The following is an incomplete work in progress. I want to find the most recent reconstruction of the Arrhenius CO₂ calculation, and see what altitudes they are actually talking about, as well as good numbers on the extinguish length and spectrum for H₂O and CO₂. I would also like to build a cheesy computer simulation that demonstrates (or doesn't) the Arrhenius results, without getting into the details of global climate models. I want to explain the thinking, not prove the result.
My impetus is an "discussion" (heated argument) with a person who runs two websites about global climate change, and about the perfidy of the Republicans who dismiss it. My concern wasn't his predilection, or the effectiveness of taunting people who's minds you want to change, it was his "appeal to authority", the oft-heard story that climate models are very complex and we must trust the experts. And the implication that we are expert in choosing experts to trust. I've never been very good at that. Instead, I've found that many baroque explanations have a core explanation that isn't simple, but doesn't require years of training to understand, often explainable to an open and techically literate mind in an hour or two. It does not speak well for most experts (career theologians and scientists alike) that they must either "out-baroque" their colleagues with explanations so cryptic that they aren't analyzable, or repeat soundbites that are familiar but very misleading. Much of the resistance to climate change ideas comes from technical people who disbelieve the obviously incorrect soundbites, but can't penetrate the arcane minutia of the climate science community. Just like their passively accepting but non-technical opponents.
The survival of humanity on the earth, and the world economy, which are fundamentally the same thing, can't be turned into a football in a battle between hostile political camps. We must collaborate to prosper, and war is failure. Those inventing enemies and initiating battles (and foisting responsibility on their opponents) are the enemies of collaboration, no matter what banner they fly. We must not give them what they want and engage them in battle - we must develop escape velocity and blow right past them, leaving them in the dust. We do not need anyone's permission to succeed.
Simplified version of the Arrhenius theory:
- Air gets colder, linearly with higher altitude
- corollary - air gets warmer linearly with lower altitude
- Air (and its constituents) gets less dense with altitude
- Water freezes out at the top of the troposphere, at pretty much the same temperature
- The temperature of the earth as seen from space produces black body radiation
- In the medium term (years) the black body radiation must balance absorbed energy from the sun
- Black body radiation in the infrared band encounters opacities due to CO₂ and water absorption at some wavelengths
- the temperature at the altitude at which a constituent becomes transparent to space is the black body temperature at which that wavelength radiates
- the highest component defines the temperature, reradiating heat coming up from below
- The behavior of gas constituents on the ground DO NOT MATTER, unless the air above is transparent to space
- when CO₂ doubles, the altitude at which it becomes transparent to space increases
- In balance, the temperature at that altitude must stay approximately the same so the power flows balance
- more distance to the ground means a higher temperature at the ground
Now we explain that in detail (much of which needs to be filled in here - more library work! MoreLater )
There's something here to piss off most ideologues, "left" and "right". The current climate change disagreement is a weapon used by these ideologues to beat each other up, rather than an attempt to understand what is going on, in order to make personal choices and form effective collaborations. In a democracy, there is a tendency to castigate others rather than think, to vote rather than act. The protection of our planet (environmentally and economically) is too important to passively assign to the actions of others - if you think there are problems (and I do) your task is to fix aspects of those problems most aligned with your skills, not defer action to others, and most especially not to whine when they don't do what you say. Perhaps they know more than you do, especially about things you don't consider worth knowing.
And your first task, if your IQ is above 70 or so, is to learn what's going on. You may not learn as much as a professional scientist or business leader, but you can learn a hell of a lot more than sound bites. You can do this with a few hours of reading. Is the survival of the human race worth that time?
The Earth is Special
We are discovering many exoplanets. We have seen a few that are earth-sized. We have seen a few that are at the right distance from their stars to potentially have an earth-like climate. But our tools aren't good enough (yet) to actually observe an earth-like climate, and it is unlikely that we will . Likely or not, our unique atmosphere of nitrogen, oxygen, water vapor, and trace amounts of CO₂ can't be found anywhere else in the solar system, and if we foul this planet, we won't get another. Our survival is dependent on atmospheric chemistry; while we can conceive of artificial habitats on Mars or Venus, or even in orbit, we can't afford them (economics matters, too). A habitable ecosystem takes a long time to build; we are here because we inherited one.
