In some ways, it is very simple. GWP is a function of two things: 1) radiative efficiency, which measures how efficiently the gas traps energy on the earth (more here); and 2) the atmospheric lifetime of that gas, which you can explore (more here). If a gas has traps more energy or has a longer lifetime in the atmosphere, it will have a higher GWP.

Take a look at the table below, cut from the IPCC’s Sixth Assessment Report. It shows GWP and other values for some of the most problematic greenhouse gases. The first column holds the different gases (aka species). Note that there are two different rows for methane: CH₄-fossil and CH₄-non fossil. And once you have noted it, feel free to ignore it at least for now. The authors decided to separate the methane that comes from fossil fuels from the methane that comes from other sources like agriculture. I will dig into the reasons for this decision in another post; for now just note that the differences in values are minor. I’ll just use the values for CH₄-fossil for the rest of this post.

Next take a look at columns four, five, and six, labeled GWP-20, GWP-100, and GWP-500. The number at the far end of the hyphen indicates the number of years. We’ll get into it more shortly but, in brief, the gases have different values over different time periods because they have different atmospheric lifetimes. There is nothing special about 20, 100, or 500 years—those are just some numbers the originators of this metric chose to show how it would change over time. Unless otherwise specified, most conversions rely on GWP-100. (I will post more about the surprising history of this metric and the choice of time period here elsewhere.)

See how the GWP values for CO₂ are all 1? That’s because CO₂ is the reference gas, a sort of common currency among greenhouse gases. By setting the table up this way, it makes it very easy to do conversions. For example, if an oil well leaks 1 tonne of CH₄ into the atmosphere, we could use the GWP-100 value to calculate that it released the equivalent of 29.8 tonnes of CO₂ or 29.8 tonnes CO₂e (It is sometimes also written CO₂eq, you can read more on all the different common climate units here.)

The thing is that, although a table in which GWP values are all calculated relative to CO₂ does make it easier to do the most common conversions, it also makes it harder to grasp the underlying concept. For this latter purpose, it will be easier to think in terms of absolute GWP, which I will abbreviate as AGWP to distinguish it from the GWP values in the table above.

In short, AGWP is the time-integrated radiative forcing caused by a greenhouse gas. What does that mean?

Take a look at the interactive graphic to the right. If you push the button on the top left, a sidebar will emerge in which you can change the values.

First get rid of N₂O by typing ‘0’ in the box and hitting return or by moving the slider all the way to the left. Next adjust the other values so that there is 1 GtCO₂ and 1 GtCH₄. Set the years to 0. Year 0 represents the day that the slug of gas was released and the 363 days that followed. (If that seems confusing, think of the way we commonly respond when someone asks us how old we are.)

• GtCO₂: 1
• GtCH₄: 1
• GtN₂O: 0
• Years: 0

Now, in the top chart, titled ‘Slug Emission Radiative Forcing vs Time,’ hover your cursor over each bar. Over the course of year 0 (which is the year that the gas was emitted), you can see that the additional CO₂ in the atmosphere will cause a shift in the earth energy balance of 0.0018 Watts per meter squared. The additional CH₄ will cause a shift of about 0.21 Watts per meter squared. Notice that the bottom chart, titled ‘Slug Emission Cumulative Radiative Forcing,’ has the same values as the top chart for now.

Next increase the number of years to 1. Now you can see the radiative forcing caused by the different gasses over two different years. In the top graph, the X axis represents time, so each year is separated. The bottom bar graph is categorical and cumulative. Each bar represents the cumulative radiative forcing caused by the gasses over all the years since they were emitted. In other words, imagine taking each of the CH₄ bars from the top graph and stacking them on top of each other to create the CH₄ bar at the bottom. The same goes for CO₂. (Note that the scale of the Y axis is different for the two graphs and will both continue to change each time you adjust one of the inputs.)

Now try setting the years to 100. Look at the cumulative radiative forcing caused by CH₄ and CO₂ in the bottom graph. These values are the absolute GWP for 100 years (AGWP-100), for each gas. The units are in Watts per square meter.

