Kevin Kilty

Recently I got around to reading my May 2020 (yes, I am that far behind) issue of Physics Today. It contained what promised to be an engaging article on tying celestial mechanics to Earth’s ice ages.[1] Indeed, the article provides many interesting points between and among celestial mechanics, climate changes, and impacts on human populations and evolution. There were some concerns in my mind about some details the article presented, which I will discuss presently, but one statement the author made caught my attention specifically.

“Changes in GHGs always precede variations in global temperatures and are therefore a clear driving force of climate change, not a response to it.”[2]

This appears to fly completely in the face of what seems to me a general opinion expressed on WUWT – that CO₂ in particular changes in response to changing global temperature, with CO₂ rising with a 800 to many thousand year lag behind rising temperature.[3] There was but a single reference provided for support of Maslin’s claim, and I immediately obtained this article.[4]  Let’s examine this claim about relative timing of CO₂ and temperature changes before moving on to the principal topics of this essay.

Does CO₂ lag or lead temperature?

There are several things about this cited research that weaken its support for Maslin’s seemingly strong claim about timing between ice ages and CO₂ fall or rise.

First, the supporting article title contains the phrase “during the last deglaciation” which restricts its findings to a period of time since the last glacial period and to smaller temperature and ice volume excursions. The physics of these processes could be quite different from the longer-term, and larger amplitude process of periodic global stadia and interstadials.

Second, the analysis in this supporting article focuses on Antarctic ice cores to the exclusion of Greenland ice core results. This exclusion is defended on the basis that the Atlantic Meridional overturning (AMOC) causes a seesawing of heat balance between the hemispheres, and thus the Greenland ice core results make a poor representation of global conditions.

Third, the premise of the article, that CO₂ is the principal driver of climate change within the time period chosen for study is supported through a comparison of temperature proxies to CO₂ concentrations against  EPICA dome C ice core. Yet, the authors spend much effort bolstering their claim through global climate modeling. I am always skeptical about modeling.  A careful inspection of the plot showing correlation between CO₂ and the global temperature stack from proxies, shows only one sigma error bars (uncertainties) and leads to a better impression of CO₂ leading temperature than what one might conclude for a 95% (nearly 2 sigma) confidence plot. The modeling support, which comes from 1000 Monte Carlo runs, suggests a global lag of temperature behind CO₂ of 460 ± 340 years with a coverage factor of only one (1 sigma). Thus a 95% confidence interval would be consistent with zero lag or even a small negative lag.

Fourth, the temperature proxy data are biased well away from polar regions and the edge of the ice sheet where Maslin’s discussion mainly focuses on feedbacks involved. Moreover, many potential global influences on the climate system are poorly constrained (dust for example). The author admits that the changes in CO₂, which levels off a millennium or more before temperature does, cannot be the sole driver of climate change. Temperature must be driven by “other aspects of the climate system”.[5] Liu, et al, come to  this same conclusion.[6]

I would say the claim put forth by Maslin has some support but is still weaker than he implies..  

A theory of growth of ice sheets

Let’s now leave the critiquing of Maslin’s claims regarding the relationship of CO₂ variations to temperature, to examine more specifically his discussion about what causes ice ages to wax and wane. First, to initiate an ice age there is a pronounced decline of insolation at 65 degrees north latitude. This, he claims, must be the result of orbital variations. This reduced insolation allows snow from the previous cold season to remain over to the next, with an attendant accumulation of thicker snow year by year. This, in turn allows a foothold for an ice-albedo feedback to provide additional cooling of the climate and the accumulation of thicker ice sheets. Meanwhile the cooling climate results in declining levels of CO₂ and water vapor in the global atmosphere which cools the climate further in a positive feedback loop.

Once ice sheets have grown to substantial thickness another feedback appears which is the ice sheets themselves pushing circum-global atmospheric circulation toward the tropics. This starves polar regions of precipitation. This negative feedback loop prevents a continually growing thickness of ice sheets and further drying of the atmosphere. It acts as a hard limit of sorts to the growth of ice sheets, and if one can compare the sum total of these processes as acting as a feedback regulator, this hard limit behaves like a relay in a refrigeration cycle — it opens to halt further cooling processes.

Over the past million years or so this process of insolation triggering a cascade of positive and negative feedback results in ice sheets growing to maximum thickness in about 80,000 years. Increasing isolation then triggers an escape from an ice age in about 20,000 years with growing greenhouse contributions from rising concentrations of CO₂ and water vapor, and a greening of regions formerly covered with ice. Except for being more rapid, deglaciation appears the reverse process to falling into an ice age.

A different view of feedback

One way of supposedly clarifying climate change is to explain it using a feedback diagram. While not really providing any clarification, these diagrams are often exceptionally simple. Just to make sure I wasn’t misstating the peer-reviewed research, I tried to find such an original diagram in the two most often cited papers, Hansen et al 1984 and Schlesinger and Mitchell 1987.[8] Neither appears to contain such a diagram. Thus I created one from an equation provided in the 1987 paper, ΔTs = ΔRTG0/(1 – f). Figure 1 nearby shows exactly the diagram this equation describes.

