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Thursday, August 11, 2022

Global Warming: How It Works

 I have a small collection on the bottom shelf of my bookcase of important books.  The books are: How Things Work (4 volumes), Roger Segalat, translated from German; The Way It Works, Robin Kerrod, 1980; The Way Things Work, translated from Italian, 1989; The Way Things Work, David McCauley, 1988; and two massive volumes on the history of science.  That’s what people do – we figure out how things work, and use that knowledge to understand and manipulate the world around us.  

A friend recently asked me, “What is the best argument that a lot of current climate change is caused by humans, through fossil fuel CO2, methane, and other green house gases?  What are the best data and arguments?”   The most important point about climate science is that we know how it works.  It isn’t speculation or correlation.  We simply know how it works.  Since the 1860s or before, people have known that glass bottles filled with CO2 heat up faster than bottles filled with air.  In 1896, the brilliant Swedish chemist Arrhenius calculated how much the earth would warm if CO2 concentration was doubled.  This happened in the same decade that we invented the manual transmission and radio transmission of Morse code, and about a decade after Edison’s electric lightbulb.  Scientific research has continued since Arrhenius, and we know how the CO2 greenhouse effect works just as well as we know how an AM radio, manual transmission, or incandescent lightbulb works.  

We’ve observed and measured the processes that trap heat in the atmosphere and we’ve made predictions of future warming and related events.  To confirm or deny the theory of global warming, scientists set up a system of instrumentation across the planet and in orbit, beginning about 30 years ago.  The data are clear – oceans are warming from the surface downwards, ice is melting in every setting on the planet, and atmospheric temperatures are rising.  We’ve seen the primary predictions of global warming and second-order climate changes robustly confirmed.  Objections and challenges to the data and interpretation have been evaluated and refuted.

How It Works
The entire spectrum of electromagnetic radiation includes gamma rays, x-rays, ultraviolet, visible light, infrared, microwaves and radio waves.  The high-energy end of the spectrum consists of very short wavelengths, including gamma rays and x-rays through visible light, while the low-energy end of the spectrum has longer wavelengths, from infrared through radio waves.  

Everything radiates electro-magnetic radiation at some wavelength.  It’s called by several names –Planck radiation, black-body radiation, or thermal infrared radiation.  The kind of radiation emitted by objects depends on temperature.  Hot objects emit high energy radiation with short wavelengths, and cool objects emit low energy radiation with long wavelengths.  The sun primarily emits energy in the visible spectrum, because it is very hot.  Atmospheric gases are transparent to the visible spectrum, so most of the sun’s energy passes through our atmosphere to reach the ground.  Visible light strikes the earth’s surface and is converted to heat.  The warmed earth also emits radiation, but at a longer wavelength (infrared) because it is cool. The earth’s infrared radiation mostly escapes back into space.  Carbon dioxide, water vapor and methane, however, are partly opaque to infrared radiation, depending on the specific wavelength.  These gases trap heat in the atmosphere, warming the air, the oceans and the ground.  The phenomenon is called the greenhouse effect, because glass will do exactly the same thing, keeping a greenhouse warm – visible light goes in, but infrared radiation is trapped inside.  

Image credit: Science News.  The yellow lines are actual IR readings from space, compared to the theoretical Planck radiation from the ocean surface shown in dark blue.  Depressions and divots in the yellow lines represent absorption of upgoing IR radiation by various greenhouse gases, notably CO2.  Differences between the yellow lines represent clear and cloudy skies, with cloud tops having cooler temperatures and a different baseline Planck profile.

The natural amount of CO2 and water vapor in the air keeps the earth at a temperature to which we’ve  become adapted.  If the earth’s atmosphere had absolutely no CO2 or H2O, the earth’s average temperature would be about 33 C colder, causing freezing conditions over the entire planet.

Of the sun’s incoming radiation (341 W/m2), about 29% (100 W/m2) is directly reflected back into space, mostly by clouds.  The remaining 241 W/m2 is absorbed by the ground and atmosphere, warming the Earth.  The Earth radiates energy back into space at a wavelength in the infrared spectrum, balancing the energy input from the sun to create a stable climate for the past 6000 years.  But the addition of greenhouse gases to the atmosphere is currently trapping 0.94% (3.2 W/m2) of the sun’s energy reaching the surface.  That heat is ultimately redistributed to the oceans, ice, and air, warming the earth.

