From Watts Up With That?

Kevin Kilty

This final part of the series explores the issue of regulation of Earth’s climate in light of a small, continuing imbalance between energy input from Sol, and outgoing LWIR – the so-called Earth Energy Imbalance (EEI). To reiterate important points from Parts I and II, we are told there is a small imbalance of magnitude 0.76 W/m², but the certainty of this number appears too optimistic. Even by the estimation of its proponents it doesn’t include all sources of bias. The so-called components of feedback into the climate system, which are responses to this imbalance, may not be any better known or understood than EEI itself; the list of likely responses is possibly incomplete.

Does a physical principle demand there be a physical climate regulator?

This is difficult to answer. It’s true that certain graphs of climate behavior during the latter Pliocene and Pleistocene suggest the operation of a regulator. Many people suggest from general physical principles that there must be one. Let’s look at this item first.

When the topic of stability of Earth’s climate arises, some people respond by invoking Le Chatelier’s principle – a principle they say applies to the general stability of complex mechanical systems. What they mean, presumably, is the atmosphere will show a limited response to increasing amounts of CO2 because a physical principle says so. A search just at WUWT produces a surprisingly large number of such references to Le Chatelier. Two dozen at least.

While it would be nice to have a general universal principle guarantee that fears of catastrophe are imagined, I am doubtful about Le Chatelier’s principle providing this.

Problems with this principle began immediately upon Le Chatelier announcing it in 1884. His first effort was difficult to explain. In attempts to clarify matters, he produced versions that were less correct, but which were so generally appealing that they were readily adopted and spread widely. Here is LeChatelier’s principle as Colina and Olivera-Fuentes translate it.[1]

“In a homogeneous mixture in chemical equilibrium, an increase in the concentration of one of

the reacting components displaces the equilibrium in the direction in which the reaction tends

to decrease the concentration of the same species.”

The first thing a person should notice is, it’s a chemical principle, not a mechanical one. Unfortunately, the original confusion led over time to increasingly hazier and more general application. Temptation arose to apply it to everything. De Heer [2] derided its “almost metaphysical interpretations”. Samuelson suggested in 1947 that it even applied to economics. As he saw things,

“The vague and often teleological Le Chatelier’s principle of thermodynamics can be formulated as an unambiguous mathematical theorem concerned with elements of definite matrices  associated with maximizing problems.”[3]

No textbook I have examined in mechanics, thermodynamics and statistical mechanics, or solid or fluid mechanics make any mention of the principle at all. It is mentioned in some textbooks on chemical thermodynamics, but not all. Some suggest it is merely a “qualitative” guide. The GSA’s Handbook of Physical Constants, which contains a wealth of thermo-chemical information about chemical systems in mineral and rock forming systems, doesn’t mention it. Probably most striking is that while some chemists insist it is among the most important concepts in chemistry,[4] it isn’t found anywhere in the 2,000+ pages of Perry’s Handbook of Chemical Engineering.  

Why this principle applies specifically to chemical equilibrium is this.

The Gibbs free energy achieves a minimum at chemical equilibrium. The minimum condition itself demands that derivatives of G with respect to its independent variables (temperature, T, pressure, P, or chemical species concentration, n) are zero at equilibrium – i.e. dG/dP=0. This later condition suggests an implicit function, F(P,T,n)=0 say, exists between P or T and n. From this implicit function one can use calculus to find the behavior of n on change of P (dn/dP). Details are available in [4].

It’s difficult to see how something similar applies to Earth’s climate which is perpetually out of equilibrium and shows all manner of transport processes. The operation of climate and weather is a mix of thermodynamics and mechanical elements. Maybe, if the mean state of the climate (if one exists) is not too far from equilibrium, a principle like minimum rate of dissipation might apply.[5] Roy Spencer has mentioned in a note to a list server that I occasionally get messages from, that the issue of energy imbalance is essentially one of vertical heat transport from surface to tropopause. I think there are reasons to disagree with this. An occasional commenter on threads here has, parameterized for lack of a better term, vertical transport by all heat transport means, and argues that convective-radiative equilibrium is hopelessly deficient as well as difficult to establish by observations.  

The topic is so complex that a separate essay is needed to even explain it. Let’s put this topic aside for now.  If there is a regulator we should find it in observations.

