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Wednesday, December 7, 2016

The Scientific Method, Redefined

In this blog post, I criticize two of my idols in science, physicists Neil Degrasse Tyson and David Deutsch.  Both of them have written or spoken about the scientific method, and both of them have missed the mark.  Dr. Tyson says that science is all about prediction, and not about explanation.  Dr. Deutsch says that science is about explanations, but gives an unsatisfactory definition of what qualifies as an explanation.  In this post, I set out my own definition for the scientific method. 

The scientific method is a search for truth through objective reasoning.  We use the scientific method to solve scientific problems, and step-by-step, we improve our understanding of reality.  When we apply the scientific method, the end product should be a good explanation for the phenomenon we are investigating.  The idea of "a good explanation" was put forward by David Deutsch, but without clear criteria for what makes a good explanation.  I think a good explanation has the following attributes:  

A good explanation must define a process which changes some aspect of reality.
The process must be observed in action.
The process must be measured and quantified.
The explanation must reconcile theory and observation.
The work must meet standards of objectivity for scientific research. 
The explanation must be verified through successful prediction of experimental results or observations of real-world changes.
The explanation will often explain other phenomena in areas unrelated to the initial inquiry.
The explanation must be subjected to peer review, and published in a reputable journal.

The Scientific Enlightenment
In general, science is the modern way that we search for truth and develop useful technologies for civilization.  The deliberate practice of scientific investigation began in the mid-1600s.  Science greatly accelerated human progress in terms of technology, understanding of the earth and the cosmos, literacy, health, prosperity, government and all other aspects of civilization.  We are living in an age of scientific enlightenment, the longest continuous period of enlightenment in history. 

The scientific method is critical to that enlightenment.  The process of objective reasoning is essential not only to science, but to most other aspects of civilization, including government, law, economics, journalism, education and medicine.  Objective reasoning is a social process, involving not just individuals, but represents how society comes to conclusions about various issues.  Objective reasoning requires academic and political freedom, free discourse and argument, unrestricted access to data and information, and equality in public debate.

We were all taught the basics of the scientific method in middle school.  According to the Oxford Online Dictionary, the scientific method consists of “systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses”.  That sounds pretty close to what I remember from middle school. 

But I now think that this description is incomplete.  What place is there in this process for human intuitions, guesses, and thought experiments?  How do we choose what to observe and measure?  What does it mean when we form a hypothesis, and where does it come from?  Where is the part about free access to primary data?   Where is the part about replicability of experiments?  Where is criticism and peer review?  Where is the part about absence of conflict of interest?  Where is publication and dissemination of results? 

I would like to convene a team of the greatest scientists to rewrite the scientific method.  I would like to enlist not only giants of scientific accomplishments, but those who have the gift of explanation of complex issues.  I want to enlist polymaths, those who have a sense of the broader meaning of objective reasoning for all humanity.  I want to ask Richard Feynman, Jacob Bronowski, Stephen J. Gould, Carl Sagan and David Attenborough.  But Feynman, Bronowski, Gould, and Sagan are all gone.  We will have to do our best without them. 

Looking further in the past, it would have been interesting to hear the opinions of Albert Einstein, Nicola Tesla, Neils Bohr and Enrico Fermi; but especially those who did not receive equality in research or recognition:  Lise Meitner, Marie Curie, Barbara McClintock, and Rosalind Franklin, but who made civilization-altering discoveries anyway.  We will also have to imagine what they would have said.

Finding Truth
In a sense, the scientific method began with the ancient Athenians.  Socrates and others advocated a process of discourse and argument to find truth.  Finding relevant truth is the goal of science. 

From that premise alone, we see that science is intrinsically democratic and egalitarian.  Conclusions must always be subject to challenge and debate.  For that there must be freedom to replicate experiments and calculations.  There must be unrestricted access to primary data, in order to review others’ work. 

Very early in my career as a geologist, I made a presentation in which I gave my interpretation of a geologic problem.  After the presentation, a wise mentor corrected me.  I learned that I must never give my conclusions in the first person.  Instead of “I say that the conclusion is X”, one should say, “The data says that the conclusion is X.”  The best analysis is always when the data speaks for itself.

The premise is that objective truth exists, and that it is accessible by everyone.  The scientific method is the process by which we analyze the world around us to illuminate objective truth for ourselves and others.

