This is a reply and extension to Pat Frank’s “Earth Abides” post (sorry, couldn’t resist) which appeared here recently. The post features an intriguing interpretation of the temperature record to deduce climate sensitivity to CO2. I thought I would try to recreate it and see where it took me. First I got the HadSST records from http://www.cru.uea.ac.uk/cru/data/temperature/.
I generally prefer to use sea-surface temperatures when looking at global trends for several reasons:
- they have a lower variance, indicating a better stability to short-term perturbations
- the surface water temperature is measured directly, eliminating some of the definitional issues of surface air temperature
- SST’s are free of siting issues, UHI, land use, and other local human climate effects
- The seas are 70% of Earth’s surface and its major heat reservoir. Temperatures can go up and down on land like a wagging tail, but the oceans are the dog.
So let’s take the SST record and fit a sinusoid to it. However, a linear fit to the secular rise simply can’t be right. It would retrodict an ice age right at the peak of the Roman Empire. Since things in nature are much more often cyclical, I tried fitting another sinusoid to the secular rise, using all the HadSST data back to 1850:
Here we have the data as dots, decadal smoothing in blue, and the fitted sum of cosines in red. (Decadal smoothing means that I convolved the data with a Gaussian with a 5-year standard deviation.) The red curve is simply the sum of two cosines, one of period 62.7 years, the other 259.9. Just how good a match is it for the data? Ignoring intra-decadal variability (weather, not climate!), let’s plot the decadally-smoothed residual:
Something very unusual happened around 1950 — that’s nearly an 8-sigma excursion. And I haven’t the slightest clue what it was. (There was a major mode shift in the PDO about that time; it was also the era of atmospheric nuclear weapon testing … and there was probably a drop in the number of pirates.) If you look at the actual data you’ll see that 1945 marks the only really drastic discontinuity in the entire record — so I feel reasonably comfortable saying that something unusual happened then. Given that the fit was so good outside the “1950 notch”, I did the fit treating the notch as an outlier (yellow line) for an even better fit (especially to recent temperatures). (That means, of course, that the model isn’t just the fit but the fit with an exception for the notch.) The red lines are one standard deviation, the magenta two. But outside of the notch, this model — a tiny one, 6 parameters — fits the decadal average SST to within 0.05 degrees for 160 years.
Here are the variances, again with the notch taken out (We take the notch out because it makes all the series correlated, so the variances wouldn’t sum. Since we explicitly say the model can’t explain the notch, we’ll concentrate on where it does match the data.):
| Raw SST data | 0.0687 |
| Model fit curves | 0.0534 |
| Residual to fit | 0.0153 |
| Data – smoothed (decadal variability) | 0.0145 |
| Smoothed – fit (model error) | 0.000513 |
In other words, decadal variability (weather!) accounts for 21% of the variance of the raw temperature series, the model accounts for 78%, leaving about 1% unaccounted for. (There’s still a tiny amount of correlation.)
But this kind of messes up the notion that there was a V-shaped piecewise linear structure to the residual across the twentieth century: the data much more clearly show a straight line with a dip than falling and rising linear trends. Yet Frank’s graph looked a lot more like the trends — what happened?
The key to the puzzle is that his data were (or included?) land temperatures, the CRUtemp data. Let’s plot that too, also as a residual to our fit curve:
Lo and behold, there really is a linear rise above the sinusoid in the land data — which isn’t there in the SST data. In other words, the divergence since 1950 is more a land-water difference than a CO2-no CO2 one. Sorry to rain on the parade, but I can’t really buy the climate sensitivity deduction. As mentioned, there are several possible explanations for the difference. We can add another one, even assuming the land temperature measurements are perfectly accurate: cloud feedbacks may operate differently over land and ocean.
Izen says:
“The graph you want is on page 7.”
No, that’s the graph you wanted, and probably the best you could come up with. And it still does not contradict what I posted earlier.
Here is another graph showing correlation between the hemispheres.
And I’m still waiting for you to post evidence showing global damage from CO2. Because if there isn’t any harm… then CO2 is harmless, and the central pillar of the wild-eyed alarmist contingent comes crashing down.
RE: tty: (June 7, 2011 at 12:21 am)
“I have often wondered if the SST anomaly in the 1940′s couldn’t simply been due to the fact that most ships were traveling in convoys 1939-45.”
I believe I read a similar explanation somewhere except it said during World War II shipping was diverted out of the usual sea-lanes due to blockades and the threat of submarine attack. This changed the actual region where these measurements were made.
J Stohrs, you wrote, “I generally prefer to use sea-surface temperatures when looking at global trends for several reasons: they have a lower variance, indicating a better stability to short-term perturbations
the surface water temperature is measured directly, eliminating some of the definitional issues of surface air temperature…”
The calculated variance of SSTs is not indicative of the accuracy of the measurements, which is almost certainly no better than about (+/-)1 C. So, use of SSTs rather than surface air temperatures doesn’t get you much. Further, bucket SSTs, which constitute more than half the 20th century record, come nowhere near even that accuracy. So, definitional issues aside, using SSTs doesn’t improve accuracy.