I have always disliked using this particular feedback diagram to explain climate change for several reasons. First, the source of energy that makes the whole loop run is implied, which is fine for electronic circuits.  Any attempt to ground it in reality with, say, energy balance, which is crucially important in discussion of climate change, is simply hopeless. Second, the feedback diagram suggests it is a matter of simple multiplication of the various blocks in the loop, when in fact the process is multiplication in the “S” domain of Laplace transforms. To transform to a time domain description requires convolution of signals against impulse response. Neither view helps clarify matters for most people. The diagram obscures time constants involved of which there are at least two within the F block. Third, this diagram contains no non-linear element, suggesting it describes a linear system which climate surely is not.

The deficiencies of this diagram are probably at the root of many disagreements over its pertinence. Possibly, though, this simplified view encourages a more fundamental problem, which is to encourage use of gain and feedback parameters observed in parts of the control domain that are inappropriate to other portions of the control domain. In other words, it suggests that the control problem is independent of amplitude, which may be at the root of the most recent criticisms Monckton, et al, level.[9]

Maslin’s article set me upon constructing a feedback diagram which addresses two of my complaints – one that applies to disturbances as great as ice ages and may have pertinence to the problem of trigger points.

Earth temperature regulation

While the effect of increasing CO₂ on present and short-term Earth temperature is commonly illustrated with a feedback diagram. I cannot say I have ever seen an attempt for the larger and greatly more complex problem of pleistocene temperature regulation. Can we consider this larger problem in terms of a feedback diagram like a temperature regulator, for example?

For guidance in this regard one might first look at the record of pleistocene ice volume, which displays the following pertinent features: 1) it shows turning points at well defined limits, and 2) it displays a periodicity that is the 40,000 year cycle of obliquity modulated by the 20,000 to 29,000 year cycle of precession of perihelion. It  clearly shows a limit-cycle having perhaps two periods both of which are subharmonics of the orbital influences.

As well defined turning points in response and a limit-cycle of operation are long established characteristics of relay control systems, I submit that Earth’s climate regulation is non-linear in much the way a relay controller in a regulator is non-linear. Figure 2 shows an appropriate modification to the simple feedback diagram of Figure 1.

To buttress my claim, Table 1 shows some selected climate features that serve to function like a relay controller (see Figure 3), or something similar to a relay. By “something similar” I mean a softer relay with a characteristic like that in the lower part of Figure 3, or something even softer such as an ArcTangent function.

Table 1. Sources of relay-like limiting of climate excursions

Source Mechanism	Limiting at high temperature or small ice volume	Limiting at low temperature or large ice volume
Hydrological cycle	Exponentially increasing rate of hydrological cycle
Atmospheric composition	Declining unit influence of a growth of atmospheric CO2 along with a limit to moistening of the atmosphere.	Increasing unit influence of a growth in CO2 along with a limit to continued drying of the atmosphere.
Albedo variation	SW influence of deepening cloud cover	Influence of dustiness on ice albedo
Atmospheric dynamics		Deflection of storm tracks

Since a person can itemize influences that limit temperature response, our system has the potential to behave like a system with a relay in it and the idea of treating it as a relay controller must have some merit. This climate relay opens to halt the effectiveness of influences tending to increase system response when the system is near its maximum; and reduce the effectiveness of influences making the Earth colder near the temperature minimum.

None of what I claim here is beyond what one could glean from a reading of the pages of WUWT from contributors such as Weekly Climate and Energy News Roundup (especially their recent summary in #482 of Professor Happer’s remarks at the Hillsdale College leadership seminar), Roy Spencer, Richard Lindzen, Willis Eschenbach, and many others too numerous to mention.

In contrast to linear control systems, there are fewer tools available for analysis of non-linear regulation. One technique is to produce successive linear approximations to construct the entire control domain. Each approximation over an infinitesimal portion of the response curve can yield information about system behavior after a small disturbance. Another method of analysis is a digital computer simulation tool. One older analytical tool used to handle non-linearity is the describing function approach. This approach requires a separate treatment for each harmonic (fourier component) of the signals circulating around the feedback loop, including the harmonics or subharmonics generated by the non-linear element.

Relay dominated regulators are known for operating in a limit cycle, and the describing function analysis will show this,[11] but the relay or relays involved in limiting the growth or shrinkage of continental ice don’t behave exactly like a relay providing temperature control for a furnace. A furnace heats a building when its relay closes while the heat losses stay constant. In this case of a “climate relay”, its closure switches off the further accumulation of ice and continued drying of the atmosphere, and maintains this limiting function while awaiting the signal from orbital parameters to begin the process of glaciation or de-glaciation. There may be no triggering points intrinsic to the N block, but there are variations of insolation input to allegedly serve this purpose.

