The Science of Everything Podcast - Episode 142: The Greenhouse Effect

Episode Date: March 30, 2024

A detailed discussion of the greenhouse effect and its impact on Earth's climate. We begin with a discussion of Earth’s energy budget, the various greenhouse gases and their interactions with longwave radiation, and a summary of major sources of greenhouse gas emisions. We then examine the mechanisms of the greenhouse effect in more detail using the idealised greenhouse model and radiative transfer models. We conclude with an analysis of the sensitivity of Earth's climate to changes in greenhouse gas concentrations, and how this interacts with the atmospheric lapse rate. Recommended prelistening is Episode 141: Natural Climate Change. If you enjoyed the podcast please consider supporting the show by making a PayPal donation or becoming a Patreon supporter. https://www.patreon.com/jamesfodor https://www.paypal.me/ScienceofEverything

you're listening to The Science of Everything podcast episode 142, the greenhouse effect. I'm your host, James Fodor. So in this episode, we're going to talk about the greenhouse effect and how it acts to warm up the Earth's climate relative to what it otherwise would be. So we'll start with talking about the Earth's energy budget and then introduce the idea of the greenhouse effect and the impact of greenhouse gases have on our atmosphere. We'll talk about the different types of greenhouse gases and their role. in trapping different types of wavelengths of radiation that's submitted from the Earth's surface. We'll talk about the idealized greenhouse model, which is a simple mathematical approach to understand the dynamics a little bit better. We'll then talk about some more of the advanced concepts

like radiative transfer models and the sensitivity of the Earth to changes in radiative forcing due to increases in greenhouse gases. Recommended pre-listening is the previous episode. 141 on natural climate change. We're continuing on in that sense. series, so recommend you listen to the previous two in order to have the context for this one. So without further ado, let's get started and introduce the idea of Earth's energy budget. This refers to the different flows of energy to the Earth from the Sun and from the Earth out to space again. So Earth receives energy from the Sun, obviously. The Sun emits radiation mostly in the visible spectrum. It has a surface temperature of about 6,000 Kelvin, and by laws of black

radiation, that means that a body at that temperature will emit mostly in the visible spectrum, and this is called short wave radiation because it's relatively short wavelength. Now Earth is much cooler than the sun, it's about 300 Kelvin, and as an approximate black body it also emits radiation, but because it's much cooler, it emits radiation at much longer wavelengths, mostly in the mid to far infrared, and this was referred to as long wave radiation. The distinction between the incoming short wave radiation and the outgoing long wave radiation is extremely important for the greenhouse effect and we'll come back to this in a moment. Now, not all of the radiation that Earth receives from the sun is absorbed by Earth. About

30% of it is reflected back into space due to the albedo of Earth, the reflectivity of Earth, particularly light coloured surfaces such as snow or deserts reflect light. And the atmosphere also reflects some light, so that contributes to the albedo of Earth. The remaining 70% or so of non-reflected light is absorbed by the Earth's surface, including the land and the ocean. Of that, about two-thirds is absorbed by the surface, and then one-third is absorbed by the atmosphere directly. Without any greenhouse gases, so ignoring the greenhouse effect for the moment, the energy absorbed by the surface of the Earth would eventually be returned to the atmosphere by a combination of long-wave radiation, convection, and evaporation. And then from there,

it would be emitted back into space. So that's what would happen without any greenhouse gases. The greenhouse effect refers to the fact that greenhouse gases in a planet's atmosphere traps some of the long wave radiation emitted by the planet's surface, thereby raising the planet's temperature. The reason why greenhouse gases are able to trap energy in this way is because greenhouse gases are transparent to shortwave radiation that comes from the sun. So that incoming shortwave radiation, that just passes straight through the greenhouse gas.

gas, it doesn't affect them because it doesn't have the right amount of energy to excite the energy levels in the greenhouse gas molecules. We'll talk more about that in a moment. However, greenhouse gases absorb long wave radiation that's emitted from the Earth's surface. So it's kind of asymmetric. The short wave can come in, but the long wave can't get out, or at least not all of it can get out. So what happens when the greenhouse gases absorb some of this long wave radiation that's been emitted by the surface? Well, this heats up the atmosphere. and again, like any body of a certain temperature, the atmosphere will emit radiation. Some of it will be emitted up towards space and some of it will be emitted down towards the Earth's

surface. But notice the difference here. Originally, the long wave radiation was emitted out into space and it all left the planet, right, and sort of cooling the planet down. But now what's happened is that because some of that long wave radiation is absorbed by greenhouse gases, half of the energy that was initially absorbed is emitted in the same direction that it was originally going in, namely out towards space, but half of it is emitted back towards the Earth's surface, thereby trapping in the heat, and this is the key mechanism by which greenhouse gases warm up the planet. They absorb long-wave radiation, emit some of it out to space, sort of as normal, as it would have done anyway, but half of it is emitted back towards the Earth's surface,

thereby warming up the planet. effectively the greenhouse gases are acting as an insulator inhibiting the outward flow of energy. The Earth's average surface temperature in the 20th century has been about 14 degrees Celsius. It's about 15 degrees Celsius these days owing to global warming. But previously it was about 14 degrees. Without the greenhouse effect, the surface temperatures of Earth would be about minus 18 degrees. So about 30 degrees cooler. So it's a very significant effect at the greenhouse effect.

The greenhouse effect is naturally occurring, so it's not something that humans have caused, but what's happening is that the burning of fossil fuels over the past 250 years or so has released substantial quantities of greenhouse gases into the atmosphere, increasing the concentration of greenhouse gases, and thereby intensifying the greenhouse effect. So the greenhouse effect is not man-made, but it's man-intensified. As a result of this, we've seen a global warming of about 1.2 degrees Celsius since the Industrial Revolution. Most of that occurring in the 20th century and the early 21st century.

Since the 1980s, we've seen a global surface temperature warming of about 0.2 degrees Celsius per decade. Just to clarify the terminology here, the term greenhouse effect comes from anality to greenhouses. So both greenhouses and the greenhouse effect work by retaining heat from the sun. But the mechanism is a bit different. So in greenhouses, you have essentially a glass box that you grow plants in. These structures prevent heat from escaping mostly by blocking convection. So convection refers to rotating currents of air, which rise up and then cool, and then the air comes back down and forms a sort of a cyclical cell of airflow

that transports heat from the surface up into the atmosphere. The greenhouse blocks that, thereby retaining that heat within the greenhouse and enabling you to grow plants that otherwise would have difficulty in in the lower temperatures. Now, greenhouse gases don't block convection because they're gases, right? They don't stop the flow of air. What they do is they block radiation, or more specifically, they absorb long wave radiation that's emitted by the surface and re-emit half of it back downwards, thereby blocking or inhibiting the flow of energy, but in this case by radiation rather than by convection. So greenhouse gases, the greenhouse gases and actual greenhouses have a similar effect,

That is, they both warm up an area by blocking heat flows, but they block heat flows by different mechanisms. The greenhouse blocks them by blocking convection physically. Greenhouse gases block radiation by absorbing it and absorbing longwave radiation and then reemitting it back towards the surface. Or they emit half of it back towards the surface. So let's talk a bit about what the greenhouse gases actually are at a chemical level. So as I said before, a compound is a greenhouse gas if it absorbed, long wave radiation or specifically infrared radiation and this occurs if the molecule has the correct energy levels corresponding to the energy of infrared photons. Now as it turns out, this typically

occurs for the vibrational motions of diatomic and triatomic molecules that are made up of different atoms. So molecular nitrogen, molecular oxygen for example are diatomic but they are composed of the same element. And so they're not infrared active. The energy levels are wrong, so they don't absorb infrared radiation. The major greenhouse gas molecules that are present in the Earth's atmosphere are carbon dioxide, methane, nitrous oxide, and tropospheric ozone. So carbon everyone's heard about. It consists of one carbon and two oxygen atoms, so that's a tri-atomic molecule. Methane actually has five atoms, although four of them are hydrogen, it's a carbon, and four hydrogens, and then nitrous oxide is two nitrogen and one oxygen. And finally,

ozone is three oxygen atoms bound together. So you can see there's a similarity there. All of the molecules in question have either three heavy atoms or one heavy atom and four light ones. So there are sort of similar size, and their vibrational motions are what enables them to absorb infrared radiation, the vibrational motions refer to the basically the stretching and compression of the atomic bonds between the different components. So because you have different types of atoms in most of these, that contributes to a difference in electrone negativity between the atoms, which is one of the factors that enables the bond energies of the vibrational motions to be of the right level to absorb infrared radiation. Now, each of these molecules is infrared active, so it can

