The Keeling Curve and Global CO2

This post is taken from a presentation which I gave at a local geologic conference in 2104, with minor modifications.

Major findings of the CO₂ study:

• Atmospheric CO₂ is rising globally as a result of human activities, principally the burning of fossil fuels. 
• Atmospheric CO₂ concentration is now about 40% higher than pre-industrial CO2 concentration.
• CO₂ emissions from fossil fuels mostly originate in the Northern Hemisphere.  A global system of monitoring stations shows the dispersion of these emissions from the Northern Hemisphere to the Southern Hemisphere.
• Atmospheric CO₂ shows a seasonal cycle that is dominated by plant growth in the Northern Hemisphere.
• The amplitude of the seasonal cycle is increasing due to human agriculture.  Agriculture accounts for about 1/3 of the seasonal cycle.
• The Southern Hemisphere has a seasonal cycle that is the opposite polarity of the Northern Hemisphere, but is very weak due to a smaller land mass and less agriculture.
• Atmospheric CO₂ concentrations and carbon isotope ratios are changing much slower than expected if all human carbon emissions remained in the atmosphere.  About half of human carbon emissions are being absorbed by carbon reservoirs (oceans, soils and biomass).  Carbon isotopes show that large volumes of atmospheric carbon are freely exchanged with carbon in carbon reservoirs.  
• The size of the carbon reservoirs exchanging carbon with the atmosphere can be estimated through the dilution of human-derived carbon isotopes in the atmosphere.  The calculation indicates that these carbon reservoirs contain about 7 times the quantity of carbon in the atmosphere.  This solution is about 40% larger than estimates using other methods.
• Human carbon emissions will continue.  Forecasts indicate that atmospheric CO₂ will reach 450 ppm by the year 2036.
• After filtering the seasonal cycle from the carbon isotope data, a multi-year cycle remains.  The multi-year cycle can be correlated with the El Nino climate cycle.  The El Nino cycle changes the rate at which atmospheric carbon is absorbed by the Pacific Ocean, and changes isotopic composition of the atmosphere.

The Keeling Curve and Global CO2

S. D. Robbins                       May 15, 2014

Abstract

The Keeling Curve is a remarkable series of atmospheric CO₂ measurements taken at Mauna Loa, Hawaii, from 1960 to the present.  The curve shows seasonal cycles and a steady rise in the concentration of CO₂, beginning about 315 ppm and currently approaching 400 ppm.   Long-term CO₂ records are also available from a number of other observatories, located from the Arctic Ocean to the South Pole.   Integration of the global dataset with carbon emissions data provides additional insights about the world’s carbon cycle. 

Atmospheric CO₂ concentrations and CO₂ carbon isotopes show seasonal and long term trends which vary by latitude.  The seasonal cycle is strongest in the Northern Hemisphere, and the Northern Hemisphere leads the Southern Hemisphere in terms of rising CO₂.  People and plants in the Northern Hemisphere cause changes in atmospheric CO₂ which propagate from the Northern Hemisphere to the Southern Hemisphere. The dispersion of CO₂ from human sources can be seen as a progression through the global data.  This progressive change is seen in bulk concentration of CO₂, in carbon isotopes of CO₂, and the amplitude of the seasonal cycle.  Long-term changes in global CO₂ are consistent with known volumes of fossil fuel emissions.   A simple model can be constructed based solely on human carbon emissions and agricultural biomass, that matches the observed seasonal cycle and long-term trends in bulk CO₂,.  This model shows that it is reasonable to conclude that human activities are influencing carbon dioxide in the atmosphere.  The Energy Information Agency (EIA) predicts rising carbon emissions for the foreseeable future, from about 35 gigatonnes CO₂ annually to nearly 50 gigatonnes CO₂ by the year 2040, in the base-case forecast.

Carbon dioxide from fossil fuels and deforestation carries a distinctive isotopic signature, which marks the movement of man-made CO₂ through the atmosphere and carbon reservoirs (soils, biomass, and oceans).  This movement of carbon, as seen in both carbon isotope data and bulk CO₂ data, reveals complexity in the carbon cycle.  Discrepancies between the datasets imply the active exchange of carbon between the atmosphere and carbon reservoirs.  More than 85% of anthropogenic CO₂ emissions, as tagged by carbon isotopes, do not remain in the atmosphere, but are absorbed by carbon reservoirs.  However, some of the anthropogenic carbon in the atmosphere is exchanged for natural carbon from carbon reservoirs, so that atmospheric CO₂ concentration is maintained at a level equivalent to about 44% of cumulative annual CO₂ emissions over the long term.  The size of carbon reservoirs is estimated at more than 7 times the volume of carbon present in the atmosphere, based on a dilution calculation of anthropogenic carbon isotopes in the atmosphere.  The role of the ocean in exchanging carbon with the atmosphere is illustrated by the correlation of atmospheric carbon isotope data with the Oceanic Niño Index (ONI), which is a measure of the El Niño/La Niña climate cycle based on sea-surface temperatures.

 

Understanding the patterns of atmospheric CO₂ may provide a tool for recognizing and measuring changes in global climate.  Additional monitoring of carbon reservoirs, particularly of the world’s oceans, will be necessary to develop a comprehensive model of the earth’s carbon cycle. 

