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