In other news, we are, after all, interested in global average surface air temperature. As the land surface is 30% of the global surface, it seems fitting to include measurements taken there.
This, “Temperatures can go up and down on land like a wagging tail, but the oceans are the dog.” isn’t entirely true either. Oceans do moderate coastal air temperatures, but internal continental temperatures are determined by, among other things, topology. I’ve fit the GISS global average land-station temperatures alone, and the oscillatory part, which I take to indicate world ocean cycles, puts about (+/-)0.1 C in the land surface anomalies. It’s true that the oceans dominate climate inertia, but the analysis is about short term (centennial) fluctuations. The effect of ocean thermal inertia is relatively low-frequency.
You wrote, “However, a linear fit to the secular rise simply can’t be right. It would retrodict an ice age right at the peak of the Roman Empire.” This imposes an incorrect inference on my analysis. It was obviously never meant to be predictive or retrodictive. It was meant to assess the trend between 1880-2010, when industrial CO2 is supposed to be influencing global air temp. To reject the linear part of the fit, because it gives absurd pseudo-predictions at long times, is analytical opportunism. It’s the same mistake, in fact, that Tamino has made. He used it to open the door for analysis, which made use of irrelevant models.
My analysis isn’t a theory of Earth’s climate. It’s an empirical analysis — data-based, in other words — looking for evidence of perturbation in a bounded data set. No more than that was ever represented. Rejection on the basis of an ice-age pseudo-hindcast for the Roman Empire is to abuse a bounded model.
Your third Figure shows that land surface air has warmed more than SST during the 20th century, and you reject the sensitivity analysis on that basis. But let’s remember that the sensitivity is about the relatively short term response of surface air temperature to additional CO2, not the sensitivity of SST. The inertia of the oceans requires a much longer term thermal response. So, it’s no surprise that ocean surface temperatures show lower intensity changes than land air temperatures.
Your first Figure, by the way, shows that you gave equal credence to SSTs measured prior to 1880, when there are very few measurements. The structure of your model appears to depend on the apparent rise in SST between 1855 and 1880. The reliability of temperatures measured during this time — land or SST — are very poor, which is one reason I began my analysis at 1880. You might want to try again starting from 1880 and see whether you get the same fit.
Pat: A very valid point about the linear fit and period of validity. I withdraw my remark about retrodiction; it was ill-considered. As I mentioned in my follow-up post, your linear + 60-year oscillation is an excellent fit for the 20th century.
The main problem with land temps for attribution is that there are so many potential confounding factors, which using SSTs finesses. It also seems likely, and this is just a guess, that there are substantively different dynamics as well.
HadSST coverage goes from 20ish in 1850 to 30ish in 1880. (Percent of the globe, not just the oceans.) You’re right that the record is less complete and less precise the farther back one goes, but the record such as it is agrees with other sources that the 1800s may have been something of a plateau.
None of this impacts what I take to be the point of both our posts, that CO2 didn’t cause the majority of the 20th century rise. Of course, it sure would be nice to know what did!
J Storrs, thanks very much for your generous reply. It’s in the spirit of science and appreciated.
I’ve consulted again, D. E. Parker, et al. (2000) “Climate Observations — The Instrumental Record” Space Sci. Rev. 94, 309-320. According to their Figure 1 land surface coverage in 1850 was about 5%, rising to about 10% by 1880 and 25% by 1900. Sea surface coverage was about 8% in 1850, rising to about 16% in 1880 and 30% in 1900.
There is a similar analysis for land surface stations in J. Hansen, et al. (1999) “GISS analysis of surface temperature change” JGR 104(D24), 30997-31022. But Hansen rests his coverage on his 1987 correlation analysis, so that that anywhere within 1200 km of any given station is covered. By his lights, in 1860, 5% of the southern hemisphere and 30% of the northern hemisphere were covered; by 1880, it’s 10% and 50%, and by 1900, 30% and 70%. These numbers are necessarily generous.
With respect, I still think that the 1850-1880 SST and global anomalies are unreliable.
“Lo and behold, there really is a linear rise above the sinusoid in the land data — which isn’t there in the SST data.”
No , what you see here is what you have already noted but forget about: land temps show more variation.
What the post 1950 section shows is a similar rise to what you have in sea data but bigger, a larger variation of the same nature.
To make any comparison you need to do the same fitting process for the land data and compare the two. Simply fitting to sea data and then noting that land is different is just stating the obvious. Much of what you are arbitrarily calling a “linear rise” is simply a question of a scaling difference.
The closeness of the fit with the two cosine terms is remarkable though you need to be careful when your data period is only about half a cycle. Lots of things bend around in a similar way to half a cycle of sine a wave but the fit is very good.
