Climatic Variability Over Time Scales Spanning Nine Orders of Magnitude: Connecting Milankovitch Cycles with Hurst–Kolmogorov Dynamics
Yannis Markonis • Demetris Koutsoyiannis Received: 9 November 2011 / Accepted: 15 October 2012 DOI 10.1007/s10712-012-9208-9
Abstract
We overview studies of the natural variability of past climate, as seen from available proxy information, and its attribution to deterministic or stochastic controls. Furthermore, we characterize this variability over the widest possible range of scales that the available information allows, and we try to connect the deterministic Milankovitch cycles with the Hurst–Kolmogorov (HK) stochastic dynamics.
To this aim, we analyse two instrumental series of global temperature and eight proxy series with varying lengths from 2 thousand to 500 million years. In our analysis, we use a simple tool, the climacogram, which is the logarithmic plot of standard deviation versus time scale, and its slope can be used to identify the presence of HK dynamics. By superimposing the climacograms of the different series, we obtain an impressive overview of the variability for time scales spanning almost nine orders of magnitude—from 1 month to 50 million years. An overall climacogram slope of -0.08 supports the presence of HK dynamics with Hurst coefficient of at least 0.92. The orbital forcing (Milankovitch cycles) is also evident in the combined climacogram at time scales between 10 and 100 thousand years. While orbital forcing favours predictability at the scales it acts, the overview of climate variability at all scales suggests a big picture of irregular change and uncertainty of Earth’s climate.
Introduction
If you thought before science was certain—well, that is just an error on your part. -Richard Feynman, The Character of Physical Law (1994 p. 71).
In the first half of nineteenth century, geologic evidence indicated that at least one glacial period existed in Earth’s geological history (Agassiz 1840; from Imbrie 1982). Some decades later, it became clear that during the Pleistocene (2,588,000–12,000 years before present time—BP), there were many glacial periods, known also as ice ages, followed by shorter interglacials, such as the one we experience since the onset of human civilization. Ice age lengths ranged from 35–45 thousand years in early Pleistocene to 90–120 thousand years in the last million years. During glacial periods, continental glaciers enlarged in length and volume, reaching the 40th parallel in some regions of the Northern Hemisphere, while similar phenomena have been identified in the Southern Hemisphere, too. Milankovitch (1941) provided an explanation for the ice ages based on Earth’s orbit variations, which was confirmed after some years by the first temperature reconstructions.
It is now well known that a succession of glaciation and deglaciation periods has not occurred all the time, but only in large periods defining an ‘icehouse climate’, such as the current (Pliocene-Quaternary) icehouse period that started about 2.5 million years ago, as well as the Ordovician and the Carboniferous icehouse periods, each of which lasted 50–100 million years (Crowell and Frakes 1970). In contrast, the ‘hothouse climates’ are characterized by warmer temperatures, abundance of carbon dioxide (concentrations up to 20–25 times higher than current) and complete disappearance of polar icecaps and continental glaciers. Recently, cosmic ray flux was proposed as the controlling factor of the transition between these states (Shaviv and Veizer 2003). As underlined by Kirkby (2007), this theory was both disputed (Rahmstorf et al. 2004; Royer et al. 2004) and supported (Wallmann 2004; Gies and Helsel 2005).
Additional findings showed that the climate of the Holocene (the last 12,000 years), earlier regarded static, was characterized by many climatic events, such as ‘Little Ice Age’, ‘Medieval Warm Period’, ‘Holocene Optimum’, ‘8,200 Holocene Event’ and ‘Bond Events’, deviating from ‘normal’ conditions for hundreds or thousands of years (Bond et al. 2001). For example, during the ‘Little Ice Age’ (1,450–1,850), the temperature of the Northern Hemisphere was about 0.6 oC below 1961–1990 average (Moberg et al. 2005; Pollack and Smerdon 2004), while the ‘Medieval Warm Period’ (950–1,250) was a period of warm climate in Europe and North America and has been related to other climatic events at various regions around the world (Grove and Switsur 1994), including China (Long et al. 2011), New Zealand (Cook et al. 2002) or even Antarctica (Hass et al. 2008).
