Cambria Math;Times New Roman;  Thank you all for being here today for the Seventh Annual Department of Atmospheric and Ocean Sciences Len Robock Lecture, supported by the estate of Len Robock.  The goal of this lecture series is to bring dynamic, high-profile speakers to speak to a general audience about topics related to atmosphere and ocean sciences.  We chose tonight's speaker, Dr. David Archer, due to the unique perspective and expert knowledge he has on climate science.  Dr. Archer has written an excellent textbook for non-science majors about global warming, called "Global Warming: Understanding the Forecast." He also wrote and co-wrote several climate outreach books for nonscientists and educators: "The Long Thaw: How Humans Are Changing the Next 100,000 Years of Earth's Climate," "The Climate Crisis: An Introductory Guide to Climate Change," and "The Warming Papers: The Scientific Foundation for Climate Change Forecast," and a Princeton Primer on "The Global Carbon Cycle." And I've actually taught a course using one of these books.  Dr. Archer developed a coursera.org online class open to the public about global warming, which has actually had over 50,000 students signed up to-date.   Archer is also a regular contributor to "Real Climate," a climate science blog written by climate scientists for journalists and the public.  Dr. Archer is visiting us from the University of Chicago Department of Geophysical Sciences, where his research focuses on the carbon cycle of the Earth and its interaction with global climate.  He has published over 80 articles, and his work has been recognized by the American Geophysical Union, who made him a Fellow in 2010.  Let's welcome David Archer to the University of Wisconsin's Seventh Annual Len Robock Lecture. 

 (audience applauds)  - Thank you, Larissa, for your great hospitality.  It's been great to visit this place.  I'd love to see it in the summer sometime.  I'm sure it's really nice.  (audience laughs) I wanted to start with a story that could have ended worse.   So, when they were developing nuclear weapons at Los Alamos, and they were gonna do the first atmospheric bomb test, the possibility was raised by Edward Teller that the blast might be energetic enough to start a fusion reaction in the atmosphere that could burn up the whole atmosphere, and end the world.  And there must have been some crucial parameter to decide  whether that was gonna happen, like an absorption cross-section or something, and they decided that the number was on the right side, and it was okay, and so, what the hell, just do it.  And it could of ended worse, right?  So this is the CO2 concentration in the atmosphere,  a plot going back a thousand years.  So the orange part, or the red part there is direct measurements from the air from Mauna Loa, and the part before that is from little bubbles of atmosphere preserved in ice cores in Antarctica.  And it's amazing that that works, but it does, and so we have these long records of atmospheric gas concentrations. 

  I'm gonna focus in this talk on the natural concentration  that was there before we started messing with it.  So about 280 parts per million, 280 molecules per million molecules of air.  And it had been about that concentration for thousands of years, more or less, as long as agriculture and human civilization and all that sort of thing.  So then, it started going up, and it is starting to provoke climate change.  And what I'm going to explain to you tonight is that the amount of climate change that we can expect to come out of this depends very strongly on what this concentration was at the beginning of the industrial time.  If it had been lower, the whole thing would have heated up much faster.  So, if you were James T. Kirk on the "Starship Enterprise,"  and you come up on some civilization, and you're told that they just discovered coal, the first think you would say is, "What is the atmospheric CO2 concentration now when you start?" 'Cause that's like the number that will determine how that episode is gonna play out.   So the absorption cross-section of the nitrogen in the atmosphere, this is a number.  But the contrast is that the people that discovered coal had no idea what that number was or the significance of it.   And so it just turned out as it was. 

  I'm gonna tell you what would have happened if that concentration had been different.  Now, this isn't exactly science because we know what that concentration was.  So I'm gonna tell you that climate change depends very heavily on what that concentration was, but we know what the concentration was.  The scientific method would be, if there's some number that is gonna control things, you measure it as well as you need to, and then you're good.  We know this number as well as we need to, so it's not like this is motivating anything new or changing anything.  It's just sort of a new perspective on the situation that we find ourselves in.   So I'm gonna start with some science and then move to alternate histories and things like that.  If you're not, if equations give you the heebie-jeebies, you can kinda just chill and pick up the thread in a little bit, all right? But I want to explain to you why the initial CO2 concentration is so important to the global warming climate event.   And we'll start from the very beginning, which the physics that determines the temperature of the planet, which is all about balancing energy  coming in from the Sun and then being shed from the planet to space.  So, geothermal heat from below, you'll find if you go and try to warm up by crouching against the sidewalk outside today, is not all that effective. 

