Another Model of Atmospheric CO2 Accumulation

I continue to model the accumulation of carbon dioxide (CO2) in the atmosphere, because the topic fascinates me.

This time, I constructed a global warming scenario driven by a pulse of anthropogenic CO2 emissions (mathematically, a slightly skewed Gaussian function), which launches in the year 1900, peaks in the year 2028, and disappears by year 2150. This model emissions rate function matches the actual trend of the increase of anthropogenic CO2 emissions (data) since the year 2000.

The point of this study is to see how a reduction of anthropogenic emissions, as by the mathematical function assumed, would influence the subsequent reduction of CO2 accumulation in the atmosphere.

The equation describing the accumulation of carbon dioxide in the atmosphere is based on these assumptions:

– 70% of the emissions accumulate in the atmosphere,

– 30% of the emissions are immediately absorbed by the oceans (surface waters),

– the only sink (mainly photosynthesis) is characterized by a relaxation time of 238 years (a characteristic time scale for the absorption process),

– emissions peak in ~2028 at 11.5GtC/y (42.1GtCO2/y) and die away skew-symmetrically thereafter. (GtC/y = giga metric tons of carbon per year; GtCO2/y = giga metric tons of carbon dioxide per year).

Figure 1 shows the resulting projected temporal profile of atmospheric CO2, in units of ppm (parts per million). Also shown is the emissions function, E(x), scaled by 50x GtC/y. The unperturbed baseline concentration is assigned as 277ppm.

The time scale, “x” in years, begins (x=0) at year 1900.

Figure 1: Time Profile of Atmospheric CO2 Concentration, for given Gaussian emissions pulse

In this scenario, the CO2 concentration peaks at 529ppm for years 180<x<200 (years 2080-2100). The continuation of this story out to year x=1200 (year 3100) is shown in Figure 2.

Figure 2: Time Profile of Atmospheric CO2 Concentration, to year 3100

Choosing a longer relaxation time (e.g., ~1000y) would significantly reduce, or eliminate, the decay of the concentration over time (the air CO2 would “never” go away). A long relaxation time would be the case if weathering were the dominant absorption phenomenon (with relaxation time ~12,000 to ~14,000 years), because the photosynthesis and absorption by the oceans sinks were saturated (as was the case during the 200,000 year-long clearing of atmospheric CO2 during the Paleocene-Eocene Thermal Maximum, PETM, 55.5 million years ago).

Figure 3 shows the increase in global temperature, in °C, corresponding to the CO2 concentration profile, shown above.

Figure 3: Average Global Temperature Increase corresponding to model CO2 concentration profile

The global temperature increase above baseline, for this scenario, is projected to peak at +1.94°C in year x=190 (2090); it arrives at +1.5°C at x=142 (year 2042).

It is obvious that if the future reality of anthropogenic CO2 emissions is an increasing trend, that the consequent time profile of atmospheric CO2 concentration will be a continuously rising trend as well. That would mean higher global temperature increases, and sooner, than those shown here.

The Gaussian emissions pulse used here is an “optimistic” scenario in that the annual rate of anthropogenic emissions peaks in 8 years, and then decreases nearly symmetrically to its profile of increase prior to 2028.

This scenario would have us avoid crossing the +2°C threshold. But, the global warming would remain above +1.5°C for the 130 years between 2042 and 2172, undoubtedly degrading many environments.

The model CO2 concentration profile found here matched data (measurements by NOAA); quite well since 2000, and adequately before that to 1960.

The important implication of this model is already well-known: if we begin reducing anthropogenic CO2 emissions very soon, and continue doing so at a steady rate so as to eliminate them completely within a century, we can avoid having Planet Earth warm up by a total of +2°C, relative to the 19th century.

The corollary to this observation is that if we instead continue increasing our CO2 emissions, it will get warmer sooner for longer.

Also, whatever we do (or don’t do) about CO2 emissions, their accumulation in the atmosphere will linger for centuries. The clearing of this atmospheric CO2 will occur on several parallel timescales:

– absorption through photosynthesis (happening daily),

– capture by the surface waters of the oceans over the course of years, decades and centuries (and eventual sequestration at the sea bottom in a surface-to-bottom mixing cycle of millennial time scale), and

– the chemical reactions of rock weathering (on a tens-of-millennia time scale).

Injecting CO2 into the atmosphere can be done instantly; removing it requires a long time.

So, it would be wise to stop emitting it.

The above report, with the addition of figures showing comparisons to data for the trends of emission rate and CO2 concentration prior to 2020, is available here (PDF file).

Gaussian Emission Function & Air CO2

Gaussian Emission Function, and Atmospheric CO2 Accumulation
(Model #7)
4 October 2020
https://manuelgarciajr.files.wordpress.com/2020/10/gaussian-emission-function-air-co2.pdf

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Reducing CO2 Emissions to Reverse Global Warming

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Reducing CO2 Emissions to Reverse Global Warming

We know that Global Warming can be reduced during the years of the century ahead of us if we — our civilization — steadily reduces its emissions of carbon dioxide gas (CO2) into the atmosphere.

Given a specific rate for the reduction of anthropogenic (our CO2) emissions:

— how long will it take to return Earth’s average temperature to its unperturbed pre-industrial level?, and

— how much higher will Global Warming (Earth’s temperature) become before it begins to decrease?

Answering these questions is the subject of my recent study. This work is based on a Carbon Balance Model, which I described in an earlier report. [1]

That model has been further refined in order to address these questions, and the details of that refinement are described in a technical report. [2]

Prior to the buildup of anthropogenic CO2 emissions in the air, the fluxes of CO2 released by the respiration of Life-on-Earth; and the fluxes of CO2 absorbed from the air by photosynthesis, the surface waters of the oceans, and rock weathering chemical reactions; were in balance. That balance is known as the Carbon Cycle.

As the rate and buildup of anthropogenic emissions increased (after ~1750, but particularly from the mid-20th century), the Carbon Cycle was perturbed out of balance, and the magnitude of that imbalance is determined by the difference between two effects: Anthropogenic Sources, and Stimulated Sinks.

The Anthropogenic Sources are:

— the CO2 emissions by the human activities of fossil-fueled energy generation and industry, and

— the CO2 emissions from land use changes (deforestation and its attendant increase of wildfires).

The Stimulated Sinks are the additional absorption of CO2 by photosynthesis and the surface waters of the oceans, because of higher atmospheric concentrations of CO2. At a sufficiently high level of atmospheric CO2 concentration, both these sinks will saturate — stop absorbing CO2. What that “sufficiently high level” is remains uncertain.

The work summarized here includes more realistic (more complicated) models of these source and sink terms in the rate equation for the change of the Carbon Balance over time.

Now I am able to quantitatively link specific rates of the reduction of anthropogenic CO2 emissions, to consequent projected histories of the slowing and then reversal of Global Warming.

Such quantitative linkages have long been featured in the super-computer models of CO2 accumulation in the atmosphere, by the major Climate Science institutes; but now I have my own quantitative version of this correlation, which is analytical (expressed as math formulas, and enumerated with a hand calculator and basic home computer).

Anthropogenic CO2 emissions in year 2020 are 42.2GtCO2/y (42.2 giga-metric-tons of CO2 per year = 42.2*10^+12 kilograms/year). This magnitude of total anthropogenic emissions, E, is the addition of our fossil-fueled and land use emissions.

I considered three cases of the intentional steady reduction of annual human-caused CO2 emissions, which are defined to decrease exponentially. The characteristic decay time of each case is: 40 years (CASE 1, a 2.5% annual reduction), 100 years (CASE 2, a 1% annual reduction), and 200 years (CASE 3, a 0.5% annual reduction).

Emissions would be reduced to half their initial rate in 28 years for CASE 1; in 69 years for CASE 2; and in 139 years for CASE 3.

If each of these reduction plans were alternatively initiated in the year 2020, then:

CASE #1, ∆t=40y:

This trend reaches a peak of 449ppm and +1.32°C in year 2048 (in 28 years); it remains above 440ppm and +1.25°C over the years 2032 to 2064 (between 12 to 44 years from now); then descends to 350ppm and +0.56°C in year 2120 (in 100 years); and 300ppm and +0.18°C in year 2140 (in 120 years).

CASE #2, ∆t=100y:

This trend reaches a peak plateau of 485ppm and +1.6°C over the years 2078 to 2088 (between 58 and 68 years from now); it remains above 480ppm and +1.56°C during years 2066 to 2100 (between 46 and 80 years from now); it descends to 350ppm and +0.56°C in year 2202 (in 182 years); and 300ppm and +0.18°C in year 2225 (in 205 years).

CASE #3, ∆t=200y:

This trend reaches a peak plateau of 524ppm and +1.9°C over the years 2125 to 2135 (between 105 and 115 years from now); it remains above 500ppm and +1.72°C between years 2075 and 2190 (between 55 and 170 years from now); and descends down to 360ppm and +0.64°C in year 2300 (in 280 years).

Message to the Humans

The singular challenge for the progressive political and social elements of our civilization is to awaken the rest of the world — and particularly the “developed” and “developing” high-emissions nations — to a full commitment (demonstrated by action) to steadily and significantly reduce anthropogenic CO2 emissions for the rest of human history.

The sooner such reduction programs are initiated, and the greater the vigor with which they are implemented, the sooner we will begin slowing the advance of Global Warming and its continuing erosion of the habitability of Planet Earth, which humans have enjoyed for over 2 million years, and particularly since the end of the Ice Ages (~11,000 year ago).

