Another Model of Atmospheric CO2 Accumulation

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

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

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

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

– 70% of the emissions accumulate in the atmosphere,

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

– absorption through photosynthesis (happening daily),

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

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

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

So, it would be wise to stop emitting it.

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

Gaussian Emission Function & Air CO2

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

<><><><><><><>

Global Warming and Ocean Acidification Accelerate

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

Carbon Dioxide Emissions

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

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

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

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

Carbon Dioxide in the Oceans

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

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

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

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

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

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

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

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

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

CO2 + H2O + CO3 —> 2HCO3

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

CO2 + H2O —> H2CO3

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

H2CO3 —> H(+) + HCO3(-)

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

H(+) + CO3(2-) —> HCO3(-)

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

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

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

CaCO3 + 2H(+) —> Ca(2+) + CO2 + H2O

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

The Rate of Global Warming is Accelerating

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

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

The Rate of Ocean Acidification is Accelerating

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

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

“Fixing” Global Warming

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

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

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

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

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

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

Notes

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

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

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

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

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

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

<><><><><><><>

Long Term Worries Are A Luxury

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

Long Term Worries Are A Luxury

It is impossible to think about long term problems when you are in the midst of an emergency. Who can worry about the balance of their bank account, or who should get elected, or global warming, when they are in the middle of a medical emergency, or a police nightmare, or a flood, or just the “normal” worries of a homeless person looking for food for themselves or their children, and a safe place to get some badly needed sleep? And this situation is repeated by the billions around the world.

Because so many people are struggling to deal with their basic survival and personal security needs, which are under assault from so many directions by the forces of human malevolence: political, economic and racial, they have no mental capacity nor psychological reserves left to expend on long term worries like global warming. That long term worry is a luxury enjoyed by people who are fortunate in life, secure and safe, and even prosperous. They are also likely to be the kind of people who are in the most anthropogenic greenhouse gas emitting classes on Earth.

I consider global warming to be an emergency, exactly as Greta Thunberg has so brilliantly broadcast to the world. Many professional “Green” activists, bloggers, book writers and internet “influencers” have advanced a variety of social behavioral adaptation schemes, and technical schemes, that governments are urged to mandate and manage in order to “transition” our current profits-above-life-itself economies to a “post carbon” alternative energy mode. In general I agree with such ideas, but I realize they are just fantasies of luxurious long term worries (LLTWs). I suppose my Marxist friends would call LLTWs a class interest.

It has finally dawned on me that the route to real action on global warming climate change is through a complete social revolution that meets the immediate survival and security needs of the great mass of humanity, and which spectrum of aspirations is being vibrantly voiced through the worldwide George Floyd protests. A psychologist might phrase this as the need for a climb up the ladder of Maslow’s hierarchy of needs. The smaller the fraction of the world’s population that is overwhelmingly taxed by scrambling for their survival and safety needs, the larger the fraction of the world’s population that can begin to enjoy the LLTW of global warming climate change.

Because meeting those many aspirations for societal renewal and social transformation are technically the easiest and quickest remedies to begin addressing the root causes of the LLTW of global warming, they should be pushed for hard by everybody who gives a damn. Thus, the George Floyd protests are really for much more than just their essential and vitally important calls for anti-racist anti-capitalist and public health actions by governments, they are also the trumpet fanfares and bugle calls for a worldwide charge up the hierarchy of popular needs, from physical survival and personal security through societal reconstruction based on indiscriminate human dignity and the wide availability of opportunity that affords achievement of personal fulfillment, and ultimately up to us “all” having the luxury to worry about global warming, and then actually act on it.

I do not think there will ever be useful action on global warming until the social needs of the masses of humanity are vigorously and effectively attended to. This is not a utopian fantasy, this is realistic hard nuts logical thinking. The first and foundation step for everything that should follow is for all of us to actually become “we.”

So, yes, I realize that implies many wished-for political, economic and social revolutions and changes, but there it is. That is what “we” need to do if we want to make “anthropogenic” a positive adjective describing our stewardship of Planet Earth, instead of leaving it with its currently negative connotation regarding our massive fouling of the most beautiful jewel known to exist in the entire Universe.

