## 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.

ScaredAmoebaat 16:50 PM on 27 June, 2010~~poor~~weak papers in the past and I suspect this attempt is just more of the same.RickGat 00:12 AM on 28 June, 2010philcat 07:35 AM on 28 June, 2010scaddenpat 07:59 AM on 28 June, 2010Moderator Response:scaddenp's suggestion that further discussion happen on the Models are unreliable thread is a good one. So please do.Ken Lambertat 23:50 PM on 28 June, 2010chrisat 01:25 AM on 29 June, 2010speed-upin sea level rise. We don't know to what extent these apparent slow downs and rises are fully real (they’re certainly at least partly real; see below). Overall the data continue to be compatible with a continuing trend in sea level equivalent to a rise somewhat above 3 mm.yr-1. This is wrong:"...entirely incompatible with the steadily increasing imbalance proposed by CO2GHG theory.If by "CO2GHG theory" you mean the rather well-founded expectation that the earth surface temperature will rise under the influence of a radiative imbalance towards a new equilibrium temperature around which it will fluctuate as a result of natural variability (i.e. the theory of enhanced greenhouse forcing), there isn't anything necessarily incompatible with the observed sea level rise data. It would be a fundamental misunderstanding to think that there should be anything necessarily "steady" about the progression of manifestations of radiative imbalance particularly when assessed over short periods. One needs to consider: (i) measurement errors. These are smaller for sea level rise measurements than for ocean heat content (OHC) measures, but they are significant as is obvious from inspection of the data . This is always a good reason for preferring longer term trends over very short time periods. (ii) real short term variability. This is likely to be large [*]. And of course we know this from simple inspection of the data. Natural variability will enhance the apparent greenhouse-forced sea level rise during some periods (El Nino, solar cycle, reduced albedo), and during other periods suppress the apparent sea level rise (La Nina, solar cycle, enhanced albedo, volcanic activity). Overall this natural variability will more or less reduce to near-zero with respect to trends. Therefore if we wish to make profound interpretations about trends, we obviously choose to assess the progression of parameters over longish periods in which this variability is averaged out. [*] For example, the redistribution of ocean heat during El Ninos and La Ninas can have very large temporary effects on sea level. It’s not unheard of the have a short term (year or so) rise of 10-15 mm.yr-1 during strong El Ninos, and largish sea leveldecreasesduring La Ninas. It’s dumb to pretend that these effects don’t occur, or to ignore them when attempting fundamental interpretations about responses to radiative imbalances.Peter Hogarthat 02:47 AM on 29 June, 2010kdkdat 07:33 AM on 29 June, 2010Doug Bostromat 07:58 AM on 29 June, 2010There is some implication that there is an "AGW theory" and that there is an argument in its support, and that said argument is a cohesive thread starting with Fourier and ending at the dreaded-extremist-boogeyman-Gore, and that failure of any chain in said argument necessarily implies "see, so no carbon policy is necessary". (I'm missing a few steps in their reasoning here, too, but that's another topic still.) I claim there is no "AGW theory" in the sense that there is an argument that four colors suffice, or more fairly, that stars follow an evolutionary path based on their mass. AGW is not an organizing principle of climate theory at all. Hypotheses, organizing principles, of this sort emerge from the fabric of a science as a consequence of a search for unifying principles. The organizing principles of climatology come from various threads, but I'd mention the oceanographic syntheses of Sverdrup and Stommel, the atmospheric syntheses of Charney and Lorenz, paleoclimatological studies from ice and mud core field work, and computational work starting with no less than Johnny von Neumann. The expectation of AGW does not organize this work. It emerges from this work. It's not a theory, it's a consequence of the theory. Admittedly it's a pretty important consequence, and that's why the governments of the world have tried to sort out what the science says with the IPCC and its predecessors. That tends to color which work gets done and which doesn't, and I think it should. As Andy Revkin pointed out, it may be time to move toward a service-oriented climatology, or what I have called applied climatology. The point is that