With decades to a century of discipline applied to this purpose, we can even reverse Global Warming. The longer we wait to do this, the worse the consequences we will have to suffer through, and the longer it would take to extricate our species — and so many other wonderful forms of Life-on-Earth — from the Hell-on-Earth we are creating by our willful and destructive ignorance.

I can only imagine such major programs of CO2 emissions reductions being synonymous with the economic, political and social uplift of the vast majority of people, because Global Warming is directly caused by the unbounded economic, political and social exploitation of the many by the few.

The fact is that we all live on the same planet, and whatever happens to it — whether worsening conflagration and flooding in the now, or eventual cooling and restoration by human commitment — will affect everybody. There is no guaranteed escape.

The CO2 accumulation model that I have described here is just this old scientist’s way of saying: We can do so much better for ourselves, and our children deserve that we try.

NOTES

[1] A Carbon Balance Model of Atmospheric CO2
11 September 2020, [PDF file]
https://manuelgarciajr.files.wordpress.com/2020/09/a-carbon-balance-model-of-atmospheric-co2.pdf

[2] Trends for Reducing Global Warming
15 September 2020, [PDF file]
https://manuelgarciajr.files.wordpress.com/2020/09/trends-for-reducing-global-warming.pdf

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Anthropogenic CO2 Emissions Are Fate

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Anthropogenic CO2 Emissions Are Fate

I developed a model of Global Warming based on the anthropogenic perturbation of the Carbon Cycle. The essence of this model is a rate equation for the evolution of the carbon dioxide (CO2) concentration in the atmosphere.

The interesting results from this model are projected trends for the CO2 concentration and the average global temperature during the next century. The character of those trends — whether rapid rises, shallow plateaus, or diminishment into the future — depend crucially on the magnitude of our civilization’s emissions of CO2, and whether those anthropogenic emissions increase or decrease with time. In the real world at present, they are increasing.

I have now been able to include the effect of linearly increasing or decreasing anthropogenic emissions into my Carbon Balance Model, which has been significantly improved.

This model also includes the effect of the increase in the rate at which atmospheric CO2 is absorbed by photosynthesis and the surface waters of the oceans, because those absorption rates are increasingly stimulated by the higher levels of CO2 in the air. This process of absorption-enhancement cannot continue indefinitely as the atmospheric CO2 concentration increases, but at what point of elevated CO2 concentration it saturates and then absorption largely shuts down, is unknown.

The third process included in the model is that of the slow absorption of atmospheric CO2 by the chemical reactions of weathering on the surfaces of rocks and soils. CO2 not “quickly” scavenged from the air by photosynthesis or the surface waters of the oceans will stay airborne for 12,000 to 14,000 years. The ~2,500ppm spike of atmospheric CO2 that occurred 55.5 million years ago took 200,000 years to clear away. That geological episode is known as the Paleocene-Eocene Thermal Maximum (PETM). At that time there was no ice at the poles, instead they were jungles and swamps with crocodiles. The global temperature at the peak of the PETM was as much as +12°C to +18°C warmer than in our pre-industrial 18th century.

I made three case studies from this model, called E-growth, E-flat, and E-fall.

E-growth

The E-growth case is driven by a relentlessly steady rise of anthropogenic CO2 emissions, based on the average upward trend of those emissions between years 1960 and 2020.

This trend arrives at 470ppm of atmospheric CO2, and a warming of +1.5°C (above pre-industrialization), in the year 2038 (in 18 years). It arrives 540ppm and +2°C in year 2055 (in 35 years); and it arrives at 800ppm and +4°C in year 2100 (in 80 years).

E-flat

The E-flat case is driven by a constant annual rate of 42.2GtCO2/y of anthropogenic emissions (42.2 giga-metric-tons of CO2 emissions per year), which is the rate in year 2020.

It arrives at 470ppm and +1.5°C in year 2041 (in 21 years); and 540ppm and +2°C in year 2070 (in 50 years); and 600ppm and +2.5°C in year 2100 (in 80 years).

E-fall

The E-fall case is driven by a steady linear reduction of anthropogenic emissions over 40 years: from 42.2GtCO2/y in 2020, to 0GtCO2/y in 2060; a reduction of 1.05GtCO2 every year for 40 years. This amount of annual reduction is 2.5% of the total anthropogenic emissions in year 2020. In this scenario, after year 2060 we would continue our civilization with zero CO2 emissions from our human activities.

This trend rises to 437ppm and +1.23°C during years 2035 to 2040 (from 15 to 20 years in the future) after which both fall. It arrives back down to 407ppm and +1°C in year 2059 (in 39 years); and 320ppm and +0.4°C in year 2100 (in 80 years).

Finally

In this year of 2020, we are presently at 417ppm and +1.08°C.

The math and physics details of this new work, as well as graphs of the trends calculated from it, are shown in the report (PDF file) linked at

A Carbon Balance Model of Atmospheric CO2
11 September 2020

Click to access a-carbon-balance-model-of-atmospheric-co2.pdf

 

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Possible Future Trends of CO2 Concentration and Global Temperature

Oakland, California, 10:15 AM, 9 September 2020, “Burning Land Eclipse”

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Possible Future Trends of CO2 Concentration and Global Temperature

Carbon dioxide gas (CO2) has been accumulating in the atmosphere since the dawn of the Industrial Revolution (~1750), because increasingly voluminous fluxes of that gas have been exhausted from the lands and the oceans, and are beyond the capacity of natural CO2 sinks to absorb completely.

Prior to the Industrial Revolution, carbon would cycle through a variety of processes that sustained the continuation of life, death, evolution and rebirth, and that all meshed into one grand balance. That balance is called the Carbon Cycle.

The explosive growth of human activity, numbers, exosomatic power, economic wealth, military overkill, and hubristic political pretensions, all spring from the access to and profligate use of heat-energy liberated from fossil fuels. Carbon dioxide is the exhaust fume from our Promethean exertions for greater conquests — and wealth.

The carbon dioxide exhausted by our civilization’s generation of heat-energy, and from our massive exploitation of once virgin land areas, is an increasingly destabilizing perturbation of the Carbon Cycle. This perturbation is called Anthropogenic Emissions.

The imbalance of the Carbon Cycle reverberates through the natural world in many ways that are increasingly harmful and dangerous to Planet Earth’s habitability for ourselves and for many other animal and plant species. The central reality of this complex of growing threats to the viability of the Biosphere is called Global Warming.

Carbon dioxide gas traps heat radiated towards space, as infrared radiation from the surface of Planet Earth, reducing our planet’s ability to regulate its temperature by cooling to compensate for the influx of solar light that is absorbed by the lands and the oceans, and stored by them as heat.

Because of the existential implications of runaway global warming — as well as the intrinsic fascination to curious minds of such a richly complex and grand human-entwined natural phenomenon — scientists have been studying global warming, and its impact on the biosphere, which is called Climate Change.

While scientists of all kinds are excited to share their findings on climate change and impress their colleagues with their new insights, members of the public are singularly interested to know how climate change will affect their personal futures. Can science offer them clear and reliable answers to their questions — and fears — and provide practical remedies and technological inoculations to ward off the threats by climate change to our existing ways of life?

Science does what it can to offer practical insights and helpful recommendations, and humanity does what it usually does when faced with a collective existential crisis: it hides from the inconvenience of drastically changing its personal attitudes and societal structures, which is in fact the only way it would be able to navigate the majority of Earth’s people through the transition to a new social paradigm; a new, sustainable and harmonious relationship between human life and Planet Earth.

While I am grateful to all the professional climate scientists — and their related life scientists who study many aspects of this complex of geophysical processes and biological organisms and systems — for making known so much of the workings of the globally warming biosphere, I am nevertheless curious to gain a quantitative understanding of it all for myself. To that end, I have devised my own phenomenological thermodynamic “toy models” of global warming. The sequence of my reports charting the evolution of my quantitative understanding of global warming, are listed at [1].

My newest report describes a rate equation for the accumulation or loss of atmospheric CO2 over the course of future time. This equation is derived from considerations of recent data on the Carbon Cycle (from the Global Climate Project), along with some mathematical assumptions about the relationships used to quantify “carbon dioxide sweepers,” the processes that scavenge atmospheric CO2.

The results of this work are projections of possible future histories of the concentration of atmospheric carbon dioxide, as well as a projection of the most likely trend of rising average global temperature.

The complete report on the new work (of which this is just a brief summary) is available at [2].

As is true of all future-casts, we will just have to wait till then to see if they were accurate, assuming we don’t do anything beforehand — collectively — to avoid the worst possibilities.

Such is the dance with the chaos and nonlinearity of the approaching future.

From the general mathematical result of this model, three possible future trends of CO2 concentration history were calculated:

CASE #1, “business as usual,” anthropogenic emissions continue at today’s level indefinitely;

CASE #2, anthropogenic emissions are immediately reduced to the point of holding CO2 concentration constant at today’s level, indefinitely;

CASE #3, anthropogenic emissions are immediately reduced to a trickle, so as to reduce the excess of CO2 in the atmosphere as quickly as possible.

Also, the trend of rising global temperature that accompanies CASE #1 was calculated.

CASE #1 is a pure growth trend, from 407.4ppm to 851.8ppm over the course of about 3,000 years (ppm = parts per million of concentration in the atmosphere).

