by Eric Grimsrud
In my first Post called “1. A Common Sense View of AGW”, I presented a simple qualitative view of the AGW problem in order to relate the essence of what the debate is primarily about. In this Post 6, we will move on to consider some basic quantitative aspects of AGW. In this section, we will be searching, in particular, for good expressions for what’s called the temperature “Sensitivity” for CO2. That number indicates the increase in average global temperature that would be caused by a doubling of its concentration. To better appreciate the immediate importance of this number, recall this. Atmospheric CO2 was at 280 prior to the Industrial Revolution. It is now 392 and rising at a rate of 2 ppm per year. Therefore, a “business as usual” course will lead to a doubling CO2 within the current century (by about 2094).
If the quantitative expression for CO2’s sensitivity is only say about 0.2 degree C, as is claimed, for example, by H. Leighton Steward in his book Fire, Ice, and Paradise, page 23, then we could indeed conclude that AGW does not pose a problem of such great immediate concern. If CO2 sensitivity is much higher, however, then we have to be very concerned about this issue and that level of concern should be in proportion to the actual value of CO2’s Sensitivity.
So what is the best way to determine or at least get a good estimate of the Sensitivity of CO2. This is being done by model calculations using huge computers to “simulate” the entire Earth. I will not be using the results of those studies here, however, because there is a much more reliable way to determine Sensitivity and that is by looking at the historical record. Even the computer modelers acknowledge this and, in fact, use that historical record to test their models. After all, the real world acts in accordance with the effects of all of the relevant variables – whether we are aware of all of them or not. So I will be taking the advice here of one of America’s most popular philosophers, a man named Yogi Berra, who is reported to have said “predictions are hard to make, especially about the future!” and “a person can observe a lot just by watching!” So let’s now do some “watching”.
In this post, we will be focusing on the “Last Major Ice Age” in which we all presently live and which began about 35 million years ago. While I understand that there have been about four previous Major Ice Ages hundreds of millions of years previously, we know much more, of course about the most recent one and have a great deal of information concerning it, as we will see.
First, let me introduce you to a single reference that I will be making extensive use of here. This reference is a paper entitled “Target Atmospheric CO2” by Hansen et al. published in The Open Atmospheric Science Journal, in 2008, volume 2, pages 217-231. This journal is available to the public and this article can be retrieved from the internet at http://www.bentham.org/open/toascj/openaccess2.htm. Use of this reference is also appropriate here because it summarizes great deal of relevant literature while providing new information and insights. In addition, a separate and even more extensive article entitled “Supplemental Material” is provided with it. In my many years of teaching, I have found it to be essential for the students to have materials from which they themselves can read and interpret the data and figures I use in the classroom. My use of this reference here will serve that purpose. At the same time, of course, all of the literature is important and will be referred to as needed. Careful considerations of this one paper, however will get us quite a ways down the road initially.
First, in order to see where the Last Major Ice Age occurred in time, please have a look at Figure 1 (all figures, unless indicated otherwise, come from the reference cited about).
Figure 1. This graph shows the temperature of the Deep Ocean over the last 65 Million years before present (My BP). (These determinations were made by the isotopic analysis of the oxygen atoms found in the CaCO3 remains of foraminifera shells found in ocean bottom core samples. Please see Hansen et al. for the details of this widely used procedure). The period of the Late Major Ice Age in indicated by the blue line beginning at about 35 My BP. Note that temperatures are shown a variations relative to the present time.
We will come back to and use this figure in future discussions, but for now will use it to gain some temporal perspective on the Last Major Ice Age. First, note the temperature rise that occurred right after the extinction of the dinosaurs, about 65 My ago. This initial rise before 50 My BP is thought to have been caused by the continental shifts at the Asia-India interface and associated volcano activity causing CO2 to increase to approximate 1500 ppm. After 50 My BP a slow and steady temperature decrease began. Until 35 My ago the world was ice free with a sea level of about 70 meters above the present level in 35 My BP and about 200 meters in 50 My BP (due to thermal expansion at high temperatures).
