Tag Archives: math

The CO2 and Temperature of the PETM

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The Paleocene-Eocene Thermal Maximum (PETM) was a 200,000 year long period 55.5 million years ago (55.5mya) at the transition from the Paleocene Epoch to the Eocene Epoch on the geological timescale, of highly elevated global temperature and carbon dioxide concentration in the atmosphere — the highest since the demise of the dinosaurs 66mya.

The average global temperature is estimated to have been +5°C to +8°C higher than it is today, which current average can be taken to be 15°C (59°F). Thus, the average global temperature during the PETM was in the range of 20°C (68°F) to 23°C (73.4°F). [1]

A recent study published by the ETH (in Switzerland) has determined that:

“Accordingly, between 57 and 55 million years ago, the mean annual air temperature at the equator where Colombia lies today was around 41°C (105.8°F). In Arctic Siberia, the average summer temperature was 23°C (73.4°F).” [2]

The cause of this elevated global temperature was a large amount of carbon dioxide (CO2) and methane (CH4) in the atmosphere. How much of each, and how did they get there? There are numerous theories and no definitive answers. My sense of a general scientific consensus is that a large swarm of volcanic eruptions in the North Atlantic volatilized layers of methane hydrates (the cold pressurized crystalized precipitates of organic matter decayed by bacterial action) on the seafloor, as well as spewing CO2; and that wildfires and the burning of peat may have contributed to the carbon emissions.

The PNAS paper presents data supporting the idea that CH4 overwhelmingly dominated the greenhouse gas load, with CO2 concentration remaining steady at ~1000±500 ppm [1]; while the ETH report states that: “At that time, the atmosphere was essentially flooded by the greenhouse gas carbon dioxide, with concentration levels reaching 1,400ppm to 4,000ppm.” (ppm = parts per million) [2]

The amount of carbon lofted into the atmosphere, according to the PNAS paper, was in the range of 2,500GtC to 4,500GtC (GtC = giga metric tons of carbon = gigatonnes C); but it cites alternative scientific studies whose estimates range from 6,800GtC to 15,400GtC. [1] Their methods of analysis were unable to determine the timescale of the emissions pulse, but it must have been well less than the 200,000 year span of the PETM, to account for its recovery back to the “normal” conditions of the early Eocene Epoch.

Methane emitted into the atmosphere will eventually oxidize to CO2 and water by chemical reactions like the following:

CH4 + 2*O2 -> CO2 + 2*H2O

CH4 + 4*O -> CO2 + 2*H2O

CH4 + O3 -> CO2 + H2O + H2.

There are many more possible reactions because there are many intermediate species formed, such as: H (atomic hydrogen), OH (hydroxyl radical), HO2, CO (carbon monoxide), H2O2 (hydrogen peroxide). So it is likely that within a few millennia of a massive CH4 release that it has all been oxidized to CO2 and water vapor.

Thus, I thought it reasonable to model the PETM temperature history as due to an emissions pulse of CO2. Specifically, that pulse is a Gaussian with a full width at half maximum (FWHM) of 4,000 years (4ky); centered at 6ky from the start of the PETM, and with a peak emissions rate of 1,456GtC/ky (1,456 GtC per 1000 years, or 1.456GtC/y). By 12ky from the start of the PETM, that pulse has come and gone leaving 6,190GtC in the model PETM atmosphere.

Figure 1, PETM CO2 pulse (12ky)

The calculated CO2 concentration added rises to 2,500ppm between 9ky and 10.5ky from the start of the PETM, (presumably there was ~280ppm, or more, prior to the emissions pulse).

Figure 2, PETM GtC/ky, GtC, CO2ppm (12.5ky)

This model assumes that the composite relaxation time for CO2 absorption from the atmosphere is 40ky. The dominant process fixing atmospheric CO2 is taken to be the weathering of carbonate and silicate rocks and soils; and the processes of both photosynthesis and the absorption by the surface waters of the oceans — which act on much shorter time scales — are assumed to be saturated because of the high concentrations of CO2 in both the air and the oceans.

The course of this model PETM atmospheric carbon excursion out to 20ky is shown in Figure 3, and out to 100ky is shown in Figure 4.

Figure 3, CO2ppm (20ky)

Figure 4, CO2ppm (100ky)

Beyond 100,000ky, the model PETM CO2 concentration falls into the range of the pre-industrial levels of ~200ppm to ~300ppm.

The model atmosphere at 0ky was taken to have 0ppm of CO2, so everything shown in the Figures is only added carbon (added CO2). The added heating caused by the added CO2 is estimated at:

+∆T °C = [CO2ppm added]/[130ppm/1°C] – 11°C,

where a baseline has been assumed of an average global temperature of 11°C at “0ppm” (actually 170ppm to 270ppm) as existed in the depths of the Ice Ages of the Pleistocene Epoch (2.58mya to 11.7kya), when the global temperature hovered about -4°C±4°C from what it was in pre-industrial times (~15°C).

The ratio 130ppm/1°C comes from my estimate of a +130ppm rise in atmospheric CO2 (280ppm to 410ppm) during the 130 years between 1890 and 2020, accompanied by an average global temperature rise of 1°C.

The calculated history of the model PETM average global temperature rise — by the above method — peaks at +8.2°C, between 9.3ky and 10ky, and is shown in Figure 5. Thus, the peak average global temperature implied was 19.2°C (66.6°F).

Figure 5, +T°C from PETM carbon pulse

If I assume that the model PETM temperature rise calculated above actually rested on a background global temperature of 15°C, similar to pre-industrial conditions (which might seem inconsistent, but there are many uncertainties), then the peak of the model PETM global temperature is 23.2°C (73.8°F).

