Niche Modeling

15
Oct
Is OHC Accelerating (II)?
Posted by David Stockwell in All

Table of contents for OHC

In tests of the rigor of the Steffen/Wong statement that “not only is the OHC increasing, it is increasing faster“, we previously used a linear regression model including natural cycles. The question was raised about the confounding of an upward trend with part of the quadratic terms representing ‘acceleration’. This risk is increased by the short run of data (only 54 years) and also because the phase of the periodic terms is a free variable. The periodic is free because both sin() and cos() are used.

The phase can be bound easily by the simplification below. I introduce 1976 as a start date for the sin() periodic, the date of the Great Pacific Climate Shift, a widely recognized change in ocean and atmospheric phenomena. The code for obtaining the probability that the model is improved by a quadratic term is then:

x<-time(SL) f<-(time(SL)-1976)*2*pi m1<-lm(SL~x+sin(f/60)) m2<-lm(SL~x+sin(f/60)+I(x^2)) f<-ftest(m1,m2) ptest<-1-pf(f[1],f[2],f[3])

The results below for existing data and data with an appended low value for 2009 show little change. The p values are 0.07 and 0.12 respectively, indicating no improvement in the model by adding a quadratic term. With the suggested alterations, we again find no empirical justification for the Senator and her advisor's statement, when we include natural cycles in the model, i.e. for OHC to be increasing faster we have to exclude natural cycles as a possible explanation.

Previous result with free phase:

The change in OHC from peak to trough is 2*2.7 or 5.4 x10²² joules, while the linear increase in heat over the same period is 0.33*54 or 17.8X10²² joules. The coefficients of the linear regression suggest periodic oceanographic phenomena could account for 30% of the increase in OHC since 1958.

Blog Action Day: Climate Change is today!

Previous in series Next in series

Tagged as:
Published by David Stockwell in: All
If you like this blog please take a second from your precious time and subscribe to my rss feed!

Bob Tisdale

David, the NODC corrected it's OHC data today.
http://bobtisdale.blogspot.com/2009/10/nodcs-co...

My apologies to Nick Stokes (who suggested caution) have been posted on the earlier thread.

davids99us

Yes, I saw it. Does not affect these analyses though.

Aslak Grinsted

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.

davids99us

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.

davids99us

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.

Nick Stokes

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.

davids99us

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.

Nick Stokes

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 to avoid confounding. A sine with several periods is close to orthogonal to a smooth function like a quadratic. But one with a fractional period is not.

davids99us

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.

Nick Stokes

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.

davids99us

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

Sign up/in

Authors

Abouts

Blogroll

Literature

Is OHC Accelerating (II)?

Table of contents for OHC

archives

tag cloud

Copyright © 2008 - 2010 Niche Modeling

Britney's Online Dating Websites