Recall the GWP values from the IPCC table 7.15 that we started with. All GWP values were unitless, and relative to CO₂. To derive GWP-100, all we need to do is divide by the AGWP of the gas in question by the AGWP-100 of CO₂. If you divide the AGWP-100 of CO₂ by itself, you will get 1, just as in the table. In other words, if you release 1 gigatonne of CO₂, it is the same as releasing 1 gigatonne of CO₂. Next divide the AGWP-100 of CH₄ by the AGWP-100 of CO₂. Although rounding errors and slightly different parameters may throw it off a little, the value should be close to 29.8, just as in the IPCC table.

Keep playing with the input values. Test out N₂O. Try deriving the GWP-20 and GWP-500 values for CH₄. Try calculating other GWP values, like GWP-1. Note how the GWP values change over different time periods as a result of the different lifetimes of the different gasses.

Here’s another way of looking at it: if the GWP-100 of CH₄ is 29.8 then, if we release 1 GtCH₄, the cumulative radiative forcing after 100 years should be the same as if we had released 29.8 GtCO₂. To test this, try leaving the CH₄ at 1 gigatonne, and bump the CO₂ up to 29.8 gigatonnes. The bars in the bottom graph should be about the same height, indicating they caused the same amount of cumulative radiative forcing.

Now look at the top graph, though. See the problem? Methane has a huge impact in the first few years, and almost none after about 40 or 50 years. In any given year following an emission, the effects of different gases will not be the same at all! GWP is such a deeply flawed metric with such huge policy ramifications that even the scientists who first came up with it were aghast, a topic I will cover in a future post.

For now, you may want to jump next to this post about the difference between warming potential and temperature.

From the moment it was created more than 30 years ago, climate scientists have known that the concept of Global Warming Potential had some major drawbacks. Since different greenhouse gases have different radiative efficiencies and different atmospheric lifetimes, there is no simple way to compare their effects. Here let’s talk about an alternative metric for comparing greenhouse gases called Global Temperature Potential, or GTP.

You can see the values for GTP-50 and GTP-100 in table 7.15 from AR6 at the bottom of this post. Note that just like GWP, the GTP values depend on time: in this case they have been calculated for 50 years and 100 years respectively. However, unlike GWP, which reflects cumulative radiative forcing over time, GTP depends only on the global average surface temperature value at the time in question. Whatever happened in the past does not matter. To put it another way, GWP reflects the area under the curve, while GTP reflects the value of the line at one point in time.

Note that GTP values are also unitless—they simply compare the temperature effects of a gas to the reference gas, which is CO₂. In other words, you might say that if you release 1 tonne of CH₄-non fossil, the resulting change in the earth’s temperature after 100 years will be 4.7 times higher than if you released 1 tonne of CO₂.

How did the IPCC derive these unitless GTP values? They first had to calculate something called Absolute GTP (AGTP). Unlike GTP, AGTP does have units—the change in global average surface temperature that will result from an emission.

To calculate AGTP, researchers used computer models to simulate the release of a greenhouse gas and then tracked the effects on global average surface temperatures over time. They used the results to create and parameterize the equation that is used in the interactive graphic here. Once you have AGTP values, it is simple to calculate GTP. You just divide the AGTP value of the gas in question by the AGTP value for the reference gas, which is CO₂.

Now let’s put these equations to work. Set the values in the interactive visualizations below to:

• GtCO₂: 1
• GtCH₄: 1
• GtN₂O: 0
• Years: 100

See how potent CH₄ is in the first few years after its release? See how its effects diminish rapidly after about 12 years? That’s because it has such a short atmospheric lifetime. Carbon dioxide, on the other hand continues to exert an effect on temperature for a very long time after its release.