CASE #2 requires that the anthropogenic emission rate be ~50% of the current rate (or 21GtCO2/y instead of 41GtCO2/y; for the units GtCO2/y defined as giga-metric-tonnes of CO2 emission per year).

This reduced rate of anthropogenic emission would just keep the CO2 concentration at 407.4ppm (from the beginning of 2019) into the near distant future (~1,600 years, and beyond), during which time the excess heat-energy presently in the biosphere would continue to degrade our weather, climate, environments, biodiversity, and planetary habitability.

CASE #3 would clear away the current excess of CO2 in the atmosphere, and then continue to reduce the atmospheric CO2 concentration to a very low level over the course of about 700 years. This would require that anthropogenic emissions be immediately reduced to about one-fifth (1/5) of their current levels, and maintained at or below that level indefinitely.

The implication is clear: if we wish to reduce the amount of CO2 in the atmosphere we have to reduce our anthropogenic emissions well below 50% of what they are today, maintain that discipline indefinitely, and wait centuries to millennia to achieve a significant reduction.

The global temperature excursion (above the average global temperature of the pre-industrial world) that accompanies CASE #1 rises steadily, though at a diminishing rate, from +1°C in 2019, to nearly +2.6°C in 2300 (~300 years). Along the way it passes +1.5°C in year 2065 (in ~40 years), and it passes +2°C in year 2120 (in ~100 years).

Global temperature would rise higher and sooner if the absorption rates of CO2 by photosynthesis and the oceans did not continue increasing — as they do today — in proportion to the increases in the atmospheric concentration of CO2. At present, increased CO2 concentration stimulates increased CO2 absorption. The model here assumes this is always true, but in reality this “sink growth” effect may saturate (be limited) at some higher level of CO2 concentration. Whether any such saturation limit on the absorption (sink) rate exists or not, is unknown.

If the +1.5°C and +2°C temperature rise milestones are truly to be avoided then it is imperative that anthropogenic emissions be drastically reduced immediately. As yet there is no sign that such reductions will occur.

The physics and mathematics of all this are fascinating, but the implications for civilization and life-on-Earth are stark.

NOTES

[1] One Year of Global Warming Reports by MG,Jr.
15 July 2020
https://manuelgarciajr.com/2020/07/15/one-year-of-global-warming-reports-by-mgjr/
Updated to 7 September 2020

[2] A Rate Equation for Accumulation or Loss of Atmospheric CO2
5 September 2020 (revised 9 September 2020)
[take a copy]
Rate Equation for Atmospheric CO2 (revised)

or view directly:

Click to access rate-equation-for-atmospheric-co2-revised.pdf

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ClimateSIM Junior, Simplified Prognostication from Unrealistic Hypothesis

Painting of the Roiling Ocean, by Ivan Konstantinovich Aivazovsky

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ClimateSIM Junior, Simplified Prognostication from Unrealistic Hypothesis

Let me call the complicated work of supercomputer climatologists “ClimateSIM Senior.” Their efforts result in very complex “computer games” that simulate, up to a point, the Earth’s climate history, past and future.

What follows is a description of “ClimateSIM Junior,” my “speculative science” effort to model Earth’s climate, using formulas devised on pads of paper and numbers arrived at with a hand-held calculator (HP45). My purpose here is to present a simplified and only mildly inaccurate picture of “what is,” and to project from that with complete positive thinking, to ‘guesstimate’ “what could be.”

For data, I used the summary of the Carbon Cycle as published by the IPCC in 2007 (reporting on 2004 data), and a variety of estimates I have made and reported on over the course of the last year. The numbers to be presented are all internally consistent for the ease of storytelling, but the realities they represent are not actually known to the exactitude implied by the numbers shown.

Finally, I am not competing with nor contradicting ClimateSIM Senior, just trying to understand it better.

In 2020, the anthropogenic emissions of carbon dioxide gas (CO2) from Earth’s land surfaces is 36.3Gt/y (Gt/y = giga metric tons per year, or units of 10^12kg/year). This composite plume is split between industrial CO2 pollution, at 29.3Gt/y, and land use (or misuse) CO2 pollution at 7Gt/y.

Natural emissions of CO2 from land surfaces are: 0.3Gt/y from volcanoes, and 440Gt/y from respiration. The total of CO2 emissions from land surfaces is 476.6Gt/y.

The yearly absorption (or fixing) of CO2 from the atmosphere by land surfaces has three components: 0.7Gt/y by weathering reactions on soils and rocks; 440Gt/y by photosynthesis as in the pre-industrial past; and an additional 0.4Gt/y by photosynthesis in recent years. The total absorption of CO2 by land surfaces is 441.1Gt/y.

At present, land is a net emitter of CO2, at the rate of 35.5Gt/y, all anthropogenic.

The natural emissions of CO2 by the oceans, at present, are: 260Gt/y of CO2 released as in the pre-industrial past; and an additional 70Gt/y released in recent decades. The net emission from the oceans is 330Gt/y.

The uptake or absorption of CO2 by the oceans is: 260Gt/y as in the pre-industrial past; with an additional absorption of 80.4Gt/y in recent decades. The net absorption by the oceans is 340.4Gt/y.

At present, the oceans are net absorbers of CO2, at the rate of 10.4Gt/y, all anthropogenic.

With lands emitting 35.5Gt/y, and oceans absorbing 10.4Gt/y of it, CO2 is accumulating in the atmosphere at the rate of 25.1Gt/y, which is equivalent to a rise in the partial pressure of atmospheric CO2 of +3.2ppm/y (ppm = parts per million). We are at 417ppm now; if nothing changes then in one year atmospheric CO2 should be at 420.2ppm.

The anthropogenic accumulation of CO2 in the oceans is 481.2Gt (my estimate; “500Gt” or “about 500Gt” are casually stated elsewhere), and the average acidity level of the oceans is at a pH of 8.1. Today’s oceans are 26% more acidic than they were in pre-industrial times, when their pH was 8.2.

Now let’s dream. Imagine that all anthropogenic CO2 emissions cease immediately and permanently. The lands would become net absorbers of CO2, at the rate of 0.8Gt/y (by weathering reactions despite volcanic outbursts, plus lingering added photosynthesis). This clearing rate is equivalent to -0.10ppm/y. The 137ppm of excess CO2 above the pre-industrial level of 280ppm would be cleared away in 1,359 years. Further accumulation of CO2 in the oceans will have ended with the cessation of anthropogenic emissions.

The global temperature would continue to rise (because of atmospheric and oceanic heat-retention effects at a higher temperature than in pre-industrial times), but at a slower and slower rate, peaking at +3.8°C of average global warming above the temperature of 1910 (and +2.8°C above today’s global average temperature), for the century 300 to 400 years from now. Cooling would ensue thereafter, with a return to pre-industrial (1910) conditions in about 1,350 years from today.

By that time the terrestrial part of the Carbon Cycle would have returned to its pre-industrial level of performance, with the land surfaces acting as net absorbers of atmospheric CO2 at the rate of 0.4Gt/y, equivalently -0.0504ppm/y of atmospheric CO2 reduction.

With the atmosphere cleared of anthropogenic CO2, and its partial pressure reduced to its pre-industrial level, the oceans could begin an extra release plume of CO2 gas at a rate of 0.4Gt/y, to be fixed by weathering reactions on land. The atmospheric concentration of CO2 would remain stable at 280ppm (with minor natural fluctuations). The anthropogenic load of CO2 in the oceans would be cleared in 1,203 years, and their acidity would return to their pre-industrial level of 8.2pH.

Nearly all of the anthropogenic caloric load accumulated by the biosphere is stored in the upper 500 to 1,000 meters of the oceans, and is concentrated at the top. With the onset of atmospheric CO2 reduction and overall biosphere cooling (more heat, as infrared radiation, being radiated into space without being blocked by an excessive CO2 “thermal blanket”), oceanic anthropogenic heat would be able to diffuse out of the waters and radiate away. Over the 1,203 year time span of oceanic de-acidification, the excess heat stored in the upper 73 meters of the oceans would be radiated away (and excess heat from the cooler depths will have diffused closer to the surface).

Logically, there would be an overlap in the time spans over which the air and oceans, respectively, are cleared of their anthropogenic loads of CO2 and excess heat, but to calculate that with any degree of believability is a job for ClimateSIM Senior.

Today, this is the best unified story I can tell about the most optimistic hypothetical case for Earth’s recovery from global warming. It lies somewhere between a quantitative engineering estimate, and a dream.

Now for some policy recommendations. My suggestions to the Economic Mandarins of the United States are as follows:

If those Mandarins are Neoliberals:

1. Use that bloated, over-equipped U.S. military colossus to invade Brazil and gain control of the Amazon Basin. Then, stop the fires, kick out the ranchers and miners, and rehabilitate the rainforest “lungs of the Earth” to tamp down the onslaught of global warming. Also, help out the Brazilian people while you are at it.

2. A second target for the same type of action as in the above, is Siberia. But be sure not to spark a nuclear war in trying to gain control of it (so, don’t be too hasty, and also use diplomacy). Remember, stabilizing the geophysical climate aids in stabilizing a reliable business climate.

If those Mandarins happen to become Socialists:

1. Use that bloated, over-equipped U.S. military colossus — if you are unwilling to dismantle it because it is a “public works” program — to implement the 2 recommendations given to the Neoliberal Mandarins.