absorb that long wave radiation coming back from the surface, but they don't all absorb in the same amounts or in the same quantities. The global warming potential is a measure of how much infrared radiation a greenhouse gas molecule will absorb over a given time frame. Because of the way the global warming potential is defined, it's set to be equal to exactly one for carbon dioxide. So basically, we're measuring everything relative to the global warming potential, the absorbing potential of carbon dioxide. In addition to the ability of the gas to absorb infrared radiation, the global warming potential is also affected by how quickly the gas leaves the atmosphere. So carbon dioxide stays in the atmosphere for quite a long time. We'll talk about its residence time

a bit more later. But for example, methane has a much shorter half-life in the atmosphere, so that would tend to decrease its global warming potential. On the other hand, it's a much better absorber of infrared radiation, so that dramatically increases its global warming. warming potential. By considering both the quantities of different greenhouse gases in the atmosphere as well as their global warming potential molecule for molecule, we can measure how important the different greenhouse gases are as contributors to anthropogenic climate change. In doing so what we find is that carbon dioxide is easily the largest contributor. However, methane is also very significant. Carbon dioxide contributes to perhaps 50% more warming than

methane. By comparison, the other greenhouse gases, nitrous oxide, ozone, chlorofluorocarbons, and hydrochlorofluorocarbons, which are man-made molecules that I hadn't mentioned, they all contribute relatively small amounts, but still measurable quantities. So although there tends to be a focus in carbon dioxide in discussions about anthropogenic global warming, it's important to recognize that there are other greenhouse gases that contribute significantly as well. Now, there is an additional infrared active gas, which I haven't mentioned, and that's water vapor. In fact, water vapor is by far the most important greenhouse gas, even more so than carbon dioxide. It drives about two-thirds of the whole greenhouse effect. That's of all of the greenhouse effect, not the enhanced greenhouse

effect due to human activity. It's important to distinguish those. So two-thirds of the entirety of the greenhouse effect, so that's that 30-degree temperature difference. Two-thirds of that is driven by water vapor. However, the residence time in the atmosphere of water molecules is very low, a few days, and its concentration varies very rapidly over time and by place, likely dependent on the weather. As such, water vapor is not an independent driver of climate, rather it's an amplifier of existing climate effects from other greenhouse gases. So if we release a bunch of carbon dioxide or methane into the atmosphere, or for that matter, if we were through a bunch of carbon dioxide or methane from the atmosphere, that would have a significant effect on the total greenhouse effect.

And as a result, that would affect changes in the amount of water vapor held in the atmosphere, which would be a feedback effect. We'll talk more about those later. But if we dumped a huge amount of water vapor in the atmosphere, that would have a very short-term effect on the order of a day or two. But very quickly, that would be rained out of the atmosphere or precipitate out, and the atmosphere would return to it. original state. So adding water vapor to the atmosphere or withdrawing water vapor to the atmosphere in an exogenous process doesn't change the equilibrium state of the atmosphere because it's turned over so quickly and so easily by a range of processes. So this is something that

is sometimes confused in the discussion around greenhouse gas emissions when you'll hear people say that human emissions of carbon dioxide are tiny compared to the greenhouse effect of water vapor. That is true, but it's largely irrelevant to the question about whether human emissions of greenhouse gases, particularly carbon dioxide, are the leading cause of climate change over the past century, because water vapor is responding to other changes in the atmosphere. It doesn't exert its own exogenous effect on the temperature or on the atmosphere. Compared to water vapor, which, as I said, stays in the atmosphere for only a few days. Other greenhouse gases stay in the atmosphere from decades to centuries, depending on which

gas we're talking about. Individual CO2 molecules have a residence time in the atmosphere of about 10 years. So on average, they stay there for about 10 years, give or take. I've seen figures of 5 to 15. It's a bit uncertain. However, that is not a measure of how long it takes the climate system to respond to changes in CO2 content. That's a measure of how long an individual CO2 molecules stays in the atmosphere. The total time taken for the climate system to adjust to human-induced changes or or changes induced by other means, is much longer on the order of several centuries, although we don't know this very accurately. The reason for this difference is because when there's additional CO2 released into the atmosphere,

some of it will be absorbed or taken up by readily accessible CO2 sinks, mostly in the upper levels of the ocean and in the soil. However, these readily accessible sinks are mostly already saturated. They can take up a bit of extra CO2, and that depends on what the partial pressure of CO2, is in the atmosphere, but they don't have a very large additional capacity. There is large additional capacity for CO2, mostly in the deep ocean, or in conversion of that CO2 into mineral forms by biological or geological processes, and some of those we discussed

in the previous episode, like the silicate weathering process. However, those processes take centuries to thousands of years, depending on which one we're talking about. Deeper oceans on the order of centuries, and geological processes probably thousands or even hundreds of thousands of years. That's why it takes a very long time for the atmosphere to adjust to human changes in CO2 concentrations. It takes at least centuries for that CO2 to start being removed from the atmosphere in significant quantities because it takes a very long time for the carbon dioxide to be removed to the deep ocean or into mineral forms.

However, as an ongoing process, individual CO2 molecules are being interchanged with CO2 molecules found in the upper level. of the ocean or in the soil. But there's no large scale net interchange of material from the atmosphere into the ocean or the soil on the scale of a few decades. There's a little bit of a response, but mostly, as I said, those stores are already fairly saturated. They'll respond a little bit if there's an increased partial pressure in the atmosphere. But to get a large scale reduction, you have to start moving that material into the deeper ocean or into mineral forms or other biological stores, and that takes a very long time. So that's another point that's sometimes confused. So some people say, well, the CO2 molecules only last like five or ten years in the atmosphere,

so human warming can't be having a prolonged effect. And that misunderstands the difference between the residence time of a single molecule and the time it takes the climate system to return to an equilibrium condition by removing the carbon dioxide from the atmosphere. And that will take many centuries or even millennia. Another important thing to understand about greenhouse gases is that just as different greenhouse gases have different efficiencies or abilities, to absorb infrared radiation, molecule for molecule, they also absorb different wavelengths of

infrared radiation. So obviously, infrared is a fairly wide region of the electromagnetic spectrum, and different types of greenhouse gases absorb different subregions within the infrared origin itself. So water vapor, I mentioned, the most potent greenhouse gas of all, absorbs many different regions in the spectrum. One of the reasons why carbon dioxide is such an effective of greenhouse gas is because two of its main absorbing areas in the spectrum, that is, two of the biggest ranges of wavelengths of infrared radiation, that it is capable of absorbing, lie roughly within the troughs of the water vapor absorption regions. So that is where water vapor can't absorb infrared radiation, because it doesn't have the right energy levels,

carbon dioxide can. And so carbon dioxide, as its concentration in the atmosphere is increased, it starts absorbing more and more of these, of the photons that lie within this range of wavelengths that water vapor can't absorb. This is important because if you have two molecules which both absorb the same subset of wavelengths within the infrared region, and one of those is already saturating that wavelength region, meaning it's absorbing pretty much all of the emitted photons from within that range of wavelengths, then adding extra concentrations of one or the other, of those two greenhouse gases won't really make any difference because all of the radiation is already

being absorbed, right? And that's why carbon dioxide has such a potent effect, precisely because some of its absorption bands lie exactly within these trough or close to these trough regions of the water vapor absorption where the water vapors are not absorbing, but carbon dioxide is absorbing. This gives rise to another misconception about the greenhouse effect, which is some people say that the main range of wavelengths that carbon dioxide absorbs at is already saturated, meaning all of the radiation in this band of wavelengths is already being absorbed by greenhouse gases. So the argument goes, if we add more carbon dioxide, it won't make any difference. Sure, there'll be more CO2 molecules in the atmosphere, but the existing concentration of CO2

is already absorbing all of the photons that are emitted within that band, so adding more CO2 molecules won't make any difference. Now, that's false on two accounts. One is that it's not true that the band of radiation where CO2 absorbs is entirely saturated. This is around a wavelength of about 15 or 16 micrometers, for those who are interested, but it doesn't really matter for our purposes. So this sort of 15 micrometer region, yeah, the central region of that is largely saturated, meaning that adding more CO2 molecules doesn't lead to greater absorption of infrared radiation

in the center of that band, because most of it's already being absorbed. But what happens is that the edges on the side of that band around like 18 micrometers on one side and about maybe 13 on the other side, those become wider in the sense that more radiation is being absorbed at the edges of this band because there's more carbon dioxide. Carbon dioxide is not as good an absorber at the sides. It's best absorbing at the middle of this region, right? But if you add more carbon dioxide to the atmosphere,