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A Few Words about CO₂ Carbon Isotopes

There are two stable isotopes of carbon, C13 and C12.   C12 is the more abundant isotope; the natural ratio of C12 to C13 is about 99 to 1.  The standard measure of carbon isotopes compares the C12/C13 isotope ratio of the sample in question to the C13/C12 ratio of a standard limestone, according to the expression:

d C13/C12 = ((C13/C12 sample  / C13/C12 standard) – 1)*1000.

This expression, commonly termed “del 13”, amplifies small but meaningful differences in the isotopes, which are diagnostic of certain processes and occurrences of carbon.  The standard is a uniform Cretaceous limestone with a d 13 value defined as zero.   Positive values indicate a heavier composition, i.e., a greater concentration of C13 than the standard.  Negative values indicate a lighter composition, i.e., a smaller concentration of C13 than the standard.

Plants fractionate carbon, favoring the lighter isotope C12.  Anything derived from plants, including oil, gas, and coal (and algae, animals and people) carries a light (negative) d C13/C12 signature.  Limestone carries a d  C13/C12 ratio near zero.  The atmosphere, in 1977, had a d C13/C12 ratio of about -7.5; it is currently about -8.3, reflecting the influence of fossil fuels.  Oceans have a slightly positive d C13/C12 ratio of dissolved inorganic carbon, although Northern Hemisphere waters show a negative ratio due to the greater use of fossil fuels in the Northern Hemisphere.  Fossil fuel CO₂ emissions and CO₂ emissions from deforestation carry a very light d C13/C12, in the range of -25 to -28.  The distinctive isotopic signature of CO₂ from fossil fuels and deforestation is useful in tracking the movement of carbon through the atmosphere and oceans.  Boden, Marland and Andres (2013) published estimates of the annual CO₂ released by fossil fuels and the d C13/C12 ratio of those emissions.  Those estimates were used in this work.  

Part 1:  The Global Record

Global CO₂ is rising, and the isotopic composition of atmospheric CO₂ is becoming lighter.

A network of observatories, mostly operated by Scripps Oceanographic Institute, monitors global atmospheric CO₂ concentrations and CO₂ carbon isotopes.   Bulk CO₂ has been monitored since 1957, and CO₂ carbon isotopes since 1977.  In all figures, data from the Northern Hemisphere is indicated in cool colors, and data from the Southern Hemisphere is indicated with warm colors.

Global CO₂ observations show a seasonal cycle and a steady rise in the concentration of CO₂.  Today’s concentration of atmospheric CO₂ is about 25% higher than in 1957, and about 40% higher than in 1800. 

The carbon isotope ratio (d C13/C12) of atmospheric CO₂ is becoming lighter, which is consistent with the isotopic signature of fossil fuels mixing with the atmosphere.

 The amplitude of the CO₂ seasonal cycle is largest in the high latitudes of the Northern Hemisphere, and diminishes southward.  The polarity of the Northern Hemisphere cycle persists to about 30 degrees South Latitude.   From that point southward, the polarity of the cycle is reversed, but with low amplitude.

Part 2:  Long Term Trends

The Northern Hemisphere leads the Southern Hemisphere in rising CO2 values and falling CO2 carbon isotope values.

The Northern Hemisphere holds 2/3 of the world’s landmass, and nearly 90% of the world’s population, fossil-fuel consumption, and agriculture.  People and plants in the Northern Hemisphere cause changes in atmospheric CO₂ which propagate from the Northern Hemisphere to the Southern Hemisphere.

The seasonal cycle in bulk CO₂ was removed by taking a one-year rolling average at each observatory.  The Northern Hemisphere leads the Southern Hemisphere in rising CO₂.  The concentration of CO₂ is highest in the Arctic, and is progressively lower by latitude to the South Pole.  The progression marks the dispersion of fossil fuel emissions from the Northern Hemisphere to the Southern Hemisphere.

The seasonal cycle in the CO₂ carbon isotope ratio was removed by taking a one-year rolling average at each observatory.   The Northern Hemisphere leads the Southern Hemisphere in terms of falling d C13/C12 of CO₂ (becoming isotopically lighter).  The isotopic composition of CO₂ is lightest near the North Pole, and becomes progressively heavier to Antarctica.  The progression marks the dispersion of fossil fuel emissions from the Northern Hemisphere to the Southern Hemisphere.

A simple model was constructed to investigate the plausibility of the idea that human activity causes changes in atmospheric CO₂.  The model begins at the global baseline CO₂ concentration in 1970.  Model inputs included 60% of global fossil fuel emissions, allocated to Northern and Southern Hemispheres by GDP.  Global agricultural biomass was scaled by year to human population, and allocated to the Northern and Southern Hemispheres by population.  Volumes of carbon were converted to CO₂ concentration by hemisphere, and defined the concentration at the poles.  Concentrations at intermediate latitudes were created by mixing concentrations from each hemisphere, with weighting by latitude.  The ease with which the model was created suggests that human activity is plausibly responsible for much of the change in atmospheric CO₂.

Part 3:  Seasonal Cycle

The Northern Hemisphere dominates the global CO₂ seasonal cycle.