Could you post the complete function of those cosines rather than just the period?
It would also be interesting if you would explain what you used to do the fits. Just hard work by hand or some fitting algorithm?
How are you filling the end of the gaussian filtered data? You should loose the first and last ten years when doing any kind of averaging since the data is incomplete. How are you padding to get a result over the full period?
Pat: Thank you in turn; it’s appreciated. The coverage figures I mentioned were from the same data files as the temps, from http://www.cru.uea.ac.uk/cru/data/temperature/. They *claim* the 1850’s are accurate to 0.2, but frankly I don’t believe them … so we may as well let it drop; the existence of the 1890 knee isn’t particularly important to either of our arguments.
J. Simpson: I fit the function
p[0]*cos(2*pi/p[1]*x+p[2]) + p[3]*cos(2*pi/p[4]*x+p[5]) + p[6]
where p is a parameter vector and x is the vector of times (just year numbers)
to the temperatures using scientific python’s scipy.optimize.leastsq optimizer
(see http://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.leastsq.html)
The resulting parameters p are [ -1.41458960e-01, 6.27587010e+01, -1.93192077e+03,
-2.91801347e-01, 2.60917034e+02, -1.88646701e+03, -8.18030465e-02]
This tells us that the cosines are period 62.7 with a minimum at 1931.9, and period 260.9 with a minimum at 1886.
(The numbers are slightly off those above since I didn’t bother to take out the notch for this reply!)
For a quick and easy gaussian endpoint straightener, divide your convolved series by the result of convolving a series of 1s with the same (normalized) gaussian.
J Storrs, about error, CRU and now UK Met implicitly claim that all measurement errors are random and cancel out in their averages. The only real errors they acknowledge are sparsity of coverage and methodological and instrumental changes. The claim of otherwise random errors does not stand up to examination (pdf download). It’s my very considered view that the global air temperature anomaly series is climatologically useless, including SST.
Capture Conc: DEICERS from Heavy Duty DESALTERS & thereby GROW more ICEMASESS in POLES & HIMALAYAS. That could be lead to AIR-CONDITIONING OF MOTHER EARTH
ferd berple says: June 6, 2011 at 11:50 am
“Why does “Climate Science” add “science” to its name? “
I’m chuckling because Tim Ball says when he got his degree the field was called “Geography”. He was studying temperature records before some of these alarmist “scientists” were born.
Excellent question why they are using phrases like “the science is settled” – don’t other fields just debate their science?
Gore, Suzuki and the IPCC say that the “science” of climate change is “settled”. Let’s think about this:
1. Science or Art?
Science determines parameters and their interconnections, ultimately arriving at “predictions” that make or break the theory that binds observations and results together in a causitive way. Climate “science” works towards “scenarios” or “projections”; Pachauri and others vigorously deny that they create predictions. So their “climate science” is not science, but an analytical type of art. Climate scientists get a sense of how things are, only, and feel their way forward with that gut understanding.
2. Settled or not?
In 1990 the IPCC had a range of scenarios higher than the 2007 IPCC report. In 1990 the study was relatively new, at least with its CO2 as prime driver, so it is reasonable that there would be adjustments to their scenarios in 17 years. However, in 2007 the science is said to be “settled”, and certain to more than 95%. If that were the case, then the scenarios would have been reduced to a result, albeit with an error range. That has not happened. We still have a catastrophic and a virtually nothing different from a continued recovery from the LIA. That means that the climate scientists still haven’t determined what the prime controlling parameters are and what the power of each is. If CO2 were determined to have a 3.75 W/m2 power with a 3.0X water vapour multiplier, then we would be told that in 2025 it WILL be X, and in 2100 it WILL be Y. But this does not yet happen: the scenarios given in 2007 by the IPCC are still as vague and multi-resulting as before. So the science also isn’t “settled”
It takes little thought to see that CAGW is based not yet on science and not yet on anything settled to a 95% certainty. Scenarios that describe a world in 39 years (2050) from what we had yesterday to an ecological disaster that drowns a billion people world wide in multi-meter sea rises and starves to death millions more in continent sized famines are so different that it is hard to understand anyone with the thinking ability of a well-trained chimpanze to believe the climate scientist understands why things happen and what they are going to do even in the near term. Belief beggars the mind, or perhaps impoverishes the mind is a closer concept.
Think of this: if Newton had said he understood the principles of gravity, and that the principles were “settled”, and he would throw a ball into the air and could be certain that it would go higher for a while and then either fly away into space or fall down again some time later, but was going with a fall-down-later scenario with a “later” time frame of 30 seconds to 5 minutes, would we be honouring Newton today?
Dunno if anyone is still following this, but Hadley have revised the SST record in a way that takes out the “notch” — see http://climateaudit.org/2011/07/11/more-misrepresentations-from-realclimate/