 It's the sunlight and the outgoing surface energy fluxes that determine the surface temperatures.  So, the sunlight is coming in at a prescribed rate,  and then the rate at which energy leaves the planet is a function of the temperature of the planet according to this formula here: Epsilon Sigma T to the Fourth Stefan-Boltzmann relation, where Epsilon and Sigma are just constants, and Temperature is raised to the fourth power.  So, the higher the temperature is, the faster the planet will shed energy.  And so it's kind of like a kitchen sink, where you turn on the faucet, and the water sort of builds up in the sink until it can go down the drain fast enough to come in to balance what's coming in from the faucet.  So the water level in the sink is kind of controlled by this through-flux of water.  The temperature of the planet is controlled by the through-flux of energy.   So to get the simplest model of a greenhouse effect, you can imagine a pane of glass in the air, suspended above the ground, and the glass lets the light from the sun go through, but it captures all of the infrared light coming up from the ground.  And then the pane of glass itself radiates infrared energy going both directions 'cause there's two sides to the piece of glass.  And so now, you can pitch this to the undergrads in your class as a sort of algebra story problem, and you gotta solve for two unknowns here, the temperature of the atmosphere and the temperature of the Earth, and what you get is, the atmosphere has a temperature that the naked planet had in the last slide because it's got to balance the energy coming in from the sun, those two arrows at the top have to balance.  But then the temperature of the Earth is hotter than it was before. 

 And this is because the pane of glass is obstructing energy from leaving the planet.  It's kind of like a little piece of carrot or something landing on the drain of your kitchen sink, and then the water level rises to a new level, where it's got more pressure to balance the water budget.   So, the real atmosphere isn't a pane of glass, and most of the gases in the atmosphere don't absorb or emit infrared light.  So they don't do this greenhouse trick.  But, if you have a molecule that is complicated enough that, when it vibrates, it creates an electrical dipole,  that will absorb and emit infrared light at the frequency that the molecule is vibrating.  So CO2, in its resting state, is a symmetrical molecule, so it wouldn't just leap out at you that it would be a greenhouse gas until you think about it a little bit.  But there are three vibrational modes, including a bending mode, right here, which is the one which is most important to Earth's climate.  So it bends, and when it's bent, it's got an asymmetry that lends it an electrical dipole.  And so that can interact with the electromagnetic light coming up from the ground.  So this is a spectrum of what the light leaving the planet looks like. 

  We've got different frequencies or wave numbers, different sort of colors of infrared light on the horizontal axis and the intensity is the vertical, and the smooth curves are blackbody curves.  Those are what the light spectrum would look like if you had an object that was emitting at all different frequencies, is what we call the blackbody.  But the dark, solid line there is what you actually see if you look down from space.  In parts of this range, like right in here,  this is called the atmospheric window, and there are no gases that absorb infrared light in that window.  So if you look down from space, what you see is the ground.  So these curves are at different temperatures,  and the ground is actually sort of halfway between the temperature that creates this curve and the temperature that creates that curve.  So you can kinda think of these curves as like a thermometer scale, kind of.  But then here, where CO2, where the frequency of light corresponds to the bending vibration frequency of the CO2, the light coming up from the ground gets absorbed, and then, that CO2 re-emits, and then more CO2 reabsorbs and re-emits, and the light has to sort of fight its way out from the surface at those frequencies.  And so, in the end, when you look down from space, what you see is CO2 that's up in the upper atmosphere where it's very cold.  And so it's following along the coldest of those black body curves there. 

 So the CO2 is ...   the total energy leaving is proportional to the area under the curve, and the CO2 is taking a big bite out of that.  So it's decreasing the energy going to space, and that makes the Earth warm up.   So, a funny thing about this phenomenon is that the amount of energy imbalance that drives  the climate to change, which is the number we call the radiative forcing, and it's in watts per square meter, but it's just a measure of how much energy we're changing, that radiative forcing is a very nonlinear function of how much CO2 you put in.  So if there's no CO2, you've got this curve here where that bite is gone.  And if you just put in a little bit, just 10 parts per million, you get this fairly strapping young peak of absorption there.   You know, you get a pretty impressive bang for your buck from just a little bit of CO2.  And then, you scale it up by a factor of 10 to a hundred parts per million, and now the peak is extending down to the coldest part  of the atmosphere there, and it's also wider than it was, so you're blocking more energy than before.  Then we do another factor of 10 to a thousand ppm, and you see the peak is still as deep as it was before because you're looking down, and you're seeing light coming from the coldest part of the atmosphere.  And changing the CO2 doesn't really change that very much. 

