Comments on: Is OHC Accelerating (II)?

By: davids99us

davids99us — Sat, 17 Oct 2009 10:23:19 +0000

Aslak, A more to the point answer to the issue of Occam's razor that you raise, is what is the reality? We know that there are cycles, we know that there might be acceleration, the question is can the correct proportion be recovered and under what conditions? The number of parameters doesn't seem like a basis for elimination of cycles, but more of a possible source of difficuly in estimating CIs.

By: cohenite

cohenite — Sat, 17 Oct 2009 06:29:16 +0000

The adjustment to NODC data [as usual the adjustment is up] still shows a down trend in recent OHC;

http://wattsupwiththat.com/2009/10/15/ocean-hea...

On top of that is the 2002-2003 'artifact' which is responsible for over 1/2 of the OHC increase in the data range has not been addressed by NODC. And speaking of temperature SST is down;

http://wattsupwiththat.com/2009/10/15/ocean-hea...

And [thermosteric] sea-level increase is shot to bits;

http://www.ocean-sci-discuss.net/6/31/2009/osd-...

Where's the heat Nick? ERBE perhaps?

By: davids99us

davids99us — Sat, 17 Oct 2009 06:18:11 +0000

Nick, You are thinking of OHC I think. Temperature is a longer record,
though the analysis you suggest would be worth doing.

By: Nick Stokes

Nick Stokes — Sat, 17 Oct 2009 04:05:02 +0000

David, “My analysis shows that periodic is the greatest contribution to temperature increases of the last 50 years”
Your analysis shows the same result for a parabolic increase plus noise. And there's nothing to indicate that would moderate. Your inference doesn't work.

By: davids99us

davids99us — Sat, 17 Oct 2009 00:46:10 +0000

Yes thats another way to look at it, though another issue I am trying to get
at is that such analysis should incorporate a universe of possible
functions: linear, quadratic or periodic. To test only quadratic is to
assume that response, so finding of significance is a circular argument.

Eg, the argument is made against natural cycles as a cause of recent AGW
that it must be shown first that cycles are capable of causing the forcing
seen in the last 50 years. However, there is a data history of strong
climate cycles of around 60 years, so the onus should be to show the
relative proportion of natural cycle vs linear or other type of forcing,
even if they are not completely understood. My analysis shows that periodic
is the greatest contribution to temperature increases of the last 50 years,
and predicts a moderation of temperature increases (as AGW alarmists are now
scrambling to explain).

That doesn't mean it is all periodic, a small linear component persists of
around 0.05C/decade, consistent with Lindzen, Spencer, Douglass etc.

By: Nick Stokes

Nick Stokes — Fri, 16 Oct 2009 10:31:31 +0000

Another version is that if you want to do what you're trying, and have the effect of each addition independently significant (or not), then the functions should be nearly orthogonal. A sine with several periods is close to orthogonal to a smooth function like a quadratic. But one with a fractional period is not.

By: davids99us

davids99us — Fri, 16 Oct 2009 10:14:24 +0000

That is your point about not enough data to discriminate, you could do the same thing with sinusoidal synthetic data. Be a different story with more data though.

By: Nick Stokes

Nick Stokes — Fri, 16 Oct 2009 09:54:24 +0000

David,
This still won't work. It's better, because fixing the phase reduces the confounding a little. But not much.

To show this, I replaced the OHC data by a vector made up of just a parabola section plus white noise. No PDO there:

set.seed(199) # fix the seed to make it reproducible
x=1:52
C=x*x+50*x-400+500*rnorm(52) # artificial data
C<-ts(C,start=1958)

Then I did an extra fit stage at the start, fitting just a line:
l0<-lm(sw~x)
l1 and l2 as before. Then I tested for the significance of first adding sin(f), then x^2.

ft<-ftest(l0,l1)
ptest<-1-pf(ft[1],ft[2],ft[3])
print(ptest) # test for adding the sin
ft<-ftest(l1,l2)
ptest<-1-pf(ft[1],ft[2],ft[3])
print(ptest) # test for further adding quadratic

Adding sin(f) showed p=.0052. Highly significant,99.5%, even though there was no PDO there.

Then adding a quadratic (x^2) showed p=0.519, not even significant at 50%. Even though the underlying function was a quadratic.

Same explanation - the sinusoid could fit the function well enough, and adding the quadratic made little improvement.

By: davids99us

davids99us — Fri, 16 Oct 2009 09:50:05 +0000

Aslak, it is penalized, but only in the case where the number of data is
few, due to the F test. In this case it probably would be, but that is what
you want after all, as you don't want to be overfitting.

Your choices probably are about the same, but refer to the discussion with
Nick, a lot hands on the prior assumptions of how you think the data should
be explained. I see the models in the RC post suggest an acceleration too,
so there is another basis for a prior belief to take into account.

I am interested in the periodics as its a clean and transparent approach. I
would never rely on just one type of model, and clearly someone should fit
PDO, cSOI, etc to OHC.

By: Aslak Grinsted

Aslak Grinsted — Fri, 16 Oct 2009 08:25:34 +0000

You compare "trend+cycle" to "trend+cycle+quadratic". The latter will be penalized for having more parameters. I think you should compare the skill of these two models:
* trend + cycle
* quadratic
I suspect that the quality of their fits will be indistinguishable when you consider the level of noise in the OHC observations. I would argue that the quadratic is the simpler model because i think the cycle model has many more free parameters.
Wavelength, and phase are specified apriori, but i would still argue that they are a quasi-free parameters. If your hypothesis is "trend+PDO", why dont you use a PDO index as predictor rather than an idealized cycle?

Note, I am not arguing against longish cycles in OHC.