Next let’s consider the implications for the carbon offset market. Carbon markets typically use GWP-100 to compare emissions. Suppose I was going to emit one tonne of CH₄ and I wanted to offset those emissions so that I could claim my operations were carbon neutral. According to the table above, I could pay somebody else to remove 29.8 tonnes of CO₂. Try setting the values in the visualizer to:

• GtCO₂: -29.8
• GtCH₄: 1
• GtN₂O: 0
• Years: 100

Logically, you might think that if something is carbon neutral, it will have no effect on temperatures. It should be as though there were no emissions at all. But from the combined line in the graph, clearly that is not the case. At first, thanks to my trade, temperatures on the earth will be hotter than they would have been if there had been no emissions at all. Then, after about 35 years, temperatures will actually be lower than they would have been in a true no-emissions scenario—a result of the different lifetimes and radiative efficiencies of the two gases. Flip that trade around and you’ll get the opposite result.

In the end, GTP suffers from many of the same drawbacks as GWP. Different greenhouse gases differ in both radiative efficiency and atmospheric lifetime. You have to set a time period of interest, and that requires judgments of value as well as science.

Or perhaps the very short life of methane just makes it fundamentally different from carbon dioxide and the topic demands a completely rethink. This post explores the another recently developed metric called GWP*.

Both Global Warming Potential (GWP) and Global Temperature Potential (GTP) were designed for a relatively straightforward goal: to enable the comparison between different greenhouse gases. For example, if someone releases a one-time ‘slug’ of methane into the atmosphere, how much impact on climate will it have compared to the release an equivalent mass of carbon dioxide.

As this post and this post discuss, even this relatively simple question is not easy to answer because the different gases have different radiative efficiencies as well as different lifetimes. One equation, two unknowns.

Now, though, consider how difficult it is to evaluate the impacts of ongoing emissions, like the methane that comes from a herd of cattle, year after year after year.

One option is to simply treat each year’s emissions as a separate event and use GWP to evaluate the impacts. In fact, that is what has been done for many years. Take a look at the graph on the top, though, labeled ‘Concentration vs Time.’

Suppose that you owned a major international beef or dairy company and that all combined, your cattle had been emitting one megatonne of methane a year.

One day you decide double the size of your operations. This would bump up the amount of methane emitted by one megatonne, so that now you are emitting two megatonnes annually. To visualize this scenario, set the values as follows if they are not there already:

• MtCH₄ at start: 1
• Change in MtCH₄ emissions: 1
• Years: 100

The solid green line represents the change in concentration of methane in the atmosphere that your operation will create. See how it climbs rapidly at first, then levels off after a few decades?

Compare that to what would happen if you were to do the same thing with equivalent quantities of carbon dioxide molecules, represented by the dotted light blue line. Because carbon dioxide has such a very long lifetime, the concentrations continue to climb for thousands of years.

Why are they so different? Think of a Ferris Wheel with little methane molecules as the riders. When the ride first opens and begins rotating, the number of riders on the wheel continues to rise. But after the wheel has made one full rotation, the number of people getting on is balanced by the number of people getting off—the number of riders stays constant.

For methane, one full rotation of the wheel takes a few decades. For carbon dioxide, it takes millennia. That dotted blue line will level off eventually, but not for a very long time.

Now back to your very large cattle operation. After that increase, you are emitting two megatonnes of methane every year. If we were to use the standard GWP-100 method to calculate your impact, we would multiply each year’s emissions by 29.8. Each year you would have to announce that you had released the equivalent of 59.6 megatonnes of carbon dioxide.

But is that really fair? Does it even do a good job of representing your impact? Based on that top chart, it doesn’t seem so.

Which is why, around 2016, some climate scientists began developing a new metric that they now call GWP* (pronounced ‘GWP star’). Their goal was to create a metric that would better represent the impacts of what they call short-lived climate forcers (SLCFs) like methane.

The effort began with the powerful computer models that so much climate science is based on, so called earth system models (ESMs). With these models it is possible to ask what effect an emission scenario will have on future temperatures.

With these data in hand, the scientists then sought to create and parameterize a simple formula that would allow people to project the impact of SLCFs like methane without having to run one of those incredibly computer-intensive ESMs.

