Why Carbon Dioxide Predicts Temperature Increases

And When It Might Not

One conclusion in an earlier essay (Climate Change in Four Easy Steps) was that the atmospheric concentration of carbon dioxide alone was an excellent predictor of past and future changes in global average temperature, and that the mechanisms causing this to be true were understood and fairly accurately calculated over 100 years ago.  Knowing the mechanisms allows us to say that the relationship has predictive power, and is more than chance correlation.  One goal of presenting that analysis was to show that the basics of climate change are relatively simple and have been known for a long time.

Any website or report on climate change will quickly get into the numerous changes in the chemistry of the atmosphere that result from agriculture, industry, energy generation and transportation.  They are many and complex.  They are real and need to be researched in detail.

Isn’t this contradictory?  If carbon dioxide alone is such a good indicator, why not just concentrate on understanding and reducing emissions of carbon dioxide?

The key here is understanding how changes in the atmosphere affect temperature, and the nature of an index.

Index first.  An index is a simpler way of summarizing a more complex system.  For example, the Dow Jones Industrial Average, the Nasdaq Composite Index and the S&P 500 might change in different ways on a given day, as they track different components of the financial system, but they tend to move in the same direction over time, acting as indexes to overall trends.  On a hot summer day, the “heat index” summarizes the interactions of temperature, humidity and other factors on how the day feels to you.  The “wind chill” index summarizes the complex of factors controlling how fast your body will lose heat on a cold winter day.

An index is never complete or perfect – it is a useful or convenient simplification, often produced to help convey the most important parts of a more complex interaction.  In a little bit we’ll encounter an example where carbon dioxide might no longer be that useful index for climate change.  But first, something on why it works so well so far.

The terms “greenhouse effect” and “greenhouse gas” have been criticized as imperfect analogies for the physical processes involved.  Svante Arrhenius, the Swedish Nobel Laureate introduced in the previous essay, employed the analogy as early as the late 1800s (although he called it the “hothouse effect”).  The term is now permanently embedded in the lexicon of climate change, as are the criticisms of it’s imperfections.

So what is the difference between the greenhouse effect and a greenhouse?  The covering on a greenhouse, either glass or plastic, is relatively transparent to incoming, visible, sunlight.  On a sunny day, the energy conveyed by that radiant light warms the interior of the greenhouse, and the covering traps the warmer air inside.  It also can reduce radiational losses of the kind described below, but that is a secondary effect.

Greenhouse gases in the atmosphere do not form a physical barrier to the movement of air, so how do they trap energy?  They do this by absorbing the invisible infrared “heat” radiation that you, me, your desk, your computer screen, soils, plants, and everything else on Earth’s surface emits.  “Night vision” binoculars work by sensing this infrared radiation emitted by the warm body of a person or animal and converting that invisible radiation into something we can see.

Absorption of this infrared radiation is the key to the greenhouse effect and to climate change.

This figure is a simplified version of the energy balance of the Earth.  All the numbers are in watts per meter square, or energy per unit area (the same “watts” used to describe your light bulbs).  Let’s step through this quickly to demonstrate the importance of the greenhouse effect. 

All the yellow arrows are dominated by visible light (we see as sunlight).  Of the 340 units received at the top of the atmosphere, a total of 100 are reflected directly back to space by clouds and particles in the atmosphere and the surface of the planet.  This total reflection of light is called albedo, and if you are on the moon, for example, this is the light you would see as the Earth.  Of the remaining 240 units, 77 are absorbed and converted to heat in the atmosphere, leaving 163 reaching and warming the surface. 

The red arrows are dominated by infrared, or longwave, or “heat” radiation.  Those two big curving red arrows between the surface and the atmosphere demonstrate the greenhouse effect.  They are the biggest exchanges in the system.  The total amount of energy transferred from the surface to the atmosphere is 398 as infrared or “heat” radiation and 105 by evaporation and movement of air from the surface (the blue arrow).  The red down arrow is infrared radiation representing energy absorbed largely by greenhouse gases (including water vapor) in the atmosphere and reradiated from the atmosphere back to the surface – the greenhouse effect.  The topmost red arrow (240 units) is infrared radiation emitted out into space.