Note that the ETH results were: +26°C at the Equator (41°C = 105.8°F) and +8°C in the Arctic during summer (23°C = 73.4°F), which are hotter for middle and tropical latitudes than in the model here.

My study here cannot rival the scientific rigor of [1] and [2] and it cannot quantify the entire complex of climate-affecting phenomena that occurred during the PETM; but it does give a clear general picture of a hyperthermal excursion caused by a massive pulse of carbon emissions into the atmosphere as occurred during the PETM.

The climate at that time was hotter and wetter, and with no polar ice; Antarctica was jungles, and the Arctic was a crocodile-infested swamp-ringed ocean.

Notes

[1] Temperature and atmospheric CO2 concentration estimates through the PETM using triple oxygen isotope analysis of mammalian bioapatite
Alexander Gehler, Philip D. Gingerich, and Andreas Pack
PNAS July 12, 2016 113 (28) 7739-7744; first published June 27, 2016;
https://doi.org/10.1073/pnas.1518116113

[2] Back to the future of climate
Peter Rüegg
ETHzürich
26 October 2020
https://ethz.ch/en/news-and-events/eth-news/news/2020/10/back-to-the-future-of-climate.html

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Another Model of Atmospheric CO2 Accumulation

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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

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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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Book and Movie Reviews by MG,Jr. (2017-2020)

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1 August 2020, was the 201st anniversary of the birth of Herman Melville. 2019 was my year to be totally immersed in Moby-Dick (for the third time), an awesome masterpiece. This is PERHAPS, the greatest novel yet written in the English language.

I’ve written previously on Melville and Moby-Dick here:

Happy 200th, Herman!
https://manuelgarciajr.com/2019/08/01/happy-200th-herman/

Moby-Dick
https://manuelgarciajr.com/2019/08/07/moby-dick/

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

The Ultimate Great American Novel
https://manuelgarciajr.com/2018/09/04/the-ultimate-great-american-novel/

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W. Somerset Maugham’s “Ten Novels And Their Authors”

Maugham wrote a book of this title, describing his picks, ranked as shown below, His essays on each are excellent.

War and Peace (Tolstoy)
Madame Bovary (Gustave Flaubert)
Pride and Prejudice (Jane Austen)
The Brothers Karamazov (Dostoevsky)
Le Père Goriot (Honoré de Balzac)
Wuthering Heights (Emily Brontë)
Le Rouge et le Noir (The Red and The Black; Stendhal)
Tom Jones (Henry Fielding)
David Copperfield (Charles Dickens)
Moby-Dick (Herman Melville)

Read by MG,Jr (from Maugham’s list), so far:

Madame Bovary (Gustave Flaubert)
The Brothers Karamazov (Dostoevsky)
Le Père Goriot (Honoré de Balzac)
David Copperfield (Charles Dickens)
Moby-Dick (Herman Melville)

I like the following, as SOME of the other novels that I think are “classics”:

The Three Musketeers (Alexandre Dumas)
Huckleberry Finn (Mark Twain)
On The Road (Jack Kerouac)
Slaughterhouse Five (Kurt Vonnegut)

The Three Musketeers is described here:

My Favorite Classics
https://manuelgarciajr.com/2017/09/18/my-favorite-classics/

Huckleberry Finn and Slaughterhouse Five are described here:

The Ultimate Great American Novel
https://manuelgarciajr.com/2018/09/04/the-ultimate-great-american-novel/

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Three movies from 2015-2016:

Heal the Living (Réparer les vivants) (2016)

Superb film by Katell Quillévéré (screen-writer and director), about life, death and organ donors. The meditative nature of this film, without excessive pathos, with a lovely piano accompaniment (most of the time except for two noisy rock songs), the lovely crisp photography possible with today’s equipment, and its seamless transitions between wakeful reality and introspective day-dreaming, and back, and its transitioning ensemble – constellation – of collaborative actors (instead of a star in front of background “support”), make this a very thoughtful and artistic film that presents fundamental truths. All these sterling qualities (except for the crisp photography) will make this film largely unpopular for US audiences, especially when spoken in French with English subtitles.
https://youtu.be/otYWveDaplo

Genius (2016)

A superb English film about legendary American authors, particularly Thomas Wolfe (author of “Look Homeward, Angel”) and really about Max Perkins, the Scribner’s (book publishing company) editor who discovered Ernest Hemingway, F. Scott Fitzgerald and, most flamboyantly, Thomas Wolfe (the movie is ostensibly about him). The heart of the story is about friendship (male friendship) collaborating in the creative artistic process, in this case to produce literary novels. Anyone who likes reading (actual books of literature, in paper), and who strives to produce excellent art that requires collaborators (particularly theater and often music, and inevitably every art) in any medium would like this movie. However, the American reviewers were not keen on this movie because they and most American audiences don’t really like reading and find the movie “slow;” it’s basically a detailed exposition of intellectual processes (and what American wants to watch that?); its lighting is “dark” (which is how it actually looks in downtown Manhattan); Americans don’t like foreigners making movies about American subjects (English actors can do any variety of American accents, but American actors can’t do English, or any other foreign accent); and the movie unrolls like a well thought-out play since it was in fact directed by an English theatrical director (with a story based on a carefully studied biography of Max Perkins).
https://youtu.be/gCvcD3IBSlc

Mr. Holmes (2015)