then even in regions where it doesn't absorb quite as well, like on the edges of this region, like 18 and 13, it's still going to be able to absorb a larger proportion of the photons that are emitted with those wavelengths. So that's one aspect of why this argument that the greenhouse effect of CO2 is saturated is incorrect, is because it may be saturated in the central region, but it's not saturated at the edges, where a higher concentration of greenhouse gases, or CO2 in this case, does lead to additional absorption. Now there's a second reason why this argument is false, but we'll come back to that in a moment

when we talk about the importance of the lapse rate. But hang on to that thought for a moment until we get there, because there are a couple of things that I want to discuss first. One is I just want to discuss greenhouse gas emissions. So we've talked about what greenhouse gases are and that they have in causing the greenhouse effect. We should know a little bit about the trend of greenhouse gases, over time and what's been happening. So I mentioned in the previous episode when we looked at

historical climatology that carbon dioxide concentrations in the atmosphere have changed dramatically over Earth's history. Typically they've been much higher in the past than they are at present. In pre-industrial time, so let's say the 18th century and in the centuries prior to that, atmospheric carbon dioxide concentrations were relatively stable at about 280 parts per million. So the absolute concentration is fairly small. We're talking parts per million, which is much less than 1%. If we go back further into prehistoric time and look at what's been happening over the most recent ice age, so the last 2 million years or so, we see that carbon dioxide concentrations have fluctuated

on roughly the 100,000-year time span of the glacial interglacial cycles that we talked about last time. And that's not surprising, because as we've discussed, there are various feedback processes that operate to adjust the concentration, to adjust Earth's concentration of carbon dioxide alongside the temperature. And what we see over the course of the last million or so years is that during the interglacial periods, like where we are now, the carbon dioxide concentration is higher, closer to 300 parts per million. Whereas during the peak of the glacial periods, such as we were in about 20,000 years ago when it's the coldest, the concentrations of carbon dioxide are much lower, down more like 200 parts per million. So that's a pretty significant

difference, a 50% or more difference over the course of, you know, 100,000 year cycle. There are many processes that contribute to that feedback processes, but we won't cover those now. We talked about some of them in the previous episode. What we want to understand here is just the trends over recent and also longer time spans. If we go back millions of years, as I said, the carbon dioxide levels were much higher. If we go back, for example, during the Triassic and the Jurassic periods, then the CO2 concentrations reached levels something like 15 or 1,600 parts per million, which is something like five times the level we have today.

And even further back, the carbon dioxide levels may have been even higher than that, perhaps 2 or even 3,000 parts per million. One question that has arisen here is how it was, was possible for the earth to remain habitable with such high concentrations of greenhouse gases. If we had those concentrations of greenhouse gases today, life would probably be impossible. Well, not microbial life, but at least human life probably wouldn't be able to be possible because of the huge amount of heat that would be trapped in and the very high temperatures we would see as a result.

One of the likely explanations for this is that, as I mentioned in the previous episode, the sun has progressively increased the quantity of radiation that it emits over geological time. I think about two billion years ago it was about 30% dimmer than it is now, something along those lines. And it's thought that that gradual increase in the amount of radiation emitted by the sun has meant that over geological time, Earth has required less and less carbon dioxide in its atmosphere to maintain a comparable temperature. So essentially as the sun is heated up, the corresponding, concentrations of carbon dioxide on Earth have decreased, maintaining comparable temperatures.

Of course, the temperatures have changed quite a lot of a geological time as well, as we talked about last time. They're about plus or minus 15 degrees either way, at the coldest compared to the hottest times. But the magnitude of that change has been muted by the gradual reduction in greenhouse gas emissions, on average. It's gone up and down, but on average, it has gone down over geological time. And it's thought that that may largely be due to the silicate weathering feedback process that I mentioned before in the previous, So basically, when the Earth is hotter, rates of chemical weathering increase, that process pulls carbon dioxide out of the atmosphere, thereby reducing the magnitude of the greenhouse effect,

thereby cooling the Earth. And vice versa, when the Earth is cooler, rates of weathering decrease, which increases the amount of carbon dioxide that's in the atmosphere, and thereby warming the planet. So there's this feedback process. There are probably others as well, such as biological feedback processes. For our purposes, though, what's important to understand is that over geological time, there has been a slow and uneven but noticeable trend of diminishing carbon dioxide concentrations. And if we go back millions of years ago, carbon dioxide concentrations were much, much higher

than they are today. That does not, however, have much bearing on issues of current understanding of the enhanced greenhouse effect due to human activity. One, because the changes in greenhouse concentrations due to natural processes are much, much slower than those, than the changes that have been occurring due to human activity, as I'll mention in a moment. So the time scales are just radically different. The second point I mentioned is that the sun has increased in its emissions over time, and so we now need less carbon dioxide to achieve the same amount of warming than we did in the past. So comparing

just the carbon dioxide concentrations is a bit misleading. And the third point is simply that there's probably not some kind of ideal carbon dioxide concentration in the atmosphere, at least within a certain range, there's probably many different possible concentrations that would be conducive to human well-being and animal well-being as well. But the issue is that humans have built our civilization of the past few thousand years on roughly 280 parts per million concentrations of carbon dioxide and the consequent types of climactic conditions that is associated with. rapidly changing those will cause a whole lot of problems because of where we've built our cities

and the types of crops we go and where we grow them and other things like that. So it's an issue of the change and the rapidity of the change. And this is a point that we'll be discussed later on when we talk about the impacts of climate change. But the bottom line there is just comparing current day CO2 concentrations to those many millions of years ago is not very informative from the perspective of assessing how problematic those recent changes are. Now when we talk about recent changes let's try to give some figures for that starting about 1750 when industrial activity really accelerated by burning of fossil fuels in the United Kingdom and then later in Europe North America and elsewhere in the world we see a

progressive increase in the concentration of greenhouse gases especially carbon dioxide in the atmosphere the growth in emissions was pretty slow at first but accelerated around the sort of late 19th century with a more rapid industrialization in many parts of central and eastern Europe. And then there was a further acceleration around the end of World War II when industrialization began in many parts of the world outside of Europe and North America. So beginning from a carbon dioxide concentration of 280 parts per million in the mid-18th century, by 1900, the concentrations had already gone up to about 300 parts per million, which is already a pretty significant increase given the relatively

modest amount of industrial activity by that point. By 1950, the concentration of carbon dioxide in the atmosphere had increased to something like 310 or a bit more parts per million, and as of December 2023, CO2 concentrations were 422 parts per million. So that represents a 140 part per million increase over pre-industrial levels, or about a 50% increase in a period of about 250 years. That is extraordinarily rapid on a geological time scale. Even when looking over the past Ice Age, the past million years or so, we see that carbon dioxide concentrations take tens of thousands of years to significantly change. As I said, over the 100,000-year period of the Ice Age cycle,

we see carbon dioxide levels change by about 100 parts per million in 100,000 years. By comparison, humans, in only 250 years, have increased the carbon dioxide concentration, by far more than that, by 140 parts per million, and still increasing. So you can see there's a massive difference here in the time scale, and also a massive difference in the maximum level, because in the past million years, the maximum concentration of carbon dioxide that we've seen is only about 300 parts per million,

and that typically occurs at the interglacial periods where the Earth is relatively warmer. Now, we're already starting from that relatively higher level, and we've already increased up to 420 parts per million, which is much, much higher concentrations of carbon dioxide than has been seen in the last couple of million years. You have to go back really before the most recent ice age to see carbon dioxide levels that high. And the effect is all the more magnified when instead of only considering carbon dioxide, you consider human emissions of other greenhouse gases, especially methane.

