Firstly 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
2018 Julian day 358, ENSO value +0.8
361, +0.8
365, +0.75

2019
JD 14, +0.75
17, +0.63

I've not bothered processing Nov or early Dec or Early 2019 , but
visually unlikely much less than ENSO 0.5 mean if at all. So unless the
end of Jan shows substantial cooling in that sector, then the next El
Nino has probably started,
with the first of the 3 quarters value as +0.6.

The following, same processing as elsewhere in this thread, is at least
consistent with that.

Gradient of the linear fit of 0.334 cm/yr agrees with the Aviso
reference value of
3.34mm per year, so some sort of validation for the reduced dataset used
for these curve-fits.
https://www.aviso.altimetry.fr/en/da...ts-images.html
70 datapoints for the complete Jason1+2+3 concattenated dataset to 01
October 2018

Linear
Y= 1.426891 + 0.334249 *x
goodness R*R = 0.98329

year Sea Level Rise (cm)
2020 8.111
2050 18.139
2100 34.851

Exponential
Y = 1.861067 -9.801611*(1-e^(0.025179*x))
R*R= 0.985352

year Sea Level Rise (cm)
2020 8.277
2050 26.578
2100 113.624
Interesting that the previous processing gave 113.528, virtually the
same, no idea if any significance to that.

Quadratic
Y = 1.921387 + 0.229779*x + 0.004398*x^2
R*R = 0.985472
year Sea Level Rise (cm)
2020 8.276
2050 24.405
2100 68.879


Best curvefit still by R*R goodness,
Indicial
Y = 2.158700 + 0.127525*x^1.290962
R*R = 0.985697

year Sea Level Rise (cm)
2020 8.256
2050 22.06
2100 50.857

upward trend still

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 .
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.
Illogical contradiction, as at some point , they will have to start
fitting a curve, so why not 2017/2018/2019? This processing includes the
heavy revisioning of the J3 data from its start , that was output to the
public 07 Dec 2018.

Global SLR to year 2100 using Dec 2017 data , 56.15 cm
data to 05 Feb 2018 projecting 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

So between 49.1cm and 60.7cm SLR to 2100, is so far, my halfpennyworth
to this fundamental topic. Well above the 34.8cm of linear "fit".

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.

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.

On Friday, January 18, 2019 at 7:43:09 PM 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.

I think there's a danger of not seeing the wood for the trees.

AGW is resulting in a rise in sea level, which is overall a very bad thing. So is chopping down the rain forests, and removing part of the sink for all the CO2 mankind is emitting.

Filling the oceans with plastic is a bad idea, there is no need to use formulae to demonstrate what the situation might or might not be in 50 years based on a number of scenarios. Just use less bl**dy plastic! Of course, it can be recycled, Maylasia takes a lot from the UK now CHina doesn't. Seems to be working well http://www.klexpatmalaysia.com/wp-co...ls-933x445.jpg

We need to minimise our impact on the planet wherever possible, that's what's important, not the endless quoting/production of figures, IMHO.

Graham
Penzance

On 18/01/2019 20:24, Graham Easterling wrote:
On Friday, January 18, 2019 at 7:43:09 PM 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.

I think there's a danger of not seeing the wood for the trees.

AGW is resulting in a rise in sea level, which is overall a very bad thing. So is chopping down the rain forests, and removing part of the sink for all the CO2 mankind is emitting.

Filling the oceans with plastic is a bad idea, there is no need to use formulae to demonstrate what the situation might or might not be in 50 years based on a number of scenarios. Just use less bl**dy plastic! Of course, it can be recycled, Maylasia takes a lot from the UK now CHina doesn't. Seems to be working well http://www.klexpatmalaysia.com/wp-co...ls-933x445.jpg

We need to minimise our impact on the planet wherever possible, that's what's important, not the endless quoting/production of figures, IMHO.

Graham
Penzance


But stubbornly holding to "fitting" a straight line to Jason data ,
falsely implies to the AGW crowd that sea-level is rising , yes, but ar
a fixed rate. Not that the rate of increase is increasing, can be seen
if you plot out concattenated J1+J2+J3 and look at it , or more
precisely analyse it , as here.
Some media referred to exponential rise a year or 2 ago, but this
analysis shows there is no current evidence for exponential rise, but
does give some sort of justified character to the rise of rise.

