A couple of posts ago I went into considerable detail on what CO2 being “logarithmic” means and how, combined with the exponential increase in radiance from the earth warming up, we arrive at very little additional warming even if we increase CO2 emissions on a massive scale. But those are just my amateur musings, right? It’s not like this is what the IPCC scientists are saying, and after all, they’re real scientists. So let’s look at the matter again with as much of the explanation as possible drawn from the IPCC literature itself.
For brief review, the commonly quoted figures from the IPCC are that pre-industrial levels of CO2 were about 280 ppm (parts per million). Their estimate is that doubling of the CO2 concentrations in the atmosphere will raise temperatures directly by about 1 degree and that feedbacks from water vapour will add another 1 to 3.5 degrees. The consensus estimate between the various scientists is a total of 3 degrees. Since 1920 (the date most often used as the beginning of the industrial age) CO2 concentrations have risen about 40% and temperatures have in fact increased, but by far less than what the IPCC projections suggested. Let’s put that aside for now and assume that the IPCC projections are accurate.
The IPCC talks about “forcing” and temperature change in the context of CO2 doubling because they accept that CO2 is logarithmic. Every doubling of CO2 has half the effect per 100 ppm of CO2 of the one before it. If we put this on a graph it looks like this:
But that’s just my graph. What about the IPCC graphs? They show the same thing, though it is presented in such a fashion that it doesn’t jump out at you right away. Here’s the graph from http://www.ipcc.ch/publications_and_data/ar4/wg1/en/figure-10-26.html of the IPCC AR4 report. It’s a bit of an eye chart so here’s the quick explanation. IPCC created a number of potential unmitigated scenarios. These are essentially a variety of economic forecasts with predictions for each of them in terms of CO2 emissions provided no formal climate mitigation policies are enacted. All of the various greenhouse gases in addition to CO2 are estimated (they too are logarithmic). The graphs at the bottom show their combined “forcing” in watts per meter squared, and the expected results. The first column is the most likely scenario based on current emissions:
The logarithmic curve is easily visible in each scenario. But cutting it off at the year 2100 is deceptive. If we were to extend that curve out, we would see that additional CO2 over about 600 ppm just doesn’t make much difference:
Even with CO2 shooting upwards, temperature change falls off. Keep in mind that the scales in the three graphs are different. CO2 is being measured in 100’s of parts per million. Our last century of fossil fuel consumption only resulted in a 100 ppm increase. Meanwhile, the watts per 100 ppm of CO2 keep falling. That scale only goes from 0 to 10. The temperature increase in degrees per 100 ppm of CO2 falls even faster because the amount of heat any body gives off increases exponentially with temperature, so it takes an increasing number of watts to get any temperature change at all. That temperature scale is only 0 to 6. Consider what this all means in terms of the worst case scenario compared directly to the best case scenario:
In the IPCC’s worst case scenario, exponential economic growth and fossil fuel consumption results in nearly 1,000 ppm of CO2 in the atmosphere by the year 2100. This implies increasing CO2 in the atmosphere six times as much this century as last century, and results in an over all world wide increase in temperature of 4.5 degrees. By 2100 in this scenario, our daily consumption of oil and equivalent fossil fuels would be on the order of 12 times as much per day as it is now. In the best case scenario, we would arrive in 2100 with about 550 ppm of CO2, but we still get a full 2 degrees of warming despite adding less than a third of the CO2 (we’re at 380 ppm right now so getting to 550 takes another 170 while getting to 1000 takes 620).
The numbers may seem a bit confusing because they don’t quite fit with the doubling of C02 standard narrative of a 3 degree increase. The standard narrative is based on pre-industrial CO2 levels of about 280 ppm and temperature at that time which was 0.5 to 1.0 degrees lower. The figures in this graphic extrapolate from current CO2 levels of about 380 pp and plot temperature increases versus the 1980 to 2000 mean. In rough summary, an additional 170 ppm in the atmosphere by 2100 raises temperatures by 2 degrees over where we are already. An additional 600 ppm adds almost four times as much, but raises the temperature 4.5 degrees, only 2.5 degrees more than that.