this amounts to application of a theory that emerged and reached mathematical and conceptual maturity entirely independent of worry about climate change. So attacks on climate change as if it were a "theory" make very little sense. Greenhouse gas accumulation is a fact. Radiative properties of greenhouse gases are factual. The climate is not going to stay the same. It can't stay the same. Staying the same would violate physics; specifically it would violate the law of energy conservation. Something has to change.For a little more on whatmustchange, how much, etc. see the rest of Tobis' post. My point in quoting Tobis is to make a helpful reminder that "falsifying" the notion of anthropogenic global warming would require an upheaval of research none of us are going to witness. So don't look to external matters such as the moon and stars or things that make graphs wiggle to put a neat "done" on the matter.Ken Lambertat 00:32 AM on 30 June, 2010Peter Hogarthat 02:48 AM on 30 June, 2010kdkdat 06:31 AM on 30 June, 2010Ken Lambertat 00:37 AM on 1 July, 2010Peter Hogarthat 07:58 AM on 1 July, 2010kdkdat 08:15 AM on 1 July, 2010philcat 08:53 AM on 1 July, 2010Ken Lambertat 00:33 AM on 2 July, 2010chrisat 01:41 AM on 2 July, 2010temporal progressionof Earth responses to enhanced greenhouse gas is poorly predictable, both in its general trend and due to this natural variability, the effect of enhanced greenhouse forcing on the Earth system is normally assessed in relation to the surfaceequilibriumtemperature response, once the climate system has re-equilibrated with the forcing. "CO2GHG theory" (as you call it!) has rather little to say about theexact progressionof climate-related parameters (like sea level) other than that these will fluctuate around the trend on the progression towards equilibrium. It is a total fallacy (and a strawman argument) to think that one should observe continuously incremental changes in any parameter of the climate system, as the latter progresses to a new equilibrium state.Ken Lambertat 00:24 AM on 3 July, 2010kdkdat 09:16 AM on 3 July, 2010kdkdat 09:29 AM on 3 July, 2010chrisat 20:17 PM on 3 July, 2010again. That's trolling. Why not simply state explicitly how you determined these apparent "offsets"? I think I know what you've done...if so it's invalid numerology. But we won't know for sure unless you tell us. TWO: linear/quadratic trends: Science isn't addressed by attempts at bullying Ken ("Prove to me that BP's quadratic approach is wrong!"). Fitting a quadratic to a temporal progression of a parameter is meaningless unless one has some independent justification for the quadratic and its particular form, and you should be careful not to be fooled by flawed analyses [*]. In the case of a relative short (18 year) period of sea level rise with significant variability from measurement "noise" and internal variability we have to be careful not to mislead ourselves with inappropriate curve fitting that is hopelessly biased by the short term variability. However we can ask a simple question about the data, namely:(see [*] below)” Given the variability in the data is the sea level rise consistent with a linear progression in time, or is it accelerating or decelerating?”If we take the data (say the unadjusted dataset with seasonal signal removed ) and project forward from the very start of the record with a linear trend of 3.2 mm.yr-1, we find that the current sea level is pretty much smack on the projected trend. That’s an inescapable fact. However one fiddles around with inappropriate curve fits and other numerological “analyses”, one can’t escape the observational fact that the sea level data is entirely consistent with a continuing linear trend of around 3.2 mm.yr-1 rise . Might sea level rise be decreasing? Possibly, but there is no evidence for such a conclusion. Might it be accelerating? Possibly, but we can’t say from the data yet. THREE: heat budget Your other points were addressed here. You're still asserting a fundamental fallacy, i.e.