If you like numbers, you can verify that all the gains and losses between space, the atmosphere and the surface sum to zero.  All three parts of the system must balance.

Notice that the amount of energy reaching the surface of the Earth through longwave radiation from the atmosphere to the ground (340 watts per meter square) is, by coincidence, the same as the amount entering the atmosphere directly from the sun and more than twice the amount of the sun’s energy that reaches the ground directly (163 watts per meter square).  This always amazes me.  This is the greenhouse effect. 

Even before we started changing the chemistry of the atmosphere, water vapor, carbon dioxide, methane and other gases were providing significant warming.  In the previous essay, I noted that Eunice Foote and John Tyndall spoke of this effect in the 1850s.  This is, in part, why we are not as cold as Mars.  Without this natural greenhouse effect, the earth would have an average temperature around zero degrees Fahrenheit, 59 degrees colder than at present, and nearly all water would be ice.  We would not be here.

Radiation from the surface to the atmosphere is driven by the temperature of the surface.  The retention of that energy by the atmosphere results from the ability of greenhouse gases to absorb thermal, infrared radiation (as discovered by Foote and Tyndall in the 1850s).  An increase in the temperature of the atmosphere causes increased reradiation back to the surface.

So what happens when we increase the concentration of carbon dioxide in the atmosphere?  The absorbance of energy radiated up from the surface of the Earth increases and the average temperature of the atmosphere increases until emissions back to the surface and out to space balance the additional energy absorbed.  In a sense, this heat energy is “recycled” a few more times before being lost to space.

The standard term used for this effect is “radiative forcing” described in watts per meter square, the same units used in the energy balance diagram above.  Essentially, additional greenhouse gases increase retention of upwelling surface radiation, increasing atmospheric temperatures and reradiation back toward the surface.

So how much have we increased this radiative forcing, and how much has that affected temperatures?  Here is one more complicated diagram with a simple message. 

Exhaustive research into greenhouse gases and other things we put into the atmosphere has been summarized in this one diagram (several similar versions can be found online).   Red bars show warming effects, blue bars cooling effects. 

The biggest blue bars are from aerosols (like dust particles) and increased cloud cover resulting from increased aerosols, that reflect sunlight back into space (some have proposed that we increase this reflection by geoengineering the atmosphere through the addition of specific types of aerosols).  The biggest red bar is for carbon dioxide, with other gases also contributing.  Some of those same aerosol particles (“soot” in the diagram), when deposited on reflective surfaces like snow, actually increase the absorbance of solar energy (hence both a blue and a red bar for aerosols).

Getting back to the value of carbon dioxide as an index, this diagram shows that carbon dioxide alone is equal to about 75% of the total net change in radiative forcing due to human activity (bottom bar in the figure).  More importantly, but not shown, this ratio of carbon dioxide forcing to total atmospheric forcing has remained relatively constant for decades. 

It is this constant ratio between the carbon dioxide effect and the total impact of all human influences on average global temperature that supports the use of this one gas as an index of our impact on global temperatures, as captured in the first graph at the top of this essay.

One final point on the figure just above.  Note that the total increase in radiative forcing is about 2.3 watts per meter square.  This is added to the 340 watts per meter square in the energy diagram above.  You could ask how an increase of less that 1% in total radiative forcing could be important.  Or you could conclude, as I do, that since this small increase has already increased average temperatures significantly, the global climate system is rather precariously perched at what we consider to be “normal” temperatures, and could be pushed into increasingly “abnormal” temperatures by small changes in radiative forcing, due to increased concentrations of greenhouse gases.

Returning to the index concept, does the strong relationship between changes in carbon dioxide and changes in temperature mean we should concentrate only on controlling carbon dioxide?  No.  The value of carbon dioxide as an index depends on the fact that all of our other influences have changed in proportion to carbon dioxide.  Reducing carbon dioxide emissions would only work as predicted by that first figure above if whatever steps we took also caused proportional changes in all the other factors as well.