The Keeling Curve is characterized by a strong seasonal cycle, dominated by the Northern Hemisphere.  The concentration of atmospheric CO₂ falls during the Northern Hemisphere growing season, when land plants remove carbon from the air through photosynthesis.  The concentration of CO₂ rises in the fall, winter and spring as decay returns carbon to the atmosphere as CO₂.

The CO₂ carbon isotope ratio d C13/C12 shows a strong seasonal cycle as a mirror image of the cycle in bulk CO₂ concentration.  Land plants in the Northern Hemisphere strongly fractionate carbon isotopes.  Plants preferentially absorb C12 during the growing season, raising the d C13/C12 ratio of the atmosphere.  During decay, plants return C12 to the atmosphere, and atmospheric d C13/C12 falls.

 

Amplitude of the seasonal cycle is relatively small in the Southern Hemisphere, reflecting a smaller land mass and sparse population.  Seasonal cycles in low latitudes of the Southern Hemisphere follow the polarity of the Northern Hemisphere, but with a phase shift.  Seasonal cycles in high latitudes of the Southern Hemisphere carry the opposite polarity to the Northern Hemisphere.

Amplitude of the seasonal cycle is increasing over the past 40 years, particularly at high northern latitudes.  The increase in amplitude correlates well to the increase in human population over the past 40 years.   By inference, the increase in seasonal amplitude also correlates to a proportional increase in human agriculture.  The correlation implies that agriculture accounts for about one-third of the amplitude of the seasonal CO₂ cycle. 

The polarity reversal of the seasonal cycle occurs at about 30 degrees South Latitude, near the southern boundary of the Hadley convection cell.  The atmosphere north of -30 degrees latitude contains air which is mixed with air from the Northern Hemisphere; CO₂ concentrations and carbon isotopes follow the seasonal cycle of the Northern Hemisphere.  The atmosphere south of -30 degrees latitude carries the seasonal cycle of the Southern Hemisphere.  This finding suggests that additional CO₂ observatories between -30 degrees and -40 degrees south latitude could monitor climate-change induced expansion of Hadley circulation, by detecting air from the Northern Hemisphere, according to the Northern Hemisphere seasonal CO₂ cycle.

Part 4:  CO₂ Emissions

Long-term changes in atmospheric CO₂ are consistent with known volumes of human CO₂ emissions.

The rate of human CO₂ emissions is increasing.  Anthropogenic CO₂ emissions, including deforestation, have grown from about 5 gigatonnes annually in 1900 to about 38 gigatonnes in 2009.  The greatest part of that increase occurred in the last 50 years.  

The average CO2 concentration of the Northern Hemisphere leads the Southern Hemisphere by 2.5 to 4 ppm CO₂.  Net annual fossil fuel emissions in the Northern Hemisphere, converted to CO₂ concentration, neatly match the difference in CO₂ concentration between the hemispheres.  Deforestation, (which is more prevalent in the Southern Hemisphere) was not included in the emissions numbers, which might account for the growing discrepancy in recent years.

Despite international efforts to reduce carbon emissions, global industrial CO₂ emissions are rising sharply.  According to the EIA base economic forecast, fossil fuel CO₂ emissions are expected to rise 45% by the year 2040, from 33 gigatonnes to 48 gigatonnes per year.  Emissions including deforestation bring the total in 2040 to 53 gigatonnes, assuming a constant rate of deforestation from 2005 to 2040.

Global average CO₂ is rising at a rate equal to about 44 percent of annual CO₂ emissions, including deforestation.  The forecast of future CO₂ concentrations, based on expected emissions, calls for world average CO₂ to exceed 450 ppm around the year 2036.  

Part 5: The Carbonsphere

The Carbonsphere consists of atmospheric carbon and all reservoirs (ocean, biomass, and soils) freely exchanging carbon with the atmosphere.

The global mix of fossil fuels has a d C13/C12 value of about -28.  Deforestation is assumed to have a d C13/C12 value of about -25.  These contrast sharply with the atmospheric d C13/C12 value of about -8, and slightly positive oceanic d C13/C12 values.  The distinctive isotopic signature of human carbon emissions allows us to track the movement of carbon through the atmosphere, and to detect the exchange of carbon with carbon reservoirs on the earth’s surface.

A 2-year lag is required for the concentration of bulk CO₂ to equilibrate from sources in the Northern Hemisphere to the Antarctic.

Differences in the behavior of bulk CO₂ and CO₂ carbon isotopes indicate the active role of carbon reservoirs in the ocean, plants, and soil in exchanging carbon with the atmosphere. 

Bulk carbon requires about a 2-year lag for CO₂ concentration to equilibrate from the Arctic to the Antarctic.  In contrast, CO₂ carbon isotopes require an 8-year lag for equilibration. 

The difference indicates that the specific molecules released by fossil fuels are cycled through carbon reservoirs and replaced in the atmosphere by other molecules from those reservoirs.  The difference in equilibration lag of bulk carbon and carbon isotopes indicates residency time in those reservoirs.

Atmospheric CO₂ concentration rises at a rate equal to about 44% of human CO₂ emissions, including deforestation.  If all human carbon emissions remained in the atmosphere, the concentration of atmospheric CO₂ would be much higher.  