What scenario trajectory are we on? We can see the CO2 concentrations being measured by NASA on line:
We’re about on track for the best case scenario based on the last 40 years of data. Of course we expect that our economy will grow, we expect that 2nd and 3rd world countries will also industrialise, and so the rate of increase will likely accelerate, though the worst case scenario seems very unlikely. The IPCC of course is recommending strong mitigation strategies either way. Just as they created a number of likely scenarios without mitigation, they created six scenarios with mitigation. They document these in Figure 5.1 of the AR4 Synthesis report (as well as other instances throughout AR4) as follows:
Unlike the first set of figures, these are calculated against pre-industrial temperatures rather than the 1980 to 2000 mean, making them a bit hard to compare. For rough comparison, let’s simply subtract 1 degree from each of them to arrive at a number that can easily be compared to current CO2 rates and the more recent 1980 to 2000 temperature range scenarios. Using scenario I to illustrate, it calls for a temperature increase of between 2.0 and 2.4 degrees over pre-industrial, about 1.0 to 1.4 degrees over 1980 – 2000.
In order to achieve that, the IPCC estimates that we would need to cut our fossil fuel consumption by 50% to 85% by the year 2015, just five years from now. Keeping in mind that since the 2nd and 3rd world countries are starting to industrialize and their consumption will grow accordingly, that means that 1st world countries would have to cut consumption even more to accommodate them. Or else subsidize their use of uneconomical alternatives through massive carbon credits.
Such a massive fossil fuel reduction world wide seems unlikely without collapsing the world economy. Scenario V on the other hand calls for consumption to peak in 50 years or so at 25% to 60% higher than current rates. That yields a temperature increase of 4.0 to 4.9 degrees over pre-industrial, or 3 to 3.9 degrees above the 1980 to 2000 mean. Yet scenario VI sees consumption peaking late in the century with consumption up 90% to 140%, double that of scenario V, but only adds another 1.2 degrees to the total. CO2 is logarithmic and these IPCC estimates reflect that. The worst case unmitigated scenarios are very little higher than the most of the mitigated scenarios! Of the mitigated scenarios, only the last three are remotely possible without devastating the global economy, and they only result in a temperature increase 1 to 2 degrees less than the worst case unmitigated scenario. Can another 2 degrees (or even 3) be that catastrophic?
Edit May 27 paragraph and graphs added:
Here are the unmitigated best and worst case scenarios compared to the IPCC mitigated scenarios. The scales are different and the unmitigated curves are calculated against 1980 to 2000 temperatures while the mitigated scenarios are calculated against pre-industrial, so be carefull how you compare them:
In brief, our current trajectory, according to IPCC data since 1940 (see above), gives us 3 degrees of warming over pre-industrial by the year 2100. For mitigation scenario III above, if we cut emissions by 30 % starting this year we will save a whopping 0.2 degrees by 2100. To demonstrate just how small a number that is, let’s consider not the 0.2 degrees we would save by cutting our economy to shreds, let’s instead consider what the worst case scenario to see what it would actually look like.
End May 27 edit
For starters, we have to understand how the IPCC arrives at its various estimates, and then put them in their proper context. This is not an effort to discredit the IPCC numbers, it is an acceptance of them at face value. Despite the fact that I think they are exagerated, I will use them as stated to demonstrate the little value there is in the IPCC proposed course of action.