The blue line starting at 35 My PB, indicates temperatures after ice began to build up on our planet, first on Antarctica and then on Greenland and then of the other continents. The world had thereby entered the Last Major Ice Age. At the very right side of the graph temperature is shown over the last few (2 or 3) million years during which ice formation was often extensive over most of the continents, including North America. Note how temperature rose and fell quite remarkably over this most recent period. This latter period includes the cold Glacial and warmer Interglacial Periods of the Last Major Ice Age. Often these glacial periods are referred to as “ice ages” in the literature. In order to avoid the confusion that thereby results, I will refer to them as “glacial periods.”
Now let’s move on the Figure 2 shown below.
Figure 2. These data were obtained from the Ice Core Records, which I’ll assume for the moment that you have heard about. By examination of these ice core samples, it is possible to determine many things including the temperature of Antarctica (and Greenland) over the last 800,000 years and the historic background concentrations of various minor components of the atmosphere. The measurements shown here of temperature and the greenhouse gases, CO2 and CH4, over time serve to illustrate an important point – their high level of reproducibility. Shown here are many measurements made by different scientific groups at different times at different locations in the Antarctic. Similar measurements from Greenland’s ice cores (not shown here) are also in close agreement The ice core records are clearly trying to tell us something about the most recent period of the Last Major Ice Age.
Now let’s move on to Figure 3 where the same sort of data are shown along with some analysis of that data.
Figure 3. (a) Measurement of two major GHG’s and also Sea Level are shown. Sea Levels can be derives by several means (see Hansen et al.) (b) Climate Forcing value have been calculated here from the GHG data and sea level data (Hansen et al. provide a good explanation to the term, Climate Forcing, at the beginning of their article). (c) From the expected Climate Forcing values, expected average global temperatures have been calculated and then compared to measured temperatures. In this case, an estimate of the average global temperature variations have been obtained by dividing the measured Antarctic temperature variations by 2. This is because temperature variations on the Antarctic are typically about twice the observed changes in average global temperature. Note that the fit between the calculated and observed temperature variations thereby obtained is very good.
[A short time out: The term, albedo, means the fraction of incoming solar radiation that is reflected back into space. The present albedo of Earth is about 0.30. During a glacial period, it is about twice that, or about 0.6 0.32 [Edit on 1/4/11]. The temperature of the Earth is primarily determined by three factors. These are sun’s intensity, the greenhouse effect and the Earth’s albedo. All of the many other detailed factors we will be discussing affect temperature by their effect on either the greenhouse effect or the albedo].
Now the reason why the general agreement between the calculated and observed temperatures shown in Figure 3c is so significant here is that this level of agreement can only be obtained using values for CO2 Sensitivity that are very much greater than the negligible level of about 0.2 degree C mentioned at the beginning of this post. The results described here could be explained only with use of a CO2 Sensitivity of about 3 degrees C for “fast feedback” processes and about 6 degrees C if slower surface albedo feedbacks were also included.
Let me explain the fast and slow feedbacks a bit more. As the temperature rises due to any “Forcing Agent” that causes a change relative to the normal, other changes also quickly occur – including increased water vapor and changes in cloud formations. All of these fast changes contribute to the CO2 sensitivity expected in the short term of a few years or a few decades. These changes can also cause slower changes in the albedo of the Earth, however, by causing the melting of sea ice or changes on land such as the conversion of barren snow covered regions to vegetated regions. While all of these factors are complicated and might be beyond our present ability to describe them well in computer simulations, Mother Nature is revealing the magnitudes of their net effects via the ice core samples.
So it appears that Mother Nature is telling us that the Sensitivity of CO2 is somewhere between 3 and 6 degrees C depending on the time span you wish to use. Figure 3b suggests that the Forcing caused by the GHG effects and the albedo effects are approximately equal. The GHG effect acts faster, but with more time, the albedo effect adds to the initial GHG effect thereby doubling the net sensitivity of the GHG’s.
All of this is can be additionally explained by bringing in Milancovitch’s calculations of the Earth’s subtle motions relative to the Sun’s position which became important during the recent glacial and interglacial periods of the Last Ice Age. A summary of this is as follows. As the Earth goes through its subtle variations of distance, tilt and precession as it revolves about the Sun, slight changes in the solar intensity in the both hemispheres occur. What happens in the Northern Hemisphere is most important because of its greater land masses. If the Northern Hemisphere happens to have a worse than average summer, the ice on it tends to grow. If it has a better than average summer, the ice on it tend to retreat. These changes in ice area cause large changes in the Earth’s albedo. In this case, we call this change a “positive feedback” because the albedo change reinforces the initial direction of change. Only after the information of the ice cores started to be revealed in the 1990’s did we realize the calculations of Milancovitch back in the 1920’s where of great importance. Until then, Milancovitch’s Theory was just one of many that awaited testing by measurements.