2. Also, immediately invade all offshore tax havens (many concentrated in the Caribbean) to repatriate tax-avoiding hoards hidden there. Use those stolen-from-the-public funds to underwrite the costs of maintaining the lives, for life, of all the nation’s people.

3. A good portion of the funds liberated from militarized and pirated-private sequestration will necessarily go to mitigating the impacts of global warming, in a variety of ways applied regionally.

4. It will also be necessary to contribute to international efforts at global warming mitigation and standard-of-living equalization, to simultaneously help meet national goals in those regards.

Being realistic, nobody really wants to hear about global warming, whether they are in government, business, or an “ordinary” member of the pubic. Government people don’t want any interruptions to their careers being in positions of power (and making money); business people don’t want any interruptions to their careers making money (and being in positions of power); and most members of the public just want an uninterrupted continuation of their comforts and entertainments — if they are not in absolute terrified panics over threats to their physical and economic survival, and don’t have the luxury of worrying about global warming.

As a result, there is no limit to how bad we can make global warning; which the Trump Administration (in the U.S.) and the Bolsonaro Administration (in Brazil) seem to be taking as a challenge.

In terms of dreams of utopia versus fears of doom and perdition, realize that the best utopia we could achieve would pale in comparison to our dreams about it, but be far superior to the conditions we live under today. If we are doomed by fate regardless of what good efforts we can make at improvement, then we will all drown together in that doom, whether we do so while exploiting each other mercilessly and quarreling bitterly, or whether we do so supporting each other in admirable solidarity. It is our epitaph to choose: nobility or ignominy. And, if we choose the former, an epitaph won’t be necessary.

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The Improbability of CO2 Removal from the Atmosphere

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The Improbability of CO2 Removal from the Atmosphere

The concentration of carbon dioxide gas in today’s atmosphere is 417ppm (parts per million). There are 10^44 gas molecules in the entire atmosphere (78% diatomic nitrogen, 21% diatomic oxygen, 1% everything else), so 1ppm is equivalent to 10^38 gas particles. The 417ppm of CO2 represents a total of 4.17×10^40 molecules.

Some people hope for new technology to remove carbon dioxide gas from Earth’s atmosphere, and then forestall the advance of global warming, or even completely eliminate it. I see this as improbable because I think any such technology would be extremely inefficient at CO2 removal, and be energy intensive as well. The process of gaseous diffusion, as with the release of CO2 into the atmosphere, requires no energy; the gases just mix, spread and dilute, and the entropy of the atmosphere increases. It is an “irreversible process” in the parlance of chemical thermodynamics. This means that the spontaneous un-mixing of gases and their re-concentration into separate volumes has never been observed. Energy must be invested to effect any such desired separation of component gases in a mixture. To explore the possibility of CO2 removal, I have quantified my sense of improbability about it, and describe that here.

Consider a hypothetical CO2 removal machine that is a tube with a filter box in the middle. Air is fanned into the tube, flows into the filter box where some of its CO2 is removed, and then flows out of the tube to rejoin the atmosphere and to slightly reduce the global average concentration of CO2. Energy is supplied to entrain air into the device, and energy is supplied to power the unspecified process that effects the CO2 removal within the filter box. The machine would operate continuously so that over time all the atmosphere would be filtered and de-carbonized.

This would be a very large machine, and most likely be a large array of identical or similar units all over the world that would comprise a composite machine. I will describe this composite as if it were a single tube. [1]

Machine #1

This machine has a filter cross-sectional area of 10,000 km^2 (10^10 m^2) into which air is fanned through at 1meter/second (2.24mph). Producing that continuous mass flow from still air requires 16GW of power, assuming an efficiency of 40% (from raw power into moving air). The filtration process is assumed to consume 40GW (1% of the power used by the United States) and be 1% effective at CO2 removal. The anthropogenic emission of CO2, at its current rate of 35.5GT/year (giga metric tons per year), is assumed to continue indefinitely (the economy!), with the oceans absorbing 29% of those emissions (10.4GT/y).

At the end of 10 years of continuous operation Machine #1 would have cleared 3.26ppm of CO2 from Earth’s atmosphere, at a cost of 1.77×10^19 Joules of energy (4.92×10^12 kilowatt-hours). Reducing the CO2 concentration to the pre-industrial level of 280ppm would require 507.6 years.

Machine #2

Clearly, improvements are required for Machine #1. So, we assume that 10% efficiency of CO2 removal can be effected by investing 400GW (10% of the power used by the United States) into the filter box. Now, the power consumption is 416GW for Machine #2. After 10 years of continuous operation 31.5ppm of CO2 would be removed from the atmosphere (bringing the concentration down to 386ppm), at an energy cost of 1.31×10^20 Joules (3.64×10^13kWh). Reducing the atmospheric concentration of CO2 back to 280ppm would require 51 years. This might seem promising except for the fact that the assumed 10% efficiency is pure fantasy.

Machine #3, All Earth’s Lands

To regain a sense of reality, consider the actual performance of the entire land surface of the Earth (1.489×10^14 m^2) acting as a CO2 removal filter. This was the case in the clearing of 2500ppm of CO2 from the atmosphere over the course of 200,000 years during the geologically brief episode of explosive global warming 55.5 million years ago, known as the Paleocene-Eocene Thermal Maximum (PETM). I described the PETM and cited numerous public-access scientific references to it in [2].

Using the same rate of CO2 removal (the e-folding time) as occurred during the PETM, in my formulation of CO2 removal machines, it transpires that the efficiency of removal by the Earth-filter (rock weathering reactions in the long term) is 8.6×10^-8 (0.0000086%). After 10 years, this Earth-machine would clear 0.42ppm of the atmospheric CO2 (bringing the level down from 417ppm to 416.6ppm). That level would be reduced to 280ppm in 3,984 years.

Machine #4

Hope in technology springs eternal for some, so maybe our Machine #2 even with a realistic efficiency can better the clearing-time set by the Earth, natural Machine #3. We accept an efficiency of 1.474×10^-7 (0.00001474%), invest 1.31×10^19 Joules of energy every year at a rate of 416GW of continuous power, and after 10 years find 0ppm of CO2 removal! In fact however long we run this machine there will always be 0ppm of CO2 removal, because the rate of technological removal is equalled by the rate of anthropogenic emissions. Reaching 280ppm is literally infinitely far away.

Machine #5

Maybe by some technological breakthrough the efficiency can be raised by a factor of 100, to 1.474×10^-5 (0.001474%). Then in 100 years Machine #5 would have cleared 0.0478ppm of atmospheric CO2 (reducing the level from 417ppm to 416.95ppm) for an investment of 1.31×10^21 Joules (3.64×10^14kWh). Achieving 280ppm would require 348,577 years. It’s hard to beat the Earth at its own game.

Best Course of Action

It should be obvious by now that our best course of action is to apply our energy resources to the betterment of our many societies and the equalization of living standards worldwide, and to the transformation of our economic activities for minimal CO2 emissions. The current catch-phrase for this transformation is “degrowth.”

During this pandemic year of 2020, the U.S. GDP shrank by 33%, and the CO2 emissions by the United States also shrank by the same proportion. Worldwide CO2 emissions shrank by 17%. Zero emissions require zero GPD, as we now know it.

Global warming will advance and its consequences will add great stresses to many human, animal and plant populations. This geophysical process could be experienced as “the collapse of civilization,” or it could be taken as a collective challenge to advance human civilization by bonds of solidarity, and the restoration of its reverence for the natural world. If we put our energy into fashioning that imperfect utopia, we would live through global warming with a justifiable sense of pride, and even have fun.

Notes

[1] Stream Tube CO2 Removal Machine
8 August 2020
Stream Tube CO2 Removal Machine
or
https://manuelgarciajr.files.wordpress.com/2020/08/stream-tube-co2-removal-machine.pdf

[2] Ye Cannot Swerve Me: Moby-Dick and Climate Change
15 July 2019
https://manuelgarciajr.com/2019/07/15/ye-cannot-swerve-me-moby-dick-and-climate-change/

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Ocean Heat, From the Tropics to the Poles

The heat being captured by the increasing load of carbon dioxide and other greenhouse gases in the atmosphere is subsequently transferred into the oceans for storage. This process — global warming — has raised the temperature of the biosphere by 1°C (or more) since the late 19th century.

Heat introduced into any material body at a particular point will diffuse throughout its volume, seeking to smooth out the temperature gradient at the heating site. If heat loss from that body is slow or insignificant, then a new thermal equilibrium is eventually achieved at a higher average temperature.

Thermal equilibrium does not necessarily mean temperature homogeneity, because the body may have several points of contact with external environments at different temperatures that are held constant, or with other external thermal conditions that must be accommodated to. Equilibrium simply means stable over time.

The heat conveyed to the oceans by global warming is absorbed primarily in the Tropical and Subtropical latitudes, 57% of the Earth’s surface. The Sun’s rays are more nearly perpendicular to the Earth’s surface in those latitudes so they receive the highest fluxes of solar energy, and oceans cover a very large portion of them.

That tropical heat diffuses through the oceans and is also carried by ocean currents to spread warmth further north and south both in the Temperate zones (34% of the Earth’s surface) and the Polar Zones (8% of the Earth’s surface).

What follows is a description of a very idealized “toy model” of heat distribution in the oceans, to help visualize some of the basics of that complex physical phenomenon.