The preceding ‘Younger Dryas’ episode is an even more impressive case of abrupt climate change that has occurred in the relatively recent climatic history. At the end of Pleistocene, when the last ice age ended and the retreat of the glaciers had begun, a rapid fall of temperature led the climatic system back to glacial conditions. The ‘Younger Dryas’ episode lasted for approximately 1,300 years (starting at *12,800 BP), covered spatially both Hemispheres and ended even more suddenly than it emerged when temperatures increased regionally up to 15 oC in few decades (Alley et al. 1993). Although the cause for this short return to an ice age period is still under debate, it has become clear that it is not associated with a single catastrophic event (such as the release of freshwater from the lake Agassiz in Gulf of Mexico or the impact of a comet) but is rather regarded as an integral part of natural variability (Broecker et al. 2010; Mangerud et al. 2010).
![clip_image001[4]](http://wattsupwiththat.files.wordpress.com/2012/11/clip_image0014.gif "clip_image001[4]"){kind=small}
All these relatively recent events cannot be attributed to the Milankovitch cycles, whose periods are much longer (see below). Thus, it is very difficult to attribute the climate variability at multiple time scales (from decades to many millions of years) to specific quantifiable causal mechanisms that would be applicable ubiquitously. A more modest goal, which is the purpose of this study, would be to characterize this variability over the widest possible range of scales that the available evidence allows. Such characterization unavoidably uses stochastic descriptions and tools, but without neglecting the influence of identifiable deterministic forcings, such as the variations in Earth’s orbit.
Such stochastic descriptions are related to the natural behaviour discovered by the hydrologist H. E. Hurst at the same period of Milankovitch’s discovery. Hurst (1951), motivated by the design of High Aswan Dam in Nile and after studying numerous geo- physical records, observed that ‘although in random events groups of high or low values do occur, their tendency to occur in natural events is greater. This is the main difference between natural and random events’. In other words, in a natural process (e.g., river flow) events of similar type are more likely to occur in groups (e.g., a series of consecutive low flow years) compared to a purely random process (white noise) where grouping of similar states is less frequent.
Unknowingly to Hurst, A. Kolmogorov had already proposed a stochastic process that described this behaviour a decade earlier (Kolmogorov 1940), although both the process and the natural behaviour became widely known after the works of Mandelbrot and Wallis (1968), Klemes (1974) and Leland et al. (1994, 1995). Over the years, this mathematical process (or variants thereof) has been given many names, such as fractional Gaussian noise (FGN), brown noise, fractional ARIMA process (FARIMA) or self-similar process, while the natural behaviour has been called the Hurst phenomenon, long-range dependence (or memory), long-term persistence or scaling behaviour (Koutsoyiannis and Cohn 2008). Here, when referring to the relevant natural behaviour, the stochastic process (definition of which will be given in Sect. 5.1) or the related stochastic dynamics, we prefix them with the term Hurst–Kolmogorov (HK) in order to acknowledge the contribution of the two pioneering researchers.
The HK behaviour, detected in numerous time series, as detailed in Sect. 3 below, indicates fluctuations at different time scales, which may reflect the long-term variability of several factors such as solar irradiance, volcanic activity and so forth (Koutsoyiannis and Montanari 2007). The multi-scale fluctuations cannot be described adequately by classical statistics, as the latter assumes independence (or weak dependence) and underestimates the system’s uncertainty on long time scales, sometimes by two, or even more, orders of magnitude (Koutsoyiannis and Montanari 2007). This underestimation, which some regard counterintuitive, will be further demonstrated below in Sect. 6. Moreover, traditional stochastic autoregressive (AR) models cannot describe these fluctuations in an adequate way, because the autocorrelation functions of these models decay faster than those of the processes they try to model (Beran 1994).