This figure simplifies many heat transfers within the atmosphere before energy is either retained on earth or returned to space.  The heat retained by greenhouse gases is given the awkward technical term "radiative forcing".

[Technical note: The sun's radiation, measured in space, has an intensity of 1364 W/m2.  There is a range of reported figures from 1361 W/m2 to 1368 W/m2, depending on the choice of instrument calibration.  The earth receives sunlight according to its cross-sectional area, equal to one-quarter of its surface area.  The earth emits radiation from its entire surface area.  So for a simplified energy budget as shown below, we have to choose a convention of adapting numbers for the cross-sectional area or the surface area of the earth.  Most displays adopt the convention of the whole earth surface area as I've done above.  This requires dividing the sun's input radiation by four, yielding 341 W/m2 to represent the average energy input across the entire earth.]

Under natural conditions, a balance develops between the incoming and outgoing radiation, which keeps the earth’s temperature stable, unless disturbed by other factors such as orbital variation.  The earth’s orbit varies over cycles of 40,000 years and 100,000 years, which triggers feedback mechanisms (including CO2 concentration and reflective ice) producing ice ages. 

Climate-change deniers are fond of saying "The climate has always been changing."  But since the last ice age, for the past 6,000 years, the climate has been stable, as proven by geological studies of sea-level, temperature-sensitive isotopes, and ice-sheet deposits.  This is the entire period of the written record of humanity.  The pre-industrial level of CO2 created a “Goldilocks” climate in which humans and nature thrived.

For the past 150 years, we have burned increasing quantities of fossil fuels – coal, oil and natural gas, and cleared or burned forests to create new farmland.

The CO2 emitted from these human activities has markedly changed the concentration of CO2 in the atmosphere, from the pre-industrial level of about 280 parts per million (ppm) of CO2, to the current level of 420 ppm CO2.  Because CO2 is such a potent greenhouse gas, this small change in atmospheric composition has a marked change in retained infrared radiation. 

You might not think that 400 parts per million is enough to change the retention of radiation in the atmosphere.  I’d like to propose a small thought experiment.  Four hundred parts per million is equivalent to four parts in ten thousand, or one part in 2,500.   One ounce of water contains about 600 drops.  Four and 1/6 ounces of water, about a half-cup, contains 2,500 drops.  Imagine, for a moment (or really try) putting one drop of opaque India ink or dark food coloring into a half-cup of water.  The ink noticeably reduces the visible light transmitted through the otherwise transparent water.  It’s the same with CO2 in the atmosphere.  

Climate Feedbacks
There are further processes known as feedback mechanisms affecting the earth’s heat budget.  Feedbacks are processes that are triggered by changes in Earth’s temperature, which either amplify (positive) or diminish (negative) the primary changes.  The strongest feedback effect is the Planck effect, a negative feedback.  As the Earth’s temperature rises, it radiates energy more strongly, counteracting the influence of greenhouse gases.  The balance between the sun’s incoming energy and the Planck effect is what caused the Earth to settle at a stable temperature.  The second strongest feedback is water vapor.  As the ocean surface becomes warmer, the equilibrium humidity in the air rises.  Also, warmer air can hold more humidity, keeping additional water vapor in the air.  Higher humidity is a positive feedback mechanism, because water vapor is itself a powerful greenhouse gas.  So as the planet warms, more heat is retained by water vapor.  As Arctic snow and ice melt, the surface reflectivity diminishes, causing positive feedback.  Climate change increases cloudiness, causing feedback effects.  Clouds are complex as a feedback mechanism, with both positive and negative impacts.  Depending on the type of cloud, the primary impact may be to reflect sunlight, or may be to retain infrared emissions from earth.  Overall, clouds are considered to be a positive feedback.  There are more complex feedbacks involving biochemistry and methane, and fast versus slow feedbacks, but these are generally an order of magnitude less significant than the physical feedbacks.  This is an area of active climate research.

The Planck effect dominates all other feedback mechanisms, and the total impact of all feedback effects is negative.  This is very good, because a simple modeling exercise shows that the global climate would soon irreversibly blow up if the total feedback were positive.  Nevertheless, there are number of authoritative sources on climate feedbacks (notably Wikipedia and Andrew Dessler’s Modern Climate Change) that neglect to mention the Planck effect among climate feedbacks and assert that the net climate feedback is positive.  This is incorrect.

