Stabilized CO2 Effect

Dr. Steven Gollmer
June 26, 2018

The April 2016 issue of Answers Magazine contained an article “ The End of Global Warming? ” which can be found at At the time I was asked to write the article, there was a discussion within conservative circles whether global warming has ended due to the apparent plateau (between 1998 and 2013) in the Annual Global Average Temperature Anomaly. I comment on several explanations (volcanoes, sunspots and natural cycles) and spent the remainder of the article introducing the concept of a new equilibrium. This idea is not original to me, but I felt it was important for a broader audience to consider.

Annual Global Average Temperature Anomaly

Upon reading this article Dr. Wu wrote a response titled “ The End of Global Warming is Not Even Close ” and can be found at In her response she took me to task on three issues: 1) Global temperature is not stabilizing, 2) We are not at, or even near, equilibrium and 3) A new equilibrium is not what we want. Although she makes some good points, I would like to comment on each of these issues.

Data analysed since 2013 has shown that the plateau is really an illusion. I acknowledged that possibility in my article when discussing natural cycles. A strong El Niño occurred in 1998 giving the impression of a sharp beginning of the plateau. However, if this year was removed from the graph, it is not clear that a plateau even exists. The most recent El Niño event (end of 2015 and beginning of 2016) was as significant as the 1998 event and removes any doubt about a plateau existing in the data. Over the next couple of years the global temperature will decrease compared to 2016 and some will revive the idea of a temperature plateau; however, this will also be an illusion. If the El Niño years are removed, it is evident that global temperatures continue to rise.

On the second issue, I agree that we are not at equilibrium because CO2 levels continue to rise. As established by Arrhenius, increasing CO2 levels in the atmosphere results in increased surface temperatures. If CO2 levels are capped, at two times its pre-industrial era level the global average temperature will rise 1.5 – 4.5 °C according to the Intergovernmental Panel on Climate Change (IPCC) report (AR5). This would be a new equilibrium level. If this cap is exceeded, the temperatures will rise even further.

I illustrated the concept of a new equilibrium as a bottle with holes. As water is added to the bottle, it runs out the holes. If the flow into the bottle increases, the water level will rise until the increased pressure at the bottom of the bottle forces water out the holes at a rate matching the inflow. Dr. Wu clarifies this illustration and then refers to the Skeptical Science web site as a critique of the water bottle model. However, this connection conflates two issues: equilibrium and saturation. (I noticed that I added to this confusion by inappropriately using the word saturation half way through my article.)

The Skeptical Science critique correctly states that the water bottle analogy is flawed because the inflow rate is constant, or nearly so (energy from the sun). Addition of CO2 is more like plugging the holes in the bottle. It makes it harder for thermal radiation to escape into space. This modification is also flawed because it infers that adding more CO2 could potentially plug all of the holes making earth's atmosphere a great heat trap leading to the extreme temperatures experienced at the surface of Venus (hot enough to melt lead).

CO2 primarily absorbs infrared radiation with a wavelength of 15 µm. At this wavelength the atmosphere is opaque and any energy escaping earth's atmosphere occurs high in the stratosphere. Opponents to Arrhenius's idea, that global warming occurs as CO2 increases, assumed that the effect of CO2 was saturated. If the hole at 15 µm is already plugged, adding more CO2 will have no additional effect. However, adding CO2 results in line absorption broadening (affecting other holes in the bottle) and also increasing the altitude at which cooling occurs (more effectively plugging a slightly leaky hole).

To illustrate the difference between equilibrium and saturation I ran several century long simulations using a low resolution climate model (GISS Model II). This model is not state of the art, but it will effectively illustrate my point. The first simulation was set at pre-industrial age CO2 levels (315 ppm) and is used as my control run. I then ran simulations at 2x CO2 levels (630 ppm), 4x CO2 levels (1260 ppm), 8x CO2 levels (2520 ppm) and 16x CO2 levels (5040 ppm ). Since I added all of the CO2 at the beginning of the simulation (not a good approach if this were done for research purposes), it takes time for the earth system to adjust to the CO2 change. However, as you see in the following plot, all of the annual global temperatures level out at a particular value. This is the equilibrium temperature associated with each CO2 scenario.