The study of natural variability of past climate can now be based on a lot of available proxy records, some of which are discussed in Sect. 4 and analysed in subsequent sections of this study. These proxies are free of anthropogenic influences that could allegedly contribute to the observed changes. It is our aim to demonstrate some evidence of the presence of HK dynamics at different time scales (spanning nine orders of magnitude). We also examine the coexistence of deterministic controls (due to orbital forcing) and stochastic dynamics and try to identify possible connections between this stochastic dynamics and the modern, obliquity-dominated, orbital theory.
![clip_image003[6]](http://wattsupwiththat.files.wordpress.com/2012/11/clip_image0036.png?quality=75 "clip_image003[6]")
Fig. 9 Combined climacogram of the ten temperature observation series and proxies. The dotted line with slope -0.5 represents the climacogram of a purely random process. The horizontal dashed-dotted line represents the climatic variability at 100 million years, while the vertical dashed-dotted line at 28 months represents the corresponding scale to the 100-million-year variability if climate was random (classical statistics approach). For explanation about the groups of points departing from the solid straight line (with slope -0.08), see Fig. 10 and its description in the text
Fig. 10 Theoretical climacograms of an HK process with H = 0.92 and two periodic processes with periods 100 and 41 thousand years, all having unit standard deviation at monthly scale, along with the climacogram of the synthesis (weighted sum) of these three components with weights 0.95, 0.30 and 0.15, respectively; the empirical climacogram of a time series simulated from the synthesis process with time step and length equal to those of the EPICA series is also plotted
Fig. 11 Climacogram of sunspot number from original data (shown in the embedded graph) from the Royal Greenwich Observatory & USAF/NOAA (http://solarscience.msfc.nasa.gov/greenwch/spot_num.txt)
Conclusions
The available instrumental data of the last 160 years allow us to see that there occurred climatic fluctuations with a prevailing warming trend in the most recent past. However, when this period is examined in the light of the evidence provided by palaeoclimate reconstructions, it appears to be a part of more systematic fluctuations; specifically, it is a warming period after the 200-year ‘Little Ice Age’ cold period, during a 12,000-year interglacial, which is located in the third major icehouse period of the Phanerozoic Eon. The variability implied by these multi-scale fluctuations, typical for Earth’s climate, can be investigated by combining the empirical climacograms of different palaeoclimatic reconstructions of temperature. By superimposing the different climacograms, we obtain an impressive overview of the variability for time scales spanning almost nine orders of magnitude—from 1 month to 50 million years.
Two prominent features of this overview are (a) an overall climacogram slope of -0.08, supporting the presence of HK dynamics with Hurst coefficient of at least 0.92 and (b) strong evidence of the presence of orbital forcing (Milankovitch cycles) at time scales between 10 and 100 thousand years. While orbital forcing favours predictability at the scales it acts, the overview of climate variability at all scales clearly suggests a big picture of enhanced change and enhanced unpredictability of Earth’s climate, which could be also the cause of our difficulties to formulate a purely deterministic, solid orbital theory (either obliquity or precession dominated). Endeavours to describe the climatic variability in deterministic terms are equally misleading as those to describe it using classical statistics. Connecting deterministic controls, such as the Milankovitch cycles, with the Hurst–Kolmogorov stochastic dynamics seems to provide a promising path for understanding and modelling climate.
The paper and SI are available here: http://itia.ntua.gr/en/docinfo/1297/
Discover more from Watts Up With That?
Subscribe to get the latest posts sent to your email.
A trivial point . The greek root for climacogram comes from the Greek κλιμαξ, klimax (genetive : , klimakos) and it means “scale”, “staircase”, and it is in the feminine gender.
Climate on the other hand comes from the greek κλιμα, clima ( genetive klimatos) and it is in the neutral gender.
Think of the plot as a plot of superimposed scales ( nothing to do with climate). .
