Does the logarithmic nature of global warming invalidate climate change claims?

Question

NOTE
It is rather unfortunate that I initially omitted the crucial part of the article I linked below (because the wording was stilted and confusing), and I was rather imprecise in my own claims. What I am specifically asking about is the two degree increase in overall earth temperature cited by most climate change experts which, if the claims of the article I cited were true, will never be reached.

I'm not asking about severe weather events, nor am I (or the article) claiming that global warming does not occur.

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According to The effectiveness of CO₂ as a greenhouse gas becomes ever more marginal with greater concentration:

According to well understood physical parameters, the effectiveness of CO₂ as a greenhouse gas diminishes logarithmically with increasing concentration and from the current level of ~390 ppmv, (parts per million by volume). Accordingly only ~5% of the effectiveness of CO₂ as a greenhouse gas remains beyond the current level.

This inconvenient fact is well understood in the climate science community. It can be accurately modeled using the Modtran program maintained and supported at the University of Chicago.

The logarithmic diminution of the effect of CO₂ is probably the reason why there was no runaway greenhouse warming from CO₂ in earlier eons when CO₂ levels were known to be at levels of several thousands ppmv.

Remarkably, IPCC Published reports , (TAR3), do actually acknowledge that the effective temperature increase caused by growing concentrations of CO₂ in the atmosphere radically diminishes with increasing concentrations. This information is in their report. It is well disguised for any lay reader, (Chapter 6. Radiative Forcing of Climate Change: section 6.3.4 Total Well-Mixed Greenhouse Gas Forcing Estimate).

Although the IPCC tacitly acknowledges that this crucial diminution effect with increasing concentrations effect exists, it certainly does not go out of its way to emphasise it. Like the Medieval Warm Period, that they attempted to eliminate with the Hockey Stick graph in 2001, the panel knows that wide public knowledge of the diminution effect with increasing CO₂ concentration would be utterly detrimental to their primary message.

From the present concentration of atmospheric CO₂ at approaching 400 ppmv, only ~5% of the effectiveness of CO₂ as a Greenhouse Gas remains. This can only give rise to a maximum of a further of ~+0.21°C. Thereafter beyond 1000+ ppmv the effect of increasing levels of CO₂ can only ever be absolutely minimal even if CO₂ concentrations were to increase indefinitely.

If this is true, then global warming is a self-regulating phenomenon; that is, it will, in effect, level off. And it will do so before reaching the levels that the climate change advocates say will cause catastrophic problems.

Is this true? And if it is, why doesn't it completely invalidate the claims of climate change advocates?

Answer 1

The claim that "... the effectiveness of CO2 as a greenhouse gas diminishes logarithmically with increasing concentration and from the current level of ~390 ppmv, ..." and that "inconvenient fact" is "well disguised for any lay reader" is one of the more ridiculous climate skeptic claims I've seen. The main metric used by climate scientists to describe the effect of carbon dioxide is called "climate sensitivity". Equilibrium climate sensitivity is the amount of warming we expect to see resulting from a doubling of atmospheric CO2. This directly tells you (provided you understand logarithms) that there is a logarithmic relationship between carbon dioxide concentrations. If ECS is 2°C per doubling that means if we raise CO2 from the pre-industrial equilibrium concentration (i.e. up to 560ppm from 280ppm) then we would expect to see a 2°C temperature rise once the climate system had fully re-equilibriated. However to get the next 2°C rise, you would need to double the atmospheric CO2 again (i.e. up to 1120 ppm) and to get a third 2°C increase you would need to double it again, up to 2240ppm.

Note that log₂(280) = 8.1293, log₂(560) = 9.1293, log₂(1120) = 10.1293 and log₂(2240) = 11.1293, so if we have y=c*log₂(x), each time we double x, y increased by c, which is why expressing climate sensitivity in °C per doubling is just saying that the relationship is logarithmic in a way that ought to be clear even to someone who doesn't know what a logarithm is. The constant c in this equation is ECS, if you use a log to a different base (e.g. ln or log₁₀) then the numeric value of c will be different, but the relationship is the same, it is just easier to explain in terms of log₂. This is hardly rocket science!