Global temperature change since pre-industrial times is about 1.1 C, so the current total feedback is -1.3 W/m2.  Combining the greenhouse gas effect with total feedback leaves a positive (warming) climate influence of 1.9 W/m2.  

Climate science predicts that the earth should be warming, due to heating resulting from the buildup of greenhouse gases.  These greenhouse gases, particularly CO2, are unquestionably from human activities (see my blog post,  We have detailed temperature records for much of the world for the past 150 year or so, and we have plentiful temperature measurements of the oceans beginning in about 1950.  However, early climate data have a few issues with data quality and coverage.

Starting around 1990, scientists put in place a comprehensive set of instrumentation specifically designed to detect and measure global warming.  These systems have corrected some of the issues of data collection from early research, and provide unprecedented coverage of our planet.  The results are unequivocal.  The oceans are warming from the surface downwards; the air is warming over the oceans; the air is warming more rapidly over land; the Arctic is warming faster than the rest of the planet; and continental glaciers, Arctic sea ice, and the Greenland and Antarctic ice caps are melting.  Other, second order effects of the heat are well-proven also, including an acceleration of rising sea level and seasonal changes in physical and biological systems.

There is simply no point to denying that global warming and resulting climate changes are happening due to human emissions of greenhouse gases.  These changes are observed to be accelerating, as expected, due to higher concentrations of greenhouse gases.  Previous predictions about climate change have been highly accurate.  There is no reason to doubt further predictions of serious to catastrophic harm from future climate change unless we greatly curtail emissions of greenhouse gases.

Appendix 1
Climate change indicators and sources
Air Temperature Over Land and Oceans

Temperature Anomaly Map, 2016-2022 vs. 1951-1980
Note Arctic warming is more intense than the rest of the planet, as predicted by the Macdonald report in 1979.  Also note that air over land is warming faster than air over oceans.
Continental Glaciers, World Glacier Monitoring Service

Arctic Sea Ice Extent (July)
Antarctic and Greenland Ice Sheets

Appendix 2, Comparison of Descriptions of Greenhouse Gas Heating
Arrhenius, 1896
“The selective absorption of the atmosphere is…of a wholly different kind [than diffusion of ultraviolet radiation]. It is not exerted by the chief mass of the air, but in a high degree by aqueous vapour and carbonic acid [CO2], which are present in the air in small quantities.  Further, this absorption is not continuous over the whole spectrum, but nearly insensible in the light part of it, and chiefly limited to the long-waved part, where it manifests itself in very well-defined absorption-bands, which fall off rapidly on both sides.  The influence of this absorption is comparatively small on the heat from the sun, but must be of great importance in the transmission of rays [thermal infrared, or long-wave radiation] from the earth.” 
Arrhenius then describes the debate over whether water vapor or CO2 has the greater influence as a greenhouse gas. 

Asimov, 1959
"The light rays of the Sun hit the air, pass through a hundred miles of it, hit the surface of the Earth, and are absorbed. The Earth heats up.  The heated Earth radiates energy at night back into space, in the form of the far less energetic infra-red.  This also passes through the atmosphere.  The warmer Earth grows, the more heat is radiated away at night.  At some particular equilibrium temperature, the net loss of radiation by Earth at night equals that gained by day so that, once the temperature (whatever it is) is reached, the Earth as a whole neither warms nor cools with time.
Carbon dioxide, however, introduces a complication.  It lets light rays through as easily as do oxygen and nitrogen, but it absorbs infra-red rather strongly.  This means that Earth’s nighttime radiation finds the atmosphere partially opaque, and some doesn’t get through.  The result is that the equilibrium temperature must rise a few degrees to reach the point where enough infra-red is forced out into space to balance the Solar input.  The Earth is warmer (on the whole) than it would be if there were no carbon dioxide at all in the atmosphere.  The warming effect of carbon dioxide is called the “greenhouse effect”.
…A recent set of calculations indicate that if the present carbon dioxide level should double, the overall temperature of the Earth would rise by 3.6 C."
Asimov was reporting on the work of G.N. Plass, published in 1958. 