So what's so special? Besides our planet's size, orbit circularity, distance from the sun, elemental composition, plate techtonics, stabilizing moon, lack of massive boloid impacts and nearby supernovas, the life that preceeded us sculpted a cozy home for itself. Specifically, it invented lignin, which turned a 20% CO₂ atmosphere into inedible, buried fossil carbon and a 20% oxygen, 0.02% CO₂ atmosphere suitable for warm blooded mammals in rough synchronization with the gradually increasing luminosity of the sun. Life is an essential component of the chemical composition of the atmosphere, and the free oxygen in our atmosphere would rapidly disappear without land plants to produce it, and sequester an enormous fraction of the biologically available carbon. This living control system has regulated the earth's climate for almost a billion years. If the feedback wasn't excellent, any of dozens of geophysical disasters would have rendered the planet uninhabitable.
We have life we do because physics supports it. A stream of high energy, low entropy photons arrives from the sun, 1360 watts per square meter on the sunlit side. Land plants convert this sunlight to usable energy, then waste heat, with a small fraction of that energy taken by animal pollinator/predators. The plants create an infrared-transparent mostly-oxygen atmosphere, and the precise nature of that atmosphere is why the earth has a surface temperature averaging 14C, rather than 460C like Venus, or -55C like Mars.
The surface temperature is not the physical planetary temperature. Humans live on the solid surface; not deep in the core, where it is extremely hot, or at the top of the troposphere, where it is very cold. First, we need to understand planetary temperature.
We normally count temperature in Fahrenheit degrees, or Celsius/Centigrade degrees. This is useful for everyday experience, but confuses the physics. Absolute temperature (the Rankine or Kelvin scales) is more physical. 14C is 287 Kelvins, and 59°F or 517° Rankine; physicists use the Kelvin scale. On the Kelvin scale, the surface temperature of Venus is 733K, Earth is 287K, and Mars is 218K.
Planets are heated by the sun - geothermal heating is small in the atmosphere. In the long term (centuries or longer) the heat absorbed by the earth (about 970 watts per square meter, noontime at the equator) is balanced by infrared radiation into space. The disk facing the sun has an area of πR2, the sphere radiating into space has an area of 4 πR2, so the Earth, on average, radiates 240 W/m2. Venus is 28% closer to the sun, and gets 93% more radiation, but reflects a lot more light - it absorbs 660 W/m2, and radiates 165 W/m2 . Mars is 52% farther from the sun, but reflects only 16% of the energy, so it gets 500 W/m2, and radiates 125 W/m2.
The radiation from a heated object (with some complications) follows the Stephan-Boltzmann black body radiation law: Power = σ T4, where σ = 5.67×10−8 W / m2 K4. A complicated way of saying that if the temperature doubles, the radiation goes up 16x; if the radiation goes up by 4%, the temperature making the radiation went up by 1%. The black body temperatures of Venus, Earth, and Mars are 232K, 255K, and 217K.
If you've been paying attention, your B.S. alarm should be sounding right about now. Why is Venus 501K hotter at the surface, Earth 32K hotter at the surface, and Mars 1K hotter at the surface?
The answer is that some of the gasses in atmospheres are infrared opaque. Oxygen and nitrogen are close to transparent to infrared. Water vapor, CO₂, and methane are opaque over significant parts of the infrared spectrum. If you looked at the Earth with infrared eyes, you would not see oceans and land, you would see a fog of high altitude water vapor, and (at different infrared "colors") a fog of CO₂ somewhat above that. Mars, with 1.6% of Earth's air density, wouldn't show much atmosphere in the infrared. In infrared, you can see the surface, which dominates the infrared emissions. Venus has 100 times the air density, and it is 97% CO₂, almost 240,000 times as much as Earth. In infrared, we can't see very far down into Venus's atmosphere.
Atmosphere and Temperature Lapse Rates
The air at the tops of mountains is colder and thinner than at sea level. Temperature measures the average energy of motion of air molecules - hot means faster moving. A molecule of nitrogen at sea level is moving (on average) 500 meters per second, and also rotating and vibrating. When it moves upwards, it loses a little bit of energy to gravity; downwards, it gains. A kilometer up, we can expect the molecules to be moving more slowly. The temperature lapse rate for dry air is -6.4K / kilometer; at the top of Everest (8.848 km) we can expect it to be 57K colder than sea level. The lapse rate for water vapor saturated air is lower ( -5.9K/km ) because water molecules are lighter, move faster at the same temperature, and lose less energy with altitude. The details are complicated, but that's the general idea.