Atmospheric CO₂ d C13/C12 falls at a rate incorporating about 12% of human CO₂ emissions. 

If all human carbon emissions remained in the atmosphere, the concentration of atmospheric CO₂ would be much higher, and the d C13/C12 isotope ratio would be much lower.  Calculations indicate that atmospheric CO₂ rises at a rate equal to about 44% of human CO2 emissions.  In contrast, CO₂ carbon isotopes indicate that only 12% of human carbon emissions remain in the atmosphere.  More than 85% of human carbon emissions, as tagged by carbon isotopes do not remain in the atmosphere, but are cycled into other carbon reservoirs.  At the same time, natural carbon, carrying a heavier isotopic signature, is exchanged from the carbon reservoirs, maintaining a bulk CO₂ concentration accumulating at a rate of 44% of human CO₂ emissions.

In the inverse of the calculation above, the d C13/C12 isotope ratio of the atmosphere shows the total volume of carbon reservoirs interacting with the atmosphere.  The calculation determines the total reservoir volume necessary to produce the observed dilution of d C13/C12 from human emissions in the air.  Carbonsphere reservoirs are assumed to be in equilibrium with the atmosphere, which is demonstrated by the relatively good fit to the solution for 30 years.  The model assumes a balance of fractionation between the carbonsphere reservoirs and the atmosphere.  The solution calls for a 6000 gigatonne carbonsphere in 1979 (including the atmosphere).  This solution is about 40% larger than estimates based on carbon inventory methods.

Part 6:  Finding Niño

The CO₂ carbon isotope record can be correlated with the El Niño/La Niña climate cycle, indicating large volumes of carbon exchange between the atmosphere and the tropical Pacific Ocean.

Multi-annual cycles, or “waves” are present in the CO₂ carbon isotope data after removing the seasonal cycle.  Lower amplitude but correlative waves also exist in the bulk CO₂ chart.  Periods of rapidly falling d C13/C12 correspond to El Niño climatic events, suggesting variability in the rate at which the tropical Pacific Ocean takes up or releases C12 to the atmosphere.  The amplitude of the waves interrupts and sometimes reverses the secular trend, indicating that the volumes of carbon exchanged sometimes exceed the volume of human carbon emissions.

A series of mathematical operations can reduce the global CO₂ isotope record to a single trace which indicates the rate at which atmospheric carbon is exchanged with the Carbonsphere.  Assuming no fractionation in the exchange process, positive values indicate a faster rate of absorption of C12 by the Carbonsphere.  Negative values indicate a slower rate of C12 absorption by the Carbonsphere.  With a slight time lag, the trace can be correlated with the Oceanic Niño Index (ONI).  The ONI is a measure of sea surface temperatures published by NOAA, indicating the prevalence of El Niño or La Niño conditions. 

The trace derived from the d C13/C12 isotope data indicates variability in the rate of exchange of C12 between the atmosphere and carbon reservoirs. That curve correlates well with the Oceanic Niño Index, a measure of the El Niño/El Niña climate cycle.  La Niña conditions, which are characterized by abnormally cool sea surface temperatures, correspond with accelerated absorption of atmospheric C12 by the ocean.  El Niño conditions, characterized by warm sea surface temperatures, correspond to decreased absorption of atmospheric C12 by the ocean. 

The quality and quantity of oceanic carbon data is weak in comparison to atmospheric CO₂ data.  Oceanic carbon data is limited by a lack of continuous readings or fixed observation sites, and is strongly influenced by local biological activity.  Nevertheless, at the broadest scale, oceanic dissolved inorganic carbon is isotopically lighter in the Northern Hemisphere, reflecting the influence of fossil fuels in the Northern Hemisphere.  Improved, systematic data collection in the oceans and other carbon reservoirs will be necessary to develop a comprehensive model of the earth’s carbon cycle.

Note: Since the original poster was presented in May, 2014, I have noticed that the low d C13/C12 values are located in the Atlantic Ocean, and may be associated with the Greenland Current.  It is possible that these values reflect a natural process, such as a significant volume of glacial meltwater lowering the d C13/C12 value of the seawater.

References:

Andres, R.J., T.A. Boden, and G. Marland. 2012.  Monthly

Fossil-Fuel CO2 Emissions: Mass of Emissions Gridded by One Degree

Latitude by One Degree Longitude.  Carbon Dioxide Information Analysis

Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak

Ridge, Tenn., U.S.A.  doi: 10.3334/CDIAC/ffe.MonthlyIsomass.2012

ftp://cdiac.ornl.gov/pub/fossil_fuel_CO2_emissions_gridded_monthly_del13C_v2012/

Andres, R.J., T.A. Boden, and G. Marland. 2009.  Monthly

Fossil-Fuel CO2 Emissions: Mass of Emissions Gridded by One Degree

Latitude by One Degree Longitude.  Carbon Dioxide Information Analysis

Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak

Ridge, Tenn., U.S.A.  doi: 10.3334/CDIAC/ffe.MonthlyIsomass.2009

ftp://cdiac.ornl.gov/pub/fossil_fuel_CO2_emissions_gridded_monthly_del13C_v2009

Andres, R.J., T.A. Boden, and G. Marland. 2012.  Annual Fossil-Fuel CO2 Emissions: Global Stable Carbon Isotopic Signature.  Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A.