Just as well the AGW lot were not aware of the recent Jason3
revisioning, which hapened to coincide with a return to upward trend
and led to a long delay in update for that public site.
(I'll place the overlay of both plots on the www so there is some public
source for it, as presumably just lost in the javascript morass of sites
such as Aviso).
Still nothing on the Aviso site as to why.
Perhaps something highly technical , change of waveguide dimensions in
weightless space perhaps, or someone placing a decimal point in the
wrong place , for the whole J3 mission.

On 18/01/2019 19:43, N_Cook wrote:

I hope you can admit , that to reach such IPCC predictions, there must
be some sort of up-curve at some point.

I'm sure that few in the scientific community believe that the rise in
sea level is _not_ going to accelerate in the coming years. The question
is how you estimate or express that likely rise and its magnitude. My
point is that the only credible way of doing so is by developing a
numerical model and not by blind curve-fitting.

Oceanography is not my field but, unsurprisingly, it looks like several
such models are well under way. Here's the results of one for instance:

https://www.nature.com/articles/s41467-018-02985-8

(I'm slightly surprised that a Nature article seems freely accessible,
but I had no trouble reading it and there even seems to be a
donwloadable PDF.)

On 19/01/2019 13:02, JGD wrote:
On 18/01/2019 19:43, N_Cook wrote:

I hope you can admit , that to reach such IPCC predictions, there must
be some sort of up-curve at some point.

I'm sure that few in the scientific community believe that the rise in
sea level is _not_ going to accelerate in the coming years. The question
is how you estimate or express that likely rise and its magnitude. My
point is that the only credible way of doing so is by developing a
numerical model and not by blind curve-fitting.

Oceanography is not my field but, unsurprisingly, it looks like several
such models are well under way. Here's the results of one for instance:

https://www.nature.com/articles/s41467-018-02985-8

(I'm slightly surprised that a Nature article seems freely accessible,
but I had no trouble reading it and there even seems to be a
donwloadable PDF.)


Detail of the Jason-3 revisioning, perhaps the AGW lot can get to the
bottom of it.
http://diverse.4mg.com/aviso25may_ma...01_overlay.jpg

01 Sep Aviso outputed curve converted to green and overlaid on the
earlier 25 May Aviso output.
Not perfect alignment as change of x and y scales and not fine enough,
discrete changes in scaling only possible in my graphics packages.
Note near coincidence of the gradients , but main point is the peak in
mid 2016 (green below blue) and peak in mid 2017 (green above blue), is
impossible to resolve even taking the scaling the other side of an ideal
superimposition.

Presumably swept under the carpet in the phrase on the Aviso site
"- for scientific and statistics reasons, period under 5 years are not
significant."

There is no "business as usual" Trump-land curve in that Nature paper,
for the early 21C situation, like on here

http://www.realclimate.org/index.php...omment-page-5/

Gives such a projection as 52cm for 2050 and 98cm for 2100
From that Nature paper ,taking 2035 peak net-zero CO2 plot as a close
stand-in for business-as-usual and the state of early 21C,
gives 22cm for 2050 and 55cm for 2100.
My analysis ,projecting on from the Jason data over one cycle of up and
down trend and best curve-fitting to the 2003 to 2018 data, from 2000 =0 cm.
Minimum 22cm rise to 2050 and 49cm for 2100
Maximum 24cm rise to 2050 and 61cm for 2100
so far , nearer the mor ebenign "2035" scenario.
Whichever way you look at these projections, a rise of the yearly rate
of global sea level rise, from the non Jason or projection fitting
linear 3.3/3.4 mm per year. I don't trust the Saral/Attica project as
its "calibrated" against tide-gauges which go up and down with
geological rates of the mm/year rate much as sea level rates, via
isostatic rebound, tectonic plate movement, human-led local water
abstraction under the tide-gauges etc
I wonder how much of this projection v. reality I will live to witness.

On 19/01/2019 08:48, N_Cook wrote:
On 18/01/2019 20:24, Graham Easterling wrote:
On Friday, January 18, 2019 at 7:43:09 PM 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.