Are there valid reasons to see the EEI as a non-problem?

My opinion is a qualified “yes”. Yes, because Earth has experienced periods of far greater average temperature, and much higher levels of both CO2 and water vapor. Qualified because the current rate of advance is possibly unlike past natural changes; if so, it could lead to trouble with natural systems that can’t keep pace. But this has been true of much of Earth history and is an explanation for some extinctions – during both periods of rapid warming and cooling.

Table 1 below summarizes some of the ranges of conditions believed to exist in various Cenozoic epochs.

Epoch	Time frame (mya)	Highest Average Temperature	CO2 (ppm) Maximum Variation	δO18 (0/00)	Notable events
Eocene	33.9-55.8	+(4-12C) over present	1000-3000+	0-2	Climate optimum; ends in an Ice age
Oligocene	23-33.9	?	500-1000	2	Ends in an Ice age
Miocene	5.3-23	+8C over present	200-1000	1-3	Climate optimum
Pliocene	2.6-5.3	2-3C over present	150-600	3-3.5

 Table 1. Data drawn from; Antarctic Climate Evolution (Second Edition), 2022 Chapters 8 and 9. [7] The Cenozoic CO2 Proxy Integration.[7] Zachos et al.[8]

What one notices is that the era  is marked by a general decline in temperature and CO2 levels, punctuated with brief excursions into hothouse climates and ice ages along with occasional spikes, positive and negative, in CO2 concentration. Tipping points, as researchers like to call them, seem endlessly in supply.  They occur, mostly, as changes in the trend of climate rather than sudden disastrous shifts that a term like tipping point implies.

The Eocene epoch saw a very warm and moist climate. Even polar regions were subtropical. Yet, the Eocene–Oligocene transition was the Cenozoic era’s largest cooling event; the climate switching from greenhouse to icehouse. It coincides with δ¹⁸O isotope records signaling a peak in glaciation in Antarctica. The climatic and biotic changes lasted for 500 kyr. Possibly a contributor to this cooling was a marked decrease in atmospheric CO2 from 1000-1500 ppm late in the Eocene to near present day levels during the Oligocene.

This defies current thinking. In addition to the drop in atmospheric CO2 levels, orbital forcing, changes in circumpolar ocean currents, and even volcanism are other possible contributors to climate change at the transition from Eocene to Oligocene. Ice-climate feedback, also thought to be a contributor to climate change, mainly follows climate and simply reinforces change already underway.

Atmospheric CO2 concentration appears to rebound rapidly following the Oligocene-Miocene transition,  with some proxy estimates as high as 1000 ppm by the earliest Miocene.

The transition from the Oligocene to Miocene epochs also involves a significant ice age. These ice age interludes in an otherwise warm period with high levels of CO2 are difficult to understand.  Naish, et al. say of the Oligocene-Miocene transition that it  “…challenges our current understanding of orbitally-paced, ocean-atmosphere carbon exchange and associated feedbacks in the climate system.”[6] But possibly these ice ages are difficult to understand only because people for decades now have relied too much on the idea of CO2 being the control knob of climate.[7]

No less enigmatic than these glacial ages are the hot house interludes,  Zachos, et al, state that a feature common to them all, whether transient or long-lived, is exceptionally warm poles. In fact, high temperatures are substantially too high for models to simulate without unreasonably high levels of CO2. Obviously climate dynamics, especially poleward heat transport, are not understood well enough to model accurately.[8]

On to the Pleistocene

The Pleistocene  epoch, which began about 2.6 Mya, is an epoch composed of alternating cold/warm periods (glacials/stadials) in which climate has become colder, continental ice volumes grown larger, and CO2 levels fall deeper, with each cycle. The top panel of Figure 1 shows that when these cycles first appeared during the early Pleistocene they did so as an oscillation with a roughly 40kyr period – a period suggestive of orbital obliquity. If ice volumes equate to global temperature then the warmest episodes of the Pleistocene epoch fall short of those in the Pliocene.  The cycles of the early Pleistocene also appear somewhat symmetrically shaped. Symmetry may only reflect poor time-resolution of data, though.