doi: 10.3334/CDIAC/ffe.db1013.2012

http://cdiac.ornl.gov/ndps/db1013_v2012.html

Boden, T.A., Andres, R.J., and G. Marland 2013. Global CO2 Emissions from Fossil-Fuel Burning, Cement Manufacture, and Gas Flaring: 1751-2010. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A.   

http://cdiac.ornl.gov/ftp/ndp030/global.1751_2010.ems

Boden, T.A., G. Marland, and R.J. Andres. 2013. Global, Regional, and National Fossil-Fuel CO2 Emissions. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A. doi 10.3334/CDIAC/00001_V2013

http://cdiac.ornl.gov/trends/emis/overview_2010.html

Ciattaglia, L., C. Rafanelli, H. Rodriguez, and J. Araujo. 2010. Atmospheric CO2 record from continuous measurements at Jubany Station, Antarctica, in Trends Online: A Compendium of Data on Global Change, Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A.

http://cdiac.esd.ornl.gov/trends/co2/jubany.html

Climate Prediction Center Internet Team, 2013, ONI Index, NOAA/National Weather Service, NOAA Center for Weather and Climate Prediction , Climate Prediction Center, 5830 University Research Court, College Park, Maryland 20740.

http://www.cpc.ncep.noaa.gov/data/indices/oni.ascii.txt

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Colombo, T., and R. Santaguida. 1998. Atmospheric CO2 record from in situ measurements at Mt. Cimone. In Trends: A Compendium of Data on Global Change. Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy, Oak Ridge, Tenn., U.S.A.

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Conti, J., et al, 2013.  International Energy Outlook, U. S. Energy Information Administration, Office of Energy Analysis, U.S. Department of Energy, Washington, D.C.    DOE/EIA-0484(2013)

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Keeling, C.D., S.C. Piper, R.B. Bacastow, M.  Wahlen, T.P. Whorf, M. Heimann, and H. A. Meijer, Exchanges of atmospheric CO2 and 13CO2 with the terrestrial biosphere and oceans from 1978 to 2000.

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On Human Opportunity

There is a small theater for visitors at the NASA Space Center in Houston, called "Destiny Theater". Every hour, every day, they show a film there called “On Human Destiny”.  This beautiful and deeply moving film documents the history of space exploration, using striking historical film footage.  The film concludes that it is our human destiny to explore space and colonize other star systems. 

I don’t believe in human destiny.  I believe in human opportunity.

There is no force which predetermined that humans should reach space, spread life to other star systems, or colonize other planets.  There is only our human potential to do so.  Whether we succeed in becoming something more than we are today or become a geological footnote in the history of a small planet depends on us.  It depends on our choices and our ability to cooperate.  It depends on our ability to work.  It depends on our ability to solve problems.   It depends on what we choose to do.  It depends on us.

Rarity of Human Life

In the history of the world, or the history of the galaxy, the evolution of the human species is an incredibly rare and improbable event.  Even given our debut as a tool-making genus about 3 million years ago, and a species capable of abstract thought 70,000 years ago, our technological civilization is an additionally unlikely and very recent development.   Against all odds, we stand on the cusp of meaningful space travel; we stand on the cusp of interstellar transmission of life.

The universe is about 13.8 billion years old.  By comparison, we have had the ability to communicate by radio broadcast for 122 years.  That is 0.0000000088^th of the lifetime of the universe.  Or consider our planet, which has existed for 4.6 billion years.  We have had the ability to communicate by radio for a fraction of 0.00000003 times the life of our planet.  Putting it another way, if aliens had randomly looked our planet at any time during the life of the planet to date, they would have had a 0.00000003th  chance of noticing that there was an intelligent species, capable of radio communication.  [Or, at least a species capable of communication, with the question of intelligence unresolved.]

Rarity of Intelligent Life in the Galaxy

The Drake Equation, formulated in 1961, describes the probability that a civilization capable of radio communication exists in the galaxy at the present time.  Many variables in the equation are poorly constrained (obviously).  But astronomical knowledge is rapidly reducing the uncertainty about the number of habitable planets in the galaxy.  The principal remaining uncertainty is the expected lifetime of a technological civilization, as pointed out by astronomers Carl Sagan and I. S. Shlovski in 1966.

The equation begins with a large number representing the number of stars in the galaxy, or the rate of star formation in the galaxy.  Factors representing some fraction of those stars successively pare down the number of potential civilizations, according to necessary criteria for life, for intelligence, for technology, and for longevity of the civilization.  The equation looks like this (from Wikipedia):

 N = R_* ^. f_p ^.n_e ^. f_l ^. f_i ^. f_c ^. L

where:

N = the number of civilizations in our galaxy with which communication might be possible (i.e. which are on our current past light cone);

and

R* = the average rate of star formation in our galaxy

fp = the fraction of those stars that have planets

ne = the average number of planets that can potentially support life per star that has planets

fl = the fraction of planets that could support life that actually develop life at some point

fi = the fraction of planets with life that actually go on to develop intelligent life (civilizations)

fc = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time for which such civilizations release detectable signals into space

Some variants of the equation use the total number of stars in the Milky Way as a starting point, rather than the rate of star formation   That number is between 200,000,000,000 and 400,000,000,000.