Clearly, there is a "diminishing returns" effect here, but (i) far from hiding it, the climatologists are explicitly pointing it out in a form more easily understood even than logarithms (ii) to get a 2°C rise, you would only need to double CO2 levels from the pre-industrial level of 280ppm, and we have raised it to 400ppm already, so this is far from impossible, given that estimates of ECS are around 1.5-4.5°C per doubling.

"there is high confidence that ECS is extremely unlikely less than 1°C and medium confidence that the ECS is likely between 1.5°C and 4.5°C and very unlikely greater than 6°C." IPCC AR5 WG1, page 924

Do a google scholar search for "climate sensitivity", or look for it in the index of the IPCC reports and read the relevent sections, far from being hushed up, climatologists talk about this a lot.

Now of course the greenhouse effect is self-limiting, for a start for that not to be the case we would require the Sun's luminosity to be infinite (as CO2 affects the Earth's radiative balance, but ultimately the energy comes from the sun), or equivalently to allow an infinite timescale (which isn't possible either). The Stefan-Boltzman law that says the power radiated per unit area rises with the fourth power of temperature is also a strongly limiting factor (but that doesn't rule out temperatures being very high due to the greenhouse effect, e.g. Venus, so that isn't much consolation ;o).

In short, a logarithmic relationship does not rule out a 2°C rise in global mean surface temperatures, double atmospheric CO2 concentrations a sufficient number of times and it will happen (once the radiative balance is restored, which doesn't happen immediately). How many doublings this requires depends on the equilibrium climate sensitivity, and according to current scientific understanding (as articulated by the IPCC AR5 WG1 report) the answer is most likely one doubling (as the most probable value is a little over 2°C per doubling), but it could be less but it is very unlikely that the number is two or more doublings (as ECS below 1°C has been essentially ruled out).

Answer 2

Yes it is logarithmic (although relative to amount of CO₂ in a sample volume of gas, not its concentration). No that doesn't invalidate climate change. If you want to read a detailed explanation for both answers, please see Skeptical Science - Is the CO₂ effect saturated?.

The mistaken idea that the Greenhouse Effect is 'saturated', that adding more CO₂ will have virtually no effect, is based on a simple misunderstanding of how the Greenhouse Effect works.

This is a summary, but I leave out some details due to space constraints (and this post is already pretty long).

It is true that the effect of CO₂ is logarithmically related to the number of atoms of CO₂ in a given volume of gas. However, this misses the critical fact that the amount of CO₂ varies with altitude due to changes in air pressure. A given volume of gas at low pressure will have fewer CO₂ atoms in it than an equal volume of gas at a higher pressure, even if the concentration is the same. The end result of that fact is that what directly causes the globe to warm isn't the increase in CO₂ levels at the ground, but rather the increase in CO₂ levels in the upper atmosphere, where the CO₂ levels are much lower and thus small changes have a much larger effect.

More specifically, what really causes global warming is an increase in the altitude at which the energy is radiated into space. Energy arrives at Earth from the sun, where it is absorbed by the land and air. This causes them both to heat up. Warmer materials radiate energy, which heads back out to space. Some of that is absorbed again by the air, which then heats up further, radiating more energy. This continues until you reach the top levels of the atmosphere, where there is so little gas to do any absorbing the energy radiated towards space escapes into space. CO₂ increases the amount of energy absorbed by the atmosphere, but does not change the amount radiated.

The amount of energy radiated is inversely related to the altitude at which it is radiated. This is because higher altitudes are colder, and colder air radiates less energy. So the higher the altitude where the energy escapes into space, the less total energy is released, and the more total energy is trapped, increasing temperatures. The altitude that determines the amount of energy lost is called the effective radiating level (or some variant of "effective (radiation|radiative|emission) (level|height|altitude)").