The exact formula for calculating GWP* has changed somewhat over the years, but in general, it depends on the idea that greenhouse gases can be divided into ‘flow’ and ‘stock’ pollutants. Under this framework, SLCFs like methane are mostly flow pollutants because the concentration depends on the flow of methane into the atmosphere.

Carbon dioxide and other long-lived climate forcers (LLCFs), on the other hand, are stock pollutants because once they get into the atmosphere they stay there for a very long time.

With that concept in mind, let’s look at the formula for calculating GWP*. Here I have used the equation that is oddly buried and written out in a footnote on p. 1016 of AR6 WGI Chapter 7: “To calculate CO2 equivalent emissions under GWP*, the short-lived greenhouse gas emissions are multiplied by GWP-100 × 0.28 and added to the net emissions increase or decrease over the previous 20 years multiplied by GWP-100 × 4.24 (Smith et al., 2021).”

What does that mean? Essentially there are two terms. The first term (emissions*GWP-100*0.28) represents the stock effects of methane. (Yes, I know we just said methane was a flow pollutant, but life is never that simple, is it?) This term serves as an acknowledgment by the GWP* developers that although most of the impacts of a change in methane emissions will occur within a matter of decades, there are some long term (as in centuries) effects as the earth reaches a new equilibrium. In other words, methane acts, in some ways, as a stock pollutant–but only 28% as much as GWP-100 would imply.

To calculate this term you just take the emissions for each year, multiply them by GWP-100, and then apply a steep discount by multiplying it by 28%.

The second term is the flow term. Think of that curve in the first graph showing how rapidly concentrations stabilize at a new level after a change in methane emissions. For 20 years after the change, each year’s emissions are multiplied by GWP-100 and then amplified by 4.24. In other words, it is those first decades, when the Ferris Wheel is not yet full and the concentrations are rising, that really count. (There’s nothing magical about the number 20, it just fits the data well.)

Take a look at the middle chart on the right. The blue line represents GWP*. The red line represents the calculation using GWP-100, and the green line shows the actual emissions. See how the blue line jumps for 20 years and then drops down to 28% of the red line?

Next look at the bottom chart. This represents the cumulative effects of the ongoing methane emissions using the different methods. See how the blue line abruptly slows its rise after 20 years, whereas the green line and the red line do not?

As it turns out, the blue GWP* line provides a pretty good estimation of the warming effects from our ongoing methane emission example.

If you are familiar with Python and want to test it yourself, you can test it using a model like FaIR. Otherwise take a look at figure 3C from Lynch et al. 2020, reproduced below. The dashed orange line represents warming. See how closely it follows GWP*?

Continued …

So should we abandon GWP for methane emissions and begin using GWP* instead? That’s what many advocates for beef, dairy, and sheep have been arguing. It’s even found support within some national governments—countries where sheep and cattle are an important part of the economy.

The thing is, switching to GWP* would be a major giveaway to any industry that generates ongoing methane emissions.

Take a look at the visualizer here. (Make sure you push enter once you change values!) Set it to:

• MtCH₄ emissions at start: 1.0
• MtCH₄ emissions at end: 1.0
• Years: 30

The visualizer assumes that the emissions have been ongoing at the “emissions at start” level for a couple of decades prior to year 0—enough time for the CH₄ levels in the atmosphere to have stabilized. And that means that if an operation keeps its CH₄ emissions at the same level into the foreseeable future, it won’t cause the CH₄ concentration in the atmosphere to go up.

Now recall that GWP* proponents do acknowledge that there are some long-term effects of methane even after it has been removed from the atmosphere. The equation takes account for this phenomenon. Still, it is much smaller than it would be using the conventional GWP definition.

As Professor Frank Mitloehner, a GWP* champion from UC Davis put it, “A constant livestock herd produces a constant amount of methane, but almost an equal amount of methane that’s produced by a constant herd is also naturally destroyed and that means when you have a slight reduction of methane per year and that reduction is 0.3% … then you are not causing additional
warming.’’

