The Problem with '12 Years'

It's like the more carbon we come across, the more problems we see.

It’s been a long year.

It’s almost exactly a year since the Intergovernmental Panel on Climate Change came out with a major report describing what 1.5°C of warming will look like (I know, it feels like an eternity ago). Today we’re at about 1 degree of warming compared to pre-industrial times, so we’re already two-thirds of the way to this threshold.

This report catapulted the idea of carbon budgets into the zeitgeist. A carbon budget tells us how much carbon dioxide we can continue to emit and still have a reasonable chance of remaining below some particular threshold of warming.

Think of a carbon budget as the amount of money that remains in our carbon bank account, and our annual carbon emissions as our annual spending. As the IPCC famously warned us a year ago, at our current rate of emissions, we’ll burn through our budget for 1.5°C of warming in about 12 years.

Actually, the report didn’t say “12 years”. They leave it to you to do the math. The IPCC came up with carbon budgets for a reasonable shot at staying below 1.5°C of warming. If you divide these budgets by our annual emissions, you’ll find that at our current rate we’ll blow through them in a little over a decade. The report concludes that unless “global CO₂ emissions start to decline well before 2030”, we will surpass the 1.5°C threshold.

So that’s where ‘12 years’ comes from. Some people believe that this a simple and effective slogan that captures the urgency of our climate crisis, and has helped galvanize people into action. Others feel that it’s overly simplistic at best, and misleading at worst, because it singles out a specific number as an all-or-nothing target, whereas in reality the effects of climate change are a continuum. As climate scientist Kate Marvel put it, “Climate change isn’t a cliff we fall off, but a slope we slide down”.

But that’s not what I want to discuss here, there are already many good pieces on this debate. Instead, I want to know where carbon budgets come from in the first place. What’s the justification for these numbers, and how accurate are they?

So in this post, I’m going to take you through how you can look at the data for yourself and come up with a rough estimate of the carbon budget.

Let’s start with the basics

You’re probably very used to seeing graphs depicting global warming that look like this. (I just doodled this, so don’t take the exact shape too seriously. )

These kinds of graphs are great for showing us how much the Earth has warmed. (And as Ronnie Chieng hilariously pointed out, they even work upside down.)

ronnie-chieng-climate-change.jpg » LiveScience

Although these graphs teach us about the past, they aren’t so helpful when it comes to predicting the future. It’s hard to tell by looking at this graph which way we’re headed, because that depends on how much carbon dioxide humans will emit in the future.

Let’s go ahead and create this graph using public data. The Global Warming Index is a measure of how much of Earth’s temperature rise is attributable to humans (so it’s removing all of the natural fluctuations in temperature).

Here’s what this looks like, wen plotted versus time (interactive version here).

Notice how it shoots up around 1970? You can compare that to a historical graph of carbon dioxide emissions and work out why that happens.

The reason this graph isn’t so useful for predicting the future is that its slope (how steeply it rises) depends on how much carbon dioxide is in the air. A future in which we take major climate action will follow a very different trajectory compared to a future that’s business as usual.

It turns out that there’s another simple way to look at our historical climate trajectory, one that’s more helpful for predicting the future.

Another way to think about warming

Here’s how it works. Imagine that you change the x-axis of the graph so that instead of measuring the years go by as we did above, we instead measure how much carbon dioxide we’ve added to the air. In that case, the graph might end up looking like this.

Every year, we add some more CO₂ to the air, so we take a step further to the right. Consequently, the Earth warms up. For every step to the right, we also take a step up. So you’d expect our trajectory to move towards the top-right.

If we make this switch, here’s what this new graph looks like (interactive).

In the graph above, the horizontal axis represents the total amount of carbon dioxide that we’ve emitted, due to both fossil fuels and land use. I pulled these numbers from the Global Carbon Project. The vertical axis measures how much the world has warmed as a consequence. Let’s call this graph a climate carbon curve.

The animation shows us the history of human-caused global warming. Every dot represents a single year of human history. Each year we emit more CO₂, so we take a step to the right. And for every step to the right, we warm up, so we take a step up. Notice that as global annual emissions accelerate, the dots get further and further apart — we’re taking bigger steps along the climate carbon curve.

Do you notice anything interesting about this graph? Let’s draw a line connecting the first and last points on this graph.

When viewed in this way, the history of climate change is surprisingly simple to understand. Aside from a bump in the 1970s, the global historical climate trajectory from 1850 to 2017 essentially follows a straight line on the climate carbon curve.