<><><><><><><>

Our Globally Warming Civilization

<><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><><>

Our Globally Warming Civilization

The 150 years of the Industrial Revolution (~1770-1920), with its catastrophic and bloody termination in World War I (1914-1918), had no noticeable effect on the global average temperature, which had hovered around 14.7 degrees Centigrade (C) since antiquity. The human population had taken 200,000 years (more or less) to grow to one billion (1B), in 1804, within the natural and majestic evolution of global climates during those 2000 centuries, (1).

By 1927, the human population had increased to 2B. The 1920s were economic boom years in the Industrialized World (give or take some post WWI German misery, the Russian Revolution, and Chinese civil warfare) with the liquid petroleum replacing the solid coal as the fossil fuel of choice for transportation vehicles; and the explosion in the craving for, and manufacture and use of, internal combustion engines and the automobiles powered by them.

After 1927 the rate of population growth increased from what it had been on average during the previous 123 years (about 8 million per year, ~8M/yr) to an average rate of 29M/yr, to accumulate another 0.7B people in the 26 years up to 1953, when the population was 2.7B. Those 26 years between 1927 and 1953 spanned the crescendo of the Roaring ‘20s, the capitalist economic collapse of 1929, the Great Depression (1929-1942), World War II (1939-1945), the Second Sino-Japanese War (1937-1945), and the Chinese Communist Revolution and Civil War (1946-1949).

I estimate that the cumulative amount of petroleum produced (pumped out and used up) by 1953 was 98.6 billion barrels (98.6 giga-barrels, 98.6Gb), (2). This implies that since about 1900, when civilization’s use of petroleum as a fuel began in earnest, it consumed 602 giga-GJ (602 x 10^18 Joules) of energy (equivalent to 168 mega-GWh = 168 x 10^9 MWh = 168 giga-mega-watt-hours) to power itself up to 1953, (3).

By 1960, the world’s human population had reached 3B, and the rate of population growth was accelerating (having been about 43M/year during the previous 7 years). From 1960 to the present day, the trend of cumulative production of petroleum, Q, has been proportional to the rising trend of human population, in the ratio of 272 barrels of oil per person (272 b/p).

Specifically, my approximating formula for Q, the accumulated production of oil in giga-barrels (Q, in Gb), given as a function of the population in billions (P, in B) for a given year within the interval 1960 to 2025 is:

Q(year) = [P(year) – 2.7B] x (272 b/p).

This approximation gives an accumulated production up to 2015 (with population 7.35B) of

Q(2015) = 1265Gb, (approximation).

By integrating the actual production rate-per-year curve (the “Hubbert curve” for world production, in GB/yr) given by Laherrere (2), I find the actual accumulated production up to 2015 to be:

Q(2015) = 1258Gb, (actual).

The rate of oil production is now likely at its peak of between 25 Gb/yr to 35 Gb/yr during this 20 year interval between 2005 and 2025, (2),(4). Thereafter, it should drop rapidly since current oil fields have diminishing production, there have been no major oil field discoveries since the 1970s and the frequency of discovery has steadily diminished since then. That means that over half of Earth’s original total reserves, estimated at 2,200Gb (2), have already been extracted. The “end-of-oil” seems destined for the last two decades of the 21st century.

Assuming all that oil was burned, up to the year 2015 (115 years since 1900), civilization would have used 7,674GGJ, (7,674 x 10^18 Joules), equivalent to 2,139GMWh, (2,139 x 10^15 Watt-hours) of energy, derived from that 1258Gb of petroleum, to power itself.

That burning would have released 398,786Gkg (~4 x 10^14 kg = ~400 giga tonnes) of CO2, (5). At present (May 2019) there are about 3,250 giga tonnes of CO2 in the atmosphere, with an average concentration of 415 parts per million by volume (415ppmv), (6). 1228 G tonnes of that CO2 is excess above the pre-industrial amount in the atmosphere. The ~400 G tonnes estimated here as the accumulated emissions from the prior burning of petroleum (up to about 2015) is only about one-third of the excess atmospheric CO2.