But what does that phrase “not causing additional warming” really mean? Let’s think of it another way. Suppose that, once every year, a burglar stole $10,000 from the homes in his neighborhood, and had been doing so for decades. Finally he gets caught. And when he is brought in front of the judge, he argues that he should be let go because even though he just stole $10,000, his action had not increased the overall burglary rate in the city.

Or what if this burglar were to take it to the next level. Suppose that he reduced his efforts and only stole $5,000 for a few years. Should he then go to the mayor and ask for a reward because he had actually reduced the city’s burglary rate? Sounds crazy, but that is exactly what GWP* would allow. Go to the visualizer and set it to:

• MtCH₄ emissions at start: 1.0
• MtCH₄ emissions at start: 0.5
• Years: 30

See how the blue line in the second graph actually dips into negative territory? If a dairy farm were to cut the size of its herd in half it could claim not just that it had reduced its emissions. It could claim to actually be generating negative emissions, as though it were sucking CH₄ out of the atmosphere.

For a much more detailed look at these issues, take a look at the report Seeing Stars: The New Metric That Could Allow The Meat And Dairy Industry To Avoid Climate Action by the Changing Markets Foundation. On p. 22 they even provide some actual emissions numbers for the meat company Tyson Foods and the dairy company Fonterra, showing how they would benefit from the use of GWP*.

Ever since the Kyoto Protocol was drafted in 1997, GWP-100 has been the commonly agreed conversion metric for reporting and comparing greenhouse gas emissions. This is the metric, for example, that is used for assessing nationally determined contributions (NDCs) under the 2015 Paris Agreement.

Since GWP-100 has such deep flaws, other conversion metrics like GTP have been proposed. Some places, like the state of New York, now use GWP-20. More recently, agricultural interests in countries like New Zealand have pushed their governments and the UN to use GWP*.

The interactive charts on the side of this page show how the use of different conversion metrics would affect reported emissions. In the top chart you can pick any country. The bars show how many megatonnes of greenhouse gas emissions the country would be responsible for in CO₂ equivalents. First, note that the amount of CO₂ doesn’t change—that’s because CO₂ is the reference gas and has a value of one for metrics like GWP-20, GWP-100, GWP-500, GTP-50, and GTP-100. GWP* is only applicable to short-lived gases like methane, so it doesn’t change the CO₂ value either.

Next let’s take a look at the values for methane. For a really graphic example, select New Zealand from the drop-down list. Recall that methane is a very potent greenhouse but that it has a relatively short atmospheric lifetime. For this reason, it has high GWP and GTP values in the short term and lower values over the long term.

New Zealand has about 25 million sheep and about 4 million cows. These ruminants emit a lot of methane! That means if New Zealand were required to report its total GHG emissions using a metric like GWP-20, they would be almost twice as high as they are with GWP-100.

On the flip side, if New Zealand were to use GWP* to report its total GHG emissions, they would only be about half as large as they are with GWP-100.

An even more dramatic example of the power of GWP* is just a short hop over the Tasman Sea. Go to the country drop-down list and select Australia. Notice that using GWP*, Australia’s methane emissions are actually negative. This is because GWP* is calculated by comparing a country’s current methane emissions to its emissions 20 years ago. In part because of a steep decline in the number of sheep, Australia’s absolute methane emissions were a lot lower in 2021 (5.1 Mt) than they were in 2001 (6.6 Mt).

Now compare Australia to Ethiopia. In absolute terms, Ethiopia emitted about 3.4 Mt of methane in 2021. That’s a lot less than Australia’s 5.1 Mt. And it is reflected in the GWP-100 values.

But if Ethiopia was required to use GWP* to report its emissions, it would have to report the equivalent of 200 Mt of CO₂. In other words, even though it emitted less methane, Ethiopia would have to report a much higher amount than Australia!

Here’s an interactive map of the world showing by what amount each country’s reported emissions would change if they used GWP* instead of GWP-100. Hover over a country to see a popup showing the percentage by which reported emissions would increase or decrease.

