## Astronomical cycles

#### Posted on 17 June 2010 by Riccardo

**Guest post by Riccardo**

Recently a new paper by Scafetta came out (a freely downloadable version can be found on arxiv but I don't know if they are exactly the same). In a few words, Scafetta connect the orbital motion of the planets with solar variability and hence on earth climate. He found a dominant 60 years cycle which, he claims, greatly downplay the anthropogenic contribution to the warming after the '70s. I won't go through the details of his analysis and the hypothesis on the yet to be discovered physical mechanism behind. Forget about physics for a moment, as Scafetta does, and think only about cycles and periods.

He does a nice and fascinating analysis of various orbital cycles which cause the motion of the sun around the center of mass of the solar system. It's assumed that in one way or another the gravitational pull affect sun activity. He then compares the power spectra from detrended Hadley's temperature data with that of the orbital cycles and obtains the nice graph reproduced below.

*Fig.1: reproduction of fig. 10B in the original paper. It shows the eight years moving average of the temperature anomaly detrended of its quadratic fit (gray); the thin black line is the same curve shifted by 61.5 years.*

The data has been detrended assuming an underlying parabolic trend. The main 60 year cycle, due to the alignment of Jupiter and Saturn, shows up very clear, but there are more. In particular, he identifies a total of 10 cycles due to combination of planets motion and one due to the moon (fig. 6B in the paper). Of those cycles, only two more are considered significant, namely those with periods of 20 and 30 years.

Fascinating. But then, a few pages later, Scafetta writes:

However, the meaning of the quadratic fit forecast should not be mistaken: indeed, alternative fitting functions can be adopted, they would equally well fit the data from 1850 to 2009 but may diverge during the 21st century.

His warning is on the problem of extrapolation of the trend in the future, which he nonetheless shows. But this sentence made me think that it's true, once we put physics aside, we're free to use the trend we like; so why parabolic? I decided to take a closer look, and this turns out to be the begining of the end.

The first and more obvious try is a linear trend and then one with a higher power. I kept the functional form y=a(x-1850)^{n}-b used by Scafetta, but let n be 1,2 or 4. Here's what I got.

*Fig.2: HadCRUT3 monthly data (grey) and the fits for n=1 (red), 2 (green) and 4 (blue).*

Already by eye inspection it may be noticed that, due to the different curvature of the fitting functions, the behaviour is different between the middle and the extremes of the range. To be quantitative, we need to calculate the residuals, i.e. the difference between the data and the trends.

The fits were performed using the raw monthly data, as shown in fig. 2, but given that we are looking for long term cycles, I smoothed the data before detrending to clean them up a bit, as Scafetta did too. The results are shown in the following figure.

*Fig.3: residuals calculated with the trend curve shown with n=1 (red), 2 (green) and 4 (blue).*

As noted before, the behaviour at the extremes of the range is opposite with respect to that at the center and the two peaks at year 1880 and 2000 get smaller on increasing n. In particular, for n=1 the curve barely flattens aroud year 2000 while for n=4 only a small short-lasting peak is left. Only with n=2 we get the three nice equal amplitude peaks.

More generally, for n=4 the claimed 60 year cycle seems to vanish after the peak at year 1940. It's not to say that the n=4 trend has more value than the n=2, but in the end we can say that the nice cyclic behaviour seen in fig. 1 depends on the choice of the trend function. It's worth to recall that its choice is arbitrary, no physics behind it.

I tested this findings with the other global surface temperature datasets (GISS and NCDC) and, not unexpectedly, they confirmed. The claim that the anthropogenic contribution to the increase in temperature after the 70s has been overestimated has then to be dismissed, at least until we can make a proper choice of the underlying trend.

Still, small, periodic and short-lasting peaks seem to be real. More accurate and hopefully physics-based studies on decadal variability are required, taking into account all possible internal and external contributions.