For starters, the IPCC refers to sensitivity in the range of CO2 doubling resulting in an increase of longwave radiance of 3.7 watts per meter squared ( 3.7 w/m2). This in turn results in direct warming of the earth, based on theoretical physics called “black body” and based on formulas by Stefan-Boltzmann of 1 degrees C. A detailed explanation of Stefan Boltzmann can be found at
Positive feedbacks from water vapour are claimed to increase this number to between 2 and 4.5 degrees, with the median consensus estimate being 3 degrees. But a Stefan-Boltzman calculation against the mean surface temperature of the earth, 15 degrees C, yields a change of 1 degree in the region of 5.5 watts, not 3.7. The reason for the discrepancy is that the IPCC calculates sensitivity against the effective black body temperature of the earth, which is different from the surface temperature. Since the earth is surrounded by an atmosphere which is a lower temperature, this makes sense. The effective black body temperature of the earth as a whole is more like -20 C. Interestingly, that’s about the temperature at 14,000 feet above sea level according to NASA’s AMSU-A satellite:
(you will need Java installed and then click on global atmospheric temperature trend and select channel 5)
So here we have our first Aha! moment. The three degrees for CO2 doubling is calculated at a much colder temperature than the surface of the earth. The same amount of additional energy flux (power) that would heat the 14,000 foot layer by 3 degrees only adds about 2 degrees at earth surface. Of course that’s based on the 14,000 foot layer being an average of -20 C and the surface being about +15. The problem is that there is nothing average at all about the earth’s surface. It is much warmer at the equator than at the poles. Summers are much warmer than winter. Mid day is (usually) warmer than night time. If an additional 3 degrees (or 4 or 5) was evenly distributed, that would be a gigantic increase. But it is not evenly distributed by day, season, or latitude. To understand the real impact, we need to not only understand the average temperature increase, but how it will be distributed.
We frequently hear words like “polar amplification” and references to the arctic regions heating up several times as fast as the rest of the planet. These things are true. The various surface station temperature records reflect this as do the satellite temperature records. Here is the northern hemisphere temperature record since 1880 according to NASA/GISS and broken down by latitude:
What we see right away is that northern hemisphere temperatures have increased by about 1 degree since 1880. But arctic region temperatures are up by 2.5 degrees. With all the excitement about the increase in arctic temperatures and the potential impact on the polar ice cap, we’ve forgotten that the average temperature increase of just 1 degree for the northern hemisphere is not only lower, but that the temperate zones and equatorial regions must be lower still in order for the average to be one degree. As we look at the graph we see that this is true. The increase since 1880 in the equatorial region is only about 0.7 degrees. So now we arrive at our second Aha! moment. Not only is the estimated temperature increase for the earth surface lower than that for the earth as a whole, but the warmest parts of the earth will see the least additional warming, and the coldest parts the most. This is precisely in agreement with APCC AR4 observations in chapter 9 of Working Group 1
Both of the graphs present the same result for two different time periods of observation. Arctic temperatures go up more than the average, temperate zone and equatorial temperatures less. If we return to the previous discussion of Stefan-Bolzmann, the physics upon which the IPCC sensitivity calculations rest, we see that this is exactly what we would expect. The following are sample calculations to illustrate the point:
P=5.67*10^-8*T^4 is the Stefan-Bolzmann formula where T is temperature in degrees K.
Arctic average temperature -20 C => +10 watts => +2.5 degrees
Equatorial average temperature +25 C => +10 watts => +1.6 degrees
We can conclude from this that Stefan-Boltzman explains some, but not all, of the lower temperature increases observed when comparing Arctic to Equatorial. Just as we expect CO2 doubling to result in a higher temperature increase at 14,000 feet than we do at earth surface, we also expect a higher temperature increase at the poles compared to the equatorial region. But that is still not the complete story. Earth’s temperatures also fluctuate by season, and by day. If we go back to NASA/GISS land data since 1881, they provide northern hemisphere temperatures broken down by season. They are not, unfortunately, also broken down by latitude, but nonetheless we can see that the same relationship applies. The cold temperatures increase more than the high temperatures:
Across the range of the graph, winter temperatures increase almost 2 degrees while summer temperatures increase by only one degree. The average temperature increase is somewhere in between. But this brings us to yet another Aha! moment. Since we already know that equatorial regions don’t fluctuate in temperature nearly as much as arctic regions, if we were to break this down by latitude, we would expect that winter temperatures in the arctic would fluctuate by an even wider ratio compared to summer. We don’t have NASA/GISS data to rely on in that regard, but we do have temperature data from DMI for the arctic 80N area since 1958
This allows us to look at the temperature fluctuations and see what cold years look like compared to warm years. The graphic below compares two of the warmest years, 2006 and 2007 to two of the coldest years, 1963 and 1964. It is very easy to see that in the coldest years, most of the change was in the depths of winter, and in the warmer years, that is also where the bulk of the temperature change occurred. To be fair, at the very top of the graph temperatures almost always converge with the annual mean almost exactly. This is because the top of the graph is just above 273 K, the melting point of ice. Once atmospheric temperatures reach that point, most of the additional energy goes into melting ice and there is no temperature increase until there is no ice left to melt. However, if we exclude the top 10% of the graph to get this issue out of the analysis, it becomes clear that almost all the temperature increases seen in the high arctic have come in the depths of winter where a small increase in energy flux results in a higher temperature increase, in keeping with Stefan-Boltzman.
