Niche Modeling

14
Oct
Is OHC Accelerating?
Posted by David Stockwell in All, Climate, Programming, Statistics

Table of contents for OHC

Code and figures to quantify the answer to the question “Is ocean heat content is accelerating?” are below. The idea is that ‘acceleration’ is synonymous with the significance of a quadratic term in a regression:

1. Annual OHC data from NODC.

2. Fit a regression model (M1) incorporating linear and periodic terms of period 60 years (to account for Pacific Decadal Oscillation):

x=time(OHC); f=x*pi*2/60; M1 = lm(OHC~x+sin(f)+cos(f))

3. Fit another regression model with the addition of a quadratic term,

M2 = lm(OHC~x+sin(f)+cos(f)+I(x^2))

4. Compare the reduction in the regression sum of squares due to the incorporation of the quadratic term, taking into account the loss of degrees of freedom due to autocorrelation (see http://en.wikipedia.org/wiki/F-test for tests of nested models)

The result below shows M1 as a solid line and M2 as a dashed line. The p value for the F test is a marginally significant 0.052 (not significant at the 95% CL) for an improvement in the model due to addition of a quadratic term.

For interest, I appended a value of 5 onto the end of the series, to anticipate the case of a precipitous fall in OHC this year. The result is below, with a non-significant p value of 0.467 for an improvement in the model due to addition of a quadratic term.

So based on these tests, taking into account the oscillation of the PDO and the autocorrelation, the empirical evidence does not strongly support an ‘acceleration’ in OHC and if it continues to decline as it appears to be doing, what support there is will vanish.

The turnkey R script and data as a zip file is here.

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Andrew

Hm, you know, I personally think that there is probably a better way to determine the presence or absence of acceleration, but this is impressive. All right, now I'll bite-I have to try some tests myself. Maybe by this weekend I'll have something.

Unfortunately the is no OHC data back during the 1911-1941 warming, which would provide a perfect test for "acceleration" IMHO.

davids99us

Thanks Andrew. If you come up with a better way - great!

Nick Stokes

David, this is not a good test for the significance of acceleration. Your data is 50 years. Your first fit includes a sinusoid of period 60 years which you've called PDO, but it is just a fit. It is not in phase with the actual PDO, having a zero about 1970. Here is a pic of how it turns out. The sinusoid is very similar to a parabola, with a minimum around 1995, and itself represents a lot of acceleration. What happens when you add a parabola to the model is that you test not for acceleration, but for the extra ability of the parabola to represent the acceleration. Naturally, that turns out to be small. The reason is that the sinusoid was already representing it well.

davids99us

Nick. The shortness of the data was one reason why I questioned the veracity of the claim made by Wong in the first place. You can't say its OK to make a speculative claim but not OK to show the claim is not
significant.

The period of the PDO and other ocean cycles is known to be around 60 years, but the amplitude and timing wrt OHC are free parameters. The cycles influence OHC, and are a common sense component of such data, i.e. its Bayesian prior probability is high, which is why I would argue that periodic terms should be included prior to testing for the presence of a speculative acceleration term, with a low Bayesian prior probability. Its an interesting and valid issue. You would need to justify why you didn't include natural cycles wouldn't you?

Nick Stokes

David, if you want to subtract a prescribed PDO function, with fixed amplitude and phase, then that is one thing. But if you just fit an arbitrary sinusoid, period 60, then that will take out PDO effects, but also anything else it can fit. And since it has a parabola shape, it can and does fit the acceleration component very well. All your test does is test for how much acceleration remains to be fitted after that.

You can see this by making your last function, instead of x^2, the difference between the fitted sinusoid and a similar parabola. This difference won't look like a parabola at all, and you wouldn't identify it with acceleration. But it will give exactly the same fit, with the same significance. You're just fitting a wrinkle on the acceleration, not the acceleration itself.

davids99us

Nick, exactly the same argument could be made if the quadratic was included first -- you could say that some periodic natural variation is being mistaken for acceleration -- which is exactly the argument I have been making for the increase in temperatures and sea level in the last half
century.

Although in the case of temperature and sea level the length of the record is two times the dominant period, and not slightly less than the dominant period.

Nick Stokes

David, yes, that's the nub of it. When you only have 50 yrs data, you can't identify uniquely what part of the signal could be a 60 year periodicity. So if there's an apparent acceleration, you can't say (from time series) whether it will continue, or turn down as a sinusoid. That's always the case; we don't know if the universe will expand forever, or contract again in a few billion years.