This is a modern and very clever modern story (i.e., not by Arthur Conan Doyle) of Sherlock Holmes near the end of his life in retirement, living as a beekeeper. The plot, photography, score, and acting by the (largely) English cast are all first rate, naturally. The film has proved popular with English and American audiences, and rightfully so. The story involves Holmes as a 93-year-old (in ~1947) who, despite failing memory, is trying to recall the details of his last case, which ended tragically and caused him to retire. The jumps between “the present” (~1947) and flashbacks (~1912) are clear, as are the transitions to the flashbacks to Holmes’s post WWII visit to Japan (1946/1947). There is enough of the “solve the mystery” element in the film to satisfy most Sherlock Holmes fans, and a thoughtful emotional-psychological thread to the story that was not ruined by an excess of pathos or icky sweetness. Of course the acting, photography and score were good and well-integrated into this polished work of cinema. Overall, nicely paced and good entertainment with wit, polish and good heart.
https://youtu.be/0G1lIBgk4PA

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Some commentary on Anti-War movies and books:

The Pentagon Papers in the Movies
[the 2003 movie is the best, and what a story!]
20 April 2018
https://manuelgarciajr.com/2018/04/20/the-pentagon-papers-in-the-movies/

Anti-War and Socialist Psychology Books and Movies
23 January 2018
https://manuelgarciajr.com/2018/01/23/anti-war-and-socialist-psychology-books-and-movies/

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Lafcadio Hearn

Lafcadio Hearn (1850-1904) was an unusual American who eventually became a Far Eastern foreign correspondent to American newspapers and magazines, and an expert interpreter of Japanese and Chinese stories, legends and fables, as well as a keen observer of how life was conceptualized and conducted in Asia (mainly Japan).

Lafcadio Hearn was born in Lefkada, a Greek island in the Ionian Sea on the west coast of Greece. He had an Irish father and Greek mother, and a difficult childhood filled with rejection. He also lived a very unusual life, for some time a newspaper crime reporter in the U.S.A. (Cincinnati, New Orleans), marriage to a Black Women at a time when mixed marriages were extremely difficult to sustain socially in the U.S., and then moving on to a foreign correspondent role, first in the French West Indies and then in Japan. There, he learned Japanese, taught in Japanese schools, married a Japanese woman and had four sons, and lived out a happy last chapter to his colorful and literary life.

A superb book by Hearn is Kwaidan, which is a book of Japanese ghost stories, and which book was the basis of an amazing 1965 Japanese art film (movie) of the same title by Kobayashi. I think Kwaidan is a masterpiece.

Gleanings In Buddha Fields is a collection of stories (the mythical, legendary and fabulous) and essays (on the realities of life), which in total immerse the reader into the zeitgeist, or context, of late 19th and early 20th century Japan.

Alan Watts noted that Lafcadio Hearn’s book Gleanings In Buddha Fields (1897) sparked (or was one of the sparkers of) his interest in Buddhism and Eastern Philosophy. I read Gleanings In Buddha Fields because I was curious to learn the source (about one of the sources) of where Alan got his Zen.

I recommend Gleanings in Buddha Fields to you (and Kwaidan).

Because some (at least one or two) of Hearn’s references to historical personalities of 19th century (and earlier) Japan are not part of modern memory, you might have to do a little Internet researching to gather some of the historical facts about the incidents Hearn was referring to (in Gleanings…), in order to fully appreciate Hearn’s presentation. But even without such deeper investigation, Gleanings In Buddha Fields is an excellent, informative, thoughtful and Zen-atmospheric book. In discovering it with your first reading, you can also imagine yourself reliving, at least in part, the juvenile awakening to Zen Buddhism experienced by Alan Watts (whose The Way of Zen is a masterpiece).

A modern collection of selected Japanese stories (including some from Kwaidan) by Hearn is the following. It is excellent, and well-researched, with a very informative introductory essay by the editor-researcher, who was Ireland’s ambassador to Japan.

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Cinema Art From 1968 For Today
18 August 2018
https://manuelgarciajr.com/2018/08/18/cinema-art-from-1968-for-today/

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The Ultimate Great American Novel
4 September 2018
https://manuelgarciajr.com/2018/09/04/the-ultimate-great-american-novel/

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All Quiet On The Western Front

“All Quiet On The Western Front,” by Erich Maria Remarque (22 June 1898 – 25 September 1970), is the greatest war novel of all time. Why? Because it vividly conveys the physical, psychological and emotional realities of being at the front face-to-face with the enemy in an all-out massively industrialized war. “All Quiet On The Western Front” is also the greatest anti-war novel of all time. Why? Because it vividly conveys the physical, psychological and emotional realities of being at the front face-to-face with the enemy in an all-out massively industrialized war.

This novel was first published 92 years ago, in 1928; and its story is set a century ago, in 1918, during World War I. This novel describes the realities of a soldier’s transformation from naïve enthusiastic recruit to hardened emotionally vacant veteran, the deadly and depersonalizing confusion of military operations, the rush and terror of frontline combat, the haphazard allocation of injuries, the slow-motion dread of being in hospital, the brief joys and overwhelming alienation and anguish of home leave, the struggle against insanity, the scant and fleeting serendipitous joys in the field, the loss of a personal past that moored one to a potentially fulfilling future in one’s culture, and the crushing of the lonely human spirit shadowed by the omnipresence of death. The human reality of this novel is timeless. Most of us casually say we are anti-war, but to truly inoculate yourself against any taste for war you must read this book and allow its story, and its feeling, to soak deep into your psyche.

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F. Scott Fitzgerald

Fitzgerald’s novel Tender Is The Night hit me like a thunderbolt. Fitzgerald drew the title from a line in John Keats’s poem “Ode to a Nightingale.” I’ve written quite a bit about Fitzgerald (follow the links to that). Below are a few of the comments about Fitzgerald and movies about him and his novels.