About 1.3Mya this pattern changed (Mid-Pleistocene Transition or MPT) to deeper glacial periods and much greater asymmetry of cooling versus warming periods. As Dawson said, “The overall pattern that the oxygen isotope exhibit is characterized by incessant switches between global cooling and warming.”[9]

Indeed, Figure 1 shows this switching from panel a through c at increasingly finer time resolution. Intense cold with warm period, and cool periods with the warmer, and warmer periods within cooler down, like a Weierstrass curve, down to the finest time resolution the ice cores allow.

During Pleistocene glacials, polar circulation cells expanded to 50 degrees north/south and even further south on the North American continent. With expansion of polar cells, the remaining weather and biomes this weather supported were compressed into a more restricted range. Tropical biomes retreated into refugia separated by broad dry savannas. The climate became dry and dusty. 

In contradiction to these mapped conditions, low-resolution GCMs of the 1970-80s suggested that ocean temperatures and atmospheric levels of water vapor were not hugely different from today. In fact, they suggest some oceanic regions were even warmer than today.

While the 41kyr cycle of Pleistocene ex ante 1.3mya seems to implicate the cycle of Earth’s obliquity as a climate driver, the MPT occurred without any significant change in orbital elements. Even considering that possibly the 100ky cycles of the late might involve cycle skipping (i.e. skipping 2 or 3 cycles of obliquity), experiments done with climate models have shown that orbital elements only, or even orbital elements in combination with reductions in CO2, are insufficient to initiate a glacial period at the most opportune times for one.[10]

The work of Rind, et al, repeated by more than a dozen other investigators over the next 12 years, and cited even a quarter century later was seen as definitive in this regard.[11,12] Thus, some internal climate dynamics seem to be involved.

Energy Balance and Escape from a Glacial

Figure 1, Panel C, suggests the Earth climbed out of the most recent glacial period in around  7,500 years time. The rapidity belies that a persistent energy imbalance of perhaps only 0.5-0.6W/m² is indicated – nearly equal to present energy imbalance estimates.

How does Earth escape the grip of a glacial when almost everything works against it?

The SB feedback always works against change. A small net positive imbalance to raise temperature, and SB radiates 60-80% of this imbalance away. The reduced concentrations of water vapor and CO2 push this figure closer to 80% than 60%. Both ice-albedo and vegetation-albedo follow changing climate rather than initiate it, and now help maintain the cold, mean atmospheric state. A dry and dusty atmosphere seems like an augmentation to the other albedo feedbacks despite making snow and ice a bit less bright.

Perhaps transport processes could do the task, although the North Atlantic conveyor of warm water was probably reduced at the time by 40% of its current value (11SV versus 18SV at present, SV=10⁶ M³/s). Feedback from changes in clouds are about all that is left to consider, which is why I said in Part II that cloud feedback being estimated as positive from the present mean climate state is possibly correct, and possibly a good thing.

Low Dimensionality Climate Regulator?

As presently practiced, climate science now seems no more than applied computer modelling. Ditlevsen argues that more insight might be gained by pursuing dynamical models with only a few degrees of freedom.[13] In effect, this is how Stommel explained the current state of the Atlantic Meridional Overturning [14] and the method Lorenz employed to demonstrate the problem of weather prediction.[15] People have used this method to explain ENSO dynamics, as well.

Ditlevsen favors a fold bifurcation model of Pleistocene climate. Eschewing catastrophe theory for now, a fold bifurcation is effectively an On/Off controller, like your home HVAC, with positive hysteresis. Figure 2 shows the comparison.

Panel A shows the fold catastrophe, with the dotted portion of the fold indicating a forbidden region which demands that transitions between two distinct states take place at different values of the controlling parameter (horizontal axis). Panel B shows the essence of an On/Off controller like a building HVAC. The controlled parameter is temperature. The controlling state is the furnace or boiler being on or off. The distance in units of the controlled variable is the hysteresis in the system, which is needed to prevent chattering. 

Panel C shows time behavior for an example system that cools according to a time constant equal to the time constant governing heating. The system displays an oscillation governed by whatever dynamic or set of parameters contributes to EEI.

This Ditlevsen On/Off controller appeared out of the Pliocene world when atmospheric CO2 levels dropped below about 350 ppm, but one shouldn’t see CO2 as its critical feature.

