = 2.270613 + 0.133686*x + 0.008761*x^2
r*r = 0.984705
year Sea Level Rise (cm)
2020 8.448
2050 30.857
2100 103.249 = 1.03m

indicial power
y=2.483612 + 0.053029^.575023
r*r = 0.984834
year Sea Level Rise (cm)
2020 8.421
2050 27.627
2100 77.397

for turn of year J3 data output in early 2012, I'll have to remember to
check whether this prediction was nearer the 8.1cm of linear or 8.4cm of
the curves.
Now J3 plot is approaching the longer term gradient, I'll move to
checking my linear fit to J3 only compared to Aviso gradient or mm/yr,
as they are getting closer.
Current Aviso J3 0.312 gradient cm/yr, my reduced datapoint gradient 0.327
revisiting previous Jason 3 data assesments
to decimal year 2018.685, aviso 0.247 gradient, me 0.192
to 2018.441, aviso 0.246 gradient, me 0.196
to 2017.964, aviso 0.241 gradient, me 0.205

A different slant on the 2 Edwards papers referred to elsewhere on this
board under Antarctica.
https://www.newscientist.com/article...creep-upwards/

On 20/02/2019 16:05, N_Cook wrote:
for turn of year J3 data output in early 2012

for early 2012 ,read early 2020

On 20/02/2019 16:05, N_Cook wrote:
y=2.483612 + 0.053029^.575023

correction
y=2.483612 + 0.053029*x^1.575023

On 26/02/2019 09:57, N_Cook wrote:
y=2.483612 + 0.053029*x^1.575023

Just because you can obtain a model fit with 6 significant figures shown
in each coefficient doesn't mean that they are right.

I'd be very surprised if anything more than the first two leading digits
were even in the right ballpark.

Instead of using R^2 as a measure of goodness of fit why don't you try
and do it using the actual residuals of the data and an estimate of the
noise to compute chi-squared. Then you can do a proper analysis and see
just how uncertain each of your coefficients are. IOW how well defined
each of them is with the others sat on their respective peak value.

--
Regards,
Martin Brown