Appreciating F. Scott Fitzgerald
https://manuelgarciajr.com/2019/04/24/appreciating-f-scott-fitzgerald/

The Poetry of Disillusionment in “Gatsby” is Beyond the Movies
https://manuelgarciajr.com/2020/04/27/the-poetry-of-disillusionment-in-gatsby-is-beyond-the-movies/

F. Scott Fitzgerald and Lost American Lyricism
https://manuelgarciajr.com/2019/06/17/f-scott-fitzgerald-and-lost-american-lyricism/

I Learn About F. Scott Fitzgerald
https://manuelgarciajr.com/2019/03/16/i-learn-about-f-scott-fitzgerald/

Two “F. Scott Fitzgerald” movies:

Last Call is based on the memoirs of Frances Kroll Ring (1916-2015), Fitzgerald’s last secretary, and sounding board, to whom he dictated his last novel The Love Of The Last Tycoon, A Western. Frances Kroll Ring’s book (1985), highly praised by both scholars and Fitzgerald aficionados for its accuracy, detail and sympathy, is about the last two years (1939-1940) of Fitzgerald’s life. Frances Kroll Ring (herself in 2002) appears at the end of the film. A very well made film, as close as we’ll ever get to “being there” with Scott. Jeremy Irons plays Scott, Neve Campbell plays Frances Kroll Ring, both excellently in my opinion. The Cambridge Companion To F. Scott Fitzgerald (2002) is dedicated to Frances Kroll Ring “with affection, gratitude, and respect from everyone who reveres F. Scott Fitzgerald as man and artist.”

Getting Straight is a fun movie of college life and protest in 1970, and centers on a much put upon ex-activist and graduate student of literature (“Harry,” played by Elliot Gould) who ultimately gives it all up (except the girl) in a very spirited defense of the art and spirit of F. Scott Fitzgerald. This movie was approvingly pointed out by Ruth Prigozy, the editor of The Cambridge Companion To F. Scott Fitzgerald. I was surprised at how many references Harry makes to characters and incidents in both Fitzgerald’s novels and in his life (with Zelda and then Sheilah Graham). The movie can be fun without having to know all these references, but it is much funnier being in the know. I thought, my god!, this bright, breezy, light-hearted confection from 1970 would be over the heads of the illiterate comic-book-cartoon-movie-consuming popular audiences of today: we’re doomed!

Last Call (2002, trailer)
https://youtu.be/uzxx8C2xWDc

Getting Straight (1970, stills and music)
https://youtu.be/vWER0TLWLuo

The Crack-Up
F. Scott Fitzgerald
[originally published as a three-part series in the February, March, and April 1936 issues of Esquire.]
https://www.esquire.com/lifestyle/a4310/the-crack-up/

The Moment F. Scott Fitzgerald Knew He Was a Failure
By Lili Anolik
Sep 22, 2015
https://www.esquire.com/entertainment/a38113/f-scott-fitzgerald-1015/

“It was a gorgeous evening. A full moon drenched the road to the lustreless color of platinum, and late-blooming harvest flowers breathed into the motionless air aromas that were like low, half-heard laughter.”
— F. Scott Fitzgerald, from The Curious Case Of Benjamin Button, section V.

“The test of a first-rate intelligence is the ability to hold two opposed ideas in the mind at the same time, and still retain the ability to function.”
— F. Scott Fitzgerald, from The Crack-Up, part I, 1936

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My Wicked, Wicked Ways, by Errol Flynn

A mostly honest book. I have always loved Flynn in the movies. A very engaging character, with his own flaws and tragedies despite all the glamour and antics. What I most like about him is that despite everything, he always sought to enjoy, to laugh, to be happy and make others happy; but a major prankster.

I think he knew he was doomed to a short life from very early on; he had contracted tuberculosis and malaria as a teenager prospecting in New Guinea in the late 1920s very early 1930s. So, he enjoyed his smokes and booze and morphine, and most of all women, who shamelessly threw themselves at him, especially after he made money but even before when broke and homeless. Besides, he pursued them very keenly, too.

Alan Watts mentioned that some Zen master from the past had said that there were two paths to enlightenment: the path of thoughtful study, meditation, good works, piety, humility and patience; and the path of debauchery leading to exhaustion of that attitude leading in turn to an awakening. This in fact is the main comparison presented in Herman Hesse’s Siddhartha. But, Watts continued, the first path is by far recommended even though its “success rate” is not particularly high, because the second path can easily be fatal (in every way) though it was considered a “sure thing” and “quicker” for gaining enlightenment: if you survived to getting to that point! The story of Siddhartha Gautama (Buddha) is in fact of a life of renunciation of a princely life of luxury and dissipation to first seek meaning through asceticism, which was ultimately found to be arid, and then to settle on the “middle way,” between asceticism and dissipation: which for today we can think of as consumerist materialism (dissipation, that is).

So, Flynn’s book was fun for me to help reflect on these ideas. Besides, it is a fun book on vignettes and quips about “golden age” Hollywood.

Errol Flynn starred in the 1938 movie, The Dawn Patrol, about WWI British fighter pilots in France. This is an anti-war movie. I describe it here:

Criminalated Warmongers
https://manuelgarciajr.com/2019/11/11/criminalated-warmongers/

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Magister Ludi (The Bead Game)

Herman Hesse received the Nobel Prize for Literature for Magister Ludi (The Bead Game). Interesting book (long), but sometimes a bit remote/slow for me. The “three tales” appended at the end are superb. I wonder if the whole big book before it was really just an enormous lead-in to them. Hesse put tremendous thought and work into this book, there are many undercurrents and subtleties that I may not have fully appreciated. I think it is basically a book about religious feeling (existentialism?) in a non-religious way; similar to the orientation of Carl G. Jung’s psychology. Both Jung and Hesse were born in religious/missionary families from Switzerland (Jung) or southwest Germany near Switzerland (Hesse, who spent much of his life till the end in Switzerland). I think Hesse was working from a view of life like looking at the Swiss Alps from a remote chalet (which is in fact where he lived).