David Hortonat 08:10 AM on 17 June, 2010it must be a tool. The problem is that almost any piece of stone (or wood) can be held in a certain way and therefore be a tool. This fallacy is particular active in the study of early human society with (often) very simple technology, and there have been many instances of "early human" tool use being postulated which have later evaporated. In fact there are objective ways you can decide if something is a stone tool, based on such things as type of stone, fracture pattern, secondary chipping, use wear, residue analysis, and a comparison between an individual item and others at the same site, or of the same age, and so on. Some you may be able to hold in your hand, most not, for many there can be endless debate about exactly how they were used. But all of this has to be based on objective research, not after the fact hypotheses. In short, you can't just look at some mathematically created cycle and then invent a reason for it and then use it to predict the future. The graph may seem to fit well in the hand, but this is almost always an illusion based on wishful thinking.Rob Honeycuttat 08:16 AM on 17 June, 2010Doug Bostromat 08:42 AM on 17 June, 2010Perhaps, this sexagenary cyclical calendar was inspired by climatic and astronomical observations.There's also a ton of other intriguing arcana on orbital phenomena. Unfortunately Scafetta goes on to claim that current models are "fundamentally" flawed because they fail to incorporate his unidentified physical mechanism and as well predicts a cooling world in the decades to come, these conclusions being the strained-metaphor equivalent of smoke belching out of the oven as Scafetta's dish is overcooked.Stephen Bainesat 08:49 AM on 17 June, 2010Ed Daviesat 09:23 AM on 17 June, 2010Tony Oat 09:37 AM on 17 June, 2010David Hortonat 10:10 AM on 17 June, 2010NewYorkJat 11:51 AM on 17 June, 2010KRat 12:41 PM on 17 June, 2010reallygood at seeing patterns. There are tons of papers in this; seeing patterns in woodland undercover (nasty critters!), environmental noise (there's somebody behind me!), and even in tea leaves (I have no idea here, I never see anything but leftover tea!). In unmitigated nature this is ahuge advantage. The cost of a false positive is a short period of panting and high blood pressure, while the cost of a false negative is much higher - being eaten by something, or clubbed by a competing caveman. However, as a result of a false positive pattern bias, we also see gnomes in Zurich manipulating currency, UFO's in clouds, conspiracies among the neighborhood pets, on and on and on. If you go looking for a pattern, you're likely to find onesomewhere. I'm much more impressed (charitable?) when someone finds that a pattern falls out of their data, andthensearch for and find a corresponding pattern in a reasonably forcing influence.NewYorkJat 14:08 PM on 17 June, 2010Stephen Bainesat 14:19 PM on 17 June, 2010Donald Lewisat 15:29 PM on 17 June, 2010Bernat 16:13 PM on 17 June, 2010Philippe Chantreauat 16:22 PM on 17 June, 2010NewYorkJat 18:18 PM on 17 June, 2010Arkadiusz Semczyszakat 18:53 PM on 17 June, 2010Arkadiusz Semczyszakat 19:08 PM on 17 June, 2010Riccardoat 19:51 PM on 17 June, 2010Arkadiusz Semczyszakat 21:05 PM on 17 June, 2010Marcusat 21:18 PM on 17 June, 2010Riccardoat 22:11 PM on 17 June, 2010johndat 23:42 PM on 17 June, 2010Albatrossat 02:38 AM on 18 June, 2010johndat 03:33 AM on 18 June, 2010Riccardoat 03:42 AM on 18 June, 2010Albatrossat 08:38 AM on 18 June, 2010Marcusat 09:38 AM on 18 June, 2010HumanityRulesat 10:09 AM on 18 June, 2010scaddenpat 10:23 AM on 18 June, 2010NewYorkJat 10:30 AM on 18 June, 2010Marcusat 12:01 PM on 18 June, 2010HumanityRulesat 14:00 PM on 18 June, 2010Albatrossat 14:25 PM on 18 June, 2010"Also,Mostof the observed increase in global average temperatures since the mid-20th century isvery likelydue to the observed increase in anthropogenic GHG concentrations.[7]""it is extremely unlikely that global climate change of the past 50 years can be explained without external forcing and very likely that it is not due to known natural causes alone. During this period, the sum of solar and volcanic forcings would likely have produced cooling,..."Also, read this There is more in the Copenhagen Diagnosis. Also consider this new paperscaddenpat 14:59 PM on 18 June, 2010'So what you're saying is that it is controversial that the 20th century is made up of 60years cycle with an underlying up trend? I can see it's a short time period to recognize a cycle'>Of course I its controversial. Its not controversial that trend is overlaid with ENSO quasi-periodic cycle. McLean et al kindly showed that you can explain much of the cycle that way. But a longer term cycle? Nope. The alternative explanation that it is response to forcing make more sense physically since no natural cycle in energy flow has so far been discovered. Perhaps also look at this Cyclical?HumanityRulesat 15:05 PM on 18 June, 2010shawnhetat 15:37 PM on 18 June, 2010Riccardoat 16:53 PM on 18 June, 2010Marcusat 16:58 PM on 18 June, 2010chrisat 19:13 PM on 18 June, 2010physicsinvolvingknown forcingsand internal variability. Thus one can independently assess the natural contributions to the 20th century and contemporary warming profile and subtract these from the warming profile “to leave a nice AGW trend”. If one does that, then according to Swanson et al (2009) [*] “Removal of that hidden variability from the actual observed global mean surface temperature record delineates the externally forced climate signal, which is monotonic, accelerating warming during the 20th century.”The other means of doing this is to model all of the contributions to the 20th century warming profile by parameterizing their contribution according to best estimates using known physics, and assess the extent to which these reproduce the warming profile. A couple of examples of this approach can be found here [**] and here [***]. In this case the “nice AGW trend” is establishedfirstaccording to known physics and included in the model, rather than "falling out" of the model as a remainder left over after removing all the contributions from internal variability a la Swanson et al.. In all of these cases the essential features of the 20th century and contemporary warming can be understood in terms of rather well understood natural and anthropogenic contributions. It’s not obvious how another phenomenological numerological analysis that lacks a basis in physics and that doesn't anyway match the empirical data very well is going to add to our understanding. That's not to say it isn't interesting. But fundamental scientific steps are missing here, namely (i) a mechanism for the supposed effect, (ii) its independent quantitation, and (iii) some physical explanation of how this "over-rules" all the known physics otherwise described in the papers cited here and elsewhere. [*]K. L. Swanson et al. (2009) Long-term natural variability and 20th century climate change.Proc. Natl. Acad. Sci. 106, 16120-16123.(see also)Zhang, R., T. L. Delworth, and I. M. Held (2007), Can the Atlantic Ocean drive the observed multidecadal variability in Northern Hemisphere mean temperature?Geophys. Res. Lett., 34, L02709[**]Hansen, J. L. et al. (2005) Earth's energy imbalance: Confirmation and implications.Science, 308, 1431-1435[***]Lean, J.L., and D.H. Rind, 2008: How natural and anthropogenic influences alter global and regional surface temperatures: 1889 to 2006.Geophys. Res. Lett., 35, L18701Ken Lambertat 20:58 PM on 18 June, 2010Berényi Péterat 21:07 PM on 18 June, 2010Posted by Riccardo at 07:37 AMMore generally, for n=4 the claimed 60 year cycle seems to vanish after the peak at year 1940. It's not to say that the n=4 trend has more value than the n=2, but in the end we can say that the nice cyclic behaviour seen in fig. 1 depends on the choice of the trend function. It's worth to recall that its choice is arbitrary, no physics behind it.Scafetta might not have provided physical explanation for his choice of n=2, but we can give it a try. If the long term trend described by the polynomial fit is supposed to be a response to the gradual buildup of CO_{2}in the climate system, and we also accept CO_{2}can be readily translated to "forcing" (two big IFs, but they areconsistentwith the mainsrteam consensus), we can make an educated guess about the correct form of the trend; not in detail, but at least about the order of polynomial to be used. CO_{2}increase was more or less exponential starting around 1850 while "forcing" (the resulting radiative imbalance at TOA - Top of Atmosphere) is proportional to its logarithmic concentration. Therefore this forcing has increased in a roughly linear manner since 1850. For a small forcing the climate system response can be considered linear. Any reasonable dynamic system should behave like this except for states close to some singularity. However, as climate during the last several thousand years have not shown wide fluctuations and we are still not very far from the average of this timespan, no singularity of the system can be too close to the present state. If the response of a linear and time-shift invariant system starts out as x^{4}for a linearly increasing excitation beginning at some instant (in this case in 1850), then its response to a step function starts as a cubic and for a Dirac delta (a brief pulse) it is quadratic. I am not talking about "climate sensitivity" here, that would involve the long term relaxation properties of the response function, it is all about the initial phase. Now. Imagine there was a general balance between incoming SW and outgoing LW radiation at TOA, so the overall balance is neutral. Then, for a brief period (let's say a month or so) this net balance is disturbed, the difference between ASR (Absorbed Shortwave Radiation) and OLR (Outgoing Longwave Radiation) increases substantially, then it is reset to zero again. How does the temperature response look like? The key point is that incoming radiative energy, if not reflected immediately back to space gets thermalized soon. If this excess heat is to stay in the system for a while, it has to be stored somewhere. But there is no other way to store it than heating up some part of the system. As there is no substance around with infinite specific heat, it implies an instant temperature increase. However, a quadratic starts from zero and for a while lingers in its vicinity. The initial phase of the impulse response can't be a quadratic, not even linear. It should start with a step. Therefore response to a linearly increasing CO_{2}forcing can only