One of them might be more accurate if it was based on a physical model
of how rising sea level and loss of permanent snow cover and glacier
mass would affect the Earth's albedo for example.

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.

I think there's a danger of not seeing the wood for the trees.

AGW is resulting in a rise in sea level, which is overall a very bad
thing. So is chopping down the rain forests, and removing part of the
sink for all the CO2 mankind is emitting.

Filling the oceans with plastic is a bad idea, there is no need to use
formulae to demonstrate what the situation might or might not be in 50
years based on a number of scenarios. Just use less bl**dy plastic! Of
course, it can be recycled, Maylasia takes a lot from the UK now CHina
doesn't. Seems to be working well
http://www.klexpatmalaysia.com/wp-co...ls-933x445.jpg


We need to minimise our impact on the planet wherever possible, that's
what's important, not the endless quoting/production of figures, IMHO.

But stubbornly holding to "fitting" a straight line to Jason data ,
falsely implies to the AGW crowd that sea-level is rising , yes, but ar
a fixed rate. Not that the rate of increase is increasing, can be seen
if you plot out concattenated J1+J2+J3 and look at it , or more
precisely analyse it , as here.
Some media referred to exponential rise a year or 2 ago, but this
analysis shows there is no current evidence for exponential rise, but
does give some sort of justified character to the rise of rise.

I think there might be just enough evidence of a very small quadratic
term in these data but you really need to use ANOVA to see if it is
sufficiently convincingly non-zero to make the grade. The scientific
community is careful not to over-egg their date unless they have a very
clear physical model that describes the process to fit against.

That said too many people (especially engineers) over fit their data.
Adding extra parameters to a fit will always improve if but unless it
explains a worthwhile fraction of remaining variance it is not valid.

Where are the numerical data in a time series form?

Another one which you might like to try is of the form

y = (a+bx)/(c+dx)

a = 1.92 b = 0.24084
c = 1 d =-0.0093

(approx) - 2050 = 26.1 but 2100 = 371.5

It is inclined to extrapolate towards a very worst case scenario.
(there is a pole in the denominator)

BTW I deduce that your x = Y - 2000

--
Regards,
Martin Brown

On 20/01/2019 16:10, Martin Brown wrote:
On 19/01/2019 08:48, N_Cook wrote:
On 18/01/2019 20:24, Graham Easterling wrote:
On Friday, January 18, 2019 at 7:43:09 PM 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.

One of them might be more accurate if it was based on a physical model
of how rising sea level and loss of permanent snow cover and glacier
mass would affect the Earth's albedo for example.

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.

I think there's a danger of not seeing the wood for the trees.

AGW is resulting in a rise in sea level, which is overall a very bad
thing. So is chopping down the rain forests, and removing part of the
sink for all the CO2 mankind is emitting.

Filling the oceans with plastic is a bad idea, there is no need to
use formulae to demonstrate what the situation might or might not be
in 50 years based on a number of scenarios. Just use less bl**dy
plastic! Of course, it can be recycled, Maylasia takes a lot from the
UK now CHina doesn't. Seems to be working well
http://www.klexpatmalaysia.com/wp-co...ls-933x445.jpg


We need to minimise our impact on the planet wherever possible,
that's what's important, not the endless quoting/production of
figures, IMHO.

But stubbornly holding to "fitting" a straight line to Jason data ,
falsely implies to the AGW crowd that sea-level is rising , yes, but
ar a fixed rate. Not that the rate of increase is increasing, can be
seen if you plot out concattenated J1+J2+J3 and look at it , or more
precisely analyse it , as here.
Some media referred to exponential rise a year or 2 ago, but this
analysis shows there is no current evidence for exponential rise, but
does give some sort of justified character to the rise of rise.

I think there might be just enough evidence of a very small quadratic
term in these data but you really need to use ANOVA to see if it is
sufficiently convincingly non-zero to make the grade. The scientific
community is careful not to over-egg their date unless they have a very
clear physical model that describes the process to fit against.

That said too many people (especially engineers) over fit their data.
Adding extra parameters to a fit will always improve if but unless it
explains a worthwhile fraction of remaining variance it is not valid.

Where are the numerical data in a time series form?