(see [*] below)"...keeping in mind that the CO2GHG theory requires that the biosphere gain 145E20 Joules/year every year."; this will never be correct no matter how many times you repeat it. ------------------------------------------- [*] the problem with Peter's seductive numerology can be seen by fitting a quadratic to thefullsatellite data set (Peter apparently fitted only 16 years of this). If one does so the already small "acceleration term" of -0.108 mm.yr^(-2) is reduced to -0.0318 mm.yr^(-2). The resulting quadratic fit is barely distinguishable from a linear fit. Scientists and skeptics aren’t fooled by flawed numerology…..Ken Lambertat 22:57 PM on 3 July, 2010chrisat 02:31 AM on 4 July, 2010” Given the variability in the data is the sea level rise consistent with a linear progression in time, or is it accelerating or decelerating?”Whether one uses a linear regression or a quadratic there is no evidence in the data that sea level rise is accelerating or decelerating. The current sea level is pretty much smack on the level it “should be” by projecting forward from nearly 18 years ago with a linear trend of around 3.2 mm.yr-1. Why does the linear regression and the quadratic give virtually the same fit? It’s because the constant of the third term of the quadratic is close to zero (it’s around 0.03, a value more than 100 times smaller than the year on year change in sea level of around 3.2). Attempting to infer an “acceleration” or “deceleration” from the sea level rise from the coefficient of a quadratic fit is simply spurious in this case. On ocean heat content and steric sea level rise. You seem surprised that”steric SLR is non-linear against OHC rise”. There’s no reason why they should be linear Ken. The steric sea level rise from a given addition of OHC depends on where the heat ends up. The same number of calories (the energy required to warm 1 gm of water by 1 oC) results in a volume expansion that depends on the water temperature (and pressure). 1 calorie of thermal energy causes an expansion of warm surface waters that is larger than the thermally-induced expansion of colder deeper water. The difference is large; up to 2-fold for heat deposited in the upper 700 metres compared to heat deposited in the deeper oceans. And we know that measurement of OHC content is very difficult; even the last few years have seen large readjustments in the data. It’s unlikely that we’re yet on top of the OHC measurements, especially in accounting for heat that is taken to depths below 700 metres. Otherwise attempting fundamental interpretations by fixing in stone uncertain numbers obtained over very short periods isn’t that helpful. As Trenberth points out [*] the entire apparent discrepancy in apparent ocean heat content, sea level rise and TOA radiative imbalance over a very short time period could be resolved if the “residual heat” ”is being sequestered in the deep oceans below the 900 m depth used for the ARGO analysis where it would contribute 0.4-0.5 mm.yr-1 sea level rise….”. We know that 0.1-0.15 W.m-2 (globally averaged) of the apparent heat imbalance can be understood in terms of the descent to a very prolonged solar minimum during the period 2003-2009. Each of these (as well as short term variations in atmospheric conditions) may be contributing to the apparent imbalance during the very short period 2004-2008. Already the sea level rise has recovered during the last couple of years, likely due to an acceleration (during this short period) in the steric sea level contribution. When these very short term uncertainties have been sorted out we’ll have a clearer picture obviously… [*]K.E Trenberth (2009) An imperative for climate change planning: tracking Earth’s global energyCurr. Op. Environ. Sustain. 1, 19–27kdkdat 08:08 AM on 4 July, 2010Ken Lambertat 23:27 PM on 4 July, 2010Peter Hogarthat 02:59 AM on 5 July, 2010chrisat 03:54 AM on 5 July, 2010”It is quite legitimate to curve fit to each separately, be it linear or otherwise to see what the individual differences are. An offset might indicate a real jump in SLR, or it could mean that linearization is not a good fit and some other relationship is applicable; or it could be an offset.”Bottom line: (a) One cannot determine “offsets” from linear fits of parts of data and extrapolating these to the “join”; that’s a mathematical fallacy. The issue of offsets in merging satellite sea level data has been considered in great detail by the relevant scientists. (b) The full satellite record is consistent with a linear progression equivalent to somewhere near 3.2 mm.yr-1. Fitting the data to a quadratic yields a fit that is very close to a straight line. There isn’t a huge amount more to be determined from the data Ken. There was a short period (2006-2008ish) where the sea level rise slowed down a bit; the last 18 months or so has seen it return to its trend level. We have to be careful not to attempt to make fundamental interpretations from these instances of short term variability.”Nine years for Topex and 7 years for Jason 1 are not 'very short time periods' when the whole AGW theory really has a 30 year history (1980 onward).”That doesn’t make a lot of sense. Why should the time period suitable for establishing reliable trends in the temporal progression