There are numerous other processes in our civilization, as well as in the natural world, that cause the emission of carbon-dioxide and its atmospheric retention in excess amounts. The main sources of CO2 emissions are the exhalations from aerobic respiration by all of Earth’s living heterotrophs, decaying plants, and volcanic eruptions. Other sources include: the burning of coal and natural gas, forest and vegetation fires caused naturally and by slash-and-burn agriculture, the bubbling out of CO2 from warming oceans no longer able to dissolve as much of that gas as before, and the massive amount of past and continuing forest clearing that has reduced Earth’s natural system of CO2 uptake — photosynthesis. The cement industry is one of the two largest producers of anthropogenic carbon dioxide, creating up to 5% of worldwide man-made emissions of this gas, of which 50% is from the chemical process and 40% from burning fuel, (7).

Methane (CH4) is a very potent greenhouse gas, being 30 times more effective than CO2 at trapping heat. “For each degree that Earth’s temperature rises, the amount of methane entering the atmosphere from microorganisms dwelling in lake sediment and freshwater wetlands — the primary sources of the gas — will increase several times. As temperatures rise, the relative increase of methane emissions will outpace that of carbon dioxide from these sources.” (8) Other sources of methane emissions are: rotting organic wastes, termite colonies, and bovine flatulence from industrialized agricultural sites. The globally warmed thawing Arctic tundra is now a region of major methane eruptions.

Up until 1974, when the human population had reached 4B, Earth’s climate system had yet to become feverish over the previous 200,000 years of collective human activity. However, at about that time the average global temperature began increasing at a historically unprecedented rate because of civilization’s heated and organic outgassing, a process which continues today as anthropogenic global warming, (9).

In fact, the date at which collective human activity began to affect and alter Earth’s climate system has now been pinpointed to somewhere between October to December 1965. That date marks the end of the Holocene Epoch of geologic history (which began 11,700 years previously, after the last Ice Age), and the beginning of the Anthropocene Epoch — the epoch of human-affected climate, globally. The physical phenomenon marking this transition is that Carbon-14, a radioactive isotope released during open-air atomic and nuclear bomb explosions between 1945 and 1963, had finally dispersed uniformly around the globe, and become absorbed into tree tissues even in the remotest parts of the world, thus recording that uniformity (10).

Between 1960 and 2025, the three rising trends of: population (P), cumulative oil production (Q), and increase of average global temperature above baseline (T – 14.7C = delta-T), are all uniformly proportional to one another.

Specifically (for years between 1960 and 2025) T, P and Q are related to each other as follows:

[T(year) – 14.7C] = [P(year) – 2.7B]/3.3B = [Q(year)/(900 Gb)],

where the forms above are each equivalent to a temperature difference relative to the baseline of 14.7C (delta-T, in degrees C).

Notice that if T = 15.7C, and P = 6B, and Q = 900 Gb, then the equality above holds, with: 1 = 1 = 1. This particular condition actually occurred during 1999.

During this 65 year interval, a 1 degree C rise in temperature (above 14.7C) is coincident with a 3.3B increase in population (above its 1953 level of 2.7B), which in turn is coincident with a production (and use) of 900Gb of petroleum.

The population is growing from 3B in 1960 to an expected 8B in 2028 during this 68 year interval, with an average population increase of +73.5M/yr. Within these 68 years, and especially during the 55 years from 1970 to 2025, the rising trends of (T – 14.7C), (P – 2.7B)/3.3B, and Q/(900Gb) are in lockstep. This period — with explosive population growth, depletion of over half of the Earth’s petroleum endowment, and with an unprecedented rate of global warming — began in the last year of the Eisenhower Administration, 1960, when John Kennedy was elected US President, and extends right up to the present (and beyond it).