Another view of this warrants consideration, however. Badly behaving On/Off controllers can develop negative hysteresis and become locked to one or the other of their controlling states. Before the MPT the climate system behaved as an On/Off controller producing symmetric excursions warm to cold and back again. At the mid-Pleistocene transition, the On/Off controller suddenly acquired negative hysteresis which locked the controller in its cold state.

Which positive feedback put us there? The climate system contains many possibilities. Zhisheng An, et al,[16] proposed that the transition is suspiciously coincident with an abnormal growth of the Antarctic ice sheets to something approaching 120% of their current extent. This in turn, pushed climatic zones north making more water vapor available to grow Northern hemisphere ice. They did not term this a positive feedback, but it certainly functions as one.

Occasionally, when orbital elements and some major feedback mechanisms work in unison, the Earth manages to return to a warmer period that cannot be maintained because the inputs are too wimpy to reach the warmer state or there is no warmer state to reach. Interglacials rapidly give way to another stadial. In this view, Earth is permanently in the colder branch of an ice age.

Pleistocene to Holocene

I have calculated that the energy imbalance bringing Earth out of its icy state at 20kya to the present warmth took place over 7,500 years was a mere 0.5-0.6 W/m². Closer inspection of global temperature [7] shows it grew mainly in two separate pulses totaling 6ky in duration indicating perhaps as much as 0.7 W/m² of effective imbalance. By effective imbalance I mean after all feedbacks are considered, but in either estimate, an imbalance not much different from the current one. An inspection of Figure 1 shows that an imbalance of approximately this magnitude characterizes the entire Pleistocene. This leads me to see the current imbalance as nothing especially unusual.

Shakun, et al, [7 ]maintain that CO2 increases prior to temperature rise in high quality proxy records implicate CO2 as the global element of change, particularly in the emergence from LGM. Yet, they point to a small temperature rise prior to the rise of global CO2. Moreover, some causative agent caused CO2 to rise in the first place. They note an anticorrelation between strength of the  AMOC and periods of most rapid CO2 rise;  implicating internal climate dynamics.

Reinforcing this view,  Dawson [9] states that the last glacial ended with the Laurentide ice sheet being thinned on its western flank as early as 17,000 ya, before other North American glaciers. This occurred even as lobes of ice continued to grow on its southern and southeastern flanks, indicating the importance of regional climate change in the emergence from the LGM rather than a global influence like CO2 or other greenhouse gasses.

By coincidence, a weather summary from Windy.com on the 27th of January shows one climate dynamic, working even nowadays, that could cause such a thing. Figure 3 shows flow of warm, moisture-laden Pacific air pushed over the Canadian Cordillera, warmed in its descent to the east, and making places even in the Yukon and Northwest Territories warmer than the central Rockies.[17]

Summary

From the Eocene through Pliocene epochs:

• Both the Eocene and Oligocene sported climate optima that are difficult to explain even at the highest possible CO2 concentration.
• Both the Eocene and Oligocene terminated with glacial episodes at CO2 levels above the presently theorized levels which will tip Earth into global boiling.
• Statements such as “ Warm polar regions are substantially too warm for models to simulate without unreasonably high levels of CO2.” or epoch to epoch transitions challenge   “…our current understanding of orbitally-paced, ocean-atmosphere carbon exchange and associated feedbacks in the climate system”, admit without saying so that there is far more to the climate system than CO2.

The Pleistocene to Holocene epochs:

• Modeling suggests that Initiating a glacial period requires an ocean so cold that Earth is already in a glacial sort of state.
• Detailed oxygen isotope records show persistent energy imbalance of the order of 0.5 W/m², plus or minus, throughout the epoch – higher still in the transition to the Holocene.
• Figure 1 demonstrates clearly that the “Mean State” of the atmosphere is one in name only. The mean state changes constantly throughout the Pleistocene – there is constant energy imbalance and lack of equilibrium.
• Climate fluctuations within the holocene are smaller than those within the Pleistocene, yet even it displays substantial variability that is difficult to explain with current paradigms.

References:

[1]-Colina, Coray & Olivera-Fuentes, Claudio. (2009). A re-examination of Le Chatelier’s Principle. Available at URL https://www.researchgate.net/publication/236998554_A_re-examination_of_Le_Chatelier’s_Principle

[2]-J. De Heer, J. Chem. Educ. 34 (1957) 375-380.