Explanations, Empiricism, and Mathematics
Physicist David Deutsch writes about the scientific method in his books “The Fabric of Reality” and “The Beginning of Infinity”.  I like Deutsch’s view, that the purpose of science is to make good explanations.  I agree with Deutsch that explanations matter. 

Empiricism is one way to make successful predictions about future events, but it is conceptually empty.  Empirical results are limited, by nature, to the specific conditions under which precedents have occurred.  As Deutsch explains, Empiricism lacks reach.  Empiricism will never take us outside the envelope of prior experience.  By extension, all forms of science which rely on empirical results are also limited.  Without explanation, we cannot know the bounds of our models, and we cannot transfer our understanding into new realms, with new insights. 

I was horrified to read an interview of celebrity physicist Neil Degrasse Tyson, in the book “But What If We’re Wrong”, by Chuck Kloosterman.  The passage is as follows:

“In physics, when we say we know something, it’s very simple.  Can we predict the outcome?  If we can predict the outcome, we’re good to go, and we’re on to the next problem.  There are philosophers who care about the understanding of why that was the outcome.  Isaac Newton [essentially] said, ‘I have an equation that says why the moon is in orbit.  I have no fucking idea how the Earth talks to the moon.  It is empty space – there’s no hand reaching out.’  He was uncomfortable about this idea of action at a distance.  And he was criticized for having such ideas, because it was preposterous that one physical object could talk to another physical object.  Now, you can certainly have that conversation.  But an equation properly predicts what it does.  That other conversation is for people having a beer.” 

NO, Dr. Tyson.  Just no.  Explanations matter.  Equations without explanations are empty, and their predictions limited.  It matters whether the unseen force causing action at a distance is made of gravitons, or if the action is caused solely by the curvature of space-time. It is precisely because Newton was unable to provide an explanation for gravity's action at a distance that the science was incomplete.  Einstein's gravity is an improvement in providing an explanation for how gravity works, but is probably not the final word on the matter.

 In college hydrology, we empirically derived equations for the flow of water through a pipe at different velocities.  Were we finished, and “on to the next problem”?   Of course not.  The equations represented processes within the pipe with physical meaning.  Only after we had observed the flow of liquid with dye tracers in transparent pipes could we assign meaning to the equations.  We could assign names to processes we observed, such as laminar flow and turbulent flow.  And those explanations give rise to practical new predictions, such as the erosion rate in the production tubing of an oil well, depending upon the velocity of the flow, and the flow regime of the fluid. 

As David Deutsch puts it, good explanations have reach.  “Reach is the ability of some explanations to solve problems beyond those for which they were created to solve.”  Thus, Newton’s theory of gravity solved the rate at which objects on earth fall to the ground, and it also solved the problem of the orbital paths of the planets. 

Observation, Theory and Experiment
There is a duality in scientific work that has existed throughout history.  Scientists come in two types: theorists and experimenters.  We can contrast Plato, for whom truth is found in the mind and imagination, with Aristotle, for whom truth is found through objective observation.  Theorists include Copernicus, Newton, Einstein ,Tesla and Feynman; observers/experimenters include Darwin, Tycho, Galileo, Edison and Fermi.  The two sides are mutually dependent, neither can make progress without the other. 

Our textbook definition of the scientific method is “systematic observation, measurement, and experiment, and the formulation, testing, and modification of hypotheses”. 

But where do we begin?  What informs our first observations?  Some scientists, including Deutsch and Stephen J. Gould, have emphasized the importance of human intuition and inspired guesswork.  These authors suggest that theory precedes observation.  I am skeptical of this claim.  It seems to me that theory must always address a problem posed by an observation.  Einstein never acknowledged the importance of the Michelson-Morey experiment as inspiration for the theory of special relativity.  But he must have been aware of this landmark experiment, which proved, against all expectations, that the speed of light is constant in all directions.  From that fact, it is possible to develop the theory of relativity.  Without that experiment, however, there is no problem to solve, and no reason to develop the explanation.

However observation begins, the scientific process must alternate between theory and experiment.  Theory shows what observations are necessary and informs experimental design.  Experimental results pose problems which new theories must solve. 