Tallbloke
I can imagine there is only a small audience presently for a new approach to climate where inclination defines a planet’s climate rather than the current and vague view of long term weather patterns shading off into climate,as far as I am concerned that latter view looks similar to the geocentric views before Copernicus introduced the dynamics of the Earth to resolve observations.
If readers can’t read a polar climate from the sequence of images of Uranus they will hardly comprehend how the old perspective of ‘no tilt/no seasons’ is modified to an equatorial or temperate climate for zero inclination.Just as Kepler modified the awkward reliance on constant orbital motion by introducing variable orbital speed,there is a bigger modification presently with the explanation of the seasons and axial precession –
“..the equator and the earth’s axis must be understood to have a variable inclination. For if they stayed at a constant angle, and were affected exclusively by the motion of the center, no inequality of days and nights would be observed.”Copernicus Chapter 11 De Revolutionibus
It is only within the last few decades through the increasing magnification power of telescopes along with sequential imaging that we can look at climate differently and specifically the ability to see the polar coordinates of a planet turn in a circle to the central Sun as they are carried around by the orbital behavior of the planet.If you or anyone else have a fixed idea in your heads on axial precession ,Milankovitch or any other idea which ignores the ecliptic axis around which the polar coordinates turn annually to the central Sun,then climate studies are effectively finished as inputs become more and more contrived just as they kept adding more and more epicycles to the geocentric theories to hold the picture together.
http://www.daviddarling.info/images/Uranus_rings_changes.jpg
Once a person sees that Uranus has a polar climate they then consider what a zero degree inclination reflects hence a planetary climate spectrum from equatorial to polar with the Earth’s 23 1/2 degree inclination giving us a largely equatorial climate.Everything else can be worked in later and that is the intensely satisfying part as that hasn’t even begun yet.It is in effect raising the standard of climate studies by modifying the explanation Copernicus give for the seasons and axial precession – the fact that it is being done in a thread on a forum rather than in open territory where it is treated with the importance it deserves speaks for itself and how much people really care about climate studies.That is not a complaint,it is what it is.
Now, if science works at its usual pace, this could be accepted wisdom in about 40 years 🙂
Hoser says:
November 4, 2012 at 11:13 pm
Try alt-248 °C.
Aggregated Std Dev? Perhaps: http://en.wikipedia.org/wiki/Standard_deviation#Combining_standard_deviations
Ever hear about the statistician who drowned in a river an average of 3 ft deep?
I’ve used the KS test, see http://www.physics.csbsju.edu/stats/KS-test.html, http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test.
Интересно, что Колмогоров также занимался с геологической историей. Об этом, я не знал.
я тоже.
Gary Pearse says:
November 4, 2012 at 2:49 pm
Regarding chaotic systems (not a big deal in this paper) that are often mentioned in terms of climate behaviour – that I don’t get. With a billion years of temp keeping within the bounds of 5 C above or 5C below average – this seems to me to be anything but chaotic. Chaos is not a thing that comes to mind when we look at a billion year+ unbroken chain of life which requires boundaries for existence. It must be the chaos of a tempest in a tea pot. Anyone care to enlighten.
Its a big subject but a few comments. Full blown chaos itself is, well – chaotic and not so interesting pattern-wise. As a dynamic system moves away from equilibrium in the direction of chaos, there is a “twilight zone” just before chaos is reached where interesting spontaneous pattern formation phenomena occur. I use the term “nonlinear-nonequilibrium pattern” although its a bit long-winded.
A comment often made about “chaos” systems is that very small initial differences lead to big differences later. This can be true but this behaviour is not exclusive to chaotic systems – deterministic systems can do the same. And addressing your point about staying within boundaries, nonlinear pattern systems often display the opposite phenomenon – an attractor. Of all the states that a system could potentially go to, the system converges to a small subset of states or locations called an “attractor”. This is sometimes called a “strange attractor” since people including climate scientists are so indoctrinated to expect everything to be tidy and linear that this nonlinear attractor behaviour seems strange. Consider smoke rising from a smouldering tip of something like a cigarette or match etc. The hot carbon atoms in principle have freedom to diffuse upwards in all directions but instead they converge into a narrow ribbon of smoke. This ribbon is a strange attractor.