Increasing CO₂ levels raises the effective radiating level. This is because more energy is being absorbed at a given altitude, and thus the higher you need to go before the energy can escape. And since those higher altitudes are colder, less energy escapes, warming the planet. And at those high altitudes, not only is CO₂ not saturated, it is at low levels where small changes are particularly significant.

This isn't just a guess, there are specific things you would expect to see if this happens. One key one is stratospheric cooling. Because less energy is being radiated into space, the highest levels of the atmosphere are also receiving less radiation (because that energy is being trapped at lower levels, as I explained in the previous paragraph). So we would expect those levels of the atmosphere to be cooling while lower levels warm. That is exactly what we see.

Further, we can use satellites to directly measure the outgoing radiation to see if it matches what we would expect from CO₂ blocking energy from escaping. All molecules have a particular pattern of how much light they absorb at a given frequency, their absorption spectrum. If CO₂ is really preventing energy from escaping, this should show up as a decreased in energy escaping that matches CO₂'s absorption spectrum (because CO₂ is blocking that energy). This has been checked, and it is exactly what we expect from CO₂-caused warming.

Answer 3

No, it is not true that it invalidates climate change claims, or the need to limit further increases in CO₂ concentration specifically as it relates to warming (we can ignore stuff like ocean acidification for this question to keep from wandering too far abroad). First of all, let's look at the source. Is the person an objective scientist, making claims and analysis from professional expertise, or from actual research? No.

The source cited in the question is a professional, paid climate science denier. He's best known for creating and hyping faux controversies by misstating facts relating to emails between climatologists and for publishing scientifically invalid misinterpretations of NOAA data. He is paid by the Heartland Institute, which is a phony industry "think tank" paid for by industrial polluters. In this case he appears to be doing the same type of spin on IPCC findings.

SourceWatch: Anthony Watts

But being a paid shill does not, in and of itself, mean he's wrong. Having a history of getting the science wrong does not mean, in and of itself, that he's getting it wrong here. It would lead one to be less likely to give the benefit of the doubt, but if he's wrong, there should be a relatively straightforward explanation of why and how he is wrong.

Here's an explanation of what's wrong with the article that Watts is citing and quoting:

Ed Hoskins' pseudo-science claptrap brings out all the nutters at WUWT

Before going any further, it will pay to go back to the logarithmic relationship between atmospheric CO₂ and global surface temperature. In short, what it means is that for every doubling of atmospheric CO₂, the surface temperature will rise by the same fixed amount, between 1.5°C and 4.5°C, probably by around 3°C over the medium term (centuries). Many deniers think it means that for every doubling of CO₂, temperature will rise much less, but that's wrong. It will go up by roughly the same amount when CO₂ doubles (at foreseeable levels). The typical science denier doesn't do maths.

Ed's article is all over the place like a dog's breakfast, but his main very wrong message is that CO₂ can rise to 1000 ppm without any bad consequences. That's just not so.

Ed's argument is that because the effect of CO₂ on temperature is logarithmic, it will only have a tiny impact as it increases. The first part is true. The relationship is logarithmic. However the second part is relative. What might seem a "tiny impact" for, say, a diurnal temperature variation would have an enormous impact if it were an increase in average surface temperature over the entire world. From our perspective, the impact on climate and ocean acidification and rising sea levels will be hugely damaging as more and more CO₂ is emitted.

A rise in atmospheric CO₂ from pre-industrial times (say 280 ppm) to 1000 ppm would mean an increase of 3.5 times. That would mean a rise in global surface temperature of somewhere between around 2.8°C and 8°C degrees or more.

According to an analysis by Steven C. Sherwood and Matthew Huber, a rise of 7°C in average surface temperature would result in a wet bulb temperature of more than 35°C in much of the world, which would stretch our physiological limits beyond tolerance. We wouldn't be able to maintain our core body temperature and would overheat. People die from heat stroke every year as it is, without a wet bulb temperature of 35°C. We cannot survive temperatures above a certain level and humidity. We can't sweat it out.