That’s a simple message. In spite of all of the complexity in climate science, there’s a direct proportionality between how much total carbon dioxide we’ve pumped out, and how much the planet has warmed as a result. For every trillion tonnes of carbon dioxide that we emit, the graph teaches us that we raise Earth’s temperature by about 0.44 degrees Celsius. To paraphrase Notorious B.I.G., the more carbon we come across, the more problems we see.

Although the exact slope might differ, this straight-line relationship is born out both through historical observations as well as through every serious climate simulation. There are dozens of scientific papers demonstrating that this relationship holds.

A caveat: We’re talking about how much the temperature rises soon after we dump greenhouse gases into the air. Climate scientists call this the effective transient response of the climate to cumulative carbon emissions (quite the mouthful). Once this carbon is in the air, the temperature will gradually continue to rise further, over centuries. The long-term temperature rise is known as the equilibrium climate sensitivity, which is a fair bit higher than the transient climate response.

Why a straight line?

It’s somewhat puzzling that this graph is so simple. What causes this straight-line relationship? Why should every unit of carbon dioxide, whether emitted in the past or the future, have the same warming effect?

If you only consider carbon dioxide in the air, then every subsequent unit of carbon dioxide does indeed have slightly less of a warming ‘bite’. That’s because the atmosphere gets increasingly saturated with CO₂ over time. It’s a bit like how throwing mud into murky water has less of an effect than throwing it into clear water.

So by itself, every additional unit of carbon dioxide that we emit would have a slightly diminishing warming effect. However, as we emit more CO₂, the oceans also become more saturated with the gas. This means that they’ll have less room to absorb carbon dioxide in the future, so a larger fraction of our emissions will end up in the air.

So we’ve got two opposing effects. As the air gets saturated with carbon dioxide, every additional unit of the gas has slightly less of a warming effect. At the same time, as the oceans get saturated with carbon dioxide, more of the gas will end up in the air.

As it turns out, these two effects cancel each other out. The result is that every new unit of carbon dioxide has approximately the same warming effect as the previous one. This is why we end up with this straight-line relationship between CO₂ and warming. (You can read more about this here, or check out the papers linked above.)

What comes next?

The big question is, where are we going to end up in the future?

We can take a reasonable guess by extrapolating out trajectory forwards.

Every possible climate future, in one graph

The yellow line represents our current trajectory, extrapolated into the future. I’ve also added a ‘cone of uncertainty’ around it. That’s because, in reality, there are bounded gaps in our knowledge (i.e., uncertainties). This cone approximately represents the uncertainty in our prediction, which comes from the underlying uncertainty in the historical measurements and analyses.

This graph isn’t telling us about just one climate future. Instead, it places a bound on every possible climate future. Trace your finger upwards along the cone of uncertainty and you’re tracing out a possible future. A high carbon future is one where your finger moves further along the cone, a low carbon future is one where your finger doesn’t move as far.

Notice that even if we shrink our annual climate emissions down to a tiny fraction of its current value, this won’t completely halt global warming. We’ll still be inching up along the cone, just taking smaller steps. The only way to stop the warming is to stop taking any steps at all. To stabilize Earth’s temperature, we need to get to zero emissions.

D.I.Y. Carbon Budgets

As promised, let’s use this graph to work out a carbon budget. By the end of 2017, we were at ~1° of warming, having emitted ~2300 billion tons of CO₂.

Trace your finger along the thin grey 1.5° line on the graph until it intersects the cone (for greater accuracy, you can zoom in with your cursor in this interactive graph).

You’ll see that it crosses the red shaded region and yellow line at about 3000, 3500, and 4200 billion tons. (These numbers are all rounded to the closest 100 billion tons.) To calculate our remaining carbon budget, subtract 2300 (where we are today) from these numbers.

So this graph tells us that as of 2018, our 1.5°C carbon budget ranged from 700 to 1900 billion tons of CO₂, with a best guess of 1200 billion tons.

Going through the same exercise for the 2°C budget, we come up with a carbon budget ranging from 1600 to 3200 billion tons, with a best guess of 2300 billion tons.

Compared to the IPCC predictions, these numbers are all on the high side. However, they’re in the ballpark of existing estimates of the carbon budget made from historical observations.

The IPCC predictions are created using climate models combined with observations. In general, this approach predicts a steeper slope for the climate carbon curve than purely historical observations do. The steeper the slope, the faster we’ll warm up. This is why the IPCC arrives at a smaller carbon budget than our simple method.

The Takeaway

We’ve seen how extending our historical trajectory forwards gives us a simple way to predict our climate future, and estimate carbon budgets. However, it’s important to keep in mind that all such estimates tend to have very large uncertainties.

