kw: analyses, greenhouse effect, climate crisis, carbon dioxide, logistic curve
Introduction
We are daily exhorted to worry about the climate, about "carbon pollution", about the "existential crisis" of "human caused global warming". As I have written elsewhere, before I was a teen I had learned how to analyze the greenhouse effect in the atmosphere of Earth caused by water vapor and carbon dioxide. Decades later I read that if the "windows" in the spectrum between the edges of the absorption bands of carbon dioxide were "closed", the total warming would be less than 4°C (7°F). Still later a series of "official" reports were issued, based primarily on computer modeling, making projections of the warming caused by increased carbon dioxide, with low, moderate, or high estimates of the temperatures that are expected. The reports are dire, the warnings are shrill. They are overdone.
This essay is not a quantitative analysis with lots of math or equations. It is conceptual, but, I hope, not simply "arm waving".
Greenhouse Gases
Water Vapor
In the past, one would see in the literature of atmospheric warming by the Sun a statement such as, "Without water in the atmosphere, the average temperature of Earth would be colder by 33°C or 59°F." This makes water vapor by far the most important greenhouse gas. We'll see more in a moment.
Carbon Dioxide
Once the infrared absorption spectrum of carbon dioxide was determined, a few scientists calculated how its concentration in the atmosphere might be adding to the greenhouse effect caused by water vapor. One of these was Svante Arrhenius. Late in the 19th Century he published his calculation that if the amount of carbon dioxide in the atmosphere were doubled (it was at that time about 300 ppm), average temperature of Earth's atmosphere would rise by between 1.5°C and 2°C (that's 2.7°F to 3.6°F).
Infrared Spectra
My first job, by which I worked my way through a couple of years of college, was performing infrared spectroscopy for a project funded by the Department of Defense. I became quite familiar with the way certain gases absorb and, when heated, emit infrared light. This image (one of many similar) shows the infrared absorption spectra of water vapor and carbon dioxide:
This chart, from an article in 2010 by Clive Best, shows the balance between solar radiation and terrestrial radiation. This time the wavelength scale starts at zero, so it includes visible and ultraviolet radiation. About 1/3 of the Sun's light is in the visible range; the cream-colored band in the image shows how it is divided up. The surface of the Earth also emits thermal radiation, at longer wavelengths, which we see in the right half. Simply put, if there were no absorption in the atmosphere, the blue "mountain" would mostly fill in under the blue curve of the three. The "blocked" radiation shows the greenhouse effect.
For clarity, three thermal infrared radiation curves are shown for different surface temperatures:
- Black: 210K = -63°C = -145°F, deep winter cold in central Siberia or Antarctica
- Blue: 260K = -13°C = +9°F, a cold winter day in Denver or London
- Lavender: 310K = 37°C = 99°F, just above body temperature, or a hot summer day in NYC
These three curves, and the red curve for the much hotter Sun, show theoretical emission from a "black body", which is a theoretically perfect absorber and perfect emitter. Just for fun, check out the lavender curve: If you get the flu and your temperature is just a couple degrees above normal, a spectrometer pointed at you would record peak radiation from your skin at about 9µm, with significant amounts in the range 5µm-22µm. To a spectroscopist, the range of wavelengths longer than 5µm, out to about 50µm, is longwave infrared, also known as thermal infrared.
Just below the red-blue section we find a combined spectrum for a generalized atmosphere ("Total Absorption and Scattering"), and then spectra for several gases, starting with water vapor and carbon dioxide. These two together produce most of the combined spectrum shown just above water vapor.
Look carefully at the rightmost absorption band for carbon dioxide. It mostly overlaps the major band for water vapor. This shows that the two gases do not act independently. When humidity is high, the differential effect of carbon dioxide is small, but in dry air, carbon dioxide has a stronger effect.
The other major absorption band for carbon dioxide, between 4µm and 5µm, is near the edges of the thermal radiation bands, so it has even less effect. It is little affected by the nearby band for water vapor.
Let's look briefly at the rest of the gases. I am disappointed that the creator of this chart chose to combine oxygen and ozone. Perhaps it was out of trust that most who read the article would know that the broad absorption at the far left, in the ultraviolet range, is for ozone, and the others are for oxygen. Anyway, it shows that oxygen, which makes up 21% of the atmosphere, is a mild greenhouse gas, while ozone, which is nearly all in the stratosphere, is a strong greenhouse gas, but only at high altitudes. Ozone's absorption of solar UV is the major reason that the upper stratosphere is warmer than the lower stratosphere.
Methane is next. It looks like a poor absorber, but that is because it occurs in very low concentration, less than two parts per billion (or less than 200,000 times the concentration of carbon dioxide). The fact that it shows up at all warns us that it will be a strong absorber if its concentration rises much. If an atmospheric sample had equal amounts of carbon dioxide and methane, the greenhouse warming by methane would be more than 80 times as much!
Nitrous oxide is also a strong greenhouse gas, but is present at very low concentration, about 300 parts per billion, or less than 1/1,000th the concentration of carbon dioxide.
Rayleigh scattering is a physical effect; the "gas" for this part is the combination of nitrogen and oxygen. A small proportion of light is scattered off the molecules of these gases, and the scattering is stronger for shorter wavelengths. It is the shorter wavelength visible light (blue), scattered from sunlight, that makes the sky blue. As a matter of fact, for any planet with an atmosphere, anywhere in the universe, unless the air is very dusty, the sky will be more blue than the star that is that planet's "sun".