So the slight motions described above are now thought to initiate a change in global temperature. Then, as expected, both the albedo of the Earth and GHG’s will follow in their expected ways. For example, if that initial orbital change causes some harming, ice will retreat and the albedo will decease – causing more heating by the Sun. At the same time, more GHG’s will be emitted by the oceans as they warm up – causing more increased temperature due to their GHG effect. A lag between the initial increasing temperature and changes in both albedo and GHG concentration is expected. These secondary changes, however, will greatly contribute to the subsequent net warming (the initial forcing of the orbital change is small relative to those of the albedo and GHG changes). For the case of CO2, the ice cores indicate that its delay of change is typically about 800 years, which is small relative to several millennia of accelerated warming that then follows.
Let’s now consider Figure 4.
Figure 4. Most of this graph should now look somewhat familiar to you. Most of it shows the record (over 800 years this time) of temperature measurements via ice core data along with just the Forcings of the GHG changes this time. The GHG forcings have been arbitrarily scaled (for convenience sake) so that they are more easily compared to the observed changes in temperature. In the very right portion of this graph, however, modern changes GHG Forcing is shown on an expanded time scale along with the global temperature (purple line – ignore the black line for now, as we will discuss it extensively in my next post concerning “the Age of Man”)
So what’s to be learned from Figure 4? First, notice how temperature has closely tracked Forcing by the GHG’s for the last 800,000 years. Yes, changes in the GHG’s follow initial temperature change, but temperature also followed subsequent changes in the GHG’s.
Now look at where we are today. During the last century changes in GHG Forcing has gotten ahead of changes in temperature. (Note also that that has never happened before during the 800,000 year record of the ice cores). This lag is due to the heat inertia of the planet (mainly its oceans) and is evident in Figure 4 only because we have used a less coarse time scale for the modern data. At the same time, we know from the long term record shown on the left that temperature will catch ups with GHG Forcing.
If we want to avoid that temperature increase in the upcoming decades the question then is can we bring the GHG Forcing down relatively quickly before temperature catches up. In addition, do we really want to increase the present GHG Forcing with “business as usual” practices? We will hopefully have that discussion soon, if we agree that there is problem here that needs to be addressed.
Looking ahead a bit, some will say that GHG’s forcing is going to come down naturally – possibly by CO2’s transport into the oceans. While the existing literature on that point will offer little hope along those lines, we will consider it and other related aspects in future posts.
The most important point I have tried to make here in this Post 6 is that the Sensitivity of CO2 is somewhere between about 3 and 6 degrees C depending on whether we are talking about a short term (say several decades) or a longer term (say several centuries) period. This deduction has come from direct measurements of the past via the ice core samples. Therefore, it appears that Mother Nature is telling us that CO2 sensitivity is likely to be about 15 to 30 times greater than more comforting, estimate of about 0.2 degrees C offered by Mr. Steward (as described above) via his greatly oversimplified and purely theoretical arguments (they can be seen on the internet at http://www.montanapetroleum.org/assets/PDF/articlesReports/2010-Treasure-State-Journal.pdf).
A General Discussion of the Ancient Atmosphere as Revealed by Figure 1.
In an effort to keep this as brief as possible, I will make just a few comments below that I think will be relevant to future discussions of AGW.
 First, note how high T became at about 50 My ago.
A major reason for the increase during the prior 10 Mys is thought to be due to continental shifts occurring at that time. Most importantly, it is thought that the then island continent of India was then moving “rapidly” northward and was crashing into and sliding under the larger continent of Eurasia. The volcanic activity associated with that event is thought to have thrown large quantities of CO2 into the atmosphere over that 10 My period, thereby increasing CO2 levels to about 1500 ppm +/- 500 ppm. (The methods used for both CO2 and temperature are probably same as used for figures shown previously in Temperature and CO2 History. If needed, we can go into those details later).
 Then note that a long slow decrease in T occurred until about 35 My ago.