Ramaswamy, 2019
“Interactions of the incoming solar radiation and outgoing longwave radiation with Earth’s surface and atmosphere affect the planetary heat balance and therefore impact the climate system.”

Also see:
Ramaswamy, Radiative Forcing of Climate Change, 2001

Ramaswamy, Radiative Forcing of Climate: The Historical Evolution of the Radiative Forcing Concept, the Forcing Agents and their Quantification, and Applications, 2019

R. J. Bantges & H. E. Brindley, On the Detection of Robust Multidecadal Changes in Earth’s Outgoing Longwave Radiation Spectrum, 2016

A. Dessler, Modern Climate Change, Third Edition, 2022

IPCC Reports, Technical Summaries, various dates.

Appendix 3, Discussion of Climate Feedback Discrepencies
Wikipedia asserts that there is a net positive feedback to warming.  However, a check of the referenced IPCC Technical Summary for AR5 (2014) is less clear and does not explicitly mention Planck radiation, the strongest negative feedback.  Andrew Dessler’s Modern Climate Change also concludes that total feedbacks are positive.  Dessler also does not mention Plack radiation as a feedback parameter.  [Dessler quantifies the total feedback relative to radiative forcing, rather than temperature change, which makes direct comparison of the feedback numbers a little more difficult.]  On the other hand, Global Climate Models, by D.L. Hartman, clearly identifies each feedback component, including Planck radiation.  Hartman states “the best estimate of the total feedback is about −1.2 ± 0.6 W m−2 K−1, but it is uncertain by about ±50%.”   The IPCC AR6 preliminary Technical Summary also concludes that total physical feedbacks are negative, with a best value of about -1.2 ± 0.7 W m−2 K−1.  I think that the value of -1.2 W m−2 K−1 is likely to be the best estimate.

Svante Arrhenius, On the Influence of Carbonic Acid in the Air upon the Temperature of the Ground, 1896.

Isaac Asimov, "No More Ice Ages?", 1959
In Fact and Fancy, 1972

Ocean heat content, NOAA 

ARGO Ocean Temperature Program Homepage 

NOAA Annual Greenhouse Gas Index 

Lambeck et al, Sea level and global ice volumes from the Last Glacial Maximum to the Holocene, 2014

Doug Robbins, atmospheric CO2 and related charts, 2022. 

NASA GISS Annual Mean Temperature over Land and over Oceans

G. Macdonald, JASONs presidential science advisory report, excerpt, 1979.
Whole report: 

Dennis Hartmann, Global Climate Models, 2016 (feedback chart)
IPCC AR6 Technical Summary (feedback chart, pg. 96)

Andrew Dessler, Introduction to Modern Climate Change, Third Edition, 2022

Sunday, June 26, 2022

Is Something Really Safe Because It Is Natural?

 A few years ago, a good friend, Alison Warn, posted a brilliant, concise FB comment about the safety and hazards from artificial and natural sources.  Here's Alison:

"Ahem: Ricin, Oleander, Hydrochloric Acid, Formaldehyde, Tuberculosis, Taipei Venom, Curare, Cyanide, Staphylococcus Aureus, Ebola, Arsenic, Methylmercury, Lead, Lionfish, Radon Gas, Saltwater Crocodiles.... need I go on?

Safety has nothing to do with source and everything to do with inherent properties such as chemical structure, radiation, germ virulence, or teeth. Some synthetic materials are indeed quite dangerous (sarin gas, anyone?) while others are harmless. Some natural materials are indeed quite harmless, while nature has also given us many of our most deadly poisons.

Being blinded by the source can be quite dangerous - it both leads us away from potentially lifesaving synthetic materials (such as promising new pharmaceuticals) and can lead to our discounting some very dangerous natural threats."


Whether something is safe or not has nothing to do with whether it is "natural" or not, and everything to do with its physical and chemical properties.  And something artificial is not necessarily any riskier than a natural substance.

Tuesday, April 26, 2022

Charts of Atmospheric CO2, Carbon Isotopes, Oxygen and Methane

 I started making charts of atmospheric CO2 in 2009, when the global average CO2 concentration was 386 ppm.  I updated my charts in 2012, at 392 ppm, and in 2017, at 405 ppm, and at the end of 2021, at 418 ppm. 