Air pressure is the weight of the gas above, compressing the gas beneath. The higher up you go, the less gas remains above you, the lower the pressure, and the lower the density. This is complicated by temperature, but (to a good approximation) as you move downwards from the vacuum of space, the weight increases, so the pressure increases, so the additional mass per meter increases, so the weight increases faster ... leading to an exponential increase in pressure and density as you move from space towards the earth. Working the other way, the density decreases with altitude. At sea level and 14C, the density is around 1.23 kilograms per cubic meter; at 6.7 kilometer altitude, the density is half that, and at 12.1 kilometers, the density is a quarter of sea level, at 1.65 km altitude, half that again. Not a perfect exponential, since the gas composition and temperature changes, but close enough for our purposes. Here's a calculator webapp for computing the behavior of the atmosphere - for our 14K average, I nudged the temperature offset by -1C from the "standard" (temperate latitude) 15C .
As the air gets colder and thinner, so does the water vapor and CO₂ in it.
Infrared Opacity of Water and CO₂
If you shine visible light through water vapor or CO₂, it is transparent. Infrared, different story. Some "colors" of infrared pass though both, some are absorbed and re-radiated by CO₂, some are absorbed and re-radiated by H₂O. These complicated molecules can bend and flex around the middle, and vibrate at infrared frequencies, making them good absorbers. Symmetric O₂ and N₂ molecules don't have these bending behaviors. Experimentally, if you shine some colors of infrared through a few meters of water vapor it is partly absorbed. Make the path half as long, or reduce the density by half, and half as much is absorbed. The same is true (for different frequencies) for CO₂.
As the air gets colder, water vapor starts to condense into ice crystals. Above the tropopause, about 12km altitude, pretty much all the water vapor has condensed, and no longer affects CO₂ transmission. Those tiny ice crystals do reflect sunlight, and that (plus sulfate particulates) reduce the light reaching the ground, lowering global average temperature. Rising vapor (it is lighter than nitrogen and oxygen) also transports heat energy upwards through the atmosphere. But it doesn't change infrared radiation much.
As the air gets less dense with altitude, the density of the CO₂ goes down, too, so the absorption path length increases. As the path length approaches the density lapse rate, the remaining atmosphere above, all the way to space, looks increasingly transparent and does not absorb and reradiate the infrared anymore. This determines the effective infrared radiation temperature for CO₂ - the apparent temperature of the atmosphere in the CO₂ color bands is the temperature of the CO₂ at the altitudes the column above becomes transparent.
So, if we double the density of CO₂ in the atmosphere, the altitude at which the atmosphere becomes transparent in the CO₂ bands goes up by a few kilometers, say from (WAG) 50km ( 269.65K, 0.98 g/m3 ) to 56 km ( 256.29K, 0.49 g/m3 ). The whole air column must heat up by a few Kelvins to increase the temperature enough to radiate the same amount of infrared power in that band. Other bands will increase more, the CO₂ bands a little less. Overall, what you would see from space, in the long term, would be a shift in the infrared color of the earth, and a very small expansion in size (moving to higher altitude), but overall, the same temperature. Down here, under a taller air column with the same temperature lapse rate, it gets hotter.
The effect isn't linear. Doubling the CO₂ raises the temperature by a few Kelvins, by pushing the radiation layer up to half the air density. Doubling the CO₂ pushes it up another half air density, and the temperature increases by about the same increment. Increasing the CO₂ by a factor of 8 does not increase the temperature by 8*T degrees, it increases it by 3*T degrees.
So what about Venus? Well, the 4C per CO₂ doubling doesn't apply in an atmosphere that is almost all CO₂, with optically opaque sulfuric acid clouds far above the surface. Instead, the Venusian atmosphere is about 27C and 0.5 atmospheres at 55km altitude; below that, things get weird. As you descend down to 100x earth atmospheric density and 90x earth pressure, you pick up about 40K fromJoule-Thomson heating. You also pick up about 500 kJ/kg of gravitational energy; with a specific heat of around 1.1kJ/kg-K, that gravitational energy turns into about 450K of heat. There is not enough free oxygen to create more than 0.3 atmospheres of CO₂ on Earth, 0.3% of Venus. So unless we somehow convert all the oceans into additional oxygen, the earth may get very hot in human terms, but it will not become Venus anytime soon.
Mea Culpa - the numbers are for illustration; I haven't done the actual calculations, over the whole atmosphere, frequency band by frequency band. This is merely to demonstrate why the behavior that matters is high in the atmosphere, not down here underneath it, where space is pretty much invisible through the intervening CO₂ and water vapor. When you see climate non-changer talking about CO₂ absorption at sea level temperatures and pressures, or some ecopanic politician talks about "CO₂ blankets", you can assume neither understands what they are talking about.