increase as x^{n}if n is not greater than 2. I am not saying Scafetta's astrological speculation makes sense, but it can not be rejected on the ground stipulated by Riccardo. You have to find another way to debunk it. Of course, as always, there is an alternative. If the underlying trend is not driven by CO_{2}but by some other secular change capable to increase its forcing in a cubic (as opposed to linear) rate, Scafetta is debunked for good. However, the very existence of this mysterious agent is an immediate death blow to consensus climate science, so if I were you, I would not take the tack.neilrieckat 21:30 PM on 18 June, 2010chrisat 21:30 PM on 18 June, 2010"Unless this 'imbalance' heat shows up in the oceans; warming is not happening.."That's an extraordinary bit of flawed deductive reasoning Ken. Since global warming clearlyishappening (all years of the 2000's warmer than all but one of the 1990's; Jan-May 2010 temperature average the highest on record), even despite the fact that the solar cycle has only just come out of a very prolonged minimum and we're in a supposed cooling ocean fluctuation "cycle"....and sea levels are continuing to rise at a rate that cannot be accounted for by land ice and glacier melt...there's something very wrong with your logic. Usually when deductive reasoning leads to conclusions that oppose extant reality, it's pertinent to look at thepremisesthat drive the logic. In your case these are clearly flawed. There is no question that OHC has risen "during the last 16 years". Has OHC stopped rising "for the last 6 years"? Probably not. The sea level data and land ice melt data are incompatible with that conclusion. As usual in science we should wait until these apparent discrepancies have been sorted out before attempting ground-breaking interpretations.....Riccardoat 21:38 PM on 18 June, 2010Berényi Péterat 22:51 PM on 18 June, 2010Riccardo at 21:38 PM on 18 June, 2010one may always show that a model is wrong using its same logicHuh?Riccardoat 00:30 AM on 19 June, 2010monckhausenat 02:00 AM on 19 June, 2010Albatrossat 02:16 AM on 19 June, 2010regional temperatures(e.g., NAO, AO, PDO) and some even of global temperatures (e.g., ENSO). Not to mention the short-term impacts of volcanism, and the known (and limited) impacts of the solar cycle. That noisy record is one of the reasons why one needs to consider 20-30 years of temperature data to derive a statistically significant trend. In addition to the very troubling problems with the paper and method identified by Riccardo: If there is some solar element to this, why does the Stratosphere continue to cool (yes O3 destruction explains some of that cooling but not all of it). Also, it would have been useful for Scafetta to quantify the forcing strength of his mechanism in WM-2. How does the strength of this alleged forcing compare to that of CO2? If real, it may have been comparable in the past, but will it be int he future as CO2 forcing continues to escalate? If his hypothesis is correct, we should see a marked downturn in global temperatures between until 2018 or so. Personally I have no intention of waiting/delaying another 8 years to (in all likelihood) see this hypothesis falsified, and I doubt very much that policy makers will either. Trying to take comfort in the belief that some hitherto undiscovered natural cycle is somehow responsible for the observed warming is not pragmatic, scientific or responsible. Especially when the overwhelming evidence and data points to an significant anthro component.Berényi Péterat 07:34 AM on 19 June, 2010Riccardo at 21:38 PM on 18 June, 2010naively looking at radiative forcings as you did reinforced my findings, if anythingI am surprised. Just try the following. As we do not know the correct exponent, look for the best fit using the forma×t, where^{ξ}-bξis also to be found. If you do it for the 160 years between 1850 and 2009,3.35(not 4) will be the optimal exponent. However, it is not because the actual trend is accelerating so fast, but because the 60 years long dominant cycle fits 2+2/3 times to this timespan. If you choose an integer multiple of 60, like 1890-2009, the optimal exponent is1.82. On the other hand if you try to fit the expression to a simple 160 years long sinusoid with a 60 year period, you may get extremely large exponents (depending on phase). Therefore the source of the apparent super-quadratic trend is the cyclic component, not secular change of forcing. On top of that the acceleration computed this way seems to diminish with time.It's not physics, just plain data analysis. Of course it could be done somewhat more correctly with joint least square fitting of trend and sinusoids, but it is a job for you or Scafetta.1850-1969 2.69 1855-1974 2.29 1860-1979 2.13 1865-1984 2.28 1870-1989 2.11 1875-1994 2.02 1880-1999 1.97 1885-2004 1.99 1890-2009 1.82kdkdat 07:42 AM on 19 June, 2010inductively, by looking at how the error component of the model changes with inclusion and exclusion of various parameters. This helps us to understand the behaviour of the system. My crude statistical analysis of climate data using these kinds of techniques clearly showed that there would have to be evidence of unprecedented quality if CO2 was not to be the main and increasing driver of the current increases in global termperature.