 So, the thousand parts per million peak is fatter than the hundred one is, and so it's definitely blocking more energy than it was at a hundred, but you're getting much less bang for your buck than you were initially.  If you put another 10 ppm on that thousand, you wouldn't even see it, whereas the first 10 ppm was huge, right?  So, this is how that radiative forcing, the watts per square meter of energy imbalance on the vertical axis there, how that depends on the concentration of CO2 for the lower curve or methane for the upper curve.  And so, if the initial concentration of CO2 was very low, and then you added a certain amount, that'd be like going from here to there.  That's a big change in watts per square meter.  Whereas, if you've got more, you're starting out from down here, and then you add the same amount of CO2, but you get a much smaller change in the radiative forcing from that because it's called the band saturation effect.  So the word band means frequency range of the light, and saturation means you've taken all there is.  So, because the absorption bands are more saturated, if you start out with more CO2, you get less climate change than you would have if you'd had less CO2 to start with.  It turns out that the radiative forcing there scales as the logarithm of the CO2.  So any doubling of the CO2 concentration gives you the same radiative forcing as any other.  So going from 10 to 20 would give you the same global warming as going from 100 to 200 or 1,000 to 2,000. 

  So, the natural CO2 concentration in the atmosphere is a slippery thing.  If we couldn't measure it directly, or even indirectly by some sort proxy measurement to sort of tell us how much there is.  If we could only figure out how much CO2 is in the atmosphere by theoretical knowledge and models, we wouldn't have a clue what it is because it's determined by a very complicated geochemical feedback system that works over very long timescales on the Earth.  So, it's sort of a thermostat, and it sort of arises  out of this cycling of carbon out of the Earth  and then back into the solid Earth.  So we start with CO2 degassing from the Earth,  and that's kind of like a driver sort of a flux, and then, so that goes into the atmosphere, maybe into the ocean, but then it exchanges with the atmosphere.  And then, the way that the carbon manages to make its way back down to the solid Earth again is through a weathering reaction, which is where rocks at the surface of the Earth dissolve in fresh water, in rainwater, and the calcium in the rocks winds up hooking up  with CO2 to make a calcium carbonate, which then gets buried at the bottom of the ocean.  So the thing about this cycle that makes a feedback, a thermostat, is the idea that the rate of the weathering,  how fast you can dissolve those rocks, depends on the climate.  It depends on how much fresh water you're washing over the rocks all the time.  So, on Earth today, you have much more weathering happening in the Amazon, where you have water flushing it all the time, than you do in the Arctic, where you're sort of water-limited.  And the idea is that, if you had more CO2 in the atmosphere  than would balance, that would mean the planet would be too tropical and too much rainfall, you would be dissolving rocks too fast, and you'd be pulling CO2 out of the atmosphere faster than you're replenishing it from the volcanoes. 

 And so it's just like this kitchen sink again, where the process of removing the carbon from the system  is like the water going down the drain in the sink.  And it is a function of the amount of carbon in the system, which affects the climate, like the water level pushes the water down the drain, and, like that, it will tend to stabilize.   So if you have a thing like fossil fuel combustion, you've got CO2,  you put a bunch of CO2 in the atmosphere, and suddenly, you're weathering faster than you were in the original steady-state.  So that means you're using up CO2 from the atmosphere faster than you're replenishing it, and so it will tend to sort of glide back down  to the initial steady-state value.  So this is a slow thing.  This is the process that will clean up after our global warming, but it's, unfortunately for us, very slow.  It has a time constant of at least a hundred thousand years, probably more like a half a million years.  So, releasing CO2 has this very, very long impact on the climate.  If you don't remember anything else, if you're like right about to fall asleep right now, remember that, and that's an important thing to remember.  So, this thermostat idea helps to solve a problem that Carl Sagan came up with called the Faint Young Sun Paradox, which is the idea that, as a Sun matures, as you make heavy atoms out of light atoms, the whole things sort of contracts, and it gets hotter. 

 And so the Sun is putting out like 25% more energy than it was four billion years ago when the Earth was younger.  And yet the climate of the Earth has this eerie, uncanny stability over all of that.  It's like you have an oven, and you're turning up the thing, but yet your cookies come out perfect at the end.  It's like, what's going on? This thermostat helps to do that, and like I say, it also will determine the longevity of what we do.   In the year 1750, in the natural world, the CO2 concentration could have been anything.  So, if the Sun had been a little hotter,  so here's a plot of a model result of what that CO2 concentration would've been as a function of the temperature of the Sun, so we're going from 5780 kelvin to 5850 kelvin,  this is a tiny, tiny, tiny change in temperature when you think about the full range of stars.  There's different classifications of stars.  The Sun is a G-type star.  So, if I were to put the limits to what a G-type star is on this plot, it would be like  the opposite ends of the room.  This is a tiny, tiny range of temperatures. 