Triggering events

Maslin credits the triggering of an ice age to orbital elements or celestial mechanics which adjusts insolation to a triggering value, just as Milankovitch’s original theory supposed. The many orbital elements involved are:

• Eccentricity of Earth’s orbit which varies from nearly zero (a near perfect circle) to a maximum value of 0.057 in a 96,000 year-long period. This leads to differences of yearly insolation of nearly 12% over this period.
• Obliquity, the angle of Earth’s axis with respect to the plane of its orbit varies from 21.8 to 24.4 degrees over a period of 41,000 years. This modulates the variation of insolation between the hemispheres, which is made even more pronounced because of the difference in proportion of land between the two hemispheres.
• Precession which involves both the precession of the equinoxes and precession of perihelion. Between these two motions it takes a variable length of time (20,800 to 29,000 years) for the orbit to revolve once with respect to a fixed orientation such as the Vernal equinox. But this is not to say that insolation values repeat exactly over this same period because all the elements are varying over different periods.

Yet, these factors cannot fully explain the march of ice ages. One of the more interesting references in the Physics Today article was Huybers’s investigation of orbital elements initiating an escape from an ice age.[12] The insolation anomaly required to trigger an end to an ice age is not a precise value, but rather a random variable. Insolation anomalies at 65 north which fail to start the escape from an ice age are in a few cases larger than insolation values that initiate an escape. Using observed oxygen isotope values as a proxy for ice volume, and for global temperatures in turn, provided Huybers the raw material to build two distributions of insolation values that fail and succeed, respectively, through a resampling process.[13]  These two distributions (which are actually joint distributions of obliquity and precession) overlap substantially and provide only about ⅔ of the explanation for deglaciation — leading to a need for some additional factors contributing to ice age start and end.

The trigger may not be entirely a matter of orbital elements. For example, an usually long summer season over southern oceans might release a sizable fraction of greenhouse gasses that had been removed from the atmosphere in the earlier cooling cycle; or, maximum insolation operating on the upwelling deep water over tropical surface oceans might do the same. Perhaps internal dynamics of the coupled ocean and atmosphere contribute as well.

Conclusions

Whatever the answer turns out to be, a person cannot look at a plot of δ¹⁸O, such as Figure 3, here, and not be struck by two things; 1) a preponderance of triggers carrying the climate out of an ice age – none seem to work oppositely during its warm phase, and 2) the smaller range of ice-volume variation prior to 2.8 million years ago. In terms of the relay-control model of climate, whatever conditions pertain to this time period the relay had smaller dead-band and the limit cycles had smaller orbit. The climate was more stable. Maslin speaks of our creating a present day super interstadial. By this he means that through altering the atmosphere by burning fossil fuels we will have delayed a start to the next ice age from near the present time to perhaps 60,000 years in the future. A more stable climate. That, my friends, sounds like awfully good news.

References:

1-Mark Maslin, Tying Celestial Mechanics to Earth’s Ice Ages, Physics Today, p.49-53, May 2020. For those readers interested in this, the article is open access for the remainder of year 2021 for people willing to register at AIP.

2-ibid. p. 51.

3-See for example Euan Mearns, https://wattsupwiththat.com/2014/12/27/vostok-and-the-8000-year-time-lag/

4-Jeremy D. Shakun, et al, Global Warming preceded by rising carbon dioxide concentration during the last deglaciation, Nature, Vol. 484, p 49-55, 5 April 2012. doi:10.1038/nature10915

5-ibid. p. 51.

6-Zhengyu Liu, et al, The Holocene Temperature Conundrum, PNAS, Published Online August 11, 2014. doi:10.1073/pnas.1407229111.

7-Hansen, J., A. Lacis, D. Rind, G. Russell, P. Stone, I. Fung, R. Ruedy, and J. Lerner, 1984: Climate sensitivity: Analysis of feedback mechanisms. In Climate Processes and Climate Sensitivity. J.E. Hansen and T. Takahashi, Eds., AGU Geophysical Monograph 29, Maurice Ewing Vol. 5. American Geophysical Union, pp. 130-163.

8-Michael E. Schlesinger,John F. B. Mitchell, Climate model simulations of the equilibrium climatic response to increased carbon dioxide. Reviews of Geophysics, 25, (4), 760-798. May 1987.

9-https://wattsupwiththat.com/2021/02/01/how-much-global-warming-should-ipccs-next-report-predict/

10-https://wattsupwiththat.com/2021/11/17/claim-climate-changed-abruptly-at-tipping-points-in-past/

Note in particular an especially pertinent observation by Dave Fair followed by one from Beng135 https://wattsupwiththat.com/2021/11/17/claim-climate-changed-abruptly-at-tipping-points-in-past/#comment-3390458

11-Charles Phillips and Royce Harbor, Feedback Control Systems, 4th Ed., Prentice-Hall, 2000. Or, Otto Smith, Control Systems Engineering, McGraw-Hill, 1958.

12-P. Huybers, Combined obliquity and precession pacing of late Pleistocene deglaciations, Nature, 480, 229, (2011). doi:10.1038/nature10626

13-For those unfamiliar with resampling, a great reference complete with exercises is, “Resampling: The new statistics, Julian Simon, 1997.” The publisher appears to be Professor Simon himself. 

via Watts Up With That?

December 8, 2021

Ice Ages, Feedback Diagrams, and Climate Triggers