In climate history of earth there are apparent discreet temperatures that are preferred, for instance in the last 2 million years the glacial and interglacial temperatures. Further back there is another stable temperature level about 10C higher than today. These temperatures that the earth seems to adopt stably, are likely to be attractors also. An attractor acts to reduce fluctuation, not increase it.
A very good book for an introduction and lucid explanation of chaos and nonlinear dynamics is “Deep Simplicity” by John Gribben, Random House.
Charles Gerard Nelson says: @ur momisugly November 4, 2012 at 1:51 pm
What orbital variations have been observed in the satellite era?
___________________________________
The one I can think of off the cuff is Length of Day and I do not mean just seasonal changes.
Gary Pearse says: @ur momisugly November 4, 2012 at 2:49 pm
…. I’m not sure the water levels in the Aswan Dam are a place one might find to detect Milankovic cycles….
You might want to look at Alexander Ruzmaikin, Joan Feynman, and Yuk L. Yung’s paper. Is solar variability reflected in the Nile River?
And here is another paper.
Late Holocene forcing of the Asian winter and summer monsoon as evidenced
by proxy records from the northern Qinghai–Tibetan Plateau
[you will have to search for the title since the link contains chinese charaters]
So there are your links of climate rainfall patterns to solar irradiance which will change over the long term thanks to the Milancovitch cycles.
Gerald Kelleher says:
November 5, 2012 at 12:31 am
Once a person sees that Uranus has a polar climate they then consider what a zero degree inclination reflects hence a planetary climate spectrum from equatorial to polar with the Earth’s 23 1/2 degree inclination giving us a largely equatorial climate.
I think I’m beginning to see what you are getting at. But doesn’t Uranus move from polar to equatorial climate every 21 years or so as it orbits the Sun?
And as the Earth’s precession advances, doesn’t the pole star stop being the pole star, because the pole is pointing elsewhere. There will always be a visually identifiable star on-axis (or near enough for sailors), but it will be a different star from the one in use a couple of thousand years ago won’t it?
Hi Gail
You are repeating as mistake that is so bound up with climate studies that it is impossible to organize and use dynamical inputs into climate without first removing this completely avoidable tragedy.The day is defined by the AM/PM cycle in that any location where the Sun is visible will
pass in front of the Sun with each rotation and each cycle is different to the next hence each of the 1461 cycles that cover 4 complete orbital circuits must be averaged to 24 hours.
The reason for the variations in the natural noon cycle is staring each and every one of you in the face,aside from daily rotation which is constant,there is another rotation to the central Sun which arises from the orbital motion of the Earth.As orbital speed varies (presently the Earth is speeding up) then so does this speed at which the planet turns – when combined with constant daily rotation you get the variations in natural noon and why we have the seasons
You can actually see the planet Uranus turn South to North in its daily cycle and East to West in its orbital cycle hence two separate axes to account for the same thing we experience on Earth –
These people at JPL do not know what they are talking about,it doesn’t matter whether you use a pendulum clock or VLBI,the conclusion drawn by Flamsteed is not only wrong by virtue that it tries to bundle two separate axes into a single one via the equatorial coordinate system,it is preventing people from modifying axial precession from a long term axial trait into an annual orbital trait.
Surely there is someone who can read the sequential images properly and interpret what looks like axial precession in context of the orbital behavior of all planets,including ours , as an annual orbital trait as the polar coordinates are carried around in a circle to the central Sun
http://www.daviddarling.info/images/Uranus_rings_changes.jpg
Leif Svalgaard says:
November 4, 2012 at 11:58 pm
tallbloke says:
November 4, 2012 at 4:35 pm
“Well, if that turns out to be correct, them amongst those wasting their time must be included people who fit cycles of implausible precision to the movements of the planets.”