of a parameter bear any relationship to the history of a scientific field? Surely the relevant considerations are scientific ones [(i) measurement error and (ii) the temporal periods of factors (El Nino, La Nina, volcanoes, solar cycle, aerosols, clouds and other atmospheric factors) that modulate the trend]. In any case our understanding of AGW has a much deeper history that dates back to the late 19th century.”And please expound on the theoretical SLR which we agree is non-linear with OHC rise (or TOA imbalance) when the major driver of TOA imbalance is a logarithmic function. What is the theoretical SLR-TOA imbalance relationship?”That’s a poorly posed question, and you possibly need to think what you are really trying to ask. On the decadal timescale the rate of sea level rise is likely approximately proportional to the absolute global temperature above a reference value that would correspond to a steady state sea level. Otherwise there are too many things mixed into your question. The rate of sea level rise may be appear rather dissociated from the TOA imbalance since it has both steric and mass components, and we know these are difficult to tease apart, especially on short timescales when stochastic and cyclic variability modulates the effects from enhanced greenhouse forcing.”There is no established mechanism nor decent measurement to support the idea of short term heat imbalance being sequestered below 900m. How do you get it down there without it showing up in the top 700m? The time lags are reputedly large due to relatively low thermal conductivity.There is direct evidence, for example here and here [*], as well as potential mechanisms [**] for recent sequestering of heat in the deep oceans. It remains to be determined whether these account for some short term apparent imbalance in energy budgets.”The Solar cycle argument I have dealt with elsewhere - but with 0.25W/sq.m reputedly as the top to bottom range of the 11 year cycle, if at the bottom the overall TOA imbalance disappears (as shown by flat OHC for the last 6-7 years); then at the top, the imbalance must be about 0.25W/sq.m. This implies an underlying imbalance of half the range which is about 0.125W/sq.m. This is a long way short of Dr Trenberth's 0.9W/sq.m imbalance.”You’ve got that quite wrong Ken. The 0.9 W/m^2 is thetotalTOA radiative imbalance. The apparent shortfall in the energy budget during the very short period 2004-2008 that Trenberth is discussing is somewhere around 0.2-0.6 W/m^2. (see page 25 of Trenberth 2009 [***]), based largely on an apparent deficiency of ocean heat in the upper oceans. Perhaps 0.15 W/m^2 might be account for by the particularly extended solar minimum, which would leave an apparent shortfall for this period of 0.05-0.45 W/m^2. As Trenberth states, this could be fully accounted for by being sequestered in the deep ocean below 900m. Trenberth points out in a recent Nature commentary that the deep ocean data for the period 2003-2008 yields a value of 0.54 W/m^2 [*]. If that were to be correct then there isn’t really a shortfall at all. The whole point about Trenberth’s recent commentaries on this issue is not to feed conspiracy theories and dodgy analyses, but to highlight the need for better monitoring systems to better monitor the climate system. As Trenberth points out in yet another commentary [*****], the recent enhanced sea level rise and increased ocean surface temperatures may be associated with a reappearance of the “missing heat”: Time will tell…. ------------------------------ [*]K. von Schuckmann, et al. (2009) Global hydrographic variability patterns during 2003–2008J. Geophys. Res. 114, C09007.[**]S. Masuda et al. (2010) Simulated Rapid Warming of Abyssal North Pacific WatersScience, in press[***]K.E Trenberth (2009) An imperative for climate change planning: tracking Earth’s global energyCurr. Op. Environ. Sustain. 1, 19–27[****]K. E. Trenberth (2010) The ocean is warming, isn’t it?Nature 465, 304.