The average global temperature will have climbed up from ~15C to ~16.2C during this interval, a relative rise of 1.4C, and a rise of ~1.5C (delta-T = ~1.5C) above the pre-industrial temperature, defined here as 14.7C (58.46 degrees Fahrenheit). That 1.5C (2.7F) warming above the pre-industrial temperature represents a tremendous amount of heat energy diffused throughout the biosphere, and the deleterious effects of that excess heat are self-evident to all: the altering of climate; the powering of violent weather; the heating and acidifying (with absorbed CO2) of the oceans, sterilizing them of marine life; the melting of glaciers and thawing of tundras; the causing of carbon dioxide and methane to bubble out of solution and frozen capture in the natural world (in a vicious feedback loop); the expansion of disease pathogens and tropical parasites; and the added stresses to both wild and farmed vegetation, and increased desertification, which result in human hunger and desperate migrations of impoverished refugees.

Now, our civilization is starting to suffocate in the lingering heat of its previous exhalations. The singular challenge to our species and to our political economies is what to do, collectively, about global warming. That challenge remains largely unanswered, and tragically denied by too many people .

Notes

1. World population is estimated to have reached one billion for the first time in 1804. It was another 123 years before it reached two billion in 1927, but it took only 33 years to reach three billion in 1960. The global population reached four billion in 1974 (14 years later), five billion in 1987 (13 years later), six billion in 1999 (12 years later), and seven billion in October 2011 (12 years later), according to the United Nations, or in March 2012 (13 years later), according to the United States Census Bureau.
https://en.wikipedia.org/wiki/World_population

World population by year
https://www.worldometers.info/world-population/world-population-by-year/

2. Jean Laherrere, World Crude Oil Production, (brown line), April 2015
https://upload.wikimedia.org/wikipedia/commons/4/46/World_crude_discovery_production_U-2200Gb_LaherrereMar2015.jpg

3. The energy released from combusting 1 barrel of oil is 6.1 giga-joules (6.1 GJ), which equals 1.7 MWh (1.7 mega-watt-hour).
https://en.wikipedia.org/wiki/Barrel_of_oil_equivalent

4. Worldwide, around 92.6 million barrels of oil were produced daily in 2017.
https://www.statista.com/statistics/265203/global-oil-production-since-in-barrels-per-day/
~73 million barrels/day in 1998, rising since.
73 Mb/day = 26.7 Gb/yr (1998)
93 Mb/day = 34.0 Gb/yr (2017)
During 20 years of production (1998-2017) the rate rose 20 Mb/day = +1 MB/day/year

5. Burning one barrel of petroleum can produce between 317kg (realistically) to 433kg (theoretically) of CO2:
Realistic
http://numero57.net/2008/03/20/carbon-dioxide-emissions-per-barrel-of-crude/
Theoretical
https://www.answers.com/Q/How_much_CO2_produced_by_burning_one_barrel_of_oil
Therefore, the CO2 emitted by combusting 1b = 317kg CO2.

6. As of January 2007, the earth’s atmospheric CO2 concentration is about 0.0383% by volume (383 ppmv) or 0.0582% by weight. This represents about 2.996×10^12 tonnes (1 tonne = 1000kg), and is estimated to be 105 ppm (37.77%) above the pre-industrial average (~278 ppmv).
https://micpohling.wordpress.com/2007/03/30/math-how-much-co2-by-weight-in-the-atmosphere/

415 ppmv of atmospheric CO2, as of May 2019
https://en.wikipedia.org/wiki/Carbon_dioxide_in_Earth%27s_atmosphere

Therefore:
(415/383) x 3000 G tonnes = 3,250 G tonnes, (May 2019).

7. Environmental impact of concrete
https://en.wikipedia.org/wiki/Environmental_impact_of_concrete

8. Methane is roughly 30 times more potent than CO2 as a heat-trapping gas
https://www.sciencedaily.com/releases/2014/03/140327111724.htm

9. I first constructed the simplified plot of average global temperature in 2004, using data from public sources. Details about that construction and the data used are given at:
Population, Oil and Global Warming, 31 May 2019 (15 March 2004)
https://manuelgarciajr.com/2019/05/31/population-oil-and-global-warming/

10. The Anthropocene Epoch began sometime between October and December 1965.
https://manuelgarciajr.com/2018/02/23/the-anthropocenes-birthday/

<><><><><><><>