When you use the global warming potential of those and take into consideration the different factors of like lifetime in the atmosphere as well as their ability to absorb different wavelengths and you calculate the number of molecules of CO2 equivalent we have of each of those other greenhouse gases and you convert that to a common measure. We arrive at a figure of something like 530-ish parts per million of CO2 equivalent in the atmosphere. So that's not literally the CO2 concentration,

but that's kind of the equivalent if you adjust the other greenhouse gases as well, especially methane. So based on that figure, we're pretty close, not quite, but pretty close to doubling the concentration of greenhouse gases in the atmosphere since pre-industrial levels over the past 250 years. And most of that effect has occurred in the past, say, century or so. So the changes here are extremely rapid. Currently, we're emitting about 32 billion tonnes of carbon dioxide every year. That quantity has increased, as I said, rapidly, especially since World War II. As of 1945, we were only emitting

about 5 billion tonnes of carbon dioxide into the atmosphere. So it's increased about sevenfold in the past 70 years or so. The rate of increase has slowed in the past decade or so, but it is still increasing. In terms of where these carbon dioxide emissions are coming from, and greenhouse gases more generally, we have a reasonably good idea. So burning of fossil fuels is the largest source of greenhouse gas emissions. It contributes about 62% of human-caused greenhouse gas emissions, or that figure is as of 2015, so it might be a bit different now. The single largest cause within that is coal-fired power stations, which contribute 20% of all greenhouse gases.

So 20% of all greenhouse gas emissions into the atmosphere, which is, that's a very inclusive number there, is just coal-fired power plants. So that's why there's such focus on cutting fossil fuel emissions, because it's by far the largest contributor to greenhouse gas emissions. There are other contributors, however, land use changes such as deforestation, mostly in the tropical regions, which introduces carbon in the atmosphere by basically what tends to happen is that the wood that's cleared from these

forest regions is burned, which releases the carbon back into the atmosphere. So that accounts for about a quarter of all anthropogenic emissions. So burning of fossil fuels plus deforestation, together account for something like 85% of all greenhouse gas emissions. Much of the rest is a can of full by animal agriculture, including enteric fermentation and release of methane from manure of livestock. That contributes significant quantities of methane into the atmosphere. The amount of methane is relatively small compared to the amount of carbon dioxide, but remember, it's far more effective as a greenhouse gas. So in terms of its equivalent effect, that's much larger. The last major source of greenhouse gas emissions is refrigeration, so chlorofluorocarbons and hydrogenated

chlorophyllular carbons are synthetic compounds that are used in fire suppression and manufacturing for refrigeration and cooling purposes. Those are also potent greenhouse gases, but the quantities of those is much, much smaller than those released by deforestation and especially burning of fossil fuels. Now that we understand a bit more about the historical time course and trajectory of greenhouse gas emissions and a bit about their source, I want to talk a bit more in detail about how the greenhouse effect actually works. And to start, we're going to talk about something called the idealized greenhouse model.

It's sometimes also called it the zero-dimensional model. This is a very simple mathematical model that's taught in university courses and is contained in the textbooks about greenhouse effect and about climate. And it's a very crude simplification of Earth and the climate, but it is very effective at illustrating the key process. operative to generate the greenhouse effect for such a simple model.

And obviously I can't describe all the equations in this audio podcast, but I want to describe the logic about what's happening so you can understand the model. It forms the foundation for more complex methods, which we'll talk about in a bit for modeling the climate, but also it's informative in its own right. So the basic idea of the there is a zero-dimensional model is that we treat Earth as a series of discrete layers. Now, this is often visualised as horizontal lines. You know, one horizontal line at the base is the surface, and then there'll be a horizontal line corresponding to the atmosphere, a bit above that. That's a simple two-layer model. You can have more layers, but let's just focus on a simple two-layer model for the moment. So essentially just the surface and then the atmosphere.

Now, they're drawn as horizontal lines, but really that horizontal dimension is just for visualization purposes. In fact, the model is zero-dimensional. So really we're just conceiving of the Earth a point and it's a point that has kind of two different layers to it, the surface and the atmosphere. And what we're going to do is we're going to model the flows of energy between those layers and in the diagrammatic representation you just draw arrows and write numbers next to them representing the magnitude of the radiation corresponding to those arrows. So this idealized greenhouse model is a very simple model we're ignoring convection completely and we're ignoring the effect of water vapor and of evaporation and

and many other clouds and many other real effects that exist in the atmosphere. We're just trying to focus on the key driving force of radiation and the trapping of radiation by greenhouse gases, which is the whole thrust of what the greenhouse effect is about. So first of all, let's talk about a planet that doesn't have any greenhouse gases in the atmosphere. So this is very simple. What we have is we have incoming solar radiation. Now about 30% of that is just reflected from the surface straight back into space.

So we can kind of forget about that because it doesn't feature further into the model. Remember, the incoming radiation is shortwave radiation, so it comes straight through the atmosphere. Although in this case, the atmosphere doesn't have any greenhouse gases in it, so the atmosphere is not doing anything anyway. So what happens is that incoming solar radiation, 70% of that is absorbed by the surface, and then that 70% is then emitted, but now at long wave lengths. So in the infrared region of the spectrum, it's absorbed as shortwave visible radiation, but it's emitted as a long wave radiation. But because the atmosphere doesn't absorb any of that because there's no greenhouse gases in the atmosphere

in this starting model, it just goes straight out into space. So 100 units of energy come in, 30 are reflected, 70 are absorbed by the surface, but then are emitted again just at a lower temperature because the surface of the Earth is at a lower temperature compared to the surface of the sun, obviously, and correspondingly at a longer wavelength.

There's a bit of math to do here using the Stefan Boltzmann Law, which is a relationship between the quantity of energy emitted by a body and its temperature. And when you plug those numbers in, using the real quantity of energy that's absorbed from the sun and a couple of other parameters, you find the equilibrium temperature of Earth is expected to be about minus 18 degrees Celsius. This is similar to the figure we gave before about the temperature of the Earth without any greenhouse gases. So without the greenhouse effect, Earth would be very cold indeed. Now, before we add in greenhouse gases to our idealized model, I want to mention

that this Stefan Boltzmann law is extremely important. And one of the important things about it is that the relationship between the energy emitted and the temperature is what's called a quartic function, meaning that it's temperature to the power of four. And what that means is when temperature goes up even a little bit, the amount of energy emitted goes up very, very rapidly, like much more than linearly, even in the much more than quadratic. It's actually a quartic, so it's to the power of four. So that means that only very small temperature changes are required to significantly change amount of energy that's emitted by a body. So that will be important later on. So just bear that

in mind that we've got this power of four there that means that there's a very strong non-linear relationship between energy and temperature. Okay, so now we're going to take our idealized model and add in a layer of greenhouse gases. So we're imagining these as if all of the greenhouse gases existed in just one layer above the earth surface. So that's obviously a big simplification. And we're going to forget about the difference between different wavelengths and different types of greenhouse gases. We're just going to pretend that they're all kind of the same. So now this complicates the model a bit. So let's walk through what the energy flows now look like. So we still have the hundred units of energy coming in from the sun in shortwave. That passes straight through the greenhouse gases because remember greenhouse gases don't absorb short wave radiation from the sun. So they still come straight in.

30 units are reflected back into space. Those are still short waves. So they're just reflected back. So they pass straight through the atmosphere once again. Greenhouse gases aren't affected by that. So now we have 70 units that are absorbed by the surface of the Earth. That's the same as before. So far. no changes. Now the surface of the Earth emits 70 units of radiation, this time long wave radiation as we know because the Earth is much cooler than the Sun so it's longer wavelength. What's different now is that this radiation is absorbed by the greenhouse gases in the atmosphere. Not all of it is absorbed, some of it makes it through, and the amount that makes it through depends on essentially how thick the greenhouse gases in the atmosphere are, not literally thick but like how what the concentration

is, the term is optical thickness. That basically just means what the concentration is of greenhouse gases in the atmosphere and how effective they are at absorbing the long wave radiation. So in this example, let's say that we have 25 units of the 70 units of energy, are able to make it through the layer of greenhouse gases. So that means that we have 45 units of energy absorbed by the greenhouse gases. What happens to that absorbed energy? Well, it heats up the greenhouse gases. which then emit long wave radiation, just like the surface of the Earth does. That energy is emitted kind of randomly in all directions, and so in this simple zero-dimensional model,

that basically means that half of it is emitted up, and half of it is emitted down, up being towards space, and down being back towards the surface of the Earth. So just to recap, we've got 70 units of energy coming up from the surface of the Earth. 25 of that manages to pass through, so that's 45 left. That 45 is absorbed by the greenhouse gases in the atmosphere, and then is emitted again, half of it up and half of it down. So let's say 22 units up and 22 units down, to round it off a bit.