Excerpts from Magister Ludi (The Bead Game), (1943)

He had also made the discovery that a spiritual man in some curious way arouses resentment and opposition in others, who esteem him from afar and make claims on him in times of distress, but by no means love or look upon him as one of themselves and are more inclined to avoid him. He had learned from experience that old-fashioned or home-made magic formulas and spells were more willingly acceptable to sick people or victims of misfortune than intelligent advice. He had learned that man prefers misfortune and external penance rather than attempt to change himself inwardly, and had found that he believed more easily in magic than in intelligence, and in formulas more readily than in experience — many things in fact which in the few thousand years that have elapsed have presumably not altered so much as many history books would have us believe. He had also learned that a man in quest of the spiritual should never abandon love, that he should encounter human desires and follies without arrogance, but should, however, never allow them to dominate him; for, from the sage to the charlatan, the priest to the mountebank, from the helping brother to the parasitical sponger, is only a short step, and people fundamentally prefer to pay a rogue or allow themselves to be exploited by a quack than to accept selflessly offered assistance for which no recompense is asked. They would not readily pay with confidence and love, but preferably with gold or wares. They cheated each other and expected to be cheated in return. One had to learn to regard man as a weak, selfish and cowardly being, but one had also to see how greatly one participated in all these characteristics and urges and longs for ennoblement.

We must no longer rely on the fact that the cream of the talented from out there flock to us and help us to maintain [our society]: we must recognise our humble and heavy responsibility to the schools of the world as the most important and the most honourable part of our task, and we must elaborate it more and more.

Times of terror and the deepest misery may arrive, but if there is to be any happiness in this misery it can only be a spiritual happiness, related to the past in the rescue of the culture of early ages and to the future in a serene and indefatigable championship of the spirit in a time which would otherwise completely swallow up the material.

Siddhartha

I love “Siddhartha” by Hesse; easy to see why that book of his is so popular. It is an “awakening” story similar to the life of Buddha, who appears as a support character to the protagonist. I said more about “Siddhartha” in my comments on Errol Flynn, above.

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After The End of The World: books by George R. Stewart, and Walter M. Miller, Jr.

Here are two classic “after the end of the world” books. In Earth Abides, George R. Stewart’s end-of-the-world is by pandemic!, and in A Canticle for Leibowitz, Walter M. Miller Jr.’s is by post nuclear war taking America back to a Medieval Period, and then eventually over a few millennia to a new rocket and nuclear age, which ends as one would expect.

Stewart was an English professor at the University of California, Berkeley, in the 1930s-1940s, and his book here is from 1949. Amazingly prescient, realistic “speculative fiction” about the subsequent lives of the few survivors of the nearly overnight pandemic.

Miller’s book is definitely different, but there are no cheesy sci-fi gadgetry nor “special effects,” despite the strangeness of the worlds he portrays. Interestingly, the monastery life that is the center of Miller’s book is similar in many ways to the monastery life that is the center of Herman Hesse’s Magister Ludi (which is also a sort-of after the end of the world book, really of a “distant” future after the end of the fascist world).

I cannot imagine Miller’s vision becoming reality, but I can easily imagine Stewart’s coming about.

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The Twilight Zone

A PERSONALLY IMPORTANT LIFE GOAL OF MINE MET!

During this 2020 summer of hiding out from the pandemic, I watched all 156 episodes of the anthology TV show, THE TWILIGHT ZONE, which originally ran between 1959 and 1964. This feat was accomplished by seeing 2 to 6 episodes a night on consecutive nights over the course of several weeks.

This show is a collective work of TV art, guided by Rod Serling, who wrote 59% of the episodes. Amazingly, despite this show being in the neighborhood of 60 years old, its anachronisms relative to today’s typical attitudes and technological paraphernalia are infrequent (as regards the attitudes) and not distracting (as regards the technicalities). But it really shines in its depiction of the inner workings of human hearts and minds, and also human heartlessness. In this most important artistic-literary aspect, The Twilight Zone has not been surpassed by television shows since.

The Twilight Zone is a sequence of — usually — morality tales (interspersed with occasional comedies) whose telling is freed imaginatively and dramatically by allowing for the arbitrary actions of mysterious metaphysical forces. It’s as if Lafcadio Hearn, Ambrose Bierce and H. P. Lovecraft had been transported 60 years into their futures to write for television. One of the most thrilling aspects of Rod Serling’s Twilight Zone is the intense social consciousness, and anti-war, anti-greed, anti-bigotry and anti-cruelty attitudes nearly every minute of the entire series exudes. The acting, by many many actors, is uniformly excellent; and the production values of all the technicalities are also very good, but also very obviously more modest than in the costly productions of TV fare today.

In seeing the entire 156 episodes in one concentrated period of time, I have gotten a very clear appreciation of The Twilight Zone’s beauty and value as art. Without intending to be blasphemous, pretentious or dumb, let me say that I can see The Twilight Zone representing, for discerning American (and beyond?) viewers of the 1960s, a thought-provoking and socially instructive film-electronic art form in the same way that the plays of Sophocles, Euripides and Aristophanes were thought-provoking and socially instructive theatrical art forms to the Fifth-century Athenians.

The bubbling cauldron of social tensions, aspirations and fears of dynamic yet troubled societies were artistically abstracted and polished into the diamond-sharp facets of intense dramatic plays, reflecting the whole of contemporary society back into itself through the fascinated gaze of its individual people. If “the eyes are the mirror of the soul” then The Twilight Zone, through TV screens, was the mirror of the collective or societal American soul, which soul is always hidden behind a flashy loud and positivist front.

If you see the whole series, looking past the incidentals of its presentation, but deep into the essence of its conception, literateness and soul, you will see and hear as sharp and accurate depictions of the personalities and preoccupations of our society today as was the case for the American society of the early 1960s, during the show’s first run 61 to 56 years ago.