Could this index, then, lose its predictive power?  Let’s explore one scenario that would break the ratio between carbon dioxide, other greenhouse gases and temperature.

In How to Avoid a Climate Disaster, Bill Gates emphasizes the need to create an all-electric economy and develop a zero-carbon electric system and grid.  This may be an achievable goal.  The current rush to electric vehicles and alternative sources of electric energy suggest that this change is already underway.

How would this bust our carbon dioxide index?

Emissions of carbon dioxide are driven largely by combustion of fossil fuels for electricity, industrial processes, transportation, and commercial and residential heating, lighting and cooling (the figures above are for the U.S. but demonstrate the concept being described here).  Gates’ goal would be to take all of the fossil fuel combustion, and all carbon dioxide emissions, out of these sectors.

Agriculture and forestry emissions are estimated to contribute only 10.5 percent of U.S. greenhouse gas emissions and is not even included as a separate sector in the figure on the left, but the mix of emitted gases is very different from the categories that are included.  The USDA estimates the mix of greenhouse gases from agriculture to be 12.3 percent carbon dioxide, 36.2 percent methane, and 51.4 percent nitrous oxide.  And some of that carbon dioxide is for electricity used in the food system, reducing that fraction even further if all electricity was carbon neutral.

So the vision of the zero-carbon, electrified economy could leave agriculture as the main source of greenhouse gas emissions, and methane and nitrous oxide would be the dominant sources of radiative forcing.  Nitrous oxide is generated mainly from the production, distribution and application of nitrogen fertilizers (Agricultural Soil Management in the figure to the right). 

Current methane emissions in the U.S. have a large energy system component.  Eliminating those sources (Coal Mining and Natural Gas and Petroleum Systems) would leave agriculture as the largest contributor.  In the figure to the right, Enteric Fermentation is a polite term for the digestion processes of domestic animals, especially cattle.  Manure management would remain in our hypothetical, carbon neutral economic system.

Gates’ solution would alter the existing ratio between carbon dioxide emissions and total radiative forcing.  The clean relationship between carbon dioxide and temperature change (first figure at the top of this essay) would no longer hold (that graph would get very messy). 

An intriguing result of this is that in an electrified, alternate energy future, agriculture, or really the entire farm-to-plate-to-waste food system, including landfills and wastewater management, could become the major remaining source of greenhouse gas emissions.  The kind of research needed to reduce these sources is very different from our current focus on carbon and energy!

Sources:

Additional background information on carbon dioxide and global temperature can be found in an earlier essay and in this article.

A more complete discussion of greenhouse gases and climate is included in:

Aber, J. 2023. Less Heat More Light. Yale University Press. New Haven, CT

The carbon dioxide data in the top figure are from the “Keeling Curve” and are available at: https://keelingcurve.ucsd.edu/.  Global average temperature data are from NASA’s Goddard Institute for Space Studies can be found here:  https://data.giss.nasa.gov/

Numbers for the diagram of the Earth’s energy budget are from:

https://www.nasa.gov/feature/langley/what-is-earth-s-energy-budget-five-questions-with-a-guy-who-knows

Many different versions of this diagram, some with slightly different numbers, can be found on the web. Thanks to Scott Ollinger for this version of the diagram with curved arrows emphasizing “recycling” of long-wave radiation.

The 59 degrees cooler estimate is drawn from the Wikipedia page on Greenhouse Gas

The figure on radiative forcing by different components of atmospheric change is from:

https://www.epa.gov/climate-indicators/climate-change-indicators-climate-forcing

Data on U.S. emissions of greenhouse gases, and the figure in the text, can be found here:

https://www.epa.gov/ghgemissions/sources-greenhouse-gas-emissions

Data on greenhouse gas emissions for agriculture in the U.S. are here:

https://www.ers.usda.gov/topics/natural-resources-environment/climate-change/

The full reference for Bill Gates’ book is:

Gates, B. 2021. How to Avoid a Climate Disaster. Alfred A. Knopf. New York.