[3]-P. Samuelson, “An Extension of the LeChatelier Principle,” Econometrica, Vol. 28, No. 2, 1960, pp. 368-379.   doi:10.2307/1907727, or P. Samuelson, “Foundations of Economic Analysis,” Harvard University Press, Cambridge, 1947

[4]-Smith, William R. “A precise, simple and general Basic Le Châtelier Principle based on elementary calculus: What Le Châtelier had in mind?” Journal of Mathematical Chemistry 58.8 (2020): 1548-1570.

[5]-Prigogine, 1967, Introduction to Thermodynamics of Irreversible Processes, 3rd Ed. Interscience Publishers.

[6]-Tim R. Naish, et al. Antarctic Ice Sheet dynamics during the Late Oligocene and Early Miocene: climatic conundrums revisited, Chapter 8, Antarctic Climate Evolution (Second Edition)

2022, Pages 363-387. And G.S. Wilson, et al, Developments in Earth and Environmental Sciences, Volume 8, 2008, Pages 369-400, Chapter 9 The Oligocene–Miocene Boundary – Antarctic Climate Response to Orbital Forcing. Also, The Cenozoic CO2 Proxy Integration Project (CENCO2PIP) Consortium, Toward a Cenozoic history of atmospheric CO2, Science, 8 Dec 2023 Vol 382, Issue 6675 DOI: 10.1126/science.adi5177

[7]-Shakun, et al, 2012,Global Warming preceded by increasing carbon dioxide concentrations during the last deglaciation, Nature, 484, p.49.

In speaking of uncertainties regarding dust and vegetation,”uncertainties notwithstanding, we suggest that the increase in CO2 concentration before that of global temperature, is consistent with CO2 acting as a primary driver of global warming,…”

[8]-James C. Zachos, et al, An early Cenozoic perspective on greenhouse warming and carbon-cycle dynamics, Nature, v 451, 17 January 2008

[9]-Alastair G. Dawson, Ice Age Earth, Routledge, 1992.

[10]-Rind, et al, Can Milankovitch Orbital Variations Initiate the Growth of Ice Sheets in a General Circulation Model? Journal of Geophysical Res., Vol. 94, No. D10, Pages 12,851-12,871, September 20, 1989

Rind, et al, ran many experiments with the GISS global climate model (GCM) in which they set insolation values to those of 106-116kya, then adjusted a number of boundary conditions. They even gave ice a head start by planting ten meter layers of ice where ice domes existed. Yet ice sheets failed to grow.

[11]-Reader, et al, 2002, On the causes of glacial inception at 116kyrBP, Climate Dynamics, 18,

383-402.

Reader, et al, repeated some of Rind, et al’s, experiments using three coupled models to establish initial conditions for an atmospheric GCM of intermediate complexity. Beyond their own efforts they summarize the results of fifteen other computer experiment investigations which verified that orbital elements alone, orbital elements plus lowered CO2, could not not initiate a glacial period. What is needed is a sufficiently cooled ocean. In other words, initiating a glacial period requires circumstances almost like a glacial period to start.

[12]-R.G. Johnson, 2014, Past and future ice age initiation, ESDD 5, 545–584. Online at: https://esd.copernicus.org/preprints/5/545/2014/esdd-5-545-2014.pdf

[13]- Peter Ditlevsen (2022) The Pleistocene Glacial Cycles and Millennial-Scale

Climate Variability, Atmosphere-Ocean, 60:3-4, 233-244, DOI: 10.1080/07055900.2022.2077172

[14]-Stommel, H.: Thermohaline convection with two stable regimes of flow, Tellus, 2, 244–230, 1961.

[15]-Lorenz, E. N.: Deterministic nonperiodic flow, J. Atmos. Sci., 20, 130–141, 1963a.

[16]-Zhisheng An, et al, Mid-Pleistocene climate transition triggered by Antarctic Ice Sheet

growth, Science, 1 Aug 2024, Vol 385, Issue 6708 pp. 560-565 DOI: 10.1126/science.abn4861

[17]-Some of the temperature contrast of southern Wyoming and central Colorado being colder than the Yukon, is the work-related cooling that goes with raising air to greater altitude. Southern Wyoming and central Colorado are the highest average terrain in the US48.