 The next figure here on the right shows how the CO2 concentration would've been different in the natural world if we had been a little bit closer to the Sun.  So, if we were 3% closer to the Sun than we are,  the natural CO2 concentration in 1750 would've been like 20 parts per million instead of the 200 that we had.  Tiny, tiny, very, very, very.  The albedo of the planet is how reflective it is.  You make a tiny change in that, a few more clouds, and you could totally change this.  And the fact that the Sun is getting hotter through time means that, if we had come to sentience and discovered coal a few hundred thousand years later, maybe a half a million years later, the Sun would be hotter enough at that point that the CO2 concentration would've been much lower in the natural state, before we start doing our thing.   So it could've been anything.  So, what I'm gonna talk about is what would have happened if it had been lower.   So, this is, we're gonna, I'm gonna assume...  the people who are discovering coal, they knew how, the temperature of the planet, so we're gonna insist that the planet have the temperature and the same biosphere, the same amount of fossil fuels, burn them at the same rate, same ocean circulation, all that stuff that we can see, but I'm gonna tweak it by tuning the Sun just a little bit up and down, no actually, tuning the CO2 degassing rate, actually, coming from volcanoes. 

 If I have more CO2 coming out, it's gotta be higher, it's like turning up the faucet.  Water level in the sink goes higher, whole thing scales up.  Or if the CO2 coming out of volcanoes had been lower, the CO2 could've been lower in the atmosphere.  Nobody would have known the difference.  So what would've happened if we had discovered coal in such a world? It's a little complicated because a lot of the carbon that we have released is not in the atmosphere now.  It's dissolving in the oceans.  So this is a plot of, the red curve is the rate of CO2 emission.   I guess this is the cumulative amount of CO2 ever emitted.  And here's what's in the atmosphere, and there's a whole bunch that's in the ocean.  The ocean is taking about half of our carbon that we release, which is a good thing. 

 One thing to be a little careful about in thinking about this is how could that have been different? If everything had been different, like I said, what would happen? Well, the fact that the ocean, it seems like the ocean, every year, takes about half of what we release.  So the simple world would be to say that the ocean and the atmosphere equilibrate quickly.  So it'll just take half of you release whatever because it just does what it does quickly.  But that's not actually true.  You can think of the ocean as sort of having two reservoirs, a surface ocean reservoir, which does equilibrate quickly, and so, if the whole ocean was just a hundred meters deep or something, maybe atmosphere and ocean would always be tightly in equilibrium.  But there's also this deep ocean that has a long time constant, and it's the biggest reservoir.  So this is where, this will hold much more carbon, but it takes much longer to get there.  And, while the surface shallow layer might equilibrate quickly enough to just always keep up with whatever you do from one year to the next, the uptake into the deep ocean kinda depends on everything you've released since like 1750.   So it's sort of ...   the top going into the shallow layer, the uptake rate is proportional to how much you released this year, probably, but how much is going into the deep is proportional to how much you've ever released because it's taking so long to equilibrate. 

  Well, it turns out that the way that the ocean takes up carbon dioxide is through a buffer chemistry reaction, where the CO2 reacts  with this guy, carbonate ion, CO3 with two minus charges.   And they go to make two of these bicarbonate molecules, which bicarbonate also has a negative charge there.  So the thing about molecules that have charges is that they don't evaporate to the atmosphere.  There's no ions in the atmosphere.  You can only have neutral molecules there.  So, when you take a CO2 that can be a gas like that, and you convert it into a bicarbonate, you're hiding it from the atmosphere.  Because once it's in bicarbonate form, it's no longer able to evaporate to the atmosphere.  So this is sort of a buffer chemistry reaction.  It allows the sea water to take up more CO2 than it would have if there were no chemistry like this, if it was just dissolving the gas, and that's like dissolving oxygen in the water.  There's no chemistry that happens, it just goes in there, and that's it. 

 So sea water can hold something like ten times as much CO2 per gallon  as it would if there were not this chemistry.  And the amount, the strength of this buffer is determined by the carbonate ion concentration, which is determined by equilibrium with calcium carbonate in the sediments.  So the calcium carbonate says how much carbonate ion there will be.  And so, it turns out, when I put this into a simple model, the ocean takes up the same fraction of the carbon regardless of what the initial CO2 concentration was, 'cause this buffer chemistry is controlled by that calcium carbonate reaction.  So here's kinda how this looks.  The top left plot you saw already, that one is how the CO2 concentration depends on the degassing rates.  That's the knob that I'm turning to drive this up and down.  And then, the lower right is how the chemistry of the ocean changes, 'cause the ocean has to deal with the CO2 thermostat saying the CO2 wants to be this.  It also has to deal with the calcium carbonate system saying the carbonate ion has to be that, and there are two degrees of freedom in that chemical system.  So we can do that by changing the total amount of carbon dissolved in the water and also something called the alkalinity, which is how much carbon you have that has minus charges in it. 