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John Keats, poet

Much feeling here, combined with a tremendous amount of work to present that feeling with refinement and grace of language, without dilution of the emotion, and without making it all seem a labored construction. Also wonderful feeling for nature and the natural world. I can’t criticize anything here, only try to learn from it. To my mind, Keats is to English poetry what Mozart is to music. Keats was a major influence on F. Scott Fitzgerald, who I see as an American “3rd generation” English Romantic poet who expressed his artistry in prose.

I have to dig into Shelley next (I have a huge tome), who was more “ferocious” than Keats. Both were very focussed artists. I’m struck by the idealism they felt and worked from.

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In Pursuit of the Unknown: 17 Equations That Changed the World, by Ian Stewart

Hello math lovers! (sic),

At one time or another a member of my family or friends has expressed an interest in:

Pythagoras’s Theorem (triangles, distance, areas, surfaces), or

Calculus (rates of change of anything and everything), or

Newton’s Law of Gravity (planetary motion, satellite trajectories), or

Pure Math (Napier’s Bones, the weirdness of the square root of -1, and Möbius Strip topology), or

Normal Distribution (the probability distribution of IQ, and “The Bell Curve” book), or

The Wave Equation (tones, semitones, musical scales, even tempering, beats within harmony), or

Fourier Transform (sines and cosines, single frequency/pitch modes and equalizers, digital camera images), or

The Navier-Stokes Equation (fluid flow, aerodynamics, F1 car design, global warming computation), or

Maxwell’s Equations (electricity, magnetism, radiation, wireless communication, TSA body scanners), or

Thermodynamics (entropy, efficiency of engines and renewable energy technology, disordering of the universe), or

Relativity (curved space-time, bent light rays, black holes, Big Bang, dark matter, dark energy), or

Quantum Mechanics (Schrödinger’s Cat, many parallel worlds, semiconductor electronics), or

Information Theory (codes, coding, data compression, digital communications), or

Chaos (species population dynamics with explosive growth and collapse, erratic unpredictability), or

Black-Scholes Equation (insane financial speculation, options, futures, derivatives, credit default swaps, the banking/real estate/financial crash of 2007-2008).

Because of that, here is my review of Ian Stewart’s 2012 book: In Pursuit of the Unknown: 17 Equations That Changed the World. Stewart says of his book: “This is the story of the ascent of humanity, told through 17 equations.”

This is an excellent enthralling book: interesting, very informative, very well written clear explanations of the mathematics and the applications of that mathematics to: classical mathematical calculations, lots of physics and related technology, information theory (codes and computers), chaos (wild swings in species populations), and the insane 21st century finance economics of our previous financial crash and its inevitable successors. This brief description does not in any way convey the complete range of this book.

On the front cover you can see the 17 (sets of) equations, which Stewart describes (and their many uses) over the course of 17 chapters. Of the 13 equations I feel confident about knowing something about (all “basic” math and/or mathematical physics), I find Stewart to be accurate and masterfully clear in his descriptions.

My only quibble is where he states about the main causes of global warming being the production of carbon dioxide and methane (gases) that: “These are greenhouse gases: they trap incoming radiation (heat) from the Sun.”

This is a collapsing of the actual mechanism, which is: the the capture of outgoing heat radiation (infrared radiation) by CO2 (most importantly) and CH4 (along with other heat-trapping molecular gases in trace amounts in the atmosphere), which upward radiated heat energy is derived from the earlier absorption (by the oceans and lands) of incoming light energy; a necessary process for cooling the Earth and stabilizing its temperature (if we didn’t mess with the process). So I would rephrase the Stewart sentence quoted as: “These are greenhouse gases: they trap outgoing radiation (heat) from the Earth.”

[If you think about it you will see that wherever the biosphere captures the incoming LIGHT from the Sun — in the air, lands or oceans — it ultimately heats to the same degree; but when our pollution intercepts and stores a greater portion of the re-radiated outward going HEAT (infrared radiation) from the biosphere than would be the case “naturally,” that the Earth’s “cooling system” is impaired and the biosphere warms up steadily, for an Earth out of heat balance.]

Regardless of this quibble, Stewart knows much much more about all the mathematics he presents and all the uses of it than I do. The 4 equations I knew nothing about (and learned about from Stewart) are: #1 Euler’s formula for polyhedra (topology); #2 information theory; #3 chaos theory (I know a little a bit about nonlinear dynamics, sensitivity to initial conditions, and limit cycles: similar to the “butterfly effect”); and #4 the Black-Scholes, or “Midas” equation that was heavily abused to produce the financial meltdown of 2007-2008. On these four, I learned a great deal from Stewart (basically everything I know about them now), and in the reading of this book I gained a sense of trust in his descriptions and pronouncements.

My only other critique of the book (and a minor one) is that there are a number of proofreading lapses (both of text and substance) that show up as typographical errors, and/or what I presume to be mischosen words (some obviously errors, others didn’t make sense to me). The few instances of these errors occur most frequently in the later chapters of the book, and none is fatal (especially if you don’t notice them). So, I agree with the praise for the book highlighted on the back cover.

I especially recommend the book for its explanation (in 8 chapters) of the physics of: classical gravity (Newtonian mechanics), waves, heat flow, fluid flow, electrodynamics, thermodynamics (entropy), relativity and quantum mechanics. I also appreciate his logical and scathing take-down of the modern hyperactive derivative-based financial speculation that dominates and threatens the world’s economies today. For me, the 8 physics chapters are superb; but there is no part of the book that is weak: “a wonderfully accessible book.”