Heat Conduction in a Static Ocean

The model is of a stationary spherical globe entirely covered by a static ocean of uniform depth. The seafloor of that ocean is at a constant temperature of 4°C (39°F), the surface waters at the equator are at 30°C (86°F), and the surface waters at the poles are at -2°C (28°F). These temperature conditions are similar to those of Earth’s oceans. These temperature boundary conditions are held fixed, so an equilibrium temperature distribution is established throughout the volume in the model world-ocean. There is no variation across longitude in this model, only across latitude (pole-to-pole). (See the Notes on the Technical Details)

Figure 1 shows contours of constant temperature (isotherms) throughout the depth of the model ocean, from pole to pole. The temperature distribution is shown as a 3D surface plotted against depth, which is in a radial direction in a spherical geometry, and polar angle (from North Pole to South Pole).

Figure 2 is a different view of the temperature distribution. Three regions are noted: The Tropical Zone (from 0° to 23° of latitude, north or south) combined with the Subtropical Zone (from 23° to 35° of latitude, north or south); the Temperate Zone (from 35° to 66° of latitude, north or south); and the Polar Zone (from 66° to 90° of latitude, north or south).

The model temperature distribution is perfectly stratified — isotherms uniform with depth — in the Tropical-Subtropical Zones, from 30°C at the surface at the equator, to 4°C at the seafloor. On entering the Temperate Zones, the isotherms arc up into a nearly radial (vertical) orientation. In the small portions of the planetary surface covered by the Polar Zones the isotherms are now more horizontally stratified because the surface waters are chillier that the those at the seafloor.

Figure 3 shows the streamlines of heat flow (the temperature gradient) for this temperature distribution. At the equator the heat is conducted down from the 30°C surface to the 4°C seafloor. As one moves further away from the equator the streamlines become increasingly lateral, until they are entirely so at 35° of latitude (north or south) where the model surface waters are at 19°C. The heat flow is entirely horizontal at this latitude, which separates the Subtropical and Temperate Zones; tropical heat is being conducted laterally toward the poles. In the Polar Zones the heat flow is up from the lower depths because the surface waters are chiller than those at depth, and because there is too little temperature variation with distance along the surface to drive a lateral heat flow.

Thermally Driven Surface Currents

Much oceanic heat is distributed by currents, and many of these occur along the surface.

The average speed of the Gulf Stream is 6.4km/hr (4mph), being maximally 9kph (5.6mph) at the surface but slowing to 1.6kph (1mph) in the North Atlantic, where it widens (information from the National Oceanic and Atmospheric Administration, NOAA).

Heat-driven equator-to-poles surface currents on the model ocean were estimated from the combination of the pole-to-pole surface temperature distribution, and thermodynamic data on liquid water. (See the Notes on the Technical Details)

The pressure built up by tropical heat in the model ocean’s equatorial waters pushes surface flows northward (in the Northern Hemisphere) and southward (in the Southern Hemisphere): from a standstill at the 30°C equator; with increasing speed as they recede from the equator, being 2kph (1.3mph) where the surface waters are at 25°C (77°F); a continuing acceleration up to a speed of 2.8kph (1.7mph) at the 35° latitude (the boundary between the Subtropical and the Temperate Zones); and an ultimate speed of 3.6kph (2.2mph) at the poles.

The currents are converging geometrically as they approach the poles, so a speed-up is reasonable. Logically, these surface currents are legs of current loops that chill as they recede from the equator, plunge at the poles, run along the cold seafloor toward the equator, and then warm as they rise to the surface to repeat their cycles.

An equator-to-pole average speed for these model surface currents is 2.8kph (1.7mph). Their estimated travel times along the 10,008km surface arc (for a model world radius of 6,371km, like that of a sphericalized Earth) is 3,574 hours, which is equivalent to 149 days (0.41 year).

Greater Realities

The model world just described is very simple in comparison to our lovely Earth. Since it does not rotate, it does not skew the north-south flow of currents that — with the help of day-night, seasonal, and continental thermodynamic inhomogeneities — creates all of the cross-longitudinal air and ocean currents of our Earth.

The irregularity of seafloor depth on Earth also redirects cross-latitudinal (pole-to-pole) and cross-longitudinal bottom currents, as do the coastlines of the continents; and the very slight and subtle changes in seawater density with temperature and salinity — neither of which is distributed uniformly throughout the body of Earth’s oceans — also affect both the oceans’s volumetric temperature distributions, and the course of ocean currents.

Recall that the model ocean is bounded by constant imposed temperature conditions at its seafloor (4°C) and surface waters (a particular temperature distribution from 30°C at the equator, to -2°C at the poles). Since this model world is otherwise suspended in a void, if these boundary conditions were removed the oceanic heat concentrated at the equator would diffuse further into the watery volume, seeking to raise the temperatures of the poles and seafloor while simultaneously cooling the equatorial region. The ultimate equilibrium state would be an ocean with a constant temperature throughout its volume.

Additionally, if it is also assumed that the now “liberated” model ocean-world can radiate its body heat away — as infrared radiation into the void of space — then the entire planet with its oceanic outer shell slowly cools uniformly toward -273.16°C (-459.69°F), which is the “no heat at all” endpoint of objects in our physical Universe.

When our Earth was in its Post-Ice Age dynamic thermal equilibrium, the “heat gun” of maximal insolation to the Tropics and Subtropics warmed the oceans there; a portion of that heat was conducted and convected into the Temperate Zones and toward the Poles; where the “ice bags” of masses of ice absorbed seasonal oceanic heat by partially melting — which occurs at a constant temperature — and then refreezing. Also, the atmosphere did not trap the excess heat radiated into space. In this way cycles of warming and cooling in all of Earth’s environments were maintained in a dynamic balance that lasted for millennia.

What has been built up in the atmosphere since about 1750 is an increasing load of carbon dioxide gas and other greenhouse gases, which have the effect of throwing an increasingly heated “thermal blanket” over our planet. Now, both the heat conduction pathways and the heat convection currents, described with the use of the model, convey increasing amounts of heat energy over the course of time. As a result the masses of ice at the poles are steadily being eroded by melting despite their continuing of cycles of partial re-freezing during winter, and additional melting during summer.

Simple mathematical models can help focus the mind on the fundamental processes driving complex multi-entangled physical realities. From there, one can begin assembling more detailed well-organized quantitative descriptions of those realities, and then using those higher-order models to inform decisions regarding actions to be taken in response to those realities, if responses are necessary. This point of departure from physics plunges you into the world of psychology, sociology, economics, politics, and too often sheer madness. I leave it to another occasion to comment outside my field of expertise about all that.

Notes on the Technical Details

The cylindrically symmetric equilibrium temperature distribution for a static ocean of uniform depth, which entirely covers a spherical planet, was solved from Laplace’s equation. The temperature of the seafloor everywhere is 4°C, the surface waters at the Equator are at 30°C, and the surface waters at the poles are at -2°C. The variation of surface water temperature with respect to polar angle (latitude) is in a cosine squared distribution. Displays of the 3D surface T(r,ɵ) show isotherms down through the ocean depths at all polar angles (ɵ). The contour lines on the stream function associated with T(r,ɵ) are heat flow streamlines, the paths of the heat gradient (which are always perpendicular to the isotherms).

Bernoulli’s Theorem was applied to surface flow from the equator to the poles (no radial, nor cross-longitudinal motion) for incompressible liquid water with thermal pressure given by:

P(T°C)=[62.25kg/m-sec^2]*exp{0.0683*[T(R,ɵ)-Tp]}

for R equal to the planetary radius to the ocean surface; Tp=-2°C; and using thermodynamic data for water between 32°F (0°C) and 100°F (37.8°C) that indicates a thermal pressure equal to 62.25kg/m-sec^2 in liquid water at 0°C; and that the density of water is essentially constant at 1000kg/m^3 (for the purposes of this model) within the temperature range of the data surveyed.

Inserting P(T°C) into the Bernoulli Theorem definition of equator-to-pole lateral (cross-latitudinal) velocity gives a formula for that velocity as a function of polar angle:

v(ɵ)=±sqrt{(2*[62.25kg/m-sec^2]/[1000kg/m^3])*exp[0.0683*(Te-Tp)]*[1-exp(-0.0683*[Te-T(R,ɵ)])]}

v(ɵ)=±(1.0523m/s)*sqrt{1-exp(-0.0683*[Te-T(R,ɵ)])}

for Te=30°C, and ± for northward (in the Northern Hemisphere) or southward (in the Southern Hemisphere) surface flows.

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Global Warming and Ocean Acidification Accelerate

The global warming of the biosphere and its consequent acidification of the oceans is a complex of geophysical, biological and ecological, and sociological phenomena that are all accelerating. There is much that humanity could do to slow that acceleration, and to enact strategies for its own protection from Nature’s escalating assaults on civilization by the grand feedback loop of anthropogenic global warming climate change, but there is really nothing humanity can do to stop it.

Carbon Dioxide Emissions

The anthropogenic emission of carbon dioxide (CO2) — the exhaust fume of economic activity — has increased steadily over the last 270 years, and explosively so for the last 70 years.

Those emissions were 5.28 billion metric tons of CO2 (1 metric ton = 1 tonne = 1000kg = 2,205 lb) in 1950, and 36.15 billion tonnes in 2017 (1 billion tonnes = 1 giga-tonne = 1 Gt). A rough quantitative characterization (analytical fit) to the historical trend of anthropogenic CO2 emissions since the early 20th century is

E = 35.5•[(YEAR-1890)/130]^2, in Gt/year.