This decrease in T is thought to be accompanied by a decrease in CO2 so that by 35 My ago, the CO2 level is thought to have decrease to about 450 +/- 100 ppm. If that approximately 1000 ppm decrease occurred smoothly over the time span between 50 and 35 My ago, the rate of that change would have been only about 0.0001 ppm per year. This is even slower than the maximum rate of CO2 change observed over the 800,000 year record of the ice cores (about 0.01 ppm) and, of course, is many orders of magnitude smaller than the present rate of change (about 2 ppm).
The major cause of this slow removal of CO2 after 50 My ago is thought to be “weathering” by which the CO2 in raindrops and in the oceans reacts with inorganic matter (rocks) and is slowly converted to solid matter such as limestone, CaCO3. The freshly exposed granite of the Himalayan Mountains (formed by India’s undermining of Asia) is thought to have facilitated this weathering process.
 Although both the CO2 and T data is not as accurate as that obtained from the ice cores, we can nevertheless deduce a rough estimate of CO2 Sensitivity from it.
A decrease from 1500 ppm CO to about 450 ppm CO2 between 50 and 35 My ago is equivalent to about 1.7 “halving” (in order words, the reverse would be about 1.7 doublings). Over that period T appears to have changed from about 13 to 5 degrees C relative to the reference T of today – a total change of about 8 degrees C. The temperature being shown here for the Ocean Bottom and the corresponding variations in average global T might be high or lower. Hansen et al. assigned this uncertainty of conversion to be about +/- 50%. Going with the 8 degree value (no conversion factor used), we come up with very rough estimate for CO2 sensitivity of about 5 degrees C with a conservative estimate of the net uncertainly of about +/- 3 degrees C.
Next it is informative to consider what type of CO2 Sensitivity this is. Is it closer the the fastback or slow feedback types discussed previously in our analysis of the ice core data? The answer is clear. During the period between 50 and 35 My ago, the Earth was a “water world” – there was no sheet ice on the planet – as there was increasingly after 35 My ago. Therefore the Sensitivity term we just estimated is of the fast feedback type for which the feedbacks of water vapor and clouds are dominant. There was no ice and its effect on albedo that needs to be consider over this period.
Now note that that the ice core data suggested that the magnitude for the fast feedback sensitivity of CO2 was about 3 degrees C, Thereby being in agreement with the rougher estimate of the same parameter just deduced from T and CO2 changes occurring between 50 and 35 My ago.
 The Paleocene-Eocene Thermal Maximum (RETM).
Note the slight peak in T seen in the year 54 My ago. This is called the RETM and is thought to have been caused by a sudden huge burst of methane thrown into the atmosphere at that time. The cause of this is generally thought to be the conversion of solid “methane-hydrates” to gaseous methane which in turn was caused by the increase in ocean bottom T occurring at that time. (Note this form of methane-containing ice is what formed and then caused the pipes to block last summer in attempts to capture the oil and methane escaping from the damaged Gulf Coast well head).
When the CH4 that entered the atmosphere during the RETM, it was oxidized quickly (within a few decades ) to CO2 thereby providing us with a unique and natural “experiment” from which to learn. One thing we learned is that is appears to have taken about 150 millennia in order to remove the excess CO2 that the RETM punched into the atmosphere. This observation is in good agreement with the very long lifetimes for EXTRA CO2 that many modelers presently claim in simulations of this process.
Another point concerning the RETM becomes clear when we consider the fact that the Earth is now literally loaded with methane hydrate deposits in their coastal sea bed. If the oceans at allowed to heat up sufficiently (and we don’t know how high a T this would require) those methane hydrated deposit will release. This event would indeed constitute what is known as a “tipping point”, at least, or even a “point of no return” as generally defined to represent two different levels of distinctly “bad news”.
 Speaking of “tipping points”, the major point of Hansen’s et al.’s paper is to show that we have already passed one with 392 ppm CO2 in the atmosphere.
He argues that the Forcing associated with that level of CO2 is moving us in the direction of an ice free world and that level of forcing – even if not raised further increased by business-as-usual putting 2 ppm additional CO2 into the atmosphere every year – has to be reduced “quickly” before the initial effects of sheet ice changes are overcome. More specifically he argues that we have to get down to 350 ppm in order to get safely away from that tipping point. Since Hansen et al. have related all of this in detail in there paper, I will stop there.