What a Greenhouse Gas Does
Let us consider, for the moment, only water vapor in an otherwise "pure" atmosphere of nitrogen and oxygen. Sunlight heats the surface, which radiates thermal infrared. Much of this is absorbed by the water vapor, which heats the atmosphere. This heat also produces thermal infrared radiation, and to a first approximation, half is aimed downward and half is aimed upward, to eventually escape into space. What goes down heats the ground, so more up-going radiation ensues. This feedback process raises the temperature of everything until the amount of radiation escaping is equal to the amount that descended from the Sun. In short: Sunlight in, IR out, with a "hang up" as some, or most, of the IR cycles between the surface and the atmosphere. The "greenhouse effect" is the "hang up".
According to Clive Best in his article, most of the possible absorption by carbon dioxide was already occurring before the Industrial Revolution. This is expressed in the diagrams above by the portions of the curves that have already reached 100%. Let's look closer at one of the diagrams:
While we are here, let us take a side trip to Venus. There, the atmosphere is almost all carbon dioxide, at a pressure of 92 atmospheres, or 1,334 psi. That is 220,000 times as much carbon dioxide as Earth's atmosphere. The tapered bands, and the smaller peaks shown, will all be at 100%, and even the little bits of hash near 10µm and elsewhere, plus others not shown here, will be at 100%. The spectrum will be a bunch of rectangles, filling much more of the total space. No wonder the temperature on Venus is above 460°C (860°F)! Of course, it "helps" that Venus gets sunlight twice as intense as that on Earth.
All these details about absorption, and the interactions between the absorption profiles of carbon dioxide, water vapor, and other gases, result in a very complex system. I hope it is evident that, in the range of a few hundred parts per million, up to one or two thousand parts per million, the extra effect of the growing margins of the absorption bands is less and less as concentration increases. There is a point of diminishing returns. Let us discuss the Logistic Curve.
The Logistic Curve
Here is one familiar situation. A weakling wants to get stronger (usually this is a guy, so I'll use male pronouns). He goes to a gym and engages a trainer. He is tested with several weights; let us assume that, for starters, he can bench press 50 pounds. That means he can't even do one pushup. He trains three times weekly, with much grit and determination. After a few months he can "bench" 80 pounds, and in a few more, he attains 100 pounds, and can now do one or two pushups. In another year he finds his one-rep bench press is approaching 200 pounds! He has quadrupled his strength, and he looks a lot better also, more filled out. Question: Can he quadruple it again? 800 pounds? Men who have trained for decades seldom exceed 500 pounds; the record for someone who never took steroids is less than 1,000. Well, then, can he attain 400 pounds? Possibly, but at that point he is likely to have joint or tendon problems. The bones and tendons he started with can't increase as much as the muscles that attach to them. Somewhere in the 200-400 pound range he has a limit.
Let's consider this graph:
The blue line is a much-studied relationship that is not well known outside mathematics and statistics departments. It is called the Logistic Curve. The red curve is an Exponential Curve, such as compound interest. The units of this graph don't matter. Many natural phenomena can be described by setting this curve in appropriate units. For example, if the red curve shows the natural ability of locusts to multiply (let's say the units along X are weeks), the blue curve shows what will happen when they eat everything nearby and must begin to migrate to find more food. They may carry along for a while and reach the "carrying capacity", or "saturation", but somewhere off the right end of the graph, the curve will fall again when the locusts have eaten everything they can reach. Or, consider our ambitious weightlifter. Let's assume "10" represents the point where he started concentrated training. His strength doubles, doubles again, and then he finds it hard to make such great gains. Eventually, he "tops out". If he's lucky, he has done this without pulling any tendons or breaking any bones. That's why he has a trainer…
How does this relate to the greenhouse effect and carbon dioxide? For the next graph I've recast the axes to make a useful analysis, at least in a general way.
The amount of absorption by carbon dioxide as its concentration increases, and the level of added heat that this causes, is also a logistic curve. If we want to make predictions about what might happen with increasing gas concentration, we need to know where we are on the curve. NOTE: The temperature scale is not intended to be highly accurate, but to show relative relationships.
Depending on which horizontal scale we use, the baseline, "pre-industrial" amount, is either the lower black circle or the lower blue circle. We don't know for sure just how much heating was already in place in pre-industrial times, compared to a situation with zero carbon dioxide. Such a "zero situation" has never occurred on Earth. But we can compare two scenarios, one using the black circles and the black scale, and one using the blue circles and the blue scale; both follow the blue curve. The implication of the dotted black curve will also be considered.
The "We are in the early stages" scenario (black scale)
Temperature has risen, as gas concentration went from 280 ppm to 420 ppm over the past 175 years, and we find ourselves a bit beyond halfway along the rising portion of the curve. The amount the curve can rise until saturation is about equal to what has already occurred.
The "We are in a later stage" scenario (blue scale)
The upper blue circle shows that we are near the top of the curve. There is a little ways to go, but even doubling or tripling the gas concentration will not push us much further.
I have not been able to discover whether the climate modeling community has picked a spot on a logistic curve, or if they are even using one.
The "This could destroy everything" scenario (black scale, black dashed line)
If the climate disaster prophets are using predictive curves at all, they are probably using one that doesn't peel over at some saturation level, but goes up forever. The portion of the blue curve between the black circles looks pretty straight, straight enough that many folks, not seeing the whole picture, will project a straight line to forever. I am pretty sure that the "impending disaster" predictions that get all the press these days (at least since the first IPCC Assessment Report in 1990) are following a linear extrapolation, such as the dashed black line.
I favor the blue circles, which imply that most of what could happen has happened already. The global climate system may gain another half degree or one degree, but not more.
That is my conclusion, dear readers. I believe we are being bullied into making drastic changes based on a nonsensical extrapolation.
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