Here are my guesses for these factors. 

My Assumptions for the Drake Equation:

80% of stars have planets.

20% of planetary systems have at least one habitable planet

20% of habitable planets develop life

1% of planets with life develop intelligence

20% of planets with intelligence develop radio technology.

The average lifetime of a radio-capable technological civilization is 2000 years. 

These assumptions yield an estimate that there is one technological civilization in the galaxy at the present time – us.  If I adjust the factors such that there are 2 civilizations in the galaxy, the average distance to another civilization would be about 35,000 light-years.  Thus the time required to communicate with another civilization would far exceed my estimate for the expected lifetime of a civilization. 

There are a number of interactive calculators for the Drake Equation available on the Internet.

Human Opportunity

“The Earth is just too small and fragile a basket for the human race to keep all its eggs in.”                                              Robert Heinlein

Against incredible odds, humanity stands on the cusp of interplanetary travel.  Some of the world’s best and brightest people are seriously making plans to colonize Mars.  And if the other planets in the solar system are too inhospitable to support an independent human civilization, scientists have discovered a thousand planets around other stars – and these are but a tiny fraction of the number that must exist. 

Still, I am reminded of the title of a 1973 book by Ben Bova: Starflight and other Improbabilities.  As we understand physics today, the speed of light is an unyielding limit.    Voyages to the stars would require generations to complete the voyage and consume vast resources.  The probability of success for any particular venture would be slim.  But the tantalizing possibility of interstellar colonization is possibly, just barely within our grasp.  A program to gain more information about other planets is the first step.

I can imagine launching miniaturized microprobes, using magnetic accelerators in space to catapult them near light speed.  Returning the data to earth is problematic; but perhaps the probes themselves could use the gravity of stars to reverse course to earth.  Alternatively, a series of relay craft, with deployable antennae could follow the probe and transmit the data back to earth. 

And if colonization of the stars proves to be impossible, we could at least do what life does: propagate itself.  We could send seed packages to other star systems which would spread the miracle of life to other worlds.  If that alone is humanity’s legacy, it would be a worthy monument that we lived, developed science and technology, and gave life a new chance on barren worlds.

If life exist on other planets (as I expect it will on some, in a simple form) we should respect and preserve that life.  But I would not let protection of speculative simple life prevent our own further development.  Earthly life has proven its ability to develop complex forms, ecosystems, intelligence and technology, and I value those more than non-sentient algae.  We do not yet know what we might achieve, but today, we appear to have achieved more than any other life in the galaxy.  We owe it to those who have gone before to reach for what more we can become.

That is the opportunity for humanity.

What We Must Do: A Short List

Colonization of the stars, by people or earthly life, will not happen by itself.  Realization of this opportunity will only happen if people actively work toward that goal, through deliberate, directed effort and management of problems facing humanity on Earth. 

You may have noticed that I highlighted the final parameter of the Drake Equation – the expected lifetime of a technological civilization.  My guess is that a technological civilization will exist for about 2000 years before self-destructing due to environmental collapse, war or other strife.  Clearly, the longer a civilization can last, the better the chances of realizing Human Opportunity.  Therefore, our first goal is to ensure the longevity of civilization for our descendants.

Here is a short list of what we must do to realize our very rare, improbable human opportunity.

1)      Bring peace to the globe. 

Nationalism was the great sin of the 20^th century, causing two world wars and countless smaller conflicts.  In the 21^st century, nationalism is still rampant, even resurgent in the first two decades of the new millennium.  Our job in the next century should be to render national borders obsolete, uniting economic interests and blurring national identity until war between nations becomes a ridiculous idea.  Global spending on the military is about 2.3% of GDP; spending on all space products and services is about 0.4% of GDP, or about 1/5 of the spending on defense.  Just imagine what we could accomplish if that ratio was reversed!

Religious conflicts also need to come to an end.  Over 3000 distinct religious sects exist on Earth, generally with each one claiming to be the single true faith.  This conviction of righteous certainty continues to plague mankind in the form of religious prejudice, intolerance, bigotry, hatred, and violence.  Religious pluralism and acceptance is necessary worldwide, in order to eliminate conflict between faiths.  Governments must be secular in order to avoid favoritism to any single faith.

Tribalism is the root of most human conflicts – the notion of “us” versus “them”, with thoughts and rhetoric which de-humanizes the enemy.  The bases for that tribalism are the familiar divides of race, religion, ethnic identity, national origin, wealth and political orientation.  Tribalism itself must be recognized as the enemy, and opposed wherever it occurs.

2)      Bring prosperity to all.

We cannot realize the full potential of mankind while a large portion of the world’ population lives in poverty.   Although great strides have been made in reducing extreme poverty, still, between one-third to one-half of the world’s population lives in poverty according to some measure – without access to adequate clean water, food, or sanitation. 

Health, nutrition, sanitation and education are the minimum requirements for full realization of a human life.  If not from the morality of fairness, then our own self-interest should motivate us to provide these things for all of humanity.  Because if we are to realize the potential of our species, we need the best performance from all of the workers, all of the scientists, and all of the geniuses on the planet.  If we do not provide these things to every young person, we are missing out on the possible contributions that we might receive. 