It's a null result - your x^2 and sin(f) etc are confounded. But your significance is not meaningful.

davids99us

Nick, granted, however if the data is sufficiently long relative to the
period length, this would be a more reliable quantitative approach. My guess
is 1.5 to two times the period length would be enough. Otherwise,
additional constraints on the phase or amplitude would be wise.

sherro

From which we can conclude that there is no mathematical basis to confidently assert that ocean heat content is accelerating or decelerating. And we can add that it could take centuries for an extrinsic temperature shock to distribute through the oceans and create a measurable ocean heat content change, let alone an acceleration/deceleration of change. Hence the small effect of adding a quadratic term to the equation.

Qualitatively, there must also be doubt that ocean heat content on a given day can be measured with adequate accuracy to fit these curves in any case. The grid cell size is large compared with the size of currents of different temperatures and the calculation is sensitive to "cut-off grade" assumptions - that is, the placement of the diffuse and ill-positioned 3D boundary where there is a temperature increment like a contour line, used in relation to measurement accuracy.

Off the cuff, is there value in comparing and contrasting smaller seas and lakes with oceans? I'd expect acceleration/deceleration to show faster in smaller volumes. But I'd assume this is standard procedure.

Nick Stokes

No, you've missed the point of the discussion above. You can't conclude that. There is significant acceleration - it has just been fitted with a portion of a cos function instead of a parabola.

sherro

Nick,

Conventionally, an acceleration requires an increase in the application of some driving force - not just a continued application at the same rate. What is the driving force that you would claim has increased and does it have the magnitude required to thus change the oceans? Geoff.

Nick Stokes

Yes, the driving force is the 1.6 or so W/m2 AGW forcing. Heat that was retained because of GHG increase and ended up in the ocean. It accelerates because GHG (and the rate of rise) have been increasing. 1.5 W/m2 is 2.4E+23 J/year, so yes, it is enough.

Andrew

Nick, the rate of change of all greenhouse forcings is pretty constant since 1979:

http://www.esrl.noaa.gov/gmd/aggi/aggi_2008.fig...

davids99us

That was what I was getting at when I suggested that the Bayesian prior for
acceleration in OHC is low. We would expect a linear increase (due to AGW),
and we would expect an oscillation similar to that seen in sea level and
temperature, both of which are shown in the model, but I don't see any
reason for an acceleration in OHC as claimed by Steffen/Wong.

Nick Stokes

Well, remember that OHC is prima facie the integral of forcing over time. Linear increase of forcing -> quadratic OHC.

davids99us

That would be if the forcing was not in equilibrium with the temperature
rise. I seem to remember controversy over this issue, with good evidence
that heat is quickly absorbed into the oceans, and the imbalance idea was
speculative.

cohenite

Nick, I don't know what your beef is with the 60 years for the PDO; there would be 2 phase shifts in that period so anything additional to an oscillation effect would be accommodated, wouldn't it? Also, has anyone explained this;

http://wattsupwiththat.com/2009/06/02/anomalous...

If this is a transitional artifact then acceleration is even more of a Dodo.

Nick Stokes

Coho, my first beef is with actually calling it a PDO. No connection is made. It's just an arbitrary 60 year cycle used as a fitting function. If it turned out to have startling correlation, you might further seek to identify it wih PDO (and explain the phase discrepancy). But you'll never get startling correlation that associates a 60 year cycle with 54 years of data. There just isn't the info you need. Instead, you end up fitting the parameters of the sinusoid to all sorts of other things that look the same over that period. And here, that includes the acceleration that DS later looks for with a parabola.

This relates to Bob's question below. These things aren't PDO or AMO. They are just sinusoids.

davids99us

Nick, It is a speculation to identify the periodic with PDO, even though the
period and phase are apparently the same. We work with the data we have,
and showing lack of statistical support does not rely on a lot of data. But
how do you feel about the speculation that OHC is increasing faster, made by
Wong/Steffen on only 54 years data?

Nick Stokes

"Increasing faster"? Well, it's true. The issue you raise is whether that apparent acceleration might be part of PDO cycle. And what I'm saying is that, from the time series data, you can't tell.

davids99us

So your position is that there is enough data to say that OHC is increasing
faster, but not enough OHC data to discriminate between acceleration and a
natural cycle. Fair enough.

My inclination to natural cycles is based on the strength of the 60 year
cycle in sea level data, even in a run of 300 years, and of course in
surface temperature data as well.

Of course the linear component could be due to AGW, or something else.