The cumulative emissions up to 2017 were 1,540Gt of CO2 (=1.54 trillion tonnes).

Carbon Dioxide in the Oceans

Of the annual CO2 emissions, about 30% are absorbed by the oceans. [1]

A rough quantitative characterization to the historical trend of CO2 absorption by the oceans is

W = 10.4•[(YEAR-1890)/130]^2, in Gt/year.

The cumulative load of anthropogenic CO2 absorbed by the oceans is 450Gt. [2]

According to [3] there are 39,000Gt of carbon currently in the oceans. Since CO2 molecules are 3.667x more massive (‘heavier’) than pure carbon atoms, this represents 143,000Gt of absorbed CO2. The cumulative mass of Earth’s oceans is 1.366GGt (=1.366•10^9 Gt). Thus, the currently absorbed CO2 is in a mass ratio to seawater of 104.7ppmm (=104.7 parts per million by mass). The “ancient” seas (without the 450Gt anthropogenic load of CO2) had 104.4ppmm of CO2.

This seemingly small addition to the CO2 in the oceans has had profound biological and ecological effects, because of the increase of oceanic acidity by 26%. [1], [4] The chemical indicator of acidity used by scientists, pH, has dropped from 8.2 for “ancient” seawater, to 8.1 for present seawater. The pH scale is logarithmic, and its numbers decrease as the solution in question becomes more acidic.

Ocean acidity impedes the ability of shell-forming marine life to produce their protective coverings. With increased ocean acidity, even the shell structures in existence are eroded. These effects make it more difficult for shell-forming marine life to survive, and as many of these life-forms are small (part of the plankton) they are essential foods at the base of the marine food chain. So the ultimate concern about escalating oceanic acidity is the potential for a collapse of marine life. One estimate of the CO2 concentration needed for “ocean death” by acidification is 400ppmm to 500ppmm. [3]

This implies that 400,000Gt to 540,000Gt more of CO2 would have to be deposited into the oceans; a task that would require 38,000 years to 52,000 years of anthropogenic emissions at the current rate (10.4Gt/year into the oceans). However, “ocean dying” is plainly evident with the current quantity of absorbed CO2, and it will only get worse at an accelerating pace as more CO2 is emitted by civilization.

The chemistry of ocean acidification is as follows. [1]

CO2 + H2O + CO3 —> 2HCO3

Carbon dioxide plus water plus a carbonate ion react to form 2 bicarbonate ions. This process occurs in three steps:

CO2 + H2O —> H2CO3

Carbon dioxide plus water form carbonic acid, which is a weakly bound molecule.

H2CO3 —> H(+) + HCO3(-)

Carbonic acid breaks up into a hydrogen ion and a bicarbonate ion.

H(+) + CO3(2-) —> HCO3(-)

The hydrogen ions liberated in the previous reaction find carbonate ions floating in seawater, and combine into bicarbonate ions. The net result is two bicarbonate ions in the seawater solution.

Shell-forming marine life capture carbonate ions, CO3(2-), to combine them with calcium into calcium carbonate, CaCO3, to form their pearls and seashells. Extracting the needed carbonate by breaking apart bicarbonate ions, instead of just collecting free-floating carbonate ions, is more energy intensive and thus a frustration of the shell-forming biology of so much marine life. So, ocean acidification by CO2 removes some of the stores of a formally available free-floating carbonate ions from the reach of shell-forming marine life.

That acidity, a function of the liberated hydrogen ions, H(+), can also dissolve existing shells. [5]

CaCO3 + 2H(+) —> Ca(2+) + CO2 + H2O

Calcium carbonate (shells) plus hydrogen ions react, dissolving the shell, into free-floating calcium ions plus absorbed carbon dioxide gas plus water.

The Rate of Global Warming is Accelerating

From what has been described up to this point, in conjunction with my previous modeling, I calculate the following tabulated results.

Note that the rate at which global temperature is increasing is accelerating, as is the rate of global warming (the Watts absorbed by the biosphere each year). Also note that entries after 2020 are necessarily projections, and are based on the assumption of existing trends (and the analytical formulas fitted to them) continuing. The entries listed for the year 2020 are pointed out to show that earlier entries are backed by data, and later entries are projections; and to note that rate of global warming for any year listed is shown as a ratio to its rate for year 2020.

The Rate of Ocean Acidification is Accelerating

From what has been described up to this point, I calculate the following tabulated results.

As in the first table, entries up to year 2020 are backed by data, while those after year 2020 are projections. Today’s oceans are 26% more acidic than the oceans of the late 19th century. An alternative comparison is that the oceans of the late 19th century were only 79% as acidic as they are today. If the current trend — of annually increasing anthropogenic CO2 emissions — continues to the end of the 21st century, then the oceans would be 144% (2.44x) more acidic than in the late 19th century; or, equivalently, almost twice as acidic as they are today. Those future acidic oceans at pH=7.8 would reproduce conditions during the middle Miocene, 14 to 17 million years ago, when the Earth was several degrees warmer and a major extinction event was occurring. [1], [4]

“Fixing” Global Warming

I see no possibility of a technical “miracle” to fix global warming; something like an anti-global-warming planetary vaccine, making civilization safe to continue with capitalism.

The CO2 in the biosphere is an extremely dilute mass within enormous masses and expanses of air and water. Removing the anthropogenic excesses of CO2 from the air and the oceans would require the filtration of an immense bulk of matter. Processes of such filtration would require immense quantities of energy, to pump and chemically “strain.” Even if we were able to generate sufficient quantities of energy to power such processes, I cannot imagine that generation to be free of CO2 emissions that would exceed whatever quantity of CO2 was strained out of the biosphere. So, I see such ideas of “technical fixes” as fantasies of the perpetual motion machine variety, and obviated by the 2nd Law of Thermodynamics (specifically, as it applies to reversing the process of diffusion).

The only lever I see humanity having with which to influence the pace of global warming is the degree of its restraint in emitting CO2 in the first place. There is no more energy-efficient counter-warming strategy we can devise. The most effective protective armor that can be devised to shield people from the potential harm that playing Russian Roulette can inflict is to not shoot themselves in the head in the first place.

The energy that we do generate and use to counteract the negative effects of global warming (not just to humans, but to thousands of other species) is best spent in transforming our societies and civilization for maximal mutual assistance and solidarity, and minimal competitive tribalism. Some of that energy would go into physical constructions to shield people from floods, inundation, excessive heat and drought; and some of that energy would go into civic arrangements for sheltering, feeding, healthcare and economic stability of all individuals, and the resettlement of those displaced by loss of habitat: by the loss of coastal land to the rising of sea level, and the loss of living space in continental interiors because of the onset of unlivable heat and loss of water.

Essential to the energy efficiency of both devising and implementing such counter-warming social transformations, it is necessary to stop wasting energy on activities without intrinsic social benefits. Specifically, we, worldwide — but most especially among the 10% wealthiest of Earth’s people, who produce 49% of anthropogenic CO2 emissions [6] — need to abandon every trace of profligate CO2-spewing lifestyles enabled by competitive and exclusionary capitalism and its plethora of bigotries, to instead join cooperatively in World Socialism without consumerist economics nor tribal animosities.

Planet Earth is the loveliest jewel we know of in the entire Universe. If we treated it as such, and each other as part of the sparkle of that gem, we would experience lives in an actual Paradise, regardless of how challenging global warming made our existence.

Notes

[1] Ocean Acidification
https://www.noaa.gov/education/resource-collections/ocean-coasts/ocean-acidification

[2] Cumulative anthropogenic CO2 absorbed by oceans is 450Gt
Previously, I showed that 1,090Gt of CO2 currently resides in the atmosphere; thus 1,540Gt – 1,090Gt = 450Gt. [450Gt/1,540Gt]•100% = 29.2%.

[3] Ocean storage of carbon dioxide
https://en.wikipedia.org/wiki/Ocean_storage_of_carbon_dioxide

[4] A primer on pH
https://pmel.noaa.gov/co2/story/A+primer+on+pH

[5] Calcium carbonate
https://en.wikipedia.org/wiki/Calcium_carbonate

[6] Image: Percentage of CO2 emissions by world population, was produced by OXFAM.

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One Year of Global Warming Reports by MG,Jr

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One Year of Global Warming Reports by MG,Jr

Over the last year, I have posted a series of reports on global warming climate change that address it in a quantitative physics, rather than qualitative and sociological manner. Those reports are listed below in chronological order. My estimation of what global warming “will look like” in the immediate and longer term future was refined over the course of producing these reports; but they are all of-a-piece on the topic.

The first report is primarily “data” for subsequent calculations (and very important). The two PDF reports are my mathematical physics notes on my calculations (the first of these being most significant). The other five are applications of the numerical results for descriptive purposes — to help the general reader understand the magnitude and duration of the global warming effect.

A number of these reports found their way onto Internet Magazines, most significantly Counterpunch, and Green Social Thought.

The versions on my blog have had minor numerical and/or typographical errors corrected (as I find them), and are followed by my comments of subsequent thoughts, with more physics on them just after they were posted.

My sociological recommendations about “what to do about climate change” are summarized in one brief paragraph at the end of Biosphere Warming in Numbers.

My purpose in doing this work should be obvious; first, for me to understand, quantitatively, the nature of global warming; and, secondly, to help “you” to understand it.

I welcome comments and questions on the topic; after all it was such inquiries that prompted me to look into this topic (scientifically) more deeply in the first place.