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Upanishads

Juan Mascaró was a superb poetic translator. His selections from the Upanishads is enthralling. His translation of the Dhammapada was also wonderful:

“As the bee takes the essence of a flower and flies away without destroying its beauty and perfume, so let the sage wander in this life.” — The Dhammapada, 49

Joseph Campbell (author of The Hero With A Thousand Faces, editor of Heinrich Zimmer’s book The Philosophies of India) said of the Upanishads: “It’s all there.”

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Books I must add to my list of essential classics:

History of the Peloponnesian War (Thucydides, translated by Rex Warner)
The Plays of Euripides
The Plays of Sophocles
L’Avare (The Miser, a play by Molière)
Phèdre (Phaedra, a play by Racine)
The Picture of Dorian Gray (Oscar Wilde)
The Moon and Sixpence (W. Somerset Maugham)
The Razor’s Edge (W. Somerset Maugham)
Brave New World (Aldous Huxley)
Homage to Catalonia (George Orwell)
1984 (George Orwell)
Collected Essays (2002, George Orwell)
Bhagavad Gita (Swami Prabhavananda and Christopher Isherwood)
Bhagavad Gita (Juan Mascaró)
Memories, Dreams, Reflections (Carl Gustav Jung)
The Autobiography of Malcolm X (Malcolm X, with Alex Haley)
Cadillac Desert (Marc Reisner)

…and others as I think of them.

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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Reducing CO2 Emissions to Reverse Global Warming
17 September 2020
https://manuelgarciajr.com/2020/09/17/reducing-co2-emissions-to-reverse-global-warming/

Global Warming Burps, Bubbles, Simmers and Sours On
24 September 2020
https://www.counterpunch.org/2020/09/24/global-warming-burps-bubbles-simmers-and-sours-on/

Another Model of Atmospheric CO2 Accumulation
5 October 2020
https://manuelgarciajr.com/2020/10/05/another-model-of-atmospheric-co2-accumulation/

The CO2 and Temperature of the PETM
2 November 2020
https://manuelgarciajr.com/2020/11/02/the-co2-and-temperature-of-the-petm/

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Carbon Dioxide Uptake by Vegetation After Emissions Shutoff “Now”

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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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Biosphere Warming in Numbers

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Biosphere Warming in Numbers

At this time, the Biosphere is warming at a rate of 3.03×10^15 Watts, which is equivalent to a temperature rate-of-rise of 0.0167°C/year. The warming rate has been increasing steadily since the 19th century, when it was on average “zero” except for natural fluctuations (plus and minus) that were hundreds of times smaller than today’s warming rate.

The total energy use by the United States in 2019 was 100 quadrillion BTU (British Thermal Units), which is equivalent to 1.055×10^20 Joules. Averaged out over the 31,557,600 seconds in a year implies a use rate of 3.34×10^12 Watts during 2019.

From the above two observations, we can deduce that the current rate of Biosphere warming on a yearly basis is equivalent to the yearly energy use in 2019 of 907 United States of Americas.

The total increase in the heat energy of the Biosphere since 1910 is 5.725×10^24 Joules, with a corresponding increase of its temperature by 1°C. That heat energy increase over the last 110 years is equivalent to 54,260 years of U.S. energy use at its 2019 amount, per year.

So, today the Biosphere is warming at a rate equivalent to it absorbing the total energy used by the U.S. in 2019, every 9 hours and 40 minutes.

In 2008, I estimated the energy of a large hurricane to be 6.944×10^17Joules. [1] Thus, 152 such hurricanes amount to the same total energy as that used by the U.S. during 2019.

The heat energy increase of the Biosphere during 2019 was 9.56×10^22 Joules, with a corresponding temperature increase of 0.0167°C. That heat energy increase is the energetic equivalent of 137,741 hurricanes. Now, of course, that Biosphere heat increase during 2019 did not all go into making hurricanes, but it should be easy enough to see that a small fraction (for a whopping amount) went into intensifying the weather and producing more and stronger hurricanes (and consequent flooding).

Two clear observations from all this are:

– the Biosphere is warming at an astounding rate, even if “we don’t notice it” because we gauge it by the annual change in average global surface temperature (which is in hundredths of degrees °C per year);

– the immense amount of heat added to the Biosphere every year is increasingly intensifying every aspect of weather and climate, and consequently driving profound changes to all of Earth’s environments.

Those environmental changes directly affect habitability, and species viability, because they are occurring at a rate orders of magnitude faster than the speed at which biological evolution can respond to environmental pressures.

What should we do about it all?

That is obvious: ditch capitalism and socio-economic inequities worldwide; ditch all forms of bigotry, intolerance, racism, war and social negativity; form a unified planetary political administration for the management of a socialist Earth; deploy reasonable technical mitigation strategies (like drastic reductions in the use of fossil fuels, transforming the transportation infrastructure); implement very deep and comprehensive social adaptation behaviors (“lifestyle changes,” eliminating consumerism, scrupulously protecting biodiversity, resettlement of populations displaced by permanent inundation or uninhabitable drought and heat, worldwide sharing of food production).

None of this will actually stop global warming, as the amount of carbon dioxide already in the atmosphere (assuming it has a lifetime there of thousands of years [2]) has us programmed to warm by about another 1°C to 2°C within two centuries, even if we immediately and permanently shut off all our greenhouse gas emissions.

But, such an improved civilization would experience the least amount of suffering — which would be equitably distributed — from the consequences of advancing global warming; and it would contribute minimally toward exacerbating future global warming.

Notes

[1] The Energy of a Hurricane
5 September 2008
https://www.counterpunch.org/2008/09/05/the-energy-of-a-hurricane/

[2] 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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Global Warming and Cooling After CO2 Shutoff at +1.5°C

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I have done further analytical modeling of global warming, using the same general method described earlier (https://manuelgarciajr.files.wordpress.com/2020/05/global-warming-model.pdf).