Yet we are still not done understanding the meaning of temperature change in the context of “average”. We’ve already seen that the average temperature change means different things at different altitudes, different latitudes and different seasons. It also means different things from day time to night time. Depending on where you are, diurnal temperature ranges can vary from small to large. In the tropics where there is high humidity, the range is small. In a desert, the range can be very large. Without going into a tremendous amount of detail, let’s take a quick look at what a given level of forcing means in terms of a daily temperature swing. Consider a hot day in the north temperate zone with an average temperature of 20 degrees. The low might be 15 and the high 30 degrees C. But the peak of 30 lasts only a few hours while the low will be spread out over most of the night time period with some of the morning and evening mixed in. Considering Stefan-Boltzman once more, the same physics that is reflected in altitude, latitude and seasonal variance, an increase of 10 watts/m2 (requiring over 1000 ppm of CO2 to achieve) would mean that the low for the evening would go up by 1.8 degrees, but the high during the day would only go up 1.6 degrees.
To review, Stefan-Boltzmann’s equations and the logarithmic nature of CO2 are confirmed by the major temperature records and by all the evidence and projections supplied in the IPCC AR4 report. They all lead to the same basic conclusions. The bulk of all warming from a strictly temperature perspective should happen, and is happening, in the coldest parts of the planet at the coldest times of the year. Put in that context, we have a very different understanding of what the worst case scenario, a rapid and unmitigated economic expansion of the global economy means, in terms of the IPCC’s estimate of a 4.5 degree temperature rise over current levels. If we consider that 4.5 degrees is calculated against the mean radiative black body temperature of the earth at 14,000 feet, we must first convert that to the mean surface temperature at 15 degrees. This translates into a surface temperature increase of 3.2 degrees. If we further break that up by latitude and season, we get very different numbers. Let’s consider three scenarios. A tropical zone with average temperature varying seasonally from +25 to +40, a south temperate zone with seasonal variation from 0 to +30, a north temperate zone with seasonal variation from -20 to plus 25 and an arctic zone from -50 to +10. Here’s what we get:
If we look at a given zone we see that the tropics experience the least warming and also the least variance. The warm season goes up 2.7 degrees, the cool season slightly more at 3. At the other end of the spectrum though, the arctic warm season goes up 3.5 degrees, not much more than the tropics. But the cold season increases a whopping 10 degrees, from -50 to -40.
Here is a bar graph showing all the zones and their winter temperature change versus the summer. Even in a worst case scenario, a massive increase in our fossil fuel consumption, summer temperatures don’t go up by the quoted 4.5 degrees. They go up less than 3 degrees for most of the planet. Almost all of the temperature increase results in warmer winters in the most bitterly cold parts of our planet.
So again we have an Aha! moment. Even at the bizarre level of world economic growth that would be required for us to reach the IPCC worst case scenario, the conclusion we should be coming to is not that the planet will somehow incinerate and kill us all. The conclusion should be that we will see somewhat warmer tropics and slightly warmer summers across the planet, but much, much milder winters. The 2.5 degrees of warming seen in the Arctic over the last century has been mostly in the winter, and as a consequence, the polar bear population is thriving. Surviving the summer is not their problem. Surviving the winter is. 2.5 degrees of warming has helped them survive the winter, but made little difference to their summers.