Another one which you might like to try is of the form

y = (a+bx)/(c+dx)

a = 1.92 b = 0.24084
c = 1 d =-0.0093

(approx) - 2050 = 26.1 but 2100 = 371.5

It is inclined to extrapolate towards a very worst case scenario.
(there is a pole in the denominator)

BTW I deduce that your x = Y - 2000


I'll try
y = (a+bx)/(c+dx)
tomorrow
As well as linear, quad, exponential (2 forms that converge) and
indicial power, I tried cubic but it was not well-behaved or would not
converge.

A close-run competitor for best curve-fit is
Y = 1.921387 + 0.229779*x + 0.004398*x^2

yes x should really be t for time and is indexed to year 2000.
csv file or tabulated data not available to the public AFAIK, matter of
transcribing graphical plots and then checking by overlaying VB version
of it over the original. Then datapoint constraints on www curve-fit
routines, hence checking the linear form gives the same gradient as
Aviso "reference" mm/year, I've got enough datapoints to be reasonably
valid.

On 20/01/2019 18:04, N_Cook wrote:
On 20/01/2019 16:10, Martin Brown wrote:
On 19/01/2019 08:48, N_Cook wrote:
On 18/01/2019 20:24, Graham Easterling wrote:
On Friday, January 18, 2019 at 7:43:09 PM 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.

One of them might be more accurate if it was based on a physical model
of how rising sea level and loss of permanent snow cover and glacier
mass would affect the Earth's albedo for example.

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.

I think there's a danger of not seeing the wood for the trees.

AGW is resulting in a rise in sea level, which is overall a very bad
thing. So is chopping down the rain forests, and removing part of the
sink for all the CO2 mankind is emitting.

Filling the oceans with plastic is a bad idea, there is no need to
use formulae to demonstrate what the situation might or might not be
in 50 years based on a number of scenarios. Just use less bl**dy
plastic! Of course, it can be recycled, Maylasia takes a lot from the
UK now CHina doesn't. Seems to be working well
http://www.klexpatmalaysia.com/wp-co...ls-933x445.jpg



We need to minimise our impact on the planet wherever possible,
that's what's important, not the endless quoting/production of
figures, IMHO.

But stubbornly holding to "fitting" a straight line to Jason data ,
falsely implies to the AGW crowd that sea-level is rising , yes, but
ar a fixed rate. Not that the rate of increase is increasing, can be
seen if you plot out concattenated J1+J2+J3 and look at it , or more
precisely analyse it , as here.
Some media referred to exponential rise a year or 2 ago, but this
analysis shows there is no current evidence for exponential rise, but
does give some sort of justified character to the rise of rise.

I think there might be just enough evidence of a very small quadratic
term in these data but you really need to use ANOVA to see if it is
sufficiently convincingly non-zero to make the grade. The scientific
community is careful not to over-egg their date unless they have a very
clear physical model that describes the process to fit against.

That said too many people (especially engineers) over fit their data.
Adding extra parameters to a fit will always improve if but unless it
explains a worthwhile fraction of remaining variance it is not valid.

Where are the numerical data in a time series form?

Another one which you might like to try is of the form

y = (a+bx)/(c+dx)

a = 1.92Â*Â*Â* b = 0.24084
c = 1Â*Â*Â*Â*Â*Â*Â* d =-0.0093

(approx)Â* - 2050 = 26.1 but 2100 = 371.5

It is inclined to extrapolate towards a very worst case scenario.
(there is a pole in the denominator)

BTW I deduce that your x = Y - 2000


I'll try
y = (a+bx)/(c+dx)
tomorrow
As well as linear, quad, exponential (2 forms that converge) and
indicial power, I tried cubic but it was not well-behaved or would not
converge.

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.

A close-run competitor for best curve-fit is
Y = 1.921387 + 0.229779*x + 0.004398*x^2

yes x should really be t for time and is indexed to year 2000.
csv file or tabulated data not available to the public AFAIK, matter of
transcribing graphical plots and then checking by overlaying VB version
of it over the original. Then datapoint constraints on www curve-fit
routines, hence checking the linear form gives the same gradient as
Aviso "reference" mm/year, I've got enough datapoints to be reasonably
valid.


--
Regards,
Martin Brown