Ancillary Elements of the Scientific Method
  • Data must be freely available, for re-calculation and verification by others.
  • The process of gathering the data must be clearly identified, so the data may be critiqued as well as the analysis.  Data gathering must be replicable by other researchers.
  • Sources of funding must be identified.  Potential conflicts of interest identified, and if possible, eliminated.
  • Results should be subject to formal peer review before general release to the press or public.
  • Results should be published in reputable journals to make the information available to other researchers.
  • Problems encountered in the research should be clearly revealed. 
  • Hypotheses should be framed in a way that allows refutation through further work.  
These ancillary processes of the modern scientific method are important, and must be observed if the results of a study are to be considered “scientific”.

Process, Observation, Measurement, Quantification, Validation
David Deutsch makes a wonderfully clear case about how the scientific method is about finding good explanations for scientific problems. The explanation of phenomena is the end goal, and it supersedes empiricism and mathematical modeling as the goal of science. 

But Deutsch falls flat when defining what makes a good explanation.  According to Deutsh, a good explanation is: “hard to vary, while still accounting for what it purports to account for.”  That’s it.   That’s the best definition given.  Deutsch gives several good examples of good explanations, and contrasts those with bad explanations, but still, the definition is weak.  There is no measure for what makes a definition hard to vary, and what the explanation should account for is left undefined.

But let’s pursue the idea of a good explanation as the goal of the scientific method.   A good explanation should answer a scientific problem.  That explanation should identify a process which transforms or changes some aspect of reality.  The process must be observable.  We should be able to measure and quantify the process.  And finally, we should be able to validate the process through experiment, or through verified predictions of some other behavior of the natural world, or both.  That’s it.

I have a former colleague who does not believe in human-caused climate change.  In his view, the world has been warming since the end of the last ice age, and the current warming of the globe is just a continuation of that trend.  Is this a good explanation?

Of course not.  This explanation has not identified any process for warming the planet, only the fact that some warming has occurred at some time in the past.  There is no observation of a current process, which is a continuation of the former process, and no measurement, quantification, or validation that the process which ended the last ice age is still operative. 

In contrast, the process of how greenhouse gases warm the earth is observed.  The buildup of greenhouse gases is observed, and the amount of heat retained by these concentrations of gases has been measured.   The total heat retained by greenhouse gases has been quantified, and can be compared to expected changes in air temperature, water temperature, volumes of melted ice and rising sea level.  Additional predictions have been made and confirmed regarding the behavior of trade winds and the frequency of extreme weather events.  This explanation has reach, and accounts for large-scale changes in the biosphere, in terms of gardening zones, movement of microclimates and timing of animal migrations.

The explanation of climate change by human emissions of greenhouse gases is a good explanation.  It is a good explanation because it identifies a process.  The process can be observed, measured, and quantified.  The measured process can be compared to predictions from theory, and verified by successful prediction of changes in the atmosphere and ocean.  And the explanation has reach in terms of explanation of seemingly unrelated phenomena. 

The scientific method is a search for truth through objective reasoning.  We use the scientific method to investigate problems in our understanding of reality.  Our goal is to develop good explanations which resolve these problems. 

The scientific method includes a number of ancillary processes to ensure the integrity of the investigation and the results.  We have made progress in understanding reality when we find a good explanation for our problem.  A good explanation meets the following criteria. 

A good explanation:
  • Must define a process which changes some aspect of reality.
  • The process must be observed in action.
  • The process must be measured and quantified.
  • The explanation must reconcile theory and observation.
  • The work must meet the standards of objectivity listed above as ancillary elements of the scientific method.
  • The explanation must be verified through successful prediction of experimental results or observations of real-world changes.
  • The explanation will often explain other phenomena in areas unrelated to the initial inquiry.
  • The explanation must be subjected to peer review, and published in a reputable journal.
Isaac Asimov, 1988, The Relativity of Wrong, 225 p.

David Deutsch, 2011, The Beginning of Infinity, 487p.
David Deutsch, 1997, The Fabric of Reality, 390 p.

Richard Feynman, 1998, The Meaning of It All, 288 p.
Richard Feynman, 1999, The Pleasure of Finding Things Out, 144 p.

Stephen J. Gould, ??, in an essay I can no longer locate.

Chuck Kloosterman, 2016, But What if We’re Wrong, 272 p.