The question addressed now is: what is the trend of temperature change after an abrupt shutoff of all CO2 emissions just as the net temperature rise (relative to year 1910) reaches +1.5°C, given the lifetime of CO2 in the atmosphere?

For this problem, it is assumed that when the temperature rise (relative to 1910) reaches ~+1.5°C, that:

– all greenhouse gas emissions cease;

– pollution grit (which scatters light) falls out of the atmosphere “instantly” (a few weeks);

– CO2 (greenhouse gas) concentration decays exponentially after emissions shutoff;

– for CO2 lifetimes [e^-1] in years: 20, 50, 100, 238.436, 500, 1,000, 10,000, 100,000;

– temperature sensitivities of cloud cover, ice cover and albedo are as in the previous model;

– all other fixed physical parameters are as in the previous model,
(https://manuelgarciajr.com/2020/06/13/living-with-global-warming/).

In general, for the 8 cases calculated, the temperature increases at a diminishing rate after the emissions shutoff, reaches a peak, then trends downward.

The longer the lifetime of carbon dioxide in the atmosphere, the later and higher is the temperature peak, and the longer it takes to cool back down to the baseline temperature of 1910, which is 1.5°C below the starting temperature for this problem.

The 4 figures below show the calculated results.


Figure 1: °C change vs. years after shutoff, for lifetimes: 20, 50, 100, 238.436 years.


Figure 2: °C change vs. years after shutoff, for lifetimes: 20, 50, 100, 238.436, 500, 1,000 years.


Figure 3: °C change vs. years after shutoff, for lifetimes: 238.436, 500, 1,000, 10,000 years.


Figure 4: °C change vs. years after shutoff, for lifetimes: 1,000, 10,000, 100,000 years.

It is evident from the figures that if the lifetime of carbon dioxide in the atmosphere is greater than 500 years, that a temperature overshoot above +2.0°C (relative to 1910) will occur before cooling begins.

If the lifetime of carbon dioxide in the atmosphere is greater than about 250 years, it will take over a century for the eventual cooling to reduce average global temperature to its baseline temperature (which is for 1910 in this model).

If the lifetime of carbon dioxide in the atmosphere is greater than 10,000 years, the temperature overshoot will take global warming past +4.0°C (above our 1910 datum) for hundreds to thousands of years, and cooling back down to the temperature at our datum would take millennia.

The clearing of carbon dioxide from the atmosphere is a slow process. The absorption of CO2 by the oceans, and the subsequent dissolution of seafloor sediments (acidifying the oceans) occur over decades to centuries. The uptake of carbon dioxide by weathering reactions in carbonate and silicate soils and rocks occurs over millennia to many tens of millennia.

It took about 200,000 years to clear away the CO2 that caused the +8°C to +12°C global warming spike that occurred 55.5 million years ago, which is known as the Paleocene-Eocene Thermal Maximum (PETM).

Beyond its intrinsic scientific interest, this study confirms what has long been known as the needed remedy: anthropogenic emissions of greenhouse gases must permanently cease as soon as possible in order to limit the ultimate extent and duration of unhealthy global warming.

My notes on the mathematical solution of this problem are available through the following link

Global Warming, CO2 Shutoff

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Climate System Response Time

The parameter “beta” is a reaction rate, or frequency, or inverse response time of the biosphere and its climate system. By my calculation, that rate is 1.329×10^-10 seconds^-1, or 0.004194 years^-1, or a response time of 238.436 years. Of course I am not saying the precision of this estimate is as suggested by all the decimal places shown, it’s just that these are the numbers that come out of my calculations, and these numbers are kept to remind me of what choices I made to eventually arrive at this result.

The parameter beta is the product:

beta = (S•a1)/C = [S•(a-cloud – a-ice)]/C,

where:

S = the insolation on the entire disc area of the Earth (1.7751×10^17 Watts),

a-cloud = the temperature sensitivity of the albedo because of the extent of cloud cover (1/°C),
for a positive quantity of: increase of albedo for a given temperature rise (5.715×10^-3 1/°C),

a-ice = the temperature sensitivity of the albedo because of the extent of ice cover (1/°C),
for a negative quantity of: decrease of albedo for a given temperature rise (1.429×10^-3 1/°C),

C = the heat capacity of the biosphere (5.725×10^24 Joules/°C).

A better determination of a-cloud and a-ice would improve the estimate of beta. I chose these quantities to be in the ratio of 4:1, as is the ratio between the cloud reflection portion of the albedo (24%) to the Earth surface portion of the albedo (6%) for the total pristine (pollution free, pre-global warming) albedo (30%).

So, beta incorporates physical parameters that characterize: solar energy, atmospheric and Earth surface reflectivity of light, and the thermodynamics of the mass of the biosphere.

Events and inputs to that Earth climate system are recognized and responded to on a timescale of 1/beta. Events and inputs with timescales less than 1/beta are blips whose impact will become evident much later, if they are of sufficient magnitude and force. Events and inputs of timescales longer than 1/beta are “current events” to the biosphere’s thermodynamic “consciousness,” and act on the climate system as it reciprocally acts on them over the course of the input activity.

Turning a large ship around takes advanced planning and much space because it’s large inertia tends to keep it on its original heading despite new changes to the angle of its rudder. Even more-so, changes in the direction of Earth’s climate, which may be sought with new anthropogenic rudder angel changes — like drastic reductions of greenhouse gas emissions — will require fairly deep time because of the immense thermodynamic inertia of that planetary system.

This means that the climate system today is responding to the “short time” impulses it was given over the previous two centuries or more; and that both the more enlightened and most stupid impulses that we give it today could take several human lifetimes to realize their full response. We are dealing with Immensity here, and our best approach would be one of respect and commitment.

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