We can confidently say that as we continue emitting carbon dioxide, we’re going to move further up the cone of uncertainty and warm up. We can use this idea to estimate when we’ll cross any particular threshold. But that’s all that these numbers are — approximate, ballpark estimates.

When people say that we have 12 years to use up our carbon budget, we should read that as ‘12 years give or take 10 or 15 years’. 12 years is not a sharp dividing line, it’s just a rough indicator of a wide range of uncertainty. What’s more, small changes in our underlying measurements and assumptions significantly shift these predictions (as the IPCC did last year). So to take this number as literal and unambiguous truth is to deeply misunderstand what it means.

That’s why some critics argue that rather than focus on impossibly precise carbon budgets, we should instead talk about when we’ll reach zero emissions. Because one thing that we can say with certainty is that so long as we’re still emitting carbon dioxide, we’re going to keep warming up.

Uncanny Skies

What Indonesia's red skies have in common with Edvard Munch's Scream

Earlier this week, I found myself fixated on footage of red skies over Indonesia. Over the past week, videos and images from the Jambi province in central Sumatra depicted a deep orange or blood-red sky, a result of sunlight scattering through the haze of human-caused forest fires.

The Jambi province is facing a health crisis caused by air pollution, with clinics seeing a surge in patients, many of whom are children. The number of fires burning in Indonesia this year is growing at a rate similar to that of 2015, when the region experienced an unprecedented air pollution crisis termed the worst environmental disaster of the year. The carbon emissions from this year’s fires are also at a record high, with nearly a million people affected by respiratory problems.

These images depict a surreal and eerie sight, bringing into focus the deep strangeness of our current predicament. In an era where we apply digital filters to dial up the vividness of natural scenes, it seems uncanny to have to remind ourselves that there are no filters. This color palette seems more befitting of dystopic science fiction than reality.

In an essay about the sensation of uncanniness, Sigmund Freud wrote that “the uncanny is that species of the frightening that goes back to what was once well known and had long been familiar”. The German word for uncanny is unheimlichkeit, literally ‘un-home-like-ness’.

This view is echoed by the novelist Amitav Ghosh. In The Great Derangement, a book about climate change and literary imagination, he writes, “It is surely no coincidence that the word uncanny has begun to be used, with ever greater frequency, in relation to climate change. […] No other word comes close to expressing the strangeness of what is unfolding around us. For these changes are not merely strange in the sense of being unknown or alien; their uncanniness lies precisely in the fact that in these encounters we recognize something we had turned away from.

Seen through this lens, the images of red skies in Indonesia are unsettling not because they’re unfamiliar, but because they bring the familiar and the unfamiliar together in jarring contrast.

Our current era is defined by a growing tide of strange and unlikely events, from thousand-year storms that revisit cities every few years, to wildfires that destroy towns and counties, to rising tides and shifting sands, to massive colonies of coral reefs bleached away, and dramatic bird and insect extinctions across the globe.

The unlikely is becoming likely. What were previously low probability events are now commonplace. It feels like rolling a dice 10 times in a row and ending up with a series of 1s.

And yet, if we look back far enough, there are often historical precedents for similarly strange and eerie events.

In 1883, the island of Krakatoa (situated between current-day Java and Sumatra) exploded in a volcanic eruption that killed tens of thousands and sent shock waves around the world. In the months that followed, people across the world witnessed dramatic, unusual skies, streaked with a fiery red caused by sunlight scattering through the volcanic haze.

(More recently, many people in the Northern hemisphere have been witnessing violet and purple colored sunsets, that were likely made more intense by a volcanic eruption in Russia in June. I remember seeing an unusually purple sunset about a month ago, and now I’m wondering if that might be related.)

In the years following the Krakatoa Eruption, the painter William Ascroft sat along the banks of the River Thames, obsessively sketching more than 500 pastel drawings of these unusual skies.
Red skies caused by the 1883 Krakatoa eruption. Wikimedia (Public Domain)

Describing these sunsets, he wrote,

“The first strong afterglow was observed November 8th, when a lurid light was seen about half an hour after sunset. It was so extraordinary that some fire engines turned out.”

In 1883 and 1884, the scientific journal Nature ran a column entitled ‘The Remarkable Sunsets’, where people wrote letters to the editor documenting their sunset observations. As the author Richard Hamblyn pointed out, the poet and priest Gerald Manley Hopkins wrote in, noting

The glow is intense, this is what strikes every one; it has prolonged the daylight and optically changed the season; it bathes the whole sky, it is mistaken for the reflection of a great fire […] more like inflamed flesh than the lucid reds of ordinary sunsets.

Meanwhile, in Norway, a painter was walking along a mