On 27/02/2018 20:46, N_Cook wrote:
On 27/02/2018 19:53, Martin Brown wrote:
On 27/02/2018 19:13, N_Cook wrote:
Best fit of cubic form to the Jasons returned to Y=0 (x=3 to 18) at
about x= 50 years, and offsetting (delaying) the x-scale, would not
converge .

Whose curve fitting algorithm are you using? There is no excuse for a
cubic polynomial fit to diverge on a decent amount of data.
(although Excel may well still do and possibly Matlab as well)

If you send me the raw data as a CSV file with time, value I would be
interested in fitting it just to see what the fit looked like.
(I am certain that I have a solution that will converge)

I have posted about such problems on the Excel groups in the past.

If you want to DIY it then rescale your data so that time is symmetrical
around the mid point and with a range of -1 to 1 - this makes the matrix
condition as well behaved as possible so even a bad algorithm can cope.
(it won't be exact but it might be much closer to a real answer)

Ie given a dataset running from MinTime to MaxTime then for each t

MyTime = (2t-(Mintime+Maxtime))/(MaxTime-MinTime)

t = Mintime Mytime = -1
t = Maxtime Mytime = 1
(subject to typos)

Unless their fitting code is hopeless this should be stable.


Y = 9.785195 + 0.250222*(x-25) -0.013375* (x-25)^2 -0.000468*(x-25)^3
converged with
R^2 = 0.982687
RMS Error = 0.225851
so larger R^2 than best Fractional power fit but also larger RMS Error
and also the awkward y=9.785195 intercept

The postulation is that if you adjust the Jason global sea level curve,
for the mass-loss and gain of Greenland via the GRACE curve, then the
result should look like the ENSO multivariate strength curve.
It is possible to convert Greenland mass-loss to global sea level, via
458 GigaTons to 1.45mm of global sea level rise
The average annnual loss is about 45GT so about 0.14mm of sea level rise
on average, from that.
The grey linear trace trace is the GRACE curve , in annual simplified
terms, wrt to this 45GT average, so above or below avearage about the
centre line, expressed as cm sea-level equivalent. Also no account taken
of likely different lag between melted ice lost to the ocean and mass
loss from the oceans as snow fall on Greenland.
Also the ENSO curve is just a curve, unrelated directly to sea-level and
no reason to treat the red and green sections equally for this purpose.
This is just a first draft, to see if there is any correlation that
could then be improved on.
The blue trace is the Jason1+2+3 curve , above and below the best fit
indicial power curve detailed before, ie the yellow line is flattened
out, to become the common centre-line. The orange curve is Jason curve
with the "Greenland" effect removed.
The red and green curve is the ENSO mulivariate curve , horizontally
scaled to match , but x shifted and vertical scaling adjusted for best
visual curve match to the orange curve. I've not seen any GRACE
mass-loss data for 2017, but ice loss was about half the previous year
and apparently more than average snow fall in the gain part of the year.
if that is so then the modified Jason, the orange curve, extended on
when data emerges, will probably resemble the positive excursion of the
ENSO curve. Not bad first go.
http://diverse.4mg.com/jason1+2+3+grace+enso.jpg
I've not yet added the later Jason data beyond decimal year 2017.91,
may as well wait until the next GRACE update.
Lag of Jason behind ENSO about 3 months and lag of Jason behind GRACE
very approximately 3 months after the midpoint of the mass-loss year
(-45GT point on average), having somewhat arbitrarily chosen the month
of maximum Greenland ice-loss , per year , as it is the more obvious
part of the repeating annual part-curve for the rectilinear plot.