Bob Tisdale

Can I ask a few basic questions? Why use the PDO, and not the AMO? The AMO has a known impact on upper level OHC through AMOC. Does the PDO?

davids99us

I could just say oceanographic cycles, but the PDO seems to have the right phase.

sherro

Nick,

Humbly I seek a clarification as I've not got into the numbers in detail. What is the 2.4E+23 J/year that you mention? Is it a total, annual figure or is it an annual increment on the previous year? How long does it take to mix through the full ocean T? What is the acceleration Joule figure per year per year?

An acceleration (say relating to velocity) will continue to increase that velocity until a bound is met. What natural event(s) do you consider will halt your postulated acceleration and reverse it? How do the brakes go on?

Your CO2 comments remind me of the Doomsday machine in Dr Strangelove. Very powerful, will end life on earth, cannot be stopped, accelerated mortality. Indeed in the script, General Turgidson has an aside "I's sure like to have a few of those Doomsday machines myself. (Or similar words). Powerful stuff, that few ppm of CO2.

Nick Stokes

2.4E+23 J/year was meant to be 1.6 W/m2 * 5e+14 m2 (Earth) * 3e+7 sec (year). And I see it should have been 2.4E+22 J/year. But it's still enough, though closer. The mixing time is very long, but doesn't affect the OHC.

I'm not sure what CO2 comments you're referring to. The 1.6 W/m2 (with error range) is the headline IPCC figure. The CO2 part comes mainly from LBL codes, which are based on well known physics.

cohenite

Well Nick, still 2 issues; even if the 50 year data period is too short to encapsule a complete PDO cycle there will still be at least 2 phase shifts during that 50 year data period, in 1976 and 1998; is the OHC movement consistent with that? And I keep asking, what is this:

http://wattsupwiththat.com/2009/06/02/anomalous...

Nick Stokes

As I mentioned above, the inferred 60 year cycle doesn't match the PDO in phase (about 10 years out). But as I say, there's too much else going on to expect the PDO to come out of this data.

Re the 2003 jump - yes, indeed. I've been recommending caution with ARGO data until the instrument issues are better understood, and getting the transition right is likely to be the hardest part.

sherro

Nick Stokes,

ow do you justify that OHC is not affected by a long ocean mixing time? I would have thought that this was a key to understanding. If there is going to be sea level change from sea temperature expansion/contraction, then the whole of the sea on average has to change T. It's not enough to show that a shallow onion skin at the surface has got a bit warmer, it's also a requirement to show that the whole ocean has got warmer. But that's becoming academic because the sea level seems not to be changing in recent years when assessed by the frame of reference used for satellite positioning. How does the sea level stay constant if the OHC is accelerating? How does an alcohol thermometer work?

BTW, what is the estimate of the accelerated energy input in J/yr/yr? What puts the brakes on? Why do we get purported OHC acceleration when the ocean temps are falling over the last decade? Indeed, how do we get falling ocean temps when CO2 is in a global mode of inexorable increase? Even if CO2 greenhouse theory worked as advertised, the long wavlength IR penetrates the sea barely at all and the UV-vis has a half-depth of several metres. Hardly a strong source to stir Mother Nature to raise OHC. Is it not more likely that the sea changes the air temp?

Do you have inside connections to get the CRU raw data from Phil Jones?

Nick Stokes

OHC is total heat. Once absorbed, it isn't changed by moving heat around.
Neither, in general, is the expansion. That's because of linearity. If you have two equal layers, the top 1C hotter than the bottom, and you then mix them, the top cools 0.5C and the bottom warms 0.5C. The bottom expands as much as the top contracts - no change in level. That's why sea level is a good indicator of OHC - maybe the best we have.

kuhnkat

"OHC is total heat. Once absorbed, it isn't changed by moving heat around."

You really ought to include the caveat that it has to stay within the ocean!! Of course, it DOESN'T stay within the ocean or the ocean would have already stopped absorbing more!!

Yup, sea level, if measured with high precision, WOULD be the best indicator we have. Even with our current measurements, it has pretty much stopped rising. As warmists claim glaciers on mountains, Greenland, and Antarctica are still net melting, that is a pretty good indicator there is a slight loss in OHC!!!

Of course, if they are NOT net melting...

Andrew

"OHC is total heat. Once absorbed, it isn't changed by moving heat around."

This is certainly true of the actual total OHC, but if it moves to or from a part of the ocean you aren't even measuring, well...

"sea level is a good indicator of OHC - maybe the best we have."