The monitoring stations are located from the far north, at 82° N in Canada to the South Pole.  Scripps Institute has managed most of these stations since the 1950s, first under the direction of Charles Keeling, and later under his son, Ralph Keeling.  I also included records from a few obsolete legacy stations that were operated by foreign governments.  I standardized my chart displays using cool colors to represent the Northern Hemisphere, and warm colors for the Southern Hemisphere.

The amplitude of the CO2 seasonal cycle varies with latitude, from high amplitude in far northern latitudes to very little amplitude at the South Pole.  The seasonal cycle is driven by seasonal plant growth and decay on lands with temperate climate, which are concentrated in the Northern Hemisphere.  Agriculture, which is also concentrated in the Northern Hemisphere, also contributes to the seasonal cycle.  I took advantage of this for my standard display, overlaying low amplitude over higher amplitude traces, so that all traces can be seen.

In general, CO2 concentration in the atmosphere is growing exponentially, a fact noted by Isaac Asimov in 1959.  In 2009, I made an exponential function, beginning at the pre-industrial CO2 concentration of 280 ppm in 1800, with an eyeball-fit to the data from 1957 to 2009.  Here’s the function, and the chart beginning in 1800, updated with CO2 data through 2021.  This chart has the “hockey stick” impression that characterizes many climate-change charts.

CO2 concentration, ppm = e(n*0.001854) + 280, where n = the number of months since Jan. 1800

This function would predict that global CO2 would pass 450 ppm in January, 2032 (ten years from now), and pass 500 ppm in August, 2043.

The exponential function seems to be slightly overstating the rate of CO2 growth since 2009, so I tried an alternate formula for the forecast in coming decades, a second-degree polynomial with a least-squares fit to the global average CO2 from 1974 to 2009.  That formula is CO2 in ppm = 0.000104*x2+0.0897*x+331.66, where x is the number of months from July, 1974.  This formula predicts global CO2 will pass 450 ppm in June, 2034, and pass 500 ppm in July, 2050. 

Certainly, these forecasts are simple extrapolations, and include none of the analysis of policies and economics which should be the basis of forecasting.  But it’s worth noting that my exponential forecast from 13 years ago is pretty much right on the money, overshooting by only one or two parts per million.  The last thirteen years has seen unprecedented growth in renewable energy technologies, but so far without significant impact on the rate of CO2 growth.  Here are the two forecasts on the same chart.

The seasonal cycle can easily be filtered from the data, leaving the long-term trend at each station.  From this, it’s easy to see that the Northern Hemisphere leads the Southern Hemisphere in rising CO2.  About 90% of fossil fuel burning happens in the Northern Hemisphere, and CO2 accumulates in the far north, while dispersing to the south. 

The difference in concentration from the far north to the South Pole has been increasing as larger volumes of fossil fuels are burned each year, from about 3 ppm in the 1980s to over 5 ppm now.  The chart below shows the difference in the one-year time-averaged CO2 concentration measured in Alert, Canada, at latitude 82° North, and the South Pole. 

The amplitude of the seasonal cycle has also been increasing in the far north.  The amplitude of the cycle increased from 15 ppm to 20 ppm since the mid-1970s.  This probably reflects increased agriculture and farm productivity in the Northern Hemisphere as world population has doubled.  Previous work showed that seasonal fossil-fuel use is volumetrically inadequate to produce the change in the atmospheric CO2 seasonal cycle.

Carbon comes in two common naturally occurring isotopes, C12 and C13.  Various processes, including life processes, sort the isotopes, favoring the accumulation of one or the other isotope.  Photosynthesis favors C12, so everything with carbon derived from plants, including lumber, your mashed potatoes, you, me, and fossil fuels is enriched in C12.  Scientists use a measure of the C13/C12 ratio written as d13C , and called delC13.  As fossil fuels are burned the C12-enriched carbon in CO2 changes the ratio of these isotopes in the atmosphere, lowering the value of delC13.  DelC13 continued to fall from 2009 to 2021, reflecting a growing fraction of carbon from fossil fuels in the atmosphere. 

Carbon isotopes in the atmosphere are also affected by the seasonal cycle of plant growth on the temperate land mass of the Northern Hemisphere.  As plants grow during the northern summer, the lighter isotope C12 is preferentially removed from the atmosphere, and returned during the winter months as plants decay.