 So the ocean can kind of adjust to accommodate all those things.  And then, the real important thing here is this fourth plot, which shows how much is going into the ocean as a function of time, as I'm gonna dump fossil fuels, CO2, into the atmospheres of these different planets.  And it's always more or less close enough, the same fraction, the same 50% is going in the oceans.  So the way that works out, then, is that you can kind of think of the atmospheric CO2 concentration as being a natural value that just stays constant throughout our time period.  And then the fossil fuel part is just gonna be this little seed, which grows exponentially.  And when we have different initial concentrations, it just pushes that whole thing up and down.  Doesn't really change the shape of that curve very much.  Okay? The next step is to figure out what is happening to the climate from this.  And so we have to calculate this radiative forcing, the watts per square meter of energy imbalance.  And that is a function of, as I said, the ratio of the initial CO2 to the one you're sort of concerned about. 

 Let's take this really low curve here, and we're calculating the radiative forcing from that.  That involves taking the natural log of it.  So over here, where the initial natural amount of carbon  is sort of negligible anymore, you're just taking the natural log of an exponential, and that just gives you a straight line.  So that's this straight line here.  So, when you get to the point where the fossil fuel part is sort of dominating,  you get this sort of straight line increase of watts per square meter per year from our continued exponential exploits there.  And then, before you get to that point, when the natural part is not negligible yet, you're kind of accelerating to that terminal stage here.  So the cool thing about this is that, if you change the natural concentration because the radiative forcing is a function of the ratios, it's like you're scaling,  you're just multiplying everything by a constant.  And the thing about multiplying an exponential by a constant is that that's just like moving it in time.  So 2e to the x equals e to the x plus natural log of 2 or something like that.  You can sort of go from a pre-exponential multiplier to something up in the exponent, which, in this case, is time. 

 So what this means is that, by dialing up and down the natural CO2 concentration, we're taking these trajectories of radiative forcing kind of accelerating and then reaching that terminal stage, and we're just moving it back and forth in time.  The slopes that they reach when they get to the terminal phase are the same, and the curvatures down in the lower part, they're all the same.  They're all the same curves, pretty much, but the timing is moving back and forth.  So it's as if, by burning coal, you're lighting a fuse.   And then the fuse is gonna burn for awhile, depending on how much CO2 is in the atmosphere.  And then, after it goes through that, it will blow up.  And how much time you have between, oh, this is cool, we've got coal, we lit this fuse, and figuring out, whoops, wait a second, this is a problem, and putting it out before it gets to the bomb, depends on how much CO2 was in the air when you start.   So...  so to go through what that looks like now, starting with lighting the fuse.   So you're looking for some kind of a clue that exponential growth is gonna happen. 

 It's a little disingenuous to insist on ingredients for exponential growth because everything about life seems to grow exponentially.  Complexity of body plans or speed of computers or whatever, but the steam engine seems like a natural place to say  this is where lit the fuse.  The very first steam engine was kind of a simple thing.  It was just designed to pump water out of mines.  And so you'd fill up a box with steam, and it would be connected to the water down there, and you would condense the steam, and the vacuum would suck water up.  Maybe you could say that extracting resources would then amplify and then turn into an exponential thing, but it's sort of a humble beginning.   But then, the real advance came with James Watt, the rotary steam engine,  because now, you've got this rotary power.  You can use it to drive locomotives, you can use it to break up rocks, you can use it to pump water, you can use it for all kinds of things.  So, there's an obvious case for your science officer on the Enterprise saying, "These people are about to really go to town "on this coal business here." All right, so then, we've lit the fuse, and it's kinda burning, but we have to figure out what's going on so we can put it out before it gets to the bomb, right? So how did that go?  The first description of the greenhouse effect that I showed you earlier comes from Joseph Jean-Baptiste Fourier,  who worked for Napoleon, actually.  And what he's mostly known for, not for being at the very foundation of Earth Science, but for heat transport and for a mathematical technique called the Fourier transform. 

 It's that same guy.  But he came up with this idea that the atmosphere could cause the Earth to be warmer by blocking heat from going out.  So this is a really impressive start.  It doesn't seem to me like it took a whole lot of abstract scientific understanding to build the steam engine.  It took being a good mechanic.  But the science that came out of that, like thermodynamics and entropy, and all these things, they came afterwards.  They weren't necessary to build the steam engine, whereas, to figure out about the greenhouse effect, you can't see infrared light.  And to understand about the energy balance and that that would set the temperature of the planet, that's really impressive, sort of abstract reasoning.   And it came a few decades after the steam engine.  So it's a good start, definitely. 