[*****]K. E. Trenberth and J.T. Fasullo (2010) Tracking Earth’s EnergyScience 328, 316-317.kdkdat 11:08 AM on 5 July, 2010Ken Lambertat 00:44 AM on 6 July, 2010JMurphyat 01:36 AM on 6 July, 2010Ken Lambert wrote :Readers might also note the convenience with which you classify time periods as short and long term. 9 years and 7 years are impossibly short term when SLR is down (short term noisy data etc), but when SLR ticks up with Jason 2 over the last 1-2 years - it is 'back on track'. So 7 years data is not long enough for my case, but 1-2 years is 'back on track' and valid for your case.Well, as a reader, I note that I cannot find a quote from chris that states the SLR is 'back on track', but I haven't had a thorough check, so perhaps you could post a link to it to make it easier to find ? I can find, however, this bit from his last post :"There isn’t a huge amount more to be determined from the data Ken. There was a short period (2006-2008ish) where the sea level rise slowed down a bit; the last 18 months or so has seen it return to its trend level. We have to be careful not to attempt to make fundamental interpretations from these instances of short term variability."And that last sentence in particular rather seems to prove you wrong in your assertion. Did you not see that ? What was that about Dunning-Kruger...?Peter Hogarthat 01:38 AM on 6 July, 2010kdkdat 09:14 AM on 6 July, 2010Ken Lambertat 23:54 PM on 6 July, 2010Ken Lambertat 00:16 AM on 7 July, 2010chrisat 02:43 AM on 7 July, 2010"due respect for the uncertainties and inconsistencies with reconciling SLR and OHC given the current state of knowledge", then that should be applied across the board. If one looks at Trenberth's analysis of the heat budget during the short period 2004-2008, then there is an apparent shortfall, although the error bars overlap. You're correct that I made a double accounting of the TSI contribution - my mistake. Otherwise the apparent shortfall during this short period amounts to ~ 0.2 - 0.69 W. As Trenberth states, this might possibly be accounted for by sequestration of some heat into the deeper oceans during this period....there may be other explanations. Is there anything more to be said about this? I don't think we can draw any particular conclusion at this time. Sea levels have risen quite rapidly during the last 18 months and as Trenberth states the recent warming may be in indication that the "missing heat" is reappearing. I expect we will have a better idea of the situation during the next few years. Otherwise I'm not sure this really merits the degree of insult and monothemic badgering that you're engaged in. Perhaps it would help if you could be a little more specific about what you are trying to achieve or what you wish to draw from the data presented by Trenberth. And you do need to address the analysis more rigorously. Your "respect for uncertainties...." and "looking hard at composite charts....", apparently equates to drawing regressions of bits of the data and noticing that these don't meet at the ends. That's simply bogus with respect to identifying offsets. I've linked to a series of papers in which the question of merging satellite sea level data is addressed in great detail. You don't seem interested in that but you should be if you sincerely have "respect for the great uncertainties.....". Likewise, wehaveanalyzed the satellite data with a quadratic fit. The quadratic fit is so close to a linear fit (the "acceleration term" of the quadratic is close to zero) that it makes little difference. So the satellite data conform rather closely to a linear fit (with some wiggles). That's a simple fact Ken. You seem sufficiently unhappy about the fact that current sea levels are pretty much smack on the long term linear trend defining the satellite era data that you feel I should be pilloried for pointing this out! Oh well....Peter Hogarthat 03:07 AM on 7 July, 2010kdkdat 07:44 AM on 7 July, 2010Ken Lambertat 23:31 PM on 7 July, 2010Ken Lambertat 23:43 PM on 7 July, 2010chrisat 00:39 AM on 8 July, 2010I deal with highly non-linear larde deflection FEA analyses every day. Many engineering relationships are non-linear, much of nature is non-linear - so what is this big deal about statistical linearity?We can fit the sea level data how one wishes. The extant fact is that the satellite data fits closely to a linear trend (somewhere around 3.4 mm.yr-1 over the whole period). We can fit the data to a quadratic. If one does this the quadratic fit is essentially the same as the linear fit. The reason is that the third term of the quadratic is as close to zero as makes no difference. The reason a linear fit is appropriate is that it allows one to address a very simple and pertinent question namely:” Given the variability in the data is the sea level rise consistent with a linear progression in time, or is it accelerating or decelerating?”Cutting through all the flak, I think we've established that the sea level data conform rather closely to a linear fit (or a quadratic with an essentially zero "acceleration term"!), that there is no justification in the data to infer that the rate of sea level rise is slowing down or speeding up, and that there is no basis in the data for insinuating "offsets" in the merging of sea level data. So some progress I would say!