So now we have probably 17 years of "best data" on which to judge this-and little other than the heat in the ocean, not how it is behaving within it. Is the heat changing it's vertical distribution? Who knows? The "best data" can't answer that question, for sure. I have to say that I don't think sea level is really a magic cure all for measuring OHC. The ARGO efforts and attempts to analyze historical data better are actually so far more important and better overall.

cohenite

Ok, if sea level is the best indicator of OHC let's go through the facts; 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-...

So where's the heat? Perhaps ERBE has the answer, page 17;

http://www.leif.org/EOS/2009GL039628-pip.pdf

Nick Stokes

Coho,
As I've said, direct measured OHC has lots of measurement noise, although the long term trend is certainly upward. The NODC data wasn't adjusted - someone got hold of an early incomplete version, prior to NODC publication of plots. Your SST link is dud.

The sea-level increase isn't shot to bits; it's still increasing. They've observed a fluctuation in the rate of increase. And if ERBE has the answer, you won't find it on p 17. In fact, it's pretty hard to find p 17. But in fact that paper says nothing about OHC, which of course a satellite can't measure. It relates changes in global flux to SST.

kuhnkat

Nick Stokes'

"The sea-level increase isn't shot to bits; it's still increasing."

Let's be precise here. Wrong. The TREND is still showing an increase. The actual Sea Level metric is flat. The OHC metric took a drop.

The statistics involved only give you probabilities. They do not give you facts.

kuhnkat

Around 2003 the Argo network went on line. At this point the OHC increased dramatically.

Now, our poor metrics on the ocean prior to the Argo network is absolutely a reasonable explanation why there might be a large difference between the computed OHC before and after.

What is more questionable is why we would compute a trend using a splicing of data when the earlier section was so obviously much lower than the Argot data.

This splice has added a large INCREASE in the trend that I simply do not see as supportable.

As the sea level did NOT show a large jump during the same period, it does not support this OHC increase either.

Would someone please show me what I missed??

cohenite

Sorry, I double-linked the adjusted OHC site, the SST link is:

http://wattsupwiththat.com/2009/10/15/global-ss...

The reason I refer to ERBE and page 17, the page where the ERBE device findings of increased TOA OLR contradict all the model predictions of a decline, is that increase in TOA OLR carries a lot of extra energy with it, energy which otherwise would be put to increasing OHC. And yes the sea-level trend is still up but the paper I link to which finds the error in the TOPEX/Jason satellite measurement shows the rate of increase is declining, from ~ 3mm pa to ~1mm pa; 1 mmpa is pretty close to the error margins but the real point is with OHC declining or flat, sea-level increase declining, SST down, atmospheric temperatures down, reasonable [sic] conclusions are that there is no AGW effect, no energy is being stored in the oceans, that the climate sensitivity distinction between the equilibrium and transient responses is probably more theoretical than actual and finally, with the ERBE empirical findings, one has to ask, what ever happened to Miskolczi?

luke33

Of course maybe the PDO doesn't really exist itself. Shakun, J. D., and J. Shaman (2009), Tropical origins of North and South Pacific decadal variability, Geophys. Res. Lett., 36, L19711, doi:10.1029/2009GL040313.

And maybe the OHC estimates need work A new perspective on warming of the global oceans
M. D. Palmer, S. A. Good, K. Haines, N. A. Rayner and P. A. Stott-
Submitted to Geophysical Research Letters – Revised August 2009

and as El Nino itself morphs into Modoki El Nino

davids99us

Luke, I think the important message of
http://www.agu.org/pubs/crossref/2009/2009GL040... is the profound effect that ENSO has on both the N and S Pacific oceans. There is also the recent Loehle paper and references therein to large amplitude of the 60-70 year natural climate cycles, potentially exceeding AGW of the last 50 years.
http://www.ncasi.org/publications/Detail.aspx?i...

"On the other hand, studies cited herein have documented a 50–70 year cycle of climate oscillations overlaid on a simple linear warming trend since the mid-1800s and have used this model to forecast cooling beginning between 2001 and 2010, a prediction that seems to be upheld by the satellite and
ocean heat content data. "

kuhnkat

Luke,

"Of course maybe the PDO doesn't really exist itself."

Just to show you how wrong you are, I agree with this statement.

Like all the ocean "cycles" they do not exist as independent entities. They are simply a group of similar measurements that scientists have decided to label as they appear somewhat regularly.

I think the best way of identifying them is by saying they are the energy flow through that portion of the earth. They do not generate the energy. The properties of the area, density, momentum, mass, radiative, conduction, convection, magnetic, electrical... all help determine how the energy is distributed and absorbed or emitted to surrounding areas.

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