  The next stop on our thing here is from a British chemist named John Tyndall, who discovered the thing about the CO2, that only some gases can absorb and emit infrared light.  They had no idea what light was.  They talked about billows of the ether, which, actually, is actually not all that far wrong, it's just different words than we use anymore.  But he had this really steampunk-ish kind of lab equipment and was able to figure out that,  'cause they were interested in the ice ages at that point.  So he was able to figure out that you don't have to change the whole math of the atmosphere to make an ice age or change the climate of the planet.  You just have to change these trace gases like carbon dioxide.   So that was at about, that was in 1850.   And then, 1896, was written my all-time favorite paper  in all of the Earth Sciences, by Svante Arrhenius.  So Arrhenius, a Swedish chemist, is also known for something other than this.  If you took freshman chemistry, you heard about the Arrhenius equation, which describes how chemical kinetics depend on temperature. 

 But he also did this amazing thing to try to estimate how much the temperature would change on the planet if you doubled the amount of CO2 in the atmosphere, which is the same metric we use today.  We call it the climate sensitivity, or delta t 2x for doubling CO2.  And it's a good metric because, like I said, climate change goes as the number of doublings.  So a climate sensitivity that was how many degrees C per parts per million of CO2 would be a weird number because it would depend on where you started, but for doubling CO2, that's a good number.  So the reason why I love this paper so much is he didn't know what the absorption spectra were  of CO2 or water vapor in the atmosphere.  He tried to figure out what that would be by using measurements of infrared light  coming from the Moon, made by a guy named Tyndall.  So Tyndall was trying to figure out, Langley, sorry, Langley, trying to figure out how hot the Moon was.  And they were just figuring about infrared light and those blackbody curves, and the warmer it is, the brighter they are.   And so he was trying to figure out how bright the Moon was by measuring how intense the infrared light coming from the Moon is in Moonlight.  And you can't see infrared light. 

 So he was sitting there in a dark laboratory at night or something, with a prism made out of salt 'cause salt is one of the few solids that you can run infrared light through and not have it absorb, and then measuring how fast a thermometer or something was warming up as the light hit it.  So it must've been really esoteric and spooky, like in a seance or something, but it was real this time.  And so what Arrhenius did is he used those measurements,  they were made as a function of the zenith angle, so if the Moon was way over here and coming in, it's gotta go through more atmosphere than if it's right overhead, and also, the temperature and the humidity so that differing amounts of water vapor for different data points.  And so Arrhenius backed out absorption coefficients for CO2 and water vapor from this silly Moonlight data and then from that, did what he called really tedious calculations to figure out how much you would warm up the planet by doubling the CO2 concentration in the atmosphere.  Incredible! In hindsight, he was lucky because the spectrum covered  by the different diffraction angles through that salt prism covered about half of the spectrum that we really needed to see.  So this has gotta be an ingredient to being a famous scientist is being really lucky, right? We all know that.  And he was very lucky.  In 1896, he basically nailed it, what the climate sensitivity is.   Beginning about 1950 is when we started to actually know what the CO2 concentration in the atmosphere is.  It's not really that difficult a measurement to make if you have a box of gas. 

 The hard part is that we breathe CO2,  and it comes out of all kinds of things and goes into things.  So if you measured the CO2 concentration in this room, for example, it would probably be about a thousand parts per million.  And then just even outside, you go outside, it would be higher than the 400 parts per million.  You can look up what the CO2 concentration in the atmosphere is because we're down in the boundary layer, and we're sorta polluting it, and it's just really hard to get the number out of all the noise.  There's seasonal cycles and all kinds of things.  So what Keeling did was set up a place on Mauna Loa,  which is this volcanic mountain in the middle of the Pacific free troposphere in Hawaii.  It's, like, the biggest middle- of-nowhere you can imagine.  Just like air all around you.  And from there, he could get rid of some of that local pollution, and he started to see the atmospheric concen-- yeah, you know.  It took him a few years of data before he said, "Whoa, that kinda going up." 'cause his boss, Roger Revelle, had just published this paper saying that he didn't think that the CO2 concentration could go up 'cause it goes into the ocean too easily. 