Although extreme poverty is diminishing, income inequality is increasing around the globe.  As economist Thomas Piketty pointed out, as long as the return on capital exceeds the rate of economic growth, the unequal distribution of wealth will increase.  Further, automation of labor through robotics and computerization is a threat to the global middle class, causing destruction of middle-income jobs.  The loss of honorable work is nothing new; it has been a theme of several dystopian novels, notably Kurt Vonnegut’s first novel, “Player Piano”, published in 1952.  Providing meaningful employment to workers will be a major economic challenge as labor is increasingly automated.  

Conflict is often rooted in inequity.   The final reason for bringing prosperity to everyone is to reduce conflict between people.  People naturally understand fairness.  People desire equality of opportunity, and a decent, honorable and respected quality of life.

The elimination of inequality includes the elimination of gender and racial discrimination.  Apart from the moral imperative of fairness, we must understand that we are unlikely to realize human potential if half of the human race is blocked from contributing to our success.   

Balancing the distribution of wealth is difficult.  It means providing equality of opportunity.  It means balancing the meritocracy of individual achievement with respect for all people.  It means providing meaningful and financially rewarding work to all laborers.  It means managing the disproportionate return on capital to the owners of capital with the need to distribute wealth throughout society.  By no means have we solved these problems, or have any solution in sight.  But providing honorable prosperity to everyone is something that we must do to achieve the potential of the human race. 

3)      Mitigate environmental damage.

Damage to our environment will shorten the lifespan of our technological civilization, reducing our chances of realizing our potential.  It should now be clear to everyone that human-induced climate change is real.  Our emissions of greenhouse gases are adding heat to the atmosphere and changing the climate in ways that may be very damaging to many people.  There is no quick fix, but we need to stabilize or reverse climate change by 2050.  Beyond climate change, we must remediate the damage to the ecosystems of the oceans due to overfishing and pollution.  We must also stop the absorption of CO2 from the atmosphere into the oceans, which is causing a significant change in ocean acidity.  We need to achieve clean air and water, particularly in newly industrialized developing countries which are rapidly causing damage to the environment.

We need to achieve our goals of environmental protection without compromising the standard of living and economic well-being of people.

4)      Continue scientific studies and space exploration.

Obviously, we will not explore and colonize space without further progress in science and technology.  We must continue to explore the planets, moons and asteroids of our solar system.  We need to continue to investigate the effects of the space environment on human physiology, so we can design spaceship environments capable of deep space flight.   We are making good progress in that direction, with concrete plans to send a manned mission to Mars.

I think an important stepping-stone will be to mine the asteroids, or bring asteroids into Earth orbit to provide construction materials for other ventures.  The technology required for these ventures will add to the general know-how of living and working in space.

Energy is a significant constraint in space exploration, as it is on Earth.  Small-scale nuclear fusion reactors seem feasible, and there are a number of research companies working on the idea.   When fusion energy is achieved, it will be a milestone for space exploration, as well as the key to ending our climate-change crisis on Earth.  For these reasons, continued funding and research into fusion power must be one of our special priorities. 

It is also not too early to think big – an independent, self-sustaining planetary colony may require a more accommodating environment than today’s environment on Mars or Venus.  Within this century, we could begin the first stages of terraforming Mars, Venus, or moons within our solar system.  The costs might be large, and it may require centuries, but the reward would be another home planet for mankind.

And private entrepreneurs are already working toward an interstellar exploration project.  The "Breakthrough Starshot" was initiated in 2016 by Russian entrepreneur Yuri Milner with a personal commitment of $100 million, and supported by Facebook founder Mark Zuckerberg.  The US agency DARPA has also given a grant called the 100 Year Starship, toward the development of the capability for interstellar travel within 100 years.

Conclusion

There is a lot to do.  But there are seven billion people capable of carrying the task forward.  We need to extend the lifetime of our technological civilization, we need to do more to ensure social equity and opportunity, and we need to work toward colonizing other planets.  The first thing is to recognize the goal and to gain alignment of many people toward that goal.

We should also acknowledge the progress that has been made over the past 300 years of the scientific enlightenment, and especially the incredible progress over the past 30 years in former "developing countries".  This progress is well documented in Hans Rosling's book Factfulness, and Steven Pinker's book Enlightenment Now.  Rosling's data visualization site Gapminder.org, is an excellent tool for seeing that progress, especially in the visualization "Health and Wealth of Nations".   https://www.gapminder.org/tools/#$chart-type=bubbles

We will not realize the potential of our species by focusing on self-interest or national interest.  We will not get there by fighting.  We will not get there by arguing about what is the correct religion and true form of God.

Although our entertainment about space provides inspiration, we will not achieve human opportunity by reading science fiction, or watching Star Wars, or playing space games.  It seems to me that people are satisfied with the dream, the fantasy that we are a space-faring people.  We will only achieve human opportunity by actually doing things that will bring us closer to space travel.

Entrepreneur Elon Musk recognizes the value and the fragility of human opportunity.  Musk made a fortune in Internet businesses with the purpose of acquiring enough capital to make a difference.  Musk started the automobile company Tesla, with the goal of reducing greenhouse gas emissions and mitigating environmental damage.  Musk founded the rocket company SpaceX, because Elon Musk sincerely wants to colonize Mars.   Few of us have the abilities or resources of Elon Musk, but everyone can do something. 