Now let's think about the effect of that. 22 units of energy are now emitted back down towards the surface of the Earth, meaning that only 22 plus the initial 25 that made it straight through actually reaches space. So this sums to approximately 50 units of energy that actually make it to space. I'm rounding a little bit for simplicity, let's call the 50 units, right? Now, that's a problem, right? It's a problem because Earth is receiving 70 units of energy from the Sun. I mean 30 were reflected as 100 initially 30 are reflected. So it's absorbing 70

But it's only emitting 50 That means there's going to be a build-up of heat or in the surface of the Earth I mean that's what happens when you absorb more energy than you release is that you accumulate energy and therefore you increase in temperature And that's exactly what happens the Earth heats up because energy is being trapped in it's not releasing, it's not emitting as much energy as it's receiving. So the surface of the earth heats up. What happens when the surface of the earth heats up? Well, remember the Stefan Boltzmann law, it says that the energy released increases to the fourth power of the temperature. So if we increase Earth's temperature just by a little bit, that dramatically increases the amount of energy that's emitted.

So now, instead of only emitting 70 units of energy, Earth will emit more units of energy, which means that more energy will be absorbed by the greenhouse gases in the atmosphere, and more will be emitted both up and down. So eventually, an equilibrium will be reached. The Earth will continue to heat up until the energy that's emitted at the top of the atmosphere, back out into space, is equal to the energy that's absorbed from the sun. And you can solve, basically, there's a simple equation, you can solve to compute what the temperature at the surface of the Earth will have to be

in order to make that balance. And it depends, as I mentioned before, on the concentration and the sort of effectiveness, the absorbativity of the greenhouse gases in the atmosphere. In this simple model, using relatively realistic parameters, but it does depend on exactly which parameters that are used, what we find is that in order for the surface of the Earth to emit enough radiation to the atmosphere, for the atmosphere to then emit enough to space to balance all of the energy coming in from the sun, it means that the temperature of the surface of the Earth has to be about 20% hotter than the temperature of the Earth.

atmosphere. Because in this model there's separate temperatures for the surface in the atmosphere because there are two different layers, right? That's the whole point of the model. At that temperature, the Earth emits about 115 units of energy, of which 25 pass straight through the greenhouse gases and escape into space, meaning that 90 units of energy are absorbed by the greenhouse gases, 40 of them are emitted back towards the surface of Earth, and 45 are emitted out into space. So if you do the sums, you work out that 25 that go straight through, plus the 45 that are emitted upwards from the atmosphere, that sums to give 70, which is the same as the amount of energy that's absorbed from the sun.

So 70 comes in, 70 goes out, now Earth is in balance. And if you're wondering, well, how does the surface of the Earth emit 115 units of energy when only 70 come in from the sun? The answer is that the total amount that's emitted by the surface of the Earth, compared to the atmosphere, the surface of the Earth, will be equal to the amount that's absorbed from the sun, which is 70, plus the amount that's absorbed coming back from the atmosphere, which is 45. So this reflects the fact that the surface of Earth has warmed up

in order to be able to emit more energy to compensate for the fact that some of the energy that it emits is absorbed by the atmosphere, the greenhouse gases in the atmosphere, and emitted back to the surface, thereby not escaping into space. So that reduces the amount of energy that escapes to space, causing an accumulation of energy in the Earth's surface, and requiring the surface of the Earth to warm up, in order to be able to increase the total emissions of energy to space,

and thereby bring the system back into balance. If you do the calculations here, applying the power of four law, remember that links energy levels to temperatures, we determined that the temperature of the surface of the Earth is expected to be around 14 or 15 degrees Celsius, which is pretty much the same as measured values. Of course, that does depend on exactly a couple of parameters that we had to plug into the model, which we won't get into,

and you can get slightly different values, if you choose different values of those parameters. Also, we have discussed here a very simple one-level case, whereas in reality the atmosphere has multiple different levels, and there's a gradation of temperatures and things like that. We can incorporate that by making the model more sophisticated, by incorporating more levels, which means the equations get more complicated,

but it doesn't change the fundamental analysis. And the fundamental point to make from this analysis is simply that we can understand and even quantitatively predict with reasonable accuracy for how, simple the model is, the process of energy accumulation by the Earth and therefore resulting temperature increases as a result of increased quantities of greenhouse gases. We don't need a very complicated model to show this. In fact, a very simple arithmetic model using just a zero-dimensional treatment of Earth and the atmosphere is sufficient to illustrate

this effect. And so I think this is a very simple but very powerful model. Now, as I said, the real Earth's atmosphere doesn't just have two layers. it has multiple layers, but also that layers aren't really distinct from each other. They're not discrete separate layers, but they sort of grade into each other. It's continuous, right? So a better treatment doesn't use separate discrete layers, but it uses calculus to integrate over infinitescally many very, very thin layers of atmosphere. And what you do is you calculate the integral weighting each tiny, infinitescidentally small layer

of atmosphere by the amount of gas in each. And that allows you to compute the total amount of emission and absorption across the entire height of the atmosphere. This can be done using what's called a radiative transfer equation, which is pretty similar to the simple zero-dimensional model that we just discussed. It's just instead of making the very simple approximation of just two layers, like the surface and one layer of atmosphere, now it allows for a much more realistic gradation of continuous layers of atmosphere with like different pressures at each layer. This model can also be extended by using what's called line-by-line radiative transfer models. What this means is that in the previous zero-dimensional

model, we just forgot about wavelength and just assumed that all of the energy is emitted and absorbed at the same wavelength. Obviously, that's not realistic, but what it does is enable us to focus on the energy flows. Every type of wavelength carries energy. It varies by the frequency, but we can still just treat the energy as a single unit. But to get a more realistic picture, we need to consider the wavelength of different wavelengths that are emitted and absorbed, because greenhouse gases absorb and emit more readily at some wavelengths compared to others. So what we can do is we can construct these radiative transfer models and compute these integrals that I mentioned for each wavelength. So that's what they mean by line by line,

basically looking at each small region of the electromagnetic spectrum separately and then computing those separately and adding them all together. Now, even this approach, which is much more sophisticated than the zero-dimensional model. But even this approach is still highly simplified. For example, we're still ignored convection. We're only talking about radiation here. We still haven't talked about the feedback effects of clouds, the lapse rate, and so forth. However, incorporating these effects becomes too difficult to do with an analytically tractable model, and we need to use complex simulations in order to be able to incorporate those. And we'll talk about these more complex climate models in the next episode. But what I wanted to

emphasize here is that these fairly simple models, such as the radiation, transfer models are still very useful for computing fairly accurate predictions about the relationship between greenhouse gas emissions and temperature changes. One thing that's been found as a result of these line-by-line radiative transfer models, for example, is that the radiative forcing as a result of doubling of carbon dioxide concentrations in the atmosphere is approximately logarithmic in the carbon dioxide concentration. And that has this nice property whereby it means that there's a relatively constant effect of of radiative forcing for every doubling of carbon dioxide concentrations, at least over a fairly

wide range, you know, like 300 to 1,000 or so, which are the kind of ranges we're interested in. That also means that there is a diminishing effect of carbon dioxide. So the first additional, say, 100 parts per million has more warming than the next 100 parts per million of warming. So that's kind of good news, but there is also tends to be an exponential increasing process whereby it's not that the amount of carbon dioxide grows by 100 units a century or something like that it's more likely to increase by a certain percentage every century. And so they sort of tends to balance itself out. But anyway, it is a useful result from these models that, roughly speaking,

a doubling of the carbon dioxide concentration in the atmosphere has a constant effect of radiative forcing. And now to understand a little bit better, let's talk about the relationship between forcing and temperature. Because remember, when we talk about radiative forcing, all that means is converting the concentration of greenhouse gases, in this case, say carbon dioxide, into the equivalent effect of the amount of energy change. Radiative forcing is measured in watts per meter squared, so that's energy per unit of surface area of the earth, that that results in. There's a couple of ways to think about this.