 So now Roger Revelle is famous for being a prescient scientist having gotten the wrong answer, but then hiring the right guy to come up with the right answer.  (audience laughs) The Revelle buffer factor came from a reviewer, I'm convinced of.  As you read Revelle's paper, he's got this whole thing, and the whole buffer chemistry I showed you, it's like he missed that, but some reviewer said, "You've gotta put this in." So he put this, "Oh yeah, this other factor of 10 there." So yeah, luck is an amazing thing.  So essentially, our understanding of the climate system matured in the early 70s.   They were discovering about aerosols that can cool the planet, and the ice ages, they were figuring out that those had happened.  But by the early 70s, it was clear that,  despite what you may read in the "Wall Street Journal," climate scientists knew that we were talking about global warming, and they were issuing public statements, this is going to happen.  Nothing really has changed since then.  I mean, we've been getting details and watching things actually happen, but in terms of first-order understanding of how this all works, it basically matured in the 70s.   So that's kind of understanding what's going on.  Now the climate impacts. 

  It was predicted in the 70s, 80s, 90s,  that by the turn of the century, the climate impacts would rise above the noise of natural variability.  And in fact, in came in 1995 that  the Intergovernmental Panel on Climate Change, which is this United Nations sponsored organization of scientists from all over the world that write these scientific assessment reports to try to synthesize what we know about climate science.  In 1995, the IPCC said, "The balance of evidence suggests a discernible human impact on climate." So, it was clear at that point to scientific analysis.   It was a done deal.  The climate is changing.  But, of course, that wasn't really enough to motivate very many people to get off of fossil fuels.   It wasn't really enough to do that.  But I would argue, based on the wonderful Paris Accord meeting that just happened last December, which I'm still sort of dancing about, that we now have reached a point where things are going bad enough that we're starting to notice it on the ground.  There are droughts that have been going for multiple years all around the world.  The whole planet is sort of dry. 

 There's all of this kind of weird weather.  And that's what motivated the Paris agreement.  It's not scientific understanding; that itself was not sufficient.  But, if it starts to mess with your crops and your bottom line, that's kinda where it goes.  So, if we accept the idea  that we've reached that point now, we can take that watts per square meter of climate forcing.   We can look across this line and see  when we would've crossed that line as a function of what the CO2 concentration in the atmosphere was in the natural case before the Industrial Revolution.   And this is what looks like.   If the CO2 concentration in 1750 had been half the concentration that it turned out to be, the climate impacts that we are experiencing today would've happened in the 1980s.  So, we knew what was going on then.  We could've said, "Oh yeah, this is what's happening. 

 We understand that." So, in that respect, we would've been as able to deal with it, intellectually, anyway, as we are now.  They didn't have as good windmills and solar cells and things like that in those days, so it would've been more of a challenge than we face.  But it would've been a similar situation to where we are.  But if it had been 1/10th the concentration that it turned out to be, it would've hit the fan in about the year 1900.  So Arrhenius had a wild idea.  He would've said, "Yeah, I know what's going on." But they didn't have the spectrum of the gases,  and really, to do this right, you need computers.  So there was a lot of work yet to do.  It would've been harder to know that things were going so strange without the instantaneous global communications that we have today.   So it would've been significantly harder for them to deal with it than it is for us.   So, just a few more slides to summarize where we are. 

  The thing about CO2 that we release to  the fast carbon cycle of the atmosphere and the ocean and the trees is that it's got this very, very long clean-up time, like I showed you, hundreds of thousands of years.  So, this is from a review paper that Peter Clark wrote that I was a grateful coauthor on, showing how, if you dump CO2 into the atmosphere, it goes up to this higher new level and basically stays there.  There's a little bit of draw down as it equilibrates with the ocean.  But that's it.  And then, you're at this new normal, essentially forever, and that also applies to the temperature.  So you see, we go up to some new temperature, and then that's it.  It doesn't come back again.   So, in terms of temperature targets, the whole Paris meeting was about, they went into it with this idea that there was a maximum temperature to the global warming climate event that we don't want to exceed.  And they went into it with a maximum temperature of 2 degrees C.  What would it take to avoid 2 degrees C? And that was, I always thought that was kind of like a bridge engineer saying, "Well, I've got this design "for a bridge for you, but it's gonna fall down, probably. 

 "It's not really safe, but it's all you really want to afford." It's not exactly safe, right? It was kind of an intellectual compromise thing.  Two degrees is warmer than the planet has been in millions of years.   So what was astonishing about the Paris meeting was that they decided on a limit of 1 1/2 degrees.  We're at about one degree already.  So 1 1/2 degrees is significantly better, as far as I'm concerned, than 2 degrees.  But the thing is, to make this happen, the way it works is that there is a linear relationship  with a lot of uncertainty between how much carbon you ever release and what the temperature you will get out of it.  So, we've burned about 500 gigatons of carbon, and that's gotten us about 1 degree C of warming.  That's where we are.  And so, to keep it at 2 degrees C,  we could burn that much again, to 1,000, or we could burn another 250 to get to 1 1/2 degrees, which is what we agreed to in Paris.  It's a very simple sort of a thing. 