Against odds of a hundred billion to one, we stand today as perhaps the only technological civilization in the galaxy.  After three and a half billion years of evolution, we are alive at the very moment when we have the intellect and capability to do something remarkable – to remake the galaxy into a home for earthly life and mankind.  We stand on the brink of colonizing the stars.  Whether we succeed or fail depends on us.  

Let's do it.
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Original post: 7/13/2016.  
Edited 4/3/2020 to add references to Hans Rosling's Factfulness, and Steven Pinker's Enlightenment Now, and references to interstellar exploration initiatives, and additions about human potential.
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References:

Drake Equation

https://en.wikipedia.org/wiki/Drake_equation

N = R_* ^. f_p ^.n_e ^. f_l ^. f_i ^. f_c ^. L

where:

N = the number of civilizations in our galaxy with which communication might be possible (i.e. which are on our current past light cone);

and

R_* = the average rate of star formation in our galaxy

f_p = the fraction of those stars that have planets

n_e = the average number of planets that can potentially support life per star that has planets

f_l = the fraction of planets that could support life that actually develop life at some point

f_i = the fraction of planets with life that actually go on to develop intelligent life (civilizations)

f_c = the fraction of civilizations that develop a technology that releases detectable signs of their existence into space

L = the length of time for which such civilizations release detectable signals into space

Drake Equation Calculators

http://www.classbrain.com/artmovies/publish/article_50.shtml

http://www.as.utexas.edu/cgi-bin/drake.pl

http://www.bbc.com/future/story/20120821-how-many-alien-worlds-exist

Planets Image

http://www.cosmosup.com/fascinating-planets-outside-the-solar-system/

Origin of Life on Earth

http://scitechdaily.com/new-evidence-on-the-origins-of-life-on-earth/

https://en.wikipedia.org/wiki/Abiogenesis

Origin of life at least 3.5 billion years ago, possibly as old as 4.1 billion years ago.  Probably originated as RNA-based life.  Gained complexity and diverse functions through time.

https://en.wikipedia.org/wiki/Eukaryote

https://en.wikipedia.org/wiki/Multicellular_organism

Multicellular life evolved independently at least 46 times.  Multicellular life arose about 3 to 3.5 billion years ago, and complex multicellular life arose about 1.5 billion years ago. 

https://en.wikipedia.org/wiki/Human_evolution

Homo habilis: 2.8 m.y. BP

Progress

Hans Rosling, 2018, Factfulness, 341p.
Hans Rosling, Ola Rosling, Anna Rosling Ronnlund; Gapminder.org.

Steven Pinker, 2018, Enlightenment Now, 576 p.

http://data.worldbank.org/indicator/MS.MIL.XPND.GD.ZS

World Bank statistics on military spending, as a percentage of GDP by country.  

Military spending is still increasing in real terms, due to the increase in global GDP.  Real military spending has increased by 2.5x since 1988.

World military spending declined from 3.4 percent of GDP in 1988 to 2.3 percent in 2015.

United States military spending has declined from 5.6 percent of GDP in 1988 to 3.3 percent in 2015.

http://www.worldbank.org/en/topic/poverty/overview

The number of people in extreme poverty has been falling rapidly.   In 1981, 44% of the world’s population lived on less than $1.90 per day.  By 1990, that number was reduced to 37% of the world’s population, and by 2012, only 12.5% of the world’s population lived on $1.90 per day. 

http://www.globalissues.org/article/26/poverty-facts-and-stats

In 1998, over 80% of the world’s population lived on less than $10 per day. 

Space Exploration

http://waitbutwhy.com/2015/05/elon-musk-the-worlds-raddest-man.html

http://waitbutwhy.com/2015/08/how-and-why-spacex-will-colonize-mars.html

https://www.tesla.com/blog/master-plan-part-deux

https://www.tesla.com/blog/secret-tesla-motors-master-plan-just-between-you-and-me

Several articles from a series about entrepreneur Elon Musk.

http://curious.astro.cornell.edu/about-us/150-people-in-astronomy/space-exploration-and-astronauts/general-questions/921-how-much-money-is-spent-on-space-exploration-intermediate

Most information seriously dated – 2005 vintage.

https://en.wikipedia.org/wiki/Budget_of_NASA

NASA 2016 budget:  19 billion dollars.

https://www.spacefoundation.org/sites/default/files/downloads/The_Space_Report_2015_Overview_TOC_Exhibits.pdf

Total global spending for space products and services was $330 billion in 2014, including commercial, military, and government scientific spending.

Given global GDP of 74.150 billion in 2015, spending on space is about 0.4 percent of global GDP.

Interstellar probes
- http://www.scientificamerican.com/article/100-million-plan-will-send-probes-to-the-nearest-star1/

- https://breakthroughinitiatives.org/Initiative/3

https://singularityhub.com/2017/06/18/why-interstellar-travel-will-be-possible-sooner-than-you-think/

https://en.wikipedia.org/wiki/Breakthrough_Starshot

https://en.wikipedia.org/wiki/100_Year_Starship