Still tilting at straw-men dalek?
Obviously, the Dalek is correct. Apparently, you consider the planet cyclomania to be like straw rather than being rock-solid.
Your reductio ad absurdum make you look more absurd than us, given that we can use our solar-planetary theory to successfully hindcast (and predict) climate change to a useful accuracy, whereas you can’t do anything of the kind with your near useless dynamology.
Larry Ledwick (hotrod) says:
November 4, 2012 at 5:43 pm
…. Hopefully it will help me get my head around this.
http://itia.ntua.gr/getfile/1135/1/documents/2011IUGG_HydrologyChange_transcript_2.pdf
________________________________________
Larry, thanks for the link. Slide 23 explains the math, however the whole presentation is worth reading. Too bad it is not something our politicians can understand, or the Climastrologists want to understand.
tallbloke says:
November 5, 2012 at 7:56 am
given that we can use our solar-planetary theory to successfully hindcast (and predict) climate change to a useful accuracy, whereas you can’t do anything of the kind with your near useless dynamology.
Ah, now it is climate change, not solar activity. Presumably the latter causes the former, or are you saying that it does not? Anyway, you have not produced any such successful predictions [you don’t know if a prediction is successful until after the fact]. On the other hand my dynamo-based forecast of SC24 has been quite successful so far.
@ur momisugly Gail Combs says:
November 5, 2012 at 7:58 am
The interesting observation I took out of that paper is that if most/all natural processes have high Hurst coef and only appear random at small time scales then this helps to explain “black swan events”
In that context a black swan event is not only not unlikely it would be expected in long time scales. Given the size of the earth and the number of natural processes we probably have one of those “exceptional events” happening every day.
Sort of puts the Russian heat wave in perspective, as not unusual at all. On a long enough time scale every region in the world will experience such a heat wave if climate is a high Hurst coef process.
Larry
Leif Svalgaard says:
November 5, 2012 at 8:16 am
my dynamo-based forecast of SC24 has been quite successful so far.
That’s bsed on a heuristic empirical observation, not a theory. You can’t use it to hindcast solar-terrestrial behaviour in the deep past, or beyond the next cycle.
In 1983 and just about the same time as the cult of modeling human activity to account for planetary temperatures was ramping up,there was a sense of dismay in the empirical community that people were no longer treating mathematical models as a tool with limitations but rather physical observations were adjusted to suit the models.It doesn’t matter if locations experience drought or floods,cold spells or heatwaves,each event can be adjusted to support the model of human activity/global warming and that is not just wrong,that is a symptom of a disorder.
“A Langrangian is not a physical thing;it is a mathematical thing – a kind of differential equation to be exact.But physics and maths are so closely connected these days that it is hard to separate the numbers from the things they describe.In fact,a month after [Philip] Morrison’s remarks,Nobel Prize winner Burton Richter of the Stanford Linear Accelerator Center said something that eerily echoed it: ” Mathematics is a language that is used to describe nature” he said “But the theorists are beginning to think it is nature.To them the Langrangians are the reality ” Discover Magazine ,1983
Even those who would outwardly appear to have common sense would not dare question the limitations of modeling however much they disagreed with the models of future weather conditions.To those pushing models of human activity as a means to control planetary temperature and even those who counter it,the models are everything and nobody bothered to consider the core planetary facts which basically mock present human understanding of climate.
They say one of the greatest human achievements was putting a man on the moon for sheer effort and human ingenuity,the greater achievement still may be bringing man back down to Earth once more where common sense and genuine creativity will prevail.
It looks like the “climacogram” is just a fancy name for the log-log gradient i.e. the Kolmogorov-Richardson fractal dimension, of temperatures with time.