 Actually, there's a couple of nonlinearities that cancel out here.  One is the nonlinearity of the temperature from the CO2, which I told you, it goes logarithmically.  But on the other hand, you have the other nonlinearity about how much goes into the ocean.  Because if you put a lotta CO2 out into the air, the ocean buffer system loses its capacity.  You run out of carbonate ion, and so then, the atmospheric fraction goes higher.  So those two nonlinearities sort of cancel each other out to give us this more-or-less linear relationship, to which you have to add a factor of 50% or something on either side uncertainty because we don't really know the climate sensitivity of the Earth as well as we would like to.  But it's, at the face of it, a fairly simple linear relationship.  It's like this piece of pie.  You eat the whole pie, you're gonna get sick.  You eat half the pie, you'll get less sick. 

 You know, how fast you eat it doesn't matter.  Well, I guess it would matter if you were eating a pie, (audience laughs) but, for the carbon, it doesn't matter.  It just matters how much you release.   So, if we're on this exponentially increasing emission rate,  now, business as usual, if were to just change the sign on the exponent and start to cut today by a few percent every year, the emissions rate would ramp down like this.  And if you add up the total amount of carbon that was ever emitted, it would come in to something like 1,000 gigatons that would get us to the 2 degrees C that they were talking about before Paris.  But then, if wait longer, we have to cut more quickly until finally, if we wait until 2040, we're pretty much done, and we have to sorta go cold turkey.  And so, the thing about this is, that how much percent per year you have to cut, that determines how expensive it will be.  So, it's kind of like this homework assignment where you tell a student that you can write a five-page paper for Friday, or you can hand it in Monday, but it's gotta be 10 pages, or Wednesday, but it became 20 pages, or Friday, but it's gotta be a book. (audience laughs) It's got this sliding kind of a scale here.   So, the thing about carbon is that we emit it doing everything that we do.  So there's no single magic bullet that can solve the problem. 

 We use it for transportation and heating and electricity and manufacturing and food and all kinds of things.  So,  what has to happen was described  in this really cool paper.  It's an old paper now, but it's still right.  They're sort of imagining, okay, so here is emissions under business as usual, and this is what they wanted to stabilize at now, and so there's no single thing you can do to go from this top curve to the lower one,  so their idea was to split this up into lots of little things, which they call wedges.  So you may have heard about wedges.  Al Gore talked about wedges.  A wedge is defined as something that you do that ramps up to cutting some amount of carbon in the future, like a gigaton of carbon per year in the year 2050 or something like that.  So, the thing about these wedges is they're small enough that there are lots of those that we could start on today.  Existing technologies.  This is a table you probably can't read very well, but it's got 15 different things on here, existing technology that could each comprise a wedge. 

 And at this time, they were saying that we needed seven wedges to stabilize carbon.  Probably we need to do more than that now, but you can sort of choose them off the menu.  So, like the first one, efficient vehicles.  They're imagining 2 billion cars in the year 2050.  If you just make them get 60 miles a gallon instead of 30, that would be a wedge.  Or windmills are a wedge, nuclear power is a wedge, all these different things you could put together as wedges.  And then, the other thing you've got to remember about fossil fuels  is that most of it is coal.  So there's a couple hundred gigatons of oil in the ground, a couple hundred gigatons of natural gas, and thousands of gigatons of coal.  So, if we were gonna try to limit to 2 degrees C, one option would be to just go cold turkey on coal right now and then burn all the rest of the gas and oil that's there, and that would get us right to 1,000 gigatons.  So, the larger point is that  the big decision about what's gonna happen with Earth's climate is what we decide to do with that coal. 

 And it's hard to wean ourselves from petroleum 'cause we like to get around, and petroleum is really good for transportation.  So, thinking about giving up traveling and stuff like that, that's kind of the hard way, but nobody is all that emotionally tied to coal, right? And we have a large fraction of the world's coal, actually, in this country.  In Illinois, actually, my state.  So, we're sitting right at ground zero.  We are in control of what's happening here, and coal is the thing to watch out for.  We keep our eyes on the ball.  That's where the action is at.   So, my conclusion is that we got really lucky.  It could've been much, much worse, and we should take advantage of this fact that the fuse burned all this time to use all of our knowledge and our technology to deal with this problem.  Much easier than it would've been, could've been if it'd been different. 

 So, thank you, very much.  (applause)