Wednesday, October 5, 2016

American Taxes Compared to Other Countries

Conservatives often say that America is one of the highest-taxed nations in the world.  My father recently told me this.  Donald Trump also said the same thing in the same words in his acceptance speech at the Republican National Convention. 

If this were true, it would be a problem worthy of examination and serious discussion.  The problem is that it isn’t true.  It isn’t remotely true.  America is one of the lowest-taxed nations in the world.  If it were true that America is a highly-taxed country, it should have a reasonable influence on American tax and spending policies.  We might infer that the United States government is inefficient, compared to other countries.  We might want to focus on cost-cutting, instead of raising revenue to close our fiscal deficit.  But it isn’t true.

Let’s look at the data.

OECD Federal Tax Burden
The Organization for Economic Cooperation and Development is a group of thirty-four countries, which includes all of the Western industrialized economies.  The organization gathers comparative economic data from all member countries.  Tax rates represent tax revenue from all sources, including businesses and individuals.  Taxes include individual income taxes, business income taxes, and all other taxes, including sales taxes, value-added taxes, excise taxes, import/export taxes, natural resource royalties and production taxes.  Tax rates are measured in terms as a percentage of GDP, which is the standard measure of the tax burden across several sources.  The data is available here:

The United States Federal tax rate is second-LOWEST of the OECD, at 10.5% in 2013 (the latest year with complete reporting).  Only Switzerland, at 9.5%, has a lower Federal tax rate.  The United States’ Federal tax rate would have to approximately double to reach the average tax rate for the rest of the OECD. 
The US tax rate has been consistently among the lowest of the OECD for years.  The following chart shows federal taxes for all OECD countries from 2008 to 2013.

OECD Total Tax Burden
The OECD also maintains records for the total tax burden for member countries.  Total taxes include Social Security (or equivalent) taxes, State and Regional taxes, and Local taxes, also measured as a percentage of GDP.   The United States total tax burden is fourth-lowest of the 34 OECD countries, behind South Korea, Chile and Mexico.
The United States total tax burden is 25% of GDP; the OECD average (ex-US) is 34%.  The United States total tax burden would have to increase 35% to reach the average total tax burden of the rest of the OECD.
The US total tax rate has also been consistently low for years.  The following chart shows total tax burden from 2008 – 2013. 
World Federal Tax Rate
The World Bank is an alternative source of tax data, including data from most nations on earth.   Only Federal or central authority tax data are available.  For the year 2011 (the recent year with the most complete reporting), the United States had the fourteenth-lowest Federal tax rate in the world.
The data is available for download on this site:

The list of countries with lower taxes than the United States is as follows:
Ethiopia, Pakistan, India, Afghanistan, Bangladesh, Central African Republic, West Bank and Gaza, Lithuania, Oman, Nigeria, Bahrain, Estonia, United Arab Emirates.

From 2009 through 2011, the United States had the lowest tax rate in the OECD, so no OECD countries appear in this list.

The time series data is a fairly messy chart, because of the number of countries included in the plot, but it is clear that the United States has consistently had among the lowest Federal tax rates in the world.

Federal Government Expenses
Taxation is one thing.  Government spending is another thing.  Data on Federal Government expenses are available from the World Bank.  As of 2011, the United States is eighth lowest of the 34 OECD countries in terms of Federal spending as a percentage of GDP.
If we assume that all countries federal governments are performing equally relative to the size of their economies, then those with the highest expenses (Portugal, Austria, Hungary, New Zealand, Greece) would be the least efficient.  The countries with the lowest expenses (Switzerland, Canada, South Korea, Japan, Spain, Chile, United States) would be considered the most efficient.
But I think it can be argued that the United States’ federal government is doing more than many other governments in terms of infrastructure, scientific research, environmental protection, etc.  Further, as of 2013 the United States is spending more than the next nine countries combined, accounting for 40% of the world’s military spending.  Military spending consumes over 50% of the nation’s $1.1 trillion-dollar discretionary budget.  Considering the burden of military spending, it is apparent that the United States Federal Government performs the remaining functions of government very efficiently.

1)  It is simply not true that the United States is one of the most highly-taxed countries in the world.   Our Federal tax burden and our total tax burden are among the lowest in the world.