Please also note, I do NOT dispute the work of professional geophysics/climate change scientists, who work at climate change institutes of various kinds around the world (e.g., meteorological, geological, atmospheric physics and chemistry, oceanographic, biological/ecological/evolutionary sciences), and who use banks of supercomputers to model the many complexities of global warming and climate change (with numerous such complexities still beyond current science’s grasp).

Ye Cannot Swerve Me: Moby-Dick and Climate Change
15 July 2019
https://manuelgarciajr.com/2019/07/15/ye-cannot-swerve-me-moby-dick-and-climate-change/

A Simple Model of Global Warming
26 May 2020
https://manuelgarciajr.files.wordpress.com/2020/05/global-warming-model.pdf

Global Warming is Nuclear War
28 May 2020
https://manuelgarciajr.com/2020/05/28/global-warming-is-nuclear-war/

Living With Global Warming
13 June 2020
https://manuelgarciajr.com/2020/06/13/living-with-global-warming/

No emissions with exponential decay of CO2 concentration: Model
18 June 2020
https://manuelgarciajr.files.wordpress.com/2020/06/global-warming-co2-shutoff.pdf

Global Warming and Cooling After CO2 Shutoff at +1.5°C
20 June 2020
https://manuelgarciajr.com/2020/06/20/global-warming-and-cooling-after-co2-shutoff-at-1-5c/

Biosphere Warming in Numbers
3 July 2020
https://manuelgarciajr.com/2020/07/03/biosphere-warming-in-numbers/

Carbon Dioxide Uptake by Vegetation After Emissions Shutoff “Now”
8 July 2020
https://manuelgarciajr.com/2020/07/08/carbon-dioxide-uptake-by-vegetation-after-emissions-shutoff-now/

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ALSO:

Global Warming and Ocean Acidification Accelerate
18 July2020
https://manuelgarciajr.com/2020/07/18/global-warming-and-ocean-acidification-accelerate/

Ocean Heat, From the Tropics to the Poles
1 August 2020
https://manuelgarciajr.com/2020/08/01/ocean-heat-from-the-tropics-to-the-poles/

The Improbability of CO2 Removal from the Atmosphere
9 August 2020
https://manuelgarciajr.com/2020/08/09/the-improbability-of-co2-removal-from-the-atmosphere/

ClimateSIM Junior, Simplified Prognostication from Unrealistic Hypothesis
16 August 2020
https://manuelgarciajr.com/2020/08/16/climatesim-junior-simplified-prognostication-from-unrealistic-hypothesis/

Facing Extinction, My View
2 September 2020
https://manuelgarciajr.com/2020/09/02/facing-extinction-my-view/

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Possible Future Trends of CO2 Concentration and Global Temperature
7 September 2020 (revised 9 September 2020)
https://manuelgarciajr.com/2020/09/07/possible-future-trends-of-co2-concentration-and-global-temperature/

The above (a brief summary) includes a web-link to the big report below.

A Rate Equation for Accumulation or Loss of Atmospheric CO2
5 September 2020 (revised 9 September 2020)
https://manuelgarciajr.files.wordpress.com/2020/09/rate-equation-for-atmospheric-co2-revised.pdf

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Major improvement on the above

Anthropogenic CO2 Emissions Are Fate
12 September 2020
https://manuelgarciajr.com/2020/09/12/anthropogenic-co2-emissions-are-fate/

For those interested in the technicalities, see

A Carbon Balance Model of Atmospheric CO2
11 September 2020
https://manuelgarciajr.files.wordpress.com/2020/09/a-carbon-balance-model-of-atmospheric-co2.pdf

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Carbon Dioxide Uptake by Vegetation After Emissions Shutoff “Now”

If all carbon dioxide emissions were immediately and permanently shut off in the year 2020 (with 417ppm of CO2 presently in the atmosphere), when would the natural uptake of CO2 by Earth’s vegetation (primarily, at first) bring the CO2 concentration down to its “ancient” level of 280ppm?; and when would the average global surface temperature return to its 1910 level (the “ancient” level, with 0°C of global warming)?

By a series of inferences based on my previous calculations of global warming, I estimate that the answers to the above questions are:

1,354 years to reach 280ppm (after an abrupt CO2 shutoff in 2020);

even so, the global temperature will rise another +2.75°C by 300 years (year 2320), remain there for a century (till year 2420), then slowly reduce to the point of 0°C of global warming (the temperature in 1910, used as my baseline for “ancient” pre-warming conditions) in the year 3374.

Figure 1, below, summarizes these findings.

FIGURE 1: CO2ppm/100 and Relative Temperature after 2020 shutoff

What follows is an explanation of how I arrived at these conclusions. It is an exercise of inductive reasoning that I present in a detailed manner for the benefit of the reader’s understanding of my logic, and to give the reader every opportunity to challenge the arguments I advance.

I proceed by making inferences from incomplete data at my disposal, linked as necessary by physical assumptions that are clearly stated, to eventually arrive at projected histories of CO2 concentration in the atmosphere, and the relative temperature (with respect to that of 1910), for the 1,354 years between 2020 and 3374.

Data on Earth’s Biomass

Humanity today comprises only 0.01% of all life on Planet Earth, but over the course of human history our species has destroyed 83% of wild mammal species. [1]

The world’s 7.6 billion people [in May 2018] represent just 0.01% of all living things. Yet since the dawn of civilization, humanity has caused the loss of 83% of all wild mammals and half of plants, while livestock kept by humans abounds. The new work cited is the first comprehensive estimate of the weight of every class of living creature and overturns some long-held assumptions. Bacteria are indeed a major life form – 13% of everything – but plants overshadow everything, representing 82% of all living matter. All other creatures, from insects to fungi, to fish and animals, make up just 5% of the world’s biomass. Farmed poultry today makes up 70% of all birds on the planet, with just 30% being wild. The picture is even more stark for mammals – 60% of all mammals on Earth are livestock, mostly cattle and pigs, 36% are human and just 4% are wild animals. Where is all that life to be found?: 86% on land, 1% in the oceans, and 13% as deep subsurface bacteria. [2]

I assume that “today” 7.7 billion humans are 0.01% of Earth’s biomass, and that the “average” human weighs 65 kilograms (kg), which is equivalent to 143.4 pounds (lb).

From this, the mass of humanity is estimated to be 5.0×10^11 kg, and the totality of biomass is estimated to be 5.0×10^15 kg.

The estimated totality of biomass can also be stated as 5,000 giga-metric-tons. A metric ton (tonne) is equivalent to 1,000 kg.

The following table lists the quantitative estimates made from the data (above) regarding the Earth’s biomass (the NOTES column in the table indicate assumptions made). Yes, there are gaps and imperfections in the table, which reflect the incomplete knowledge I begin with.

Mass of CO2 in the Atmosphere

The mass of Earth’s atmosphere is 5.2×10^18 kg.

To a good approximation, Earth’s atmosphere is made up of diatomic nitrogen (N2), at 79%, and diatomic oxygen (O2) at 21%. The molecular weight of an N2 molecule is 28 (atomic mass units); and the molecular weight of an O2 molecule is 32 (atomic mass units). A conceptual “air” molecule is defined as having a molecular weight that is 79% that of N2 plus 21% that of O2; that value is 28.8 atomic mass units (AMU).

A carbon dioxide molecule has a molecular weight of 44 atomic mass units (the carbon atom contributes 12 AMU, the two oxygen atoms contribute 32 AMU, combined). So, a CO2 molecule is 1.526x heavier than an “air” molecule.

The concentration of CO2 in the “ancient” atmosphere was 280ppmv (parts per million by volume). The mass (weight) of that ancient (original or baseline) quantity of atmospheric CO2 is thus:

(280ppmv) x (5.2×10^18 kg) x (1.525) = 2.22×10^15 kg.

The mass (weight) of the CO2 presently in the atmosphere (417ppmv) is estimated by a simple ratio:

(417ppm/280ppm) x 2.22×10^15 kg = 3.31×10^15 kg.

The difference between the masses of CO2 today, and in the “ancient” (pre 1910) atmosphere, is the “excess” CO2 driving global warming. The quantity is:

(3.31×10^15 kg) – (2.22×10^15 kg) = 1.09×10^15 kg.

That is 1,090 giga-tonnes.

A second route to estimating the mass of CO2 in the atmosphere is as follows.

Modeling of the huge CO2 spike that occurred 55.5 million years ago and that produced the Paleocene-Eocene Thermal Maximum (PETM) was described in [2], drawing on work cited in [3] and [4].

5,000 billion tonnes of carbon were quickly injected into the model atmosphere, producing a concentration of 2,500ppmv of CO2. The modeling showed the excess CO2 being cleared from the atmosphere by a variety of processes, down to a level of about 280ppmv by 200,000 years.

I interpreted the statements about this modeling, in both [3] and [4], to mean that 5,000 billion metric tonnes of carbon (which happened to be bound in carbon dioxide molecules) — but not 5,000 gigatons carbon dioxide — were injected into the model atmosphere.

The ratio of the molecular weight of carbon dioxide, to the atomic weight of carbon is 44/12 = 3.667.

The quantity of injected CO2 (2,500ppmv) in that model is then:

(3.667) x (5,000×10^9 tonnes) x (1,000 kg/tonne) = 1.834×10^16 kg.