I wondered how Ed Hoskins came up with his magical thinking. He went back to the third assessment report of the IPCC for some reason, back thirteen years to 2001. He wrote:

quotes the same passages as the OP here

He thinks that something "is well disguised". Well, it looks as if it is so "well-disguised" that Ed himself cannot understand it. Thing is, it doesn't "radically diminish". He wrote about the IPCC publishing views about the effect of CO₂ up to 1000 ppm, but doesn't show it. Instead he shows charts from denier Steve Milloy who admits that what he writes is junk science. (That's the name of his blog.)

So does the IPCC publish views about the effect of CO₂ up to 1000 ppm? There were only four mentions of the words "1000 ppm" in the latest IPCC report, and three of them referred to the same period in Earth's history, the Early Eocene Climatic Optimum. (The other was a reference to stomata.) Here are two of them:

During the Early Eocene (52 to 48 million years ago), atmospheric CO₂ concentration exceeded ~1000 ppm when global mean surface temperature was 9°C to 14°C higher (medium confidence) than for pre-industrial conditions. [IPCC AR5 WG1:TS.2.8 Changes in Carbon and Other Biogeochemical Cycles] The EECO [Early Eocence Climatic Optimum] represents the last time atmospheric CO₂ concentrations may have reached a level of ~1000 ppm (Section 5.2.2.2). There were no substantial polar ice sheets, and oceanic and continental configurations, vegetation type and distribution were significantly different from today. Whereas simulated SAT are in reasonable agreement with reconstructions (Huber and Caballero, 2011; Lunt et al., 2012) (Box 5.1, Figure 1d), there are still significant discrepancies between simulated and reconstructed mean annual SST, which are reduced if seasonal biases in some of the marine proxies are considered for the high-latitude sites (Hollis et al., 2012; Lunt et al., 2012). Medium confidence is placed on the reconstructed global mean surface temperature anomaly estimate of 8°C–14°C. [IPCC AR5 WG1: 5.3.1 High CO₂ Worlds and Temperature]

In other words, the last time when the atmospheric concentration was 1000 ppm or more was 52 to 48 million years ago and the global mean surface temperature was 9°C to 14°C higher than it was in pre-industrial times in this modern era. Does that seem like a tiny effect to you? Does it strike you as inconsequential that vast areas of land would become uninhabitable because the wet bulb temperature would be intolerable for humans?

In a nutshell, being logarithmic doesn't magically cap the upper bound. If we more than double the atmospheric CO₂ (currently around 400 ppm) to 1000 ppm, we will see more than the amount of warming stated in the question. And that ignores a lot of other factors, as well, but since the basic concept is wrong, we don't need to delve into that.

Answer 4

The first part of the claim is:

the effectiveness of CO2 as a greenhouse gas diminishes logarithmically with increasing concentration and from the current level of ~390 ppmv, (parts per million by volume). Accordingly only ~5% of the effectiveness of CO2 as a greenhouse gas remains beyond the current level.

Expressions using logarithmic functions have been published for radiative forcing and temperature.

For example in New Estimates of Radiative Forcing due to well Mixed Greenhouse Gases there is the approximate expression:

ΔF = 5.35ln(C/C₀)

where "ΔF" is change in radiative forcing and "C" is CO2 concentration.

However, contrary to the claim, a logarithmic function, such as ln(C), approaches infinity as C approaches infinity. There is no limit to the amount of forcing as C increases.

Secondly, it is immediately obvious that the above equation is just an approximation valid in a limited range, ln(C) approaches negative infinity as C approaches 0, ridiculously predicting zero CO2 concentration results in an infinitely negative amount of forcing.

A more detailed formula is available from Model Forcasts of Global Climate Changes at page 9360:

ΔT = f(C) - f(C₀)

f(x) = ln(1 + 1.2x + 0.005x² + 0.0000014x³)

C₀ = 315ppmv

where ΔT is change in temperature

The above formula is said to be valid up to 1000 ppmv, where upon a 2 °C increase relative to 1958 has already been exceeded. This model does not consider feedback mechanisms.