After filtering the seasonal cycle, we see that the Northern Hemisphere leads the Southern Hemisphere in falling DelC13.  As an aside, the residual fluctuations in the trend have a strong correlation to the Oceanic Nino Index (ONI), reflecting sea surface temperatures in the Pacific.

Interestingly, if all of the carbon released by fossil fuels stayed in the air, the DelC13 value would be much lower, about -13, instead of -8.5.  The measured dilution of carbon with the isotope signature of fossil fuels provides a way of estimating the volume of all carbon reservoirs exchanging carbon with the atmosphere.  Currently, the reservoirs freely exchanging carbon with the atmosphere have a carbon mass of about 5200 gigatonnes, before accounting for additional carbon in the system from new burning of fossil fuels.  That’s about 6 times the mass of carbon currently in the atmosphere.

Atmospheric oxygen is also influenced by burning of fossil fuels.  Oxygen is consumed, causing atmospheric O2 to fall.  The atmosphere is about 21% oxygen, and the decline is only about 0.08%, so there is no threat to breathing.  Still, the decline can be measured precisely.  The decline in oxygen is reported in units per meg, which is equivalent to ppm in this range of values.

After filtering the seasonal cycle, we see that the Northern Hemisphere leads the Southern Hemisphere in oxygen decline, because most fossil fuels are burned in the Northern Hemisphere.  The total volume of oxygen decline is very close to the expected consumption of oxygen considering the reported volumes of fossil fuels burned and deforestation, as reported in this previous post.

Atmospheric methane (C4) is also increasing as a result of human emissions.  Methane is a much more powerful greenhouse gas than CO2, but has a shorter lifespan.  CO2 has a half-life of 120 years, while methane has a half-life of about 10 years.  This is why the climate scientists use the parameter GWP (global warming potential) to represent the different strength of various greenhouse gases over an effective time frame.  The GWP of CO2 equals 1, by definition, for all time intervals.  For methane, the warming potential over 20 years (GWP-20) is 84 – 87, and over 100 years is 28 – 36.  Over shorter intervals, methane is an even stronger greenhouse gas.  Currently, methane concentration in the atmosphere is about 1.9 ppm (i.e. 1900 ppb).  In absolute terms, methane warmed the earth by about 0.52 W/m2, compared to 2.11 W/m2 for CO2, for the latest year reported by NOAA, 2020.  All other greenhouse gases combined contributed another 0.55 W/m2.  Methane also has a seasonal cycle in both hemispheres with high values in the summer and low values in the winter, but I don’t know the explanation for the seasonal cycle. 

As the concentrations of CO2 and methane in the air rise, the atmosphere will absorb heat at a faster rate, leading to destructive climate change.  Temperatures and climate change will not stabilize until carbon emissions reach zero.  I will update my charts on carbon emissions when summary data for 2021 is released in the BP Statistical Summary of World Energy in July.  Apart from a small pandemic-related decline in emissions in 2020, the world continues to add CO2 to the atmosphere at an ever-increasing rate.  If the world had acted to reduce emissions three decades ago, simply reducing emissions might have been a reasonable policy.  However, in our current situation, outright elimination of carbon emissions is required to avoid some level of catastrophic consequences. 

Globally, we need to reduce emissions to 50% by 2035, and to zero some time between 2050 and 2070.  I am very pessimistic that we have the public understanding or political will to reach these goals.  As Bill Gates wrote in 2021, "To avoid a climate disaster, we have to get to zero greenhouse gas emissions….The case for zero was, and is, rock solid.  Setting a goal to only reduce our emissions—but not eliminate them—won’t do it.  The only sensible goal is zero.”


CO2, CO2 carbon isotopes, oxygen and methane data, including obsolete CO2 stations

Isaac Asimov, "No More Ice Ages?" prediction and commentary on global warming,
in Fantasy and Science Fiction, Jan. 1959, republished in Fact & Fancy, 1962 and Asimov on Chemistry, 1974. 

Global Warming Potential,uses%20a%20different%20value.).

GWP-20 for methane = 84 to 87; GWP-100 for methane = 28 to 36 (also reported as 25)

Radiative Forcing for various greenhouse gases