“Log-log” behaviour is characteristic of systems exhibiting nonequilibrium pattern behaviour. It means in this case that small changes happen all the time, big changes more rarely, really big changes very rarely – in a log-log pattern. The most important thing to understand about such changes is that these changes can be generated BY THE SYSTEM ITSELF. One does not have to conjure up a new story of soot or CO2 or methane or farting or volcanoes or ozone for every single wiggle of the curve, as present day climatologists do. The system changes BY ITSELF.
It can however be of the periodically forced variety of nonlinear oscillation, so there can be a role for external forcing, but possible a complex, non-obvious relationship between forcing and emergent signal. It could also be a mixture of strong forcing (e.g. the 41,000 yr and 100,000 yr Milankovich signal) and weak forcing (other oscillatory inputs), resulting in a more complex and variable oscillation. There are, however, nonforced oscillatory systems. The Belousov-Zhabotinsky reactor for instance has both forced and non-forced instances.
tallbloke says:
November 5, 2012 at 8:04 am
That’s based on a heuristic empirical observation, not a theory. You can’t use it to hindcast solar-terrestrial behaviour in the deep past, or beyond the next cycle.
Shows how little you know. Here is the detailed theory http://www.leif.org/research/Jiang-Choudhuri-2007.pdf
Where is yours?
As the poleward drift of magnetic field has a strong random element, confident prediction is never possible more than one cycle ahead. Hindcast is possible if the polar fields are known. As we only know the polar fields for the last 100 years or so, no further hindcast is possible. But we can say something about the past: http://www.leif.org/EOS/Choudhuri-Karak-2009.pdf
All based on solid physics, with theory, equations, numbers, the works.
What do you have? Nothing, as far as I can tell from your various postings.
phlogiston says:
November 5, 2012 at 8:57 am
“…possibl[y] a complex, non-obvious relationship between forcing and emergent signal.”
Tidal forces may provide an answer. Tidal forces are dissipative, that is, they convert macro kinetic energy into heat. They are small but persistent. Dissipative forces will tend to bring the kinetic energy of the planetary orbital ensemble to its lowest available energy configuration (second law of thermodynamics – maximum entropy principle). This involves harmonics and overtones, and if I understand the present paper correctly it will tend to raise the variability of the shorter periods of measurement compared with the longer periods, since shorter cycles dissipate energy more rapidly. Other systems that show this propensity are musical instruments (harmonics help to dissipate energy) and atoms (spontaneously emit photons – the complex arrangement of electron orbitals and the way they are preferentially filled is an obvious illustration of the maximum entropy principle). This helps to explain the ratios observed in the planetary orbits and the self-similarity (resonance) that the solar system exhibits. It means that our earthly climate will continue to vary as it must to help bring the kinetic energy of the solar system to its lowest available state, but also that the variability will decrease with time as the process progresses. .
Ideally, the reviews should not be anonymous. Both the reviews and the author’s rebuttals or responses should be published with the paper. People don’t fight duels today so the element of social engineering inherent in the anonymous peer review methodology is no longer called for. It would also reveal “buddy” review and the action of known axes being ground and bones picked and the structure of scientific cliques.
[snip . . unintelligible . . mod]
“”””””…..Gerald Kelleher says:
November 5, 2012 at 8:24 am
“A Langrangian is not a physical thing;it is a mathematical thing – a kind of differential equation to be exact.But physics and maths are so closely connected these days that it is hard to separate the numbers from the things they describe.In fact,a month after [Philip] Morrison’s remarks,Nobel Prize winner Burton Richter of the Stanford Linear Accelerator Center said something that eerily echoed it: ” Mathematics is a language that is used to describe nature” he said “But the theorists are beginning to think it is nature.To them the Langrangians are the reality ” Discover Magazine ,1983…..”””””
Maybe Mathematics and Physics are related; but it would be a mistake to equate either of those with “nature”.
Both Mathematics, and Physics , are pure fiction, that we made up out of whole cloth in our head.