2)  The United States government does a lot of things that make its citizens safe, things that cannot be done by individual contributions.  These things cost money.  America would be a terrible country if the government stopped doing these things.

3) Over half of the discretionary budget goes to the military, leaving less than half to do everything else.  What the government does with the rest of the money is very efficient by comparison to other countries.

4)  We’ve had a 35-year experiment in systematic under-taxation.  Perhaps we’ve had more economic growth as a result.  Perhaps government is more efficient as a result.  But we are stealing from our children by continuing to run deficits.  It isn’t fair and it isn’t right.  We need to raise taxes and pay our bills.

5)  The tax revenue/GDP parameter is a way to measure fairness.  If an American is paying 10% of gross income in Federal tax (not including Social Security and Medicare payroll taxes), including all unrealized and deferred capital gains (401k, IRA), then they are pulling their weight.  But due to the complexity of the tax system, it is not clear who is pulling their weight and who is not, and there is a widespread perception that the system is unfair.

I think most Americans would agree that we should reform our tax system to make it simpler, more transparent, and give all taxpayers confidence that the system is fair.
A version of this post also appears on the blog Debatably Political, located at this URL:

Monday, August 22, 2016

Optimistic and Pessimistic Societies

Physicist David Deutsch has a chapter called “Optimism” in his wide-ranging book “The Beginning of Infinity”.  Deutsch writes about the idea of optimistic and pessimistic societies, as exemplified by ancient Athens and Sparta, in the fifth century BCE.  It seems to me that the duality of optimism or pessimism explains much about human thinking and behavior, both as individuals and societies.  The idea is particularly striking when applied to American political parties in 2016.

To state the obvious, when faced with uncertainty, an optimist expects good things to happen and a pessimist expects bad things to happen.  Our attitudes and actions are built from those expectations.  An optimist plans for success; a pessimist takes precautions for failure.  An optimist expects normal traffic on the way to the airport, expects to check in easily and clear security without problems.  A pessimist expects difficulty at some point, and allows extra time. 

It should be clearly understood that neither optimists nor pessimists are necessarily correct.  Most of the time, the optimist meets the expected normal conditions, but some of the time misses a flight.  The pessimist spends much more time sitting at the gate waiting for departure, but rarely misses a flight.  Each of them simply experiences different costs and benefits.

David Deutsch generalizes optimism and pessimism to societies.  

Optimistic Societies
Optimistic societies expect the best from the unknown.  Optimistic societies welcome change, because they expect change to be good.  Optimistic societies value the diversity of ideas and seek innovation in science, industry, art, and culture.  Optimistic societies value non-conformity in youth and in education.  Optimistic societies are open to immigration and integration with other cultures.  Optimistic societies value individual freedom, and are permissive with regard to social behavior.

Ancient Athens is Deutsch’s example of an optimistic society.  Fifth-century Athens was a free-wheeling place, the site of the world’s first formal democratic government.  Pericles, in 431 BCE, speaks of a people who live at ease, who are lovers of the beautiful in all things, whose strength is in knowledge rather than laborious military training.   He describes a society of non-exclusiveness, where people freely do as they please in their private lives without fear of criticism from neighbors. 
Pericles noted his city’s openness to foreigners as a strength (although he also noted the increased risk due to information which could be transmitted to enemies).  The ancient Athenian society produced an unparalleled flowering of civilization from a few people in a small place and a brief time.   Athens produced the greatest advances in science, ethics, mathematics, art, literature, government and philosophy in the ancient world.  Ancient Athenians even explored the theory of knowledge itself – something not tackled seriously by Western philosophers until the 20th century.

Pessimistic Societies
Pessimistic societies avoid change, because they expect bad things and fear the unknown.  Pessimistic societies value conformity and obedience to authority.  Pessimistic societies especially emphasize conformity and obedience in children, and traditional values in education.  Pessimistic societies fear foreign aggression and foreign influence, so they are militaristic and intolerant of foreigners.  Pessimistic societies are authoritarian, and emphasize the importance of police in maintaining law and order.  The military, the police, religion and other symbols of authority are glorified.  Past wars and the dead from those wars are memorialized and revered, to reinforce the moral obligation for obedience to authority.  Oppositional opinions and news sources are repressed. Pessimistic societies share many characteristics of fascist societies.  