Open this graphic in a new window

Notice how richer countries like those in Europe and Australia and New Zealand would see significant reductions in their reported emissions. Meanwhile, many poorer countries including several in Africa would have to report much higher emissions.

This is one of the main criticisms of GWP*: it would reward countries that have been emitting methane for a long time and punish other, often poorer, countries that are now growing their economy. It doesn’t seem fair.

Next look to the right side again and take a look at the bottom chart, which shows a comparison for five countries with very different types of emissions. Because emissions values are so different in scale, the Y axis shows values as a percent of their values under GWP-100. Select a metric at the top to look at how it would change these countries’ reported emissions compared to GWP-100. 

As a result of its extensive tropical rainforest, Costa Rica absorbs a lot of carbon dioxide, enough to make up for almost all of its CO₂ emissions. A metric that discounts the importance of methane, like GWP-500 substantially reduces its emissions. Heavily industrialized Japan, on the other hand, emits a lot of CO₂. Changing metrics hardly changes its emissions at all. 

In sum, the choice of metric can have an enormous impact on a country’s reported emissions. And while I haven’t shown it here, the same thing applies to any company or organization that reports emissions. Want to claim your company or country is climate neutral? Try switching your metric.

Other greenhouse gases, like methane (CH₄), have a much shorter lifetime. On average, a CH₄ molecule only lasts about 10 or 12 years in the atmosphere before it is broken down.

The interactive graph below represents the persistence, or lifetime, of greenhouse gases in the atmosphere. The Y axis is the fraction of the original “impulse” that remains, so changing the absolute amount of gas released in the slider on the left will not change it. The X axis shows the time that has elapsed since the original emission in years. Suppose you were to release one gigatonne of CO₂ (GtCO₂). At that moment (year 0) one GtCO₂ would be in the atmosphere. Each year thereafter, some of that CO₂ would be eliminated. After 20 years, for example, only 0.6 GtCO₂ would remain.

CO₂ is a very stable molecule. It is primarily eliminated from the atmosphere by plants, which use it for photosynthesis, and by absorption in the ocean. Set the years slider on the left to 1,000 and you will see that even after a millennium, about 25% of that original impulse remains in the atmosphere.

Methane, on the other hand, breaks down relatively quickly. As it circulates in the atmosphere, a series of chemical reactions transform it into other molecules including CO₂. After only a few decades, most of it is gone. The different atmospheric lifetimes of the different greenhouse gases have important implications for climate mitigations.

If you’d like to examine it in more detail, the parameters and equations used to calculate the “impulse response functions” for these gases comes from the IPCC here, here, and here.

In this post, I’ll focus on the four units that are commonly used when quantifying emissions and greenhouse gases:

• GtCO₂ (gigatonnes of carbon dioxide)
• GtC (gigatonnes of carbon)
• ppm (parts per million)
• GtCO₂e (gigatonnes of carbon dioxide equivalent)

GtCO₂

Let’s start with that first letter, G. That stands for giga, a prefix that means 1 billion, 1,000,000,000 or, in scientific notation, 1×10⁹. You can find a list of other prefixes you may run across here. Weirdly, when you write out ‘gigatonne,’ the g is lowercase. But when you use the abbreviation, as in ‘Gt’ the ‘G’ is always capitalized. Even more weirdly, according to the rules of scientific notation, that rule doesn’t apply to some of the other prefixes, like the ‘k’ in ‘kt’ and kilotonne. That letter is supposed to be lowercase in both instances. Why? Because when the French invented the metric system, they didn’t get higher than one thousand. And also so you can waste time going down this Quora rabbithole. 