More details - CO₂ is heavier than N₂/O₂, so it gets less dense faster with altitude. Also, the dry air in the stratosphere ionizes and forms ozone, which absorbs solar UV, which adds heat to the thin air. So the temperature plateaus at 216.5K from 11 to 21km, then rises to 269.50K at 47km, then starts dropping again above 51km.
BUT, it ISN'T all about fossil fuel
Some folks blame the fossil fuel industries for the CO₂ rise, and they certainly are contributors, though they do so only because we keep buying their products. However, when Svente Arrhenius first figured this out in the 1890s, CO₂ was already in the 280 ppm range, far higher than the 180 ppm that 10 thousand year old ice cores show. He computed that the fossil fuel consumption (almost all coal) of the time would double CO₂ in a few thousand years. But CO₂ had already increased by 50% from prehistoric levels, in spite of tiny and localized fossil fuel consumption. So, what is the driver that nearly doubled CO₂ from 180ppm to 315ppm in 1960, when the scary Mauna Loa CO₂ graph begins?
Agriculture-driven land use change. Crops and cows. See the eye opening 2010 article by Rieck et al in Tellus. The big industrial runup occured around world war 2, when we devoted vast resources to destroying vast resources.
2000 years ago, most of the places we now call deserts were grasslands, and many of the places that are now farmland were forests. The degraded lands in modern Iraq used to be part of the "fertile crescent". The archeological sites scattered through the "desert" west of the Rockies supported abundant life before humans got there. Native Americans hunted animals using fires to panic and concentrate animals. They left ample archeological evidence of large human populations. Indeed, much of the forest understory in the Pacific Northwest was missing from frequent fires, until Europeans drove off the aboriginals with disease and firearms. The invaders chopped down the trees to clear the land for farms, and destroyed the native prairie grasses with overgrazing.
All plant life is not the same. Annual crops are optimized for high "shoot-to-root" ratio; growth above ground that becomes sellable product. Native grasses have roots going down many meters. Some trees go farther into the earth than they do into the sky. Not to reach water, but to reach phosphates and other nutrient minerals in the rock, which the roots exchange with carbonates. Long term, this is where atmospheric carbon ends up, to eventually run off into the ocean, to be subducted back under the continental crust.
Untilled natural soil is rich in elemental carbon, and the CO₂ density is much higher in the soil than it is above ground. Agriculture released all this soil carbon into the atmosphere. Modern fertilized crops do not sequester carbon for more than the growth season.
The effects of land use change, CO₂ and rainfall and temperature changes on plant growth, and agricultural runoff on coastal margins (where the majority of ocean biological activity is concentrated) is complex. But if we entirely eliminate all energy generation by combustion, while increasing the conversion of nature to crop and meat production, we can expect CO₂ to keep rising. It doesn't matter how slowly you add CO₂ if you destroy the removal mechanisms.
Stewart Brand (a Stanford trained ecologist, not a wannabe) has some workable (though very politically incorrect) ideas about the solutions. Moving more of the population to cities ( reduced birthrate, increased efficiency ), crops bio-engineered for lower land use, and nuclear power. His ideas are excellent, and have about zero percent chance of adoption in the US, where half the population pretends there is no problem, and half pretends there is no solution, and both believe in magic pixie dust instead of frugal living and hard work. Fortunately, the US is only 4% of the world's population, and if we disappear, we will hopefully take our media-fogged ignorance and hostility with us. Some of the other 96% are plenty smart enough to figure out better ways to live, and some Americans might survive cultural suicide by learning from them.
Implications for Life
The increased oxygen and decreased CO₂ made warm-blooded mammals and birds possible, which coevolved with C4 (low-CO₂ tolerant photosynthesis) angiosperm plants. This "hostile takeover" of the land ecosphere mostly occured during the last 100 million years, and global glaciations were among the weapons "we" used to suppress the C3 life that preceeded us. We can return to conditions that favor other lifeforms instead of us. Life is tenacious, and will thrive in whatever conditions we can manage to create. But our kind of life, dependent on angiosperms and breathable air, may not. If we ignore our environmental needs, or worse, we solve the wrong problems in a bass-ackwards way, we will learn about our own fragility.
I am a pessimistic optimist; I think intelligence is also tenacious, though future substrates for intelligence may take other forms, from gene-engineered "mutants" to artifically enhanced machines. While they may be grateful for destroying our paradise and creating theirs, I would rather express my gratitude for billions of years of natural evolution by helping it continue.