Annual Global Average Temperature Anomaly

You also see that adding more CO2 increases the average surface temperature of the earth. In this model doubling CO2 results in a temperature increase of 4.3 °C. This is on the high end of the impact reported by the IPCC.

To determine if a saturation effect is taking place I plotted the equilibrium temperatures against the amount of CO2. Although adding CO2 increases the surface temperature, increasing CO2 by the same amount, has less of an effect. Adding 315 ppm to the control run increases the temperature by 4.3 °C. However, adding 315 ppm to the 8x CO2 simulation increases the temperature by 0.7 °C. If the CO2 effect were to saturate, at sufficiently large amounts of CO2 adding 315 ppm would result in a temperature increase of 0 °C and we would reach a CO2 saturation temperature.

Annual Global Average Temperature Anomaly

The shape of this plot fits a log function with high accuracy. Since log functions have no asymptote (check your favorite calculus textbook and look up limits), there will be no saturation temperature. Increasing CO2 levels will continue to increase surface temperatures, although at decreasing effectiveness. I tried a 32x CO2 simulation; however, the model failed to run to completion because one of its internal parameters exceeded an acceptable value and the program was terminated. In spite of the failure, the data from the previous runs fit a log plot so well that I have confidence that the same trend would continue if the fail condition were corrected.

Hypothetically, you could add enough CO2 to earth's atmosphere to reach Venusian temperatures; however, I would not anticipate that happening. First, earth is further from Venus and, therefore, sunlight is less intense. This effectively reduces the inflow in the bottle analogy. Second, earth has a large percentage of surface water. Water vapor is also a greenhouse gas and would have a heating effect as higher temperatures evaporate more water (plugging different holes than CO2 does). However, net cooling of the atmosphere due to water vapor occurs low in the atmosphere and is influenced by the dynamics of the troposphere. Also, water vapor can condense in the atmosphere producing clouds, which in turn affect how much sunlight is reflected back into space. These complex interactions make it impossible to predict the effects of global warming using simplistic analogies, such as water bottles. This is why there needs to be a continued effort to study the impacts of climate change using earth system climate models, which are able to capture the intricacies of such a complex system as the earth.

This now leads to the final critique, which is “Is this new equilibrium what we want?” I, like most people, do not like change. We know what the earth is like now and we don't want to see the changes that come with an increased global temperature. Studies across multiple disciplines have looked at the impact of a 2 °C temperature increase. It is clear that what might look like a modest temperature increase, can have significant impacts on agriculture, ecosystems, land habitability, national security, etc. Will this increase be the end of the world? I doubt it, but we will not be able to ignore the impact and it will have negative effects. What about a 4 °C change or higher?

Dr. Wu mentions the unprecedented rate at which CO2 in the atmosphere is increasing. This is a completely different discussion; however, I will end with the following observation. For those who minimize the impact that humans have on the CO2 levels in the atmosphere and on the environment in general fall into the continuum fallacy, or the argument of the beard. When I was born, earth's population was 3 billion. By the time I die (assuming I live to a reasonable age) earth's population will be 9 billion. If the population can triple in my lifetime, at what point will mankind have a significant impact on the earth? In addition, technology has multiplied the impact that one person can have on the environment. My dad supported his family by farming 350 acres of land. Agribusiness makes that model no longer feasible and now the ‘small’ family farm needs to be 1000+ acres to be viable.

Advancements in technology and increases in population impact the environment. This is an inescapable fact. At this point in history the salient question is “What is the most responsible way forward?” In my article I conclude with the statement that we need to be good stewards of God's creation. It is good stewardship to limit the impact mankind has on the environment. However, it is also good stewardship to aid the poor, who will be most impacted by environmental change. Personally and nationally, what is the right balance to strike between these two as well as other demands on our time, talents, finances and resources? That will always be the question responsible citizens need to consider.

Edited 6/27/18