You can think of it as in, when we increase the carbon dioxide concentrations by a certain amount, how much of a change in outgoing radiation does that result in at the top of the atmosphere. So typically that's going to reduce the outgoing radiation at the top of the atmosphere because it's trapping in the energy, right, as we just discussed. Alternatively, you could think about it in terms of how much extra radiation would we need to receive from the sun in order to have the same effect on the Earth's energy balance as this amount of increased concentration of CO2. It's kind of equivalent, whichever way you want to think about it. But that's why it's called radiative force, because it's introducing a change into the radiation balance that we just talked about, which will then

lead to a change in temperature. So the question, of course, is what is the relationship between changes in radiative forcing and changes in temperature? So as I just mentioned, line-by-line radiative transfer models, as well as other techniques, estimate that there's a roughly logarithmic relationship between carbon dioxide concentration and radiative forcings. And specifically, what we expect from these results is that each doubling of green, of carbon dioxide concentrations in the atmosphere results in a forcing of about 3.7 watts per meter squared. That's a relatively large effect. Remember that the changes in solar forcing from the sun owing to either the 11 year sunspot cycle or just sort of periodic wanderings of the

of the radiance of the sun amount to only about one watt per meter squared and that's effect on the earth is actually diminished because it's spread out over the entire surface of the earth, not only the quarter of it that actually faces the sun. So a 3.7 watts per meter squared effect of doubling greenhouse gas emissions is very significant, much larger than any effect of changing solar forcings that we've seen over the past decades or even centuries. Now, to understand the effect that that's likely to have on temperature, we need to have a relationship between the forcing and the temperature. This figure here is known as the climate sensitivity. The sensitivity refers to how much will Earth's climate once it reaches the near

equilibrium, how much will the temperature change in response to a particular amount of forcing? This number is a very controversial one, and we'll come back to that in a moment. But first, let's talk about how much of a forcing we've actually seen as a result of human activity over the past couple of centuries. So as I said, at the beginning of the Industrial Revolution, greenhouse gas concentrations were about 280 parts per million. That's increased to 420 parts per million considering just CO2, or if we're considering all greenhouse gases, it's gone up to about 520 parts per million. So because all greenhouse gases contribute to warming, we should probably use that higher number. And because we've converted everything into equivalent concentration of CO2,

we can just use the CO2 forcings measure. So 520 parts per million is about an 85% increase relative to greenhouse gas concentrations in 1750. That leads then to a radiator forcing of about 3.3 watts per meter squared. Not quite a doubling, so a bit less than the 3.7 from doubling, about 3.3 watts per meter squared. Now then comes the issue of the sensitivity. This figure is something that the IPCC, the international panel on climate change, discusses at length in their periodic reports. Because the amount of temperature change resulting from a change in forcing is affected by many different factors, including the many climate feedbacks that we'll look at in a moment. There's no easy way to calculate this number, and the number that you get depends on exactly

what factors you've included. So let me briefly walk through a number of factors that are included and talk about how the estimated sensitivity changes as you include more factors. The first factor to be included is simply the Stefan Boltzmann response to radiative forcings. So we know about this, we've just talked about it. As the temperature of Earth increases, the energy that's emitted by the surface of the Earth increases to the fourth power of that temperature increase. That by itself is a very strong negative feedback. So essentially, as the Earth warms up even a little bit, Earth emits much more radiation relative to previously. And that means that the Earth then cools that much faster relative to what it would have previously. It's not a true

feedback because it's a direct part of the radiative forcing sort of in temperature response process. It's not a kind of a separate process like the water vapor or the ice albedo feedbacks we'll talk about later. But it's a feedback that's sometimes included along with the other feedbacks. And it's a starting point for computing the sensitivity. So if you just use the Stefan Boltzmann law to take the derivative with which forcing's changed with temperature and then plug in the relevant values, you get a sensitivity value of about point. of about 0.25 degrees per watts per meter squared. So in other words, for every watts per meter square of forcing that the atmosphere has, the equilibrium temperature of the surface of the earth will

increase by about 0.25 degrees. That's not a very high number, but it's still significant, obviously. So using this number, a doubling of greenhouse gas concentrations would increase equilibrium temperatures by about 1 degree. As I've said, it's still quite significant. But this is a gross underestimate of the sensitivity parameter because we haven't looked at any of the feedbacks. If we now add a bit more complexity to our model and use a radiative convective equilibrium model, so this is one that doesn't just factor in the temperature change, but also looks at exchanges of energy via radiation and convection between the surface of the earth and the atmosphere, we can get a better estimate in particular of how much

water vapor will be added to the atmosphere as a result of the increased temperatures. These models are still relatively simple, but much more complex. complicated than the zero-dimensional idealized models that we talked about. These are basically using radiative transfer methods to compute the amount of radiation transferred between the surface and the atmosphere, and also incorporating the effects of convection to see how much water vapor will likely change as a result of the increased temperatures. Because water vapor, as we've discussed, is the most potent greenhouse gas. It's just that it doesn't result in external changes to the climate because it responds to changes in the climate, because of its short residence time in the atmosphere.

When we use these models to incorporate the feedback effects of weather vapor, we get a combined sensitivity of Stefan Boltzmann temperature feedback plus water vapor feedback of about 0.5 Kelvin per watts per meter squared, so about a double sensitivity. Now from there, there are still further feedbacks that we want to include, including, as I mentioned before, ice albedo, clouds and others. Those are much more difficult to model. I'll talk in a moment about how we can model some of those.

But the point I wanted to make is that even if we just include the fairly simple methods of temperature change resulting from radiation flows, plus water vapor changes resulting from radiation and convection, we get a combined sensitivity of 0.5. Now, the best estimates of the IPCC have varied over the years, but haven't changed much from about 0.8. in the recent reports they've provided a range of values but mean estimates so the best estimate is about 0.8 and those are based on very complicated models and a range of techniques the point though is that we can get a fairly good estimate of the sensitivity parameter by just including even the most simplest of feedback so the temperature change from stephen bolzman resulting in more energy release plus the feedback of water vapor that gets you to 0.5 which you know is lower than but not dramatically different from from 0.8. So although those feedbacks alone, without considering others, would underestimate the

warming, it doesn't change the fundamental picture, which is the point that I want to make, that you don't need extremely complex models to get a reasonable estimate of radiative forcing changes or of climate sensitivity changes. Let's then take this figure of about 0.8 as our best estimate of the climate sensitivity. And plugging this in, what we get is basically we just take 0.8, multiply that by 3.3, which is the radiative forcing due to greenhouse gas emissions since 1770 or so. And we get an increase in equilibrium surface temperatures of about 2.6 degrees, which is, as I said, very significant. Typically in recent history, we would expect to see changes of about at maximum 1 degree per millennium. When going from the peak of the cold period during the ice age to the

interglacial period, we see warming of may. maybe one degree per millennium and the equilibrium change that we're expecting from just the amount of greenhouse gases that have been emitted in the past 250 years of 2.6 Kelvin. However, it's also true that that figure of about 2.6 is about double the measured temperature change of about 1.2 Kelvin over this period of time. So why are we seeing such a dramatic difference between the estimated temperature change and the measured temperature change due to the greenhouse gas emissions? The main reason for this is because, as you may have picked up, this sensitivity parameter refers to the equilibrium temperature response.

So that means that it's the temperature response once the climate system has reached a new equilibrium after the injection of greenhouse gases. As we've discussed, it takes quite a while for this new equilibrium to be reached. I'll talk a bit more about this when we get into climate feedbacks and climate models about exactly why it takes so long for the equilibrium to be reached, but it's thought that it will take centuries for the Earth's climate system to reach a new equilibrium of temperature. So this 2.6 degrees change is essentially the amount of warming that we've committed to based on the greenhouse gas emissions that have already occurred.

Now, some of those emissions won't last for that entire time. Methane is removed from the atmosphere fairly quickly, so that will then come, that will be then a reduction in the greenhouse gas concentrations, of course we're emitting more of it, but if we just stopped emissions tomorrow, then the equilibrium temperature response from existing emissions would be 2.6 degrees, but that would come down over time as, say, methane is removed from the atmosphere. And then over a much longer time span of probably millennia, carbon dioxide would also be removed from the atmosphere by the deep ocean and biological and geological processes. And then the carbon dioxide would gradually return to pre-industrial levels.

But if we ignore those processes and just ask the question, how much would the temperature change if the amount of greenhouse gases that we've already emitted just stayed in the atmosphere, then the answer is eventually we'd expect 2.6 degrees of warming. And that would occur for a period of centuries. The transient climate response refers to how much of a temperature response we get on the order of, I think it's 20 years it's defined as. So about 20 years from when the emissions occur, how much of a temperature response is there. And that is estimated to be about half of the equilibrium response.

And so that matches up very well with how much we'd expect given the amount of greenhouse gases that have been emitted, relative to the temperature increase we'd expect, and then about half of that gets you to roughly the measured value of 1.2 degrees. So we see fairly good agreement between the estimated sensitivity values in the transient case and the measured temperature changes. But the important lesson to be drawn here is that even if we stopped emissions tomorrow completely, the climate would continue to warm probably for centuries to come, assuming we didn't pull out any further greenhouse gases from the atmosphere, because of the kind of built-in warming that we've already accrued, because we haven't reached equilibrium yet,

that the planet is still more than a degree away from equilibrium. And this is sometimes referred to as climate inertia, that you can't just look at the warming that's already happened from the greenhouse gases that have been emitted. You have to think about how much warming will there be in the future as a result of the greenhouse gases that have already been emitted. And then, of course, you've got to factor in while we're continuing to emit greenhouse gases. So predicting what the temperature will be at different points in the future becomes quite difficult

because you've got to factor in all of these different cases. Now, the last thing that I wanted to discuss in this episode, drawing back to something that I mentioned a bit earlier, which is this claim that the absorption of infrared radiation that's emitted from the surface is saturated, particularly around the key absorption region of a about 14 or 15 micrometers of carbon dioxide. Now, as I said, this claim is false because although the central region of that band is saturated, the edges are not saturated. So increasing carbon dioxide concentrations do lead to increased absorption at the boundaries of that emission band.

Plus, also, of course, that doesn't say anything about methane and other greenhouse gases, which are not saturated. But just looking at carbon dioxide here. Now, I mentioned that there was a second aspect to this, however. And this is the effect on the lapse rate, which I wanted to then discuss just briefly now. And this is a bit of a subtle point, which I think is not communicated very well in a lot of public discussion about this point, even public science communication. So I want to try to articulate this. So far, we've talked about the greenhouse effect in terms of long wave radiation being absorbed by greenhouse gases in the atmosphere,

which leads to an emission of long wave radiation back towards the surface of the earth, causing the earth to heat up. increase in temperature until it restores balance of outwardly emitted radiation with incoming solar radiation. And the claim was that as we increase the concentrations of greenhouse gases in the atmosphere, that leads to absorption of more and more regions of the spectrum, resulting in less and less of this long wave radiation that's able to make it into space. That is true, and that is an important mechanism of the greenhouse effect. However, there is an additional aspect to this that's not often discussed very clearly. And that is the effect of emission height. So it's not just a question about whether radiation is emitted or is absorbed or not by the

atmosphere. Because in fact, what actually happens to most of the radiation, I mean, it depends on which region you're talking about, but particularly if we talk about around that like 15 micrometer band where CO2 is a particularly good absorber, most of the radiation in that band is absorbed within a matter of, I think, a few meters of the Earth's surface. You know, the troposphere is like 10, 12 kilometers high, right? And then there's a stratosphere above that. So a few meters is sort of hardly anything. The point there being that essentially none of the radiation that's emitted by the surface of the Earth,

at least in that band, makes it anywhere near to escaping the atmosphere, because it's all absorbed very close to the surface of the Earth. So you might wonder, what does adding more carbon dioxide, then due to anything if it's already being absorbed right near the surface of the earth. Like, what difference is that going to make? It seems that there's already more than enough greenhouse gases to absorb everything. Well, as we said, that's not true for radiation that's either side of the key band. But the other important aspect here is that radiation isn't just absorbed once and for all by the atmosphere. In those simple zero-dimensional idealized model that we talked about, there was

only one atmospheric layer. And radiation was either absorbed by that layer or it wasn't. And it went straight through and got back into space. But as we said, that's not how the real atmosphere works. The real atmosphere has sort of as multiple layers, or in reality really, there aren't distinct layers. It's a gradation of decreasing pressure with altitude, going up, you know, tens of kilometers. And so the correct way to model that is to use a radiative transfer model where you actually look at the concentration of the optical density, so it's called, of greenhouse gases at each kind of level, infinitesimal level of the atmosphere as you go upwards. The pressure, decreases, so the total amount of carbon dioxide is decreased, but its relative concentration stays

pretty much the same with altitude. And so you integrate over that to compute how long it's going to be taken on average for a photon at a given wavelength to be absorbed. And so a more realistic understanding of what's happening here is that, let's say you emit the Earth emits a photon at 15 micrometers. That travels, I don't know, 10 meters up and then is absorbed by a molecule of CO2. Now, individual photons are not re-emitted because it's not the same photon, but you can imagine if we absorb 10 photons at 10 meters, maybe five of them will be emitted upwards and five of them will be emitted downwards. And then of those five they're emitted upwards, let's say all of them are absorbed again within another 10 meters. And so then we've got, say, two and a half on average that are emitted up and two and a half that are emitted down, right? So what we actually have is this progressive emission and absorption of radiation.

Lower levels of the atmosphere are warmer, so they have a higher temperature, so they emit more in total than higher levels. So that's how you can get this balance between the fact that higher levels of the atmosphere can only get radiation that's been able to somehow get through all of the lower layers. So it's sort of like if you're moving through the defences of a castle, right? You can only get to the inner layers if you've passed through all the outer layers. But that would seem to mean that hardly any energy would get to the top of the, the atmosphere right because eventually it's going to be absorbed by one or the other of the layers right well to compensate for that we need more energy going upwards than then goes downwards and the way that

that sort of balances out is that the lower levels of the atmosphere warm up more than higher levels of the atmosphere and that gives rise to what's called the lapse rate well there's actually multiple reasons why the lapse rate exists but one of the reasons why the lapse rate exists is because of this absorption of long wave radiation by greenhouse gases in the atmosphere in the troposphere at least So lower levels are more readily able to absorb radiation because it doesn't have to travel as far to get to it, right? It's kind of easy to get to the lower levels. So they emit lots to higher levels. Higher levels of the atmosphere, it's harder for them to get radiation coming from below.

Remember, we're just talking about long wave radiation from the Earth's surface now. It's harder to get up there. But to compensate, there's more energy that's sort of coming from below because of the higher temperatures of lower levels. Whereas the higher layers, they emit much less because they're cooler. They're cooler. So this is how you're able to get the balance. It's a bit complicated to try to sort of picture this. But the basic point is that this lapse rate, this temperature gradient going from warmest

at the surface to coolest at the top of the troposphere, is critical for the enhanced greenhouse effect. I've seen some sources say that the lapse rate is critical for the greenhouse effect as a whole. And this is not correct. You don't need to have a lapse rate in order for the greenhouse effect to take place. What's critical, what's important rather, is that the lapse rate is critical for the enhanced greenhouse effect that's produced by adding extra concentration of greenhouse gases.

So this effect of the lapse rate isn't required to have any greenhouse effect at all, but it is critical for the enhanced greenhouse effect that's produced by humans emitting more greenhouse gases, more carbon dioxide relative to what was in the atmosphere previously. So let's understand what's happening here. Basically what's happening is that the long wave radiation that's emitted by the Earth's surface doesn't get straight through the atmosphere. It doesn't get absorbed once and then emitted and then it gets out. It's actually being absorbed and emitted many, many times by different levels in the atmosphere. Eventually, in a kind of a slow leapfrog process, if you like, the energy is able to iteratively get higher and

higher up in the atmosphere until it reaches the top of the atmosphere. It actually doesn't have to reach the true top of the atmosphere, but we'll just call it the top of the atmosphere for simplicity to illustrate the region where most of the emission occurs. The atmosphere gets thinner and thinner as you go up, so as the altitude increases, it gets easier and easier for infrared radiation to escape the atmosphere. What this means is that there is a certain altitude, a certain height above the Earth's surface, where at that point most of the radiation that's emitted from that point finally escapes for good. Energy that's absorbed at 10 meters height in the atmosphere, or even 5 kilometers height in the

atmosphere is probably not escaping for good. It's probably going to be absorbed once, twice, or many times before it can make it out of the atmosphere, because there's still so much more atmosphere on top of it. At some point, if you keep going up and the atmosphere keeps getting thinner, you reach a point where energy that's emitted from this level will probably escape, or like most of it will escape, right? It's a graded process, right? So it's not like suddenly it escapes when previously it doesn't, but as you go further upwards, eventually more and more of the emitted radiation escapes for good. It goes out to space. And that's kind of critical because it's only radiation that escapes out into space

that's able to balance the incoming energy from the sun and contribute to that energy balance. Anything else kind of adds to the greenhouse effect, and any energy that doesn't get out to space that's trapped within the atmosphere, adds to the greenhouse effect and continues to increase temperatures. So as we go up and up higher and higher, eventually the highest levels, we reach levels where most of the energy that's emitted escapes fully out into space. as we just discussed, however, in order to balance out the energy flows, and also for other reasons, that there's a temperature lapse rate, a gradation of temperatures from highest at the surface to

lowest at the top of the troposphere, that's the lowest level of the atmosphere. All of this means that if we increase the concentration of greenhouse gases, that makes it harder for energy that's emitted at the surface of the earth to get out into space, because the atmosphere is thicker than it was before. It still eventually will escape into space, but to do so, it has to get to a higher altitude. Basically, if you imagine that the atmosphere has to reach a certain level of, that the total vertical distance of atmosphere, the total optical thickness,

that the radiation has to pass through in order to escape to space, can't be too big, otherwise it'll be absorbed again and it sort of has to start from scratch, right? If we add more carbon dioxide, more greenhouse gases to the atmosphere, the optical thickness of the atmosphere increases. And so in order to compensate, the energy has to kind of start, if you like, from higher up. When I say start, it means that energy won't be able to finally escape the atmosphere unless it doesn't have as far to travel.