Ancient Sparta, as a pessimistic society, provides the counterpoint to Athens.  Noticeably, there are no Spartan historians, no Spartan playwrights, no Spartan philosophers.  Almost everything we know about the Spartans comes from their rivals, the Athenians.  But 2400 years later, half-way around the world and in another language, “Spartan” is still a synonym for discipline and deprivation.  Spartan society was completely militarized.  Sparta was based on a slave economy, with slave provided by military conquest.  Its educational practices were harsh, disciplinarian and directed toward military service.   Sparta was intolerant of differences; it valued conformity and absolute obedience to authority.  Sparta did not seek improvement, except in military matters.  Sparta did not seek improvement; it abhorred change.

Optimism and Pessimism in American Politics
It seems to me that our current political divide and culture wars relate to an optimistic or pessimistic outlook.  Progressives embrace diversity and change, while conservatives seek to revert to the status quo of the late 1950s.  Attitudes towards immigration, cultural and sexual diversity, religious tolerance, militarization and authority – all seem to relate to the division between optimism and pessimism described by David Deutsch.  In most measures, Democrats are the party of optimism, and Republicans are the party of pessimism.  This is why Barack Obama successfully energized Democratic voters with his message of hope and change.  And Obama himself is the embodiment of diversity within American politics.

Donald Trump’s acceptance speech for the nomination of the Republican party paints a dark (and inaccurate) picture of America.  It is a thoroughly pessimistic speech, written to appeal to a thoroughly pessimistic partisan following.  Donald Trump’s supporters have one of the most distinctive demographic form of any in recent election history.  Trump’s supporters are America’s aging white majority, who look back to the 1950s and 1960s as their template for what the country should be.  This demographic group is still strong, but it is fading in significance with every passing year.

Caveats and Conclusions
To be fair, neither individuals nor societies are strictly optimistic or pessimistic.  I know a man who is a classic pessimist in most things.  He arrives at the airport two hours before flight time; he is very conservative about investments and spending.  However, he climbs mountains – technical climbs of thousands of feet, alone, in winter!  Clearly, this is the behavior of an optimist!  

Likewise, the apparently optimistic culture of Athens had pessimistic traits.  The democracy of Athens convicted Socrates of heresy and corruption of youth, and sentenced him to death for his crimes, in 399 BCE.  This is not what we expect of the tolerant society described by Pericles.   Sparta, also, was not completely pessimistic.  Spartan culture granted more rights to women than Athens, including the right to own property and the right to divorce.  These are values we associate with progressive, optimistic societies.  So there are no pure endpoints in the optimistic/pessimistic spectrum.

Further, to reiterate a point I made at the beginning of this post, neither optimists nor pessimists are necessarily correct.   Sparta conquered Athens in 404 BCE, ending the Athenian enlightenment.  Deutsch describes several examples of optimistic cultures through history, all of which advanced civilization but subsequently failed.  [Deutsch writes, "If earlier experiments in optimism had succeeded, our species would be exploring the stars, and you and I would be immortal."]  Our current period of enlightenment has lasted than any other, but optimism does not have a good track record for sustained dominance.

I do believe that human progress is necessarily tied to optimism.  Cultural and scientific advances occur slowly, if at all, in a conservative, authoritarian, static society.  Human progress requires openness to foreign influences, globalization of the economy, acceptance and tolerance of cultural differences.  So count me as a citizen of Athens and an optimist!

David Deutsch, 2011, The Beginning of Infinity, 487p.; chapters “Optimism”, pp. 196 – 222, and “A Dream of Socrates, pp. 223 – 257.

Plato, Apology, 399 B.C.E., a retelling of Socrates unsuccessful oral defense at his trial for impiety and corruption, in Five Dialogs, trans. by G. Grube and J. Cooper, pp. 21 – 44.

Pericles, 431 B.C.E., Funeral Oration,

Xiao-Yu, 2016, in a free-write piece on Ari’s Blog.  I particularly liked Xiao-Yu’s choice of illustrations contrasting the cultures of Athens and Sparta.

Thomas Cahill, 2003, Sailing the Wine-Dark Sea; Why the Greeks Matter, 304 pp.

Tuesday, August 9, 2016

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


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. 

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.

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