If we were to choose a more reasonable growth expectation like a 1% year over year increase in CO2 levels, we would arrive at about 660 ppm by the end of this century which the IPCC suggests would be a temperature increase of about 3 degrees over the 1980 to 2000 mean, which is still a higher number than the most likely scenario from the IPCC of 2 degrees. Using the ideal black body calculation against a three degree rise from 255 K, we get 11.7 w/m2 and we can do the chart again to see how 660 ppm stacks up:
In this much more realistic scenario, with no mitigation, we arrive at fossil fuel consumption over double our current rates by the end of the century, and put almost three times as much CO2 into the atmosphere as we did in the previous century. While an additional three degrees still sounds alarming on the surface, the same rules apply. We would expect only 2 degrees or less in the summer, the bulk of the increases would be experienced mostly as milder winters. Even the hottest days will be experienced more as warmer evenings than as high mid day temperatures.
We could take this analysis to another level still. Consider that in northern areas, winters are long. If you get far enough north, it is pitch black for months at a time. Winter can be eight months long leaving only four more for spring, summer and fall to split between them. If the temperature goes up 10 degrees in winter, the average for the year would be met with an even smaller temperature rise in the summer than what was calculated above. The same holds true for night and day. Even when sunlight is evenly divided between day and night, the peak temperature is brief, similar to the DMI graphs at the beginning of this article. As a consequence the heating during the cool part of the day takes up a larger portion of the day, and the average is met with less peak temperature rise. I like math, but that level of detail I’m not excited about. If you’ve followed along this far, you get the idea.
The bottom line is that if we review the worst case unmitigated scenario, we only save one to two degrees against any of the scenarios that are remotely practical. If we then take that two degrees and distribute it by latitude and by season, we find that we will have accomplished almost nothing. Instead of +40.6 on a very hot day in the tropics, it will be +40. A nice summer day in the north will be 15.9 instead of 15. And instead of -36 in the middle of winter it will be -40. And gasoline will be $22.00 per gallon.
My critics will at this point say I have left some things out and I have. The temperature model I have presented is not valid if one takes into account snow melt. In my example of the Arctic with a -50 winter and a +10 summer, this would imply snow melting and much of the additional w/m2 would go into driving a state change (from snow to water) rather than a temperature change when spring arrives. This is a fair criticism and modifying these formulas to account for that is a whole study unto itself. The point however, is that the bulk of the temperature change comes in the depths of winter, and a winter at -40 instead of -50 is certainly not catastrophic to our biosphere. For northern temperate zones, the snow will still melt, it will just melt faster, summer will be a bit nicer and winters will be a lot milder. Would the ice caps and glaciers melt? There is no doubt that they would be impacted by any warming at all, but let’s note that the polar ice cap doesn’t melt any faster at -40 than it does at -50. In addition, the IPCC predicts considerably more precipitation, so the question becomes, does the relatively small temperature increase in the summer melt season (which is very short in the first place) off set the increased snowfall in the winter (which is still long)? I can only observe that despite large temperature increases of 2.5 degrees over the last century, ice seems within normal bounds at both the arctic and Antarctic, and IPCC predictions of sea level rise have fallen far short of estimates. You can check Arctic sea ice extent here
and you can see Antarctic sea ice extent here
The other two objections regard rainfall and drought due to changing climate patterns, and increased extreme weather. I will do my best with the first objection, and I will put the second to rest rather forcefully.