The thicker the atmosphere is, then the less distance in the atmosphere, like vertical distance, the energy will be able to travel before it's absorbed again. So more greenhouse gases means a thicker atmosphere. So the thicker the atmosphere, the optically thicker the atmosphere, the shorter a distance can radiation travel in that atmosphere before it gets absorbed again. And so therefore, the altitude at which you have to get to before the energy can assess. or mostly the energy can escape, gets higher up because now the atmosphere is thicker, so we can't travel through as much of it before escaping. Now by itself, this wouldn't necessarily mean that much. Well, so what if the energy is being emitted at a higher altitude? What difference does that make? It's being emitted, right? Well, the key different, the reason this is so

important is because of the lapse rate. When the energy is emitted at a higher altitude, it's emitted by a region that is at a lower temperature, because that's what the lapse rate is. It means that higher up you go within the troposphere, the lower the temperature. What does this mean? Well, it means, effectively, the key feedback that we talked about, remember the Stefan Boltzmann law, and the feedback that that gives. As the temperature increases, the energy that's emitted increases dramatically by a power of four because of that, you know, T of the power of four relationship. So a small increase in temperature results in a much, much bigger increase in the amount of energy emissions. In this case, though, we're going the opposite direction.

The ambospheres become optically thicker because of more greenhouse gases, which means that radiation energy can't travel as far to get out of the atmosphere. And so it escapes from the atmosphere at a higher altitude than it previously was able to, because it can't travel as far to get out. So it has to sort of start off from higher up to get out. And what that means is that there's a lower temperature at the emission altitude than there was before. It's not like there's one height where all of the radiation is emitted from, but what you can compute is an average emission height, right?

Some is emitted from higher, some from low, but on average you can calculate the emission height. and the average emission height goes up when more greenhouse gases are in the atmosphere because it's optically thicker and so it's harder to escape. So you can't, you have to shorten the distance to escape and so that's a higher emission altitude. That high emission altitude occurs because of the lapse rate at a lower temperature. And lower temperature means by a factor of four less energy emitted. So even a small temperature difference, brought about by small altitude difference, means a pretty big reduction in the amount of energy emitted. Well, what does the, does that mean? Well, what it means is that the surface temperature, and therefore the temperature

of the lower atmosphere as well, it all has to heat up even more in order to increase the energy emissions back again, because remember, this process of greenhouse gas emission leading to warming is occurring in order to restore the balance between absorbed radiation from the sun and emitted long wave radiation. If we reduce the amount of emitted long wave radiation as a result of lower temperatures where the average level of emission is, then what we're going to have to do is shift out the whole lapse rate curve. Basically, that means that every region of the atmosphere warms up. So it warms up at the surface, warms up at the lower atmosphere, mid-atmosphere, and it warms up at the higher atmosphere as well. So the higher

atmosphere is still much cooler than the surface. That's still the lapse rate still there. The slope is roughly the same, right? That's not really what's changing, not much. But the point is that everything is shifting up. Everything is going up in temperature, relative to what it would otherwise be, in order to offset this effect of lower temperatures at the higher average emission altitude. And this is actually the most important effect contributing to the enhanced greenhouse effect, the extra greenhouse effect brought about because of human emissions. So a paper that's looked at this quite rigorously that I used as a source here estimates that about 90% of the increased greenhouse effect resulting from increased CO2 emissions,

relative to pre-industrial levels, is due to the increased, average emissions altitude. Remember, that's not 90% of the whole greenhouse effect, the whole greenhouse effect being that like 30 degree difference from what the temperature is to what it would be if we didn't have any greenhouse gases. Rather, it's 90% of the difference between the greenhouse effect in 1750 and the greenhouse effect now because of all the extra greenhouse gases we've emitted. So that's an important distinction to make. But nevertheless, most of the enhanced greenhouse effect is actually brought about by this increased emission altitude, not actually because of more absorption over a wider range of wavelengths.

That does contribute, but it's a small proportion. So I hope that was reasonably clear. That last part is a bit technical. The key point to understand there is that more greenhouse gases in the atmosphere means that the atmosphere gets optically thicker, which means essentially that it's harder for radiation to pass through it, but without getting absorbed again. And each time a bit of radiation gets absorbed, some of it will be emitted upwards again, and half of it will be emitted downwards again.

And so the thicker the atmosphere is, the more difficult it is for radiation to eventually escape. Eventually the radiation will escape to space, but only once it reaches a point where all of the remaining atmospheric thickness above it is thin enough. The more greenhouse gases are in the atmosphere, the higher up that emissions altitude, average emissions altitude, will have to be.

And because of the lapse rate, meaning that temperatures increase with altitude, the temperature that higher average emissions altitude, is lower when there's more greenhouse gases. So more greenhouse gases means higher average emissions altitude, which means lower average temperature of emission. And a lower average temperature of emission means much less energy emitted at that temperature

because of the power of fall law, of the Stefan Boltzmann law, in order to compensate and get the emission back up again because the total has to equal the incoming radiation from the sun, the total has to go up again. In order to compensate for that, what happens is that the whole planet has to warm up, like the surface and all of the atmosphere levels below,

up until the average emissions height, it all has to warm up. So the lapse rate kind of stays the same, but it all shifts across to get higher temperatures across the board. So this effect of the average emissions height, leading to reduce temperatures at the emission level, thereby increasing temperatures across the board, is actually the major contributor to the enhanced greenhouse effect. And it is the ultimate reason why it's false to argue that we don't have to worry about extra CO2 emissions because absorption in the energy band region is mostly absorbed by CO2, particularly the 15 micrometer region, is mostly saturated. We saw that that's not even true because the bits on the side of that band still can absorb more energy, that they're not

saturated, and so there's that point. But then there's the more important point, probably 90% of the point in terms of increased temperatures, which is simply that, yeah, but the average emissions altitude is increasing. And because of the lapse rate, that means that the temperature is lower there, and in order to compensate, the whole atmosphere warms up. So there is these two sort of distinct effects here, which is sort of the amount of absorption you have sort of in new regions of the electromagnetic spectrum that previously didn't have much absorption. And then there's the effect of higher altitudes of average emission due to the increased optical thickness. Now, both of these are caused by the same underlying process. They're both caused by increased concentration.

of CO2. It's just a slightly different mechanism that leads to the overall end result of greater radiative forcing and therefore higher temperatures. So the short take home there is simply that increased greenhouse gas concentrations in the atmosphere lead to a trapping in of energy that previously escaped out of the Earth's atmosphere but now is not in order to for Earth to return to equilibrium where the amount of energy coming in is balanced by the amount of energy going out. The temperature of the Earth needs to increase, which thereby by this different Boltzmann law increases the amount of emitted radiation, bringing the system back into balance. And that's fine sort of thermodynamically from a point of view. The downside is the temperature goes up.

And as we've seen, from a near doubling of the total greenhouse gas concentrations in the atmosphere in the past 250 years, that is expected, given the sensitivity estimates that we have, to result in about a 2.6 degree increase in equilibrium temperatures and has already led to about a 1.2 degree increase in temperatures. The rest of it being temperature increases which we've kind of committed to but haven't happened yet because the climate system takes a while to adapt. So in the next episode we will talk about in more detail about some of the climate feedbacks that we discussed in this episode briefly. We'll talk about some more of those and the effects that they have on climate feedbacks. And then we'll talk about how some of these can be incorporated into climate models, more sophisticated computational

models of the climate as a whole. And finally, we'll conclude by looking at some of the markers of recent climate change being anthropogenic. We've talked about the mechanisms by which it occurs. We'll talk about some of the specific evidence and so-called markers or fingerprints that really demonstrate beyond any reasonable doubt that recent warming is anthropogenic, is human-made. So until then, thanks very much for listening. I hope you enjoyed this episode. If you would like to support the podcast, consider giving it a favorable review on iTunes or Spotify or the aggregate of site of your choice. You can also send me an email. My address is Fods12 at gmail.com. That's FODDS1.2 at gmail.com. If you'd like to support the podcast

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