By simple ratios I estimate the masses of CO2 at both 280ppmv and 417ppmv:

(280ppmv/2500ppmv) x (1.834×10^16 kg) = 2.05×10^15 kg,

(417ppmv/2500ppmv) x (1.834×10^16 kg) = 3.06×10^15 kg.

Note that by the first method of estimating these masses I arrived at:

2.22×10^15 kg, at 280ppmv,

3.31×10^15 kg, at 417ppmv.

The agreement between the two methods is heartening. So, continue.

Notice that the mass of CO2 per ppm is:

1.834×10^16kg/2500ppm = 7.34×10^12kg/ppm; equivalently 7.34giga-tonne/ppm.

Lifetime of CO2 in the Atmosphere

The modeling of the PETM described in [2], [3] and [4] showed that after about 10,000 years after the “quick” CO2 injection, the concentration had been reduced to about 30% of its peak level, so to about 750ppm.

This means that the mass of atmospheric CO2 was reduced by 12,840 giga-tonnes (from 18,340 giga-tonnes to 5,500 giga-tonnes) over the course of 10,000 years.

Assuming that this reduction occurred at a uniform rate (linearly) implies that the rate was -1.284 giga-tonne/year, or -1.284×10^12 kg/yr.

The Earth during the PETM (55.5 million years ago) and the Eocene (between 56 and 35 million years ago) was ice-free. The Arctic was a swamp with ferns, Redwood trees and crocodiles; and the Antarctic was a tropical jungle. The quantity of vegetation over the surface of the Earth must certainly have been at a maximum.

Roughly half of the CO2 injected into the model of the PETM atmosphere (mentioned earlier) was drawn out by a combination of photosynthesis, uptake by the oceans, and some dissolution of seafloor sediments (chalk deposits), by 1,000 years. About 30% remained at 10,000 years, and that was further reduced (to about 280ppm, or 11% of the 2,500ppm peak) by 200,000 years by the processes of weathering of carbonate rocks, and then silicate rocks.

If the linear reduction rate of -1.284 giga-tonnes/year (estimated for the first 10,000 years of CO2 reduction during the PETM) were operative for the next millennia or two, the excess 1,090 giga-tonnes of CO2 presently in the atmosphere could be cleared down to 280ppm within:

(1,090 giga-tonnes)/(1.284 giga-tonne/year) = 849 years.

However, since 13 million years ago Antarctica has been in a deep deep freeze; and the Arctic has also been a region of deep cold, ice, and minimal vegetation. Also, “since the dawn of civilisation, humanity has caused the loss of 83% of all wild mammals and half of plants.” [1]

So this combination of natural and anthropogenic reductions of Earth’s vegetation from it’s peak during the Eocene would mean that the process of extracting CO2 from the atmosphere by photosynthesis will be slower. For the moment, I assume at half the rate given earlier, or -0.642 giga-tonnes/year. At that rate, clearing the current CO2 excess (linearly) would take 1,698 years.

In [5] I described my model of how average global surface temperature can be influenced by the exponential decay of CO2 in the atmosphere, after an abrupt and permanent cessation of CO2 emissions. I call the time constant (parameter) used in the exponential function that models the longevity of CO2 in the atmosphere, it’s “lifetime.” In [5], I showed a number of post-shutoff temperature histories, each characterized by a specific value of the lifetime parameter, which in mathematical jargon is called the “e-folding time.” The exponential function is reduced to 36.79% of its peak value when the elapsed time is equal to the e-folding time (e^-1).

The case of the e-folding time being 10,000 years (in my model) has the excess CO2 cleared out of the atmosphere by 1,300 years after the abrupt shutoff of emissions (when global warming is at +1°C, as it is now). That “10,000 year case” is shown in Figure 3 of reference [5], and will be described further below.

It also happens that 10,000 years was found to be the time span required to reduce the CO2 concentration in the model PETM atmosphere to about 30% to 40% of its beginning peak value.

So, I infer that 10,000 years is a reasonable estimate of the lifetime parameter (e-folding time) for CO2 in the atmosphere, and that the present excess of CO2 in the atmosphere (417ppm – 280ppm = 137ppm) would be cleared — if there were an immediate and permanent cessation of emissions — within about 1,300 years, which is similar (in this speculative modeling) to the 1,698 years clearing time gotten by halving an estimated clearing rate during the PETM, above.

A linear rate of decrease of 137ppm over 1,300 years would be -0.11ppm/year (this number will be further refined below).

Reduction of excess CO2 concentration after Abrupt Shutoff
(given a 10,000 year e-folding parameter)

Using the “10,000 year case” post-shutoff temperature change history, just noted [5], the following is observed:

The global temperature relative to “now” (2020, at +1°C) is:

above +2.75°C, at 300 to 400 years (net >3.75°C),
above +2.4°C, at 212 to 550 years (net >3.4°C),
above +1.6°C, at 110 to 766 years (net >2.6°C),
above +1.0°C, at 55 to 900 years (net >2°C),
above +0.5°C, at 30 to 1,100 years (net >1.5°C),
above +0°C, at 0 to 1,100 years (net >1°C).

200 years after the temperature overshoot dips below +0°C (below the 1°C of global warming above “ancient” we have now), further cooling returns the global temperature to its level in 1910 (“ancient,” as used here). This is the behavior, over a span of 1,300 years, of the “10,000 year case” calculated in reference [5].

So, I assume that a CO2 “lifetime” of 10,000 years (e-folding time parameter) would result in a reduction of the atmospheric concentration of CO2 from 417ppm (“now”) to 280ppm (“ancient”) in about 1,300 years. That would be a 32.8% reduction of concentration down to a level of 67.2% of the present peak; a linear rate of decrease of 137ppm/1,300years = 0.105ppm/yr (this number will be further refined, below).

Earlier (above) I had found that the mass of CO2 per ppm is:

7.34×10^12kg/ppm, equivalently 7.34giga-tonne/ppm.

If so, then the weight of CO2 removed per year (at -0.105ppm/yr) is:

7.71×10^11kg/yr, equivalently 0.771 giga-tonnes/yr.

The present excess of CO2 is 1,090 giga-tonnes. Clearing it in 1,300 years would imply a uniform (linear) removal rate of 0.839 giga-tonnes/yr.

I will average the two estimates just given for the CO2 removal rate, to settle on:

0.805 giga-tonnes/yr = 8.05×10^11kg/yr

as the CO2 removal rate.

Earlier (above) I found the mass of the present excess of CO2 in the atmosphere to be 1,090 giga-tonnes. It would take 1,354 years to clear away that excess, given a uniform removal rate of 0.805 giga-tonnes/yr.

That reduction of 137ppm over 1,354 years implies a uniform rate of -0.1012ppm/yr.

Earlier (above) I found the total mass of Earth’s plants to be 4,100 giga-tonnes, equivalently 4.10×10^15 kg. The present excess of atmospheric CO2 (1,090 giga-tonnes) is equivalent to 26.6% of the present cumulative mass of all of Earth’s vegetation (plants). The uptake per year is equivalent to 0.0196% of the current total mass of Earth’s plants.

CO2 uptake occurs within the continuing carbon cycle of:

– carbon dioxide absorbed by plant photosynthesis,

– plants consumed as food by animals (heterotrophs),

– organic solids and wastes absorbed by the soil (decay, nutrients, peat, oil, coal),

– carbon dioxide absorbed by the oceans and used to make shells and corals,

– organic gases emitted to the atmosphere (like methane, CH4, which is soon oxidized to CO2 and water vapor),

– re-release of plant-bound carbon to the atmosphere by wildfires,

– mineralization of CO2 by the weathering of carbonate, and then silicate rocks

From “final” quantities and rates determined in all the above, the following projected histories of the reduction of CO2 concentration (in ppm), and global warming (average global temperature excursion above its level in 1910), after an abrupt cessation of CO2 emissions “now,” are determined and tabulated. This is my estimation of the 1,464 year global warming blip projected to occur between 1910 and 3374.

 

Figure 1, at the top of this report, is a graph of this table.

It is important to note that the conclusions of inductive reasoning — as is the case with this exercise — are viewed as supplying some evidence for the truth of the conclusion. They are not definitive as is the case with proofs by deductive reasoning.

In other words, I did the best I could with what I have. Only the unrolling of the future can supply us the definitive answers.

Notes

[1] Humans just 0.01% of all life but have destroyed 83% of wild mammals – study
https://www.theguardian.com/environment/2018/may/21/human-race-just-001-of-all-life-but-has-destroyed-over-80-of-wild-mammals-study

[2] Ye Cannot Swerve Me: Moby-Dick and Climate Change
15 July 2019
https://manuelgarciajr.com/2019/07/15/ye-cannot-swerve-me-moby-dick-and-climate-change/

[3] Global Warming 56 Million Years Ago, and What it Means For Us
30 January 2014
Dr. Scott Wing, Curator of Fossil Plants,
Smithsonian Museum of Natural History
Washington, DC
[1:44:12]
https://youtu.be/81Zb0pJa3Hg

[4] CO2 “lifetime” in the atmosphere
National Research Council 2011. Understanding Earth’s Deep Past: Lessons for Our Climate Future. Washington, DC: The National Academies Press.
Figure 3.5, page 93 of the PDF file, page numbered 78 in the text.
https://doi.org/10.17226/13111

[5] Global Warming and Cooling After CO2 Shutoff at +1.5°C
20 June 2020
https://manuelgarciajr.com/2020/06/20/global-warming-and-cooling-after-co2-shutoff-at-1-5c/

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