Next, the lowercase ‘t’. It’s attached to that ‘giga’ and it stands for ‘tonne.’ A ‘tonne’ is the same as a ‘metric ton’ which is 1,000 kilograms, or about 2,205 pounds. (It’s not quite the same as a US ton (2,000 lbs.) or a long or imperial ton (2,240 lbs.), but they’re pretty close. You can probably ignore the differences (unless you are designing a Mars orbiter).¹

CO₂, of course, stands for carbon dioxide, so one GtCO₂ is one billion tonnes of CO₂. That’s a lot. So much that it can be hard to wrap your mind around it, even if you know that it is about the same mass as 250 million elephants. At least now, though, the next time you see that unit, you’ll have a strange image in your head of some French elephants about to land on Mars, which should be enough to slow you down.

GtC

Onward to GtC. The ‘C’ in that unit stands for the element carbon. And now we start getting into the confusing stuff. Sometimes scientists prefer to quantify the amount of CO₂ in terms of the carbon alone. For example, instead of seeing: “Globally, the burning of fossil fuels produced 37 GtCO₂,” you might see, “Globally, the burning of fossil fuels produced 10 GtC of CO₂.” 

Huh?

Well, in fact, those two statements are saying the same thing. Here’s where the chemistry (and some simple math) comes in. Carbon has an atomic mass of 12.² The atomic mass of oxygen is  16. That means that the molecular mass of CO₂ is about 44 (12+16+16). And in turn, a carbon dioxide molecule weighs 3.67 (44 ÷ 12) times as much as a carbon atom. Ergo, there are about 10 GtC present in that cloud of 37 GtCO₂ that were released.

The math is pretty easy, but the carbon dioxide calculator on the right will do the work for you if you’d like. Change the number in one of the boxes and then press enter. The other boxes will automatically adjust.

ppm

Both GtCO₂ and GtC are commonly used to describe emissions. By contrast, ‘ppm’ is commonly used when talking about gases that are already in the atmosphere.

Note that ppm is a unit of concentration. Just as percent stands for ‘parts per hundred,’ ppm stands for ‘parts per million.’ You may also run across ‘ppb’ which stands for parts per billion. You can easily convert between these units. One percent is the same as 10,000 ppm, which is the same as 10,000,000 ppb.

Concentrations like ppm are commonly used when calculating or discussing the greenhouse effect. Why? Because it is not the absolute mass of a greenhouse gas like CO₂ that determines how much energy is trapped by the atmosphere. Rather, it depends on the number of molecules of CO₂ per unit of volume, which is to say concentration.

Now we have covered the first three units: GtCO₂, GtC, and ppm. If you’re a little confused, don’t worry, I promise you’re not the first one. The good news is that it is relatively easy to convert between these three different units. We already covered the conversion between GtC of CO₂ and GtCO₂: 1 GtC of CO₂ = 3.67 GtCO₂. 

You can also calculate the conversion from GtC of CO₂ to ppm in the atmosphere if you’d like. You just need to know the number of molecules in a GtC of CO₂ and the total number of all the gas molecules in the atmosphere. In case you don’t want to do that, though, I’ll just tell you. Emitting 2.13 GtC of CO₂ will increase the concentration of CO₂ in the atmosphere by 1 ppm.

Back to the carbon dioxide calculator. If you increase the concentration of CO₂ in the atmosphere by 1 ppm is the same as adding 2.13 GtC of CO₂ which is the same as adding 7.81 GtCO₂.

GtCO₂e

Finally, let’s talk about ‘GtCO₂e.’ That ‘e’ on the end stands for ‘equivalent’ and it comes into play when other greenhouse gases besides CO₂ enter the chat, gases like methane or nitrous oxide (N₂O). At its simplest, GtCO₂e uses CO₂ as a common currency, allowing the comparison and even the trading of the different greenhouse gases. Think of the way the US$ is used in international markets. In this case, though, the exchange rate is based on an estimate of the potency of the different gases over 100 years known as the Global Warming Potential, or GWP-100.

Conceptually, scientifically, and as a matter of policy, GWP-100 is a deeply problematic (and fascinating) metric, but I’ll leave that for another post. For now, just know that the Intergovernmental Panel on Climate Change (IPCC) has assigned every greenhouse gas a GWP-100 value. Methane (CH₄) from fossil fuels, for example, has a GWP-100 of 29.8, meaning that releasing one gigatonne of methane causes as much warming as 29.8 gigatonnes of CO₂.