Nothing in any branch of mathematics actually exists anywhere in nature; there are no points or lines or circles, or spheres, or anything else from mathematics. And the Physics, is really a descriptive model of another fiction, that we believe closely emulates nature in its behavior.
It is a tribute to the giants who constructed our models of Physics, and the mathematical tools to manipulate those models (not nature), that they gave us a way to deal with something probably far too complex for us to really understand.
phlogiston says:
November 5, 2012 at 8:57 am
“It looks like the “climacogram” is just a fancy name for the log-log gradient i.e. the Kolmogorov-Richardson fractal dimension, of temperatures with time.
“Log-log” behaviour is characteristic of systems exhibiting nonequilibrium pattern behaviour. It means in this case that small changes happen all the time, big changes more rarely, really big changes very rarely – in a log-log pattern.”
===================================================================
Thanks for a good explanation of something, that as someone said earlier, is “way above my pay grade.” Searching Kolmogorov-Richardson on Google, I found entries for Richardson-Kolmogorov. One had a good cartoon to explain the concept.
Since we speak of “hundred year floods” and “ hundred year storms,” it looks like this log-log gradient is a good way to look at climate. In my Google search it appears as though Koutsoyiannis used this technique first to look at rain fall patterns. Looks like a good tool for further use.
Leif Svalgaard says:
November 5, 2012 at 9:28 am
But we can say something about the past: http://www.leif.org/EOS/Choudhuri-Karak-2009.pdf
All based on solid physics, with theory, equations, numbers, the works.
What do you have? Nothing, as far as I can tell from your various postings.
Quoting from the second paper you’ve linked:
“Following this approach, we stop the code at a sunspot minimum after obtaining a relaxed
periodic solution. Then, in the northern hemisphere, we multiply A(r, ) above r = 0.8R⊙ by a factor
N,
whereas we use the factor
S for the southern hemisphere. To get good results, we have to make another
assumption which we agree is somewhat ad hoc.”
Lol. Is that it? Solid physics? I think not.
This model output simulating solar variation from planetary frequencies also observed in real empirical solar data is a lot more like the real thing.
http://tallbloke.wordpress.com/2011/07/31/bart-modeling-the-historical-sunspot-record-from-planetary-periods/
“equations, numbers, the works.” and no ad hoc fudges.
Your team has some catching up to do.
tallbloke says:
November 5, 2012 at 12:17 pm
“Following this approach, we stop the code at a sunspot minimum after obtaining a relaxed
periodic solution”. Lol. Is that it? Solid physics? I think not.
Some reasonable assumptions are always needed when data is sparse. That you do not understand the physics is your own failing.
This model output simulating solar variation from planetary frequencies
No mechanism, no physics, just simulating some numerology. But the proof is in the pudding. Produce your 21st century prediction and your 17th century hindcast, then come back here.
tallbloke says:
November 5, 2012 at 12:17 pm
“To get good results, we have to make another assumption which we agree is somewhat ad hoc.” Lol. Is that it? Solid physics? I think not.
I note you have no comment on the first paper which describes the physics. The second paper shows that it is possible to get a Maunder Minimum with an assumption on asymmetry.
You neglect to quote the conclusion of the paper:
“We have shown that different characteristics of the Maunder minimum can be explained very elegantly on the basis of the simple ansatz that, as a result of randomness in the Babcock–Leighton process, the poloidal field at the end of the last cycle before the Maunder minimum fell to a rather low value in the northern hemisphere and also became small in the southern hemisphere due to the diffusive coupling between the hemispheres. While we are carrying on an analysis to show that this ansatz can be justified on statistical grounds, the fact that calculations based on this ansatz agree with observational data so extremely well gives credence to this ansatz. Our model explains why the Maunder minimum started abruptly, but ended with a more gradual growth of cycle strengths”
This shows the strength of a real physical theory: that you can play ‘what if’ games and explore different scenarios.