The IPCC AR4 report in fact includes projections for increased rainfall. Rainfall pretty much has to increase given that the whole notion of 1 degree of CO2 forcing becoming 3 degrees due to positive feedbacks is based on substantial increases in atmospheric moisture. That does not mean however that some areas won’t get less rain and some more. The AR4 report takes the trouble to predict both temperature and rainfall by latitude:
As can be seen from the chart, The IPCC AR4 report suggests that precipitation will increase for most of the planet with a few narrow latitude bands seeing a few percentage points less. How accurate is this? I’m not the one to ask, but again, let’s look at the worst case scenario. The areas of reduced rainfall are limited. The great droughts of the 1930’s were followed by an extended cooling period until the late 1960’s. The warming since then has surpassed the temperatures of the 1930’s, but the droughts have not returned, so they (or those specific ones in any event) were not driven by warmer temperatures. True, additional precipitation could also lead to flooding and other problems. So much of what is in the IPCC AR4 report is factually accurate, but presented to be more dramatic than it is. I don’t know if that is the case for precipitation forecasts, but I will make this observation. We are not animals. We build houses to control the climate within them, we build damns to hold the water where we need it and we irrigate where there isn’t enough. Animals run away or die when confronted with change. We are humans and we have a much broader range of choices (almost all of them enabled by fossil fuels). If precipitation sky rockets I think few countries will wring their hands. They’ll be too busy building hydro electric damns to capture the cheap power.
I will close with a discussion of extreme weather events. The IPCC narrative is that a warmer planet implies a larger amount of energy stored in various systems. If an extra 3.7 w/m2 is being retained on the planet due to CO2 doubling, plus 7.4 w/m2 more from water vapour feedback, it by default must be stored somewhere in the system. Since there is more energy in the system as a whole, there is more potential for storms, hurricanes, cyclones and so on to occur and draw on all that extra energy, resulting in more frequent and more intense weather events. Of all the distortions and misrepresentations contained in the various predictions for our climate, this one is perhaps the most troubling. Yes there is more energy stored in the system, but the manner in which it is stored suggests that extreme weather events will decrease, not increase.
Energy can be stored, but for it to move there must be a difference in potential. If you have two lakes with water in them, but they are at the same elevation, water will not flow between them. It doesn’t matter if the lakes are one kilometre across or ten kilometres. It doesn’t matter if they are connected by a garden hose or an aqueduct. One lake must be higher than the other for water to flow. Wind doesn’t blow unless there is a pressure difference between two areas. Hook two fully charged car batteries in parallel and nothing will happen. In parallel the positive terminals are connected to each other and the same with the negative terminals. Since the voltage potentials are the same, nothing happens. If you connect them in series, positive to negative and then the second positive to the first negative… I am warning you not to do this. The sparks could well blind you, you could start a fire, and if you actually manage to get a good connection, your jumper cables will melt and weld themselves solid. When there is a large difference in potential energy, stuff happens.
Weather in the short term and climate in the long term are both driven by the same thing. There are natural processes that create energy potential differences. The earth spins, heating up each day and cooling off each night. This causes convection as hot air rises and pulls cold air in below. It causes pressure changes which drive wind. It causes water to evaporate which winds up as rain that fills lakes that flow into rivers. Every single feature there is that we call weather, is driven by natural processes that create differentials in energy potential which deplete themselves as anything from a breeze to a cyclone to a hurricane. Our long and short term weather is driven by energy differentials that cause circulation of energy from the high temperature tropics to the poles:
I have just spent the last several pages demonstrating via the IPCC’s own data, theory, and published reports, that the arctic zones will heat up more than the tropics, that winters will heat up more than summers, and that nights will warm up more than days. I’ve confirmed with the NASA/GISS temperature records that these things are true, and the IPCC has imbedded that very conclusion in many of their graphs and calculations. In other words, while there may be more energy in the system, the energy potential difference is diminished by warming. From night to day, from latitude to latitude, and from season to season the theoretical physics and the observed results show that the end result is less temperature differential daily, seasonally and geographicaly. As those are the very things that drive weather, we must conclude that extreme weather events are less likely, not more.
May 27 edit
Observation bears this out. Hurricane frequency and cyclone intensity have been in decline despite warming world temperatures and increasing ocean heat content:
end May 27 edit
Given the opportunity to vote for climate change options, I shall choose the one that provides for fewer extreme weather events, milder winters, more fresh water, bigger crop yields and more arable land farther north and at higher elevations. On a really hot day I will run an air conditioner, and if need be a diesel generator to run that. The CO2 is good for the crops. An extra degree in summer won’t hurt me or the rest of the biosphere in any meaningful way. 40 below on the other hand tends to wear on one as one ages. Even the polar bears are on side.