You’ll run into this GtCO₂e unit anytime the discussion is focused on the aggregate impacts of an activity, organization, or region. For example, in the year 2021, the United States emitted about 6 GtCO₂e of greenhouse gases.

The good news is that once again, the conversions are relatively easy. On the right there is another calculator for fossil-fuel methane. Since CH₄ has a molar mass of 16 and carbon has a molar mass of 12, 1 GtC of CH₄ is equal to 1.33 (16 ÷ 12) GtCH₄. You can find the GWP-100 values for other common gases in the IPCC table below.

1. In 1999, a US$125 million Mars orbiter crashed after a 10 month journey because one team was using the metric system while another was using British Imperial units. ︎
2. Yes, I’m simplifying and avoiding using units here! More specifically, 6.02214076×10²³ atoms of carbon have a mass of about 12 grams. ︎

Table 7.15 from IPCC Sixth Assessment Report, WGI, Chapter 7, p. 1017

Let’s focus first on the energy-in part of Earth’s energy balance. Take a look at the diagram below. Everything in the universe, or at least everything that has a temperature above absolute zero, emits energy known as electromagnetic radiation. The wavelength that a body emits depends upon the temperature of the object itself. Shorter wavelengths carry more energy. With a blistering average temperature of about 5,800°C, the Sun emits radiation in what we call the ultraviolet, visible, and infrared parts of the electromagnetic spectrum.

Note, though, that these terms say much more about us than they do about the the sun’s light itself. There is nothing special about what we call visible light. It is just that, because it helped our forebears to survive and reproduce, we evolved sensors that could detect that part of the spectrum. Ultraviolet is just that part of the spectrum beyond violet that we cannot perceive with our eyes, and infrared is the same thing on the other side. To make it easier, I will refer to the energy emitted by the sun as solar or shortwave radiation from hereon.

Of course since the Sun is a sphere, the vast majority of the energy it emits travels in other directions and never comes near the Earth. The outer edge of the Earth’s atmosphere, however, does receive some solar radiation—an average of about 340 Watts per meter squared. Some of this incoming energy bounces off clouds and other particles in the atmosphere and never makes it to the earth. Some is absorbed by the atmosphere itself. Some of the energy that does make it to the earth is immediately reflected upwards back into the atmosphere—the so-called albedo. And of course some of this incoming solar energy is absorbed by the earth itself—warming the land and the oceans and everything upon them.

Next, let’s look at the energy out part of the earth energy budget. Just like the Sun, the Earth also emits electromagnetic radiation. However, since it is so much cooler—about 15°C—the earth emits longwave radiation in that part of the spectrum we call infrared. Some of this energy goes directly out to space. Much of it though is absorbed by gases in the atmosphere like water vapor, carbon dioxide, and methane. When these gases eventually reradiate the energy themselves, some of it is directed back at the earth, some at other gas molecules and so on. As it ricochets around between and within the earth and the atmosphere, the radiative energy is slowed or prevented from escaping into space. In other words, these gases act like a blanket or greenhouse, causing the earth to be warmer than it would otherwise be.

If the concentration of greenhouse gases in the atmosphere increases, the temperature of the Earth will also increase. A warmer Earth will emit more radiation until eventually a new equilibrium is reached.

Which finally brings us back to the concept of radiative forcing. Recall the basic equation. In a stable system: energy in = energy out. If you change either side of that equation you will cause radiative forcing. If the change causes the equilibrium temperature of the Earth to go up, it is called positive forcing. If it causes the equilibrium temperature to go down, it is negative forcing. Think of all of the radiative interactions that I described in the previous paragraphs—reflection, albedo, absorption. Launching a giant space mirror that prevented sunlight from reaching the Earth would reduce the energy in and cause negative radiative forcing. Pumping carbon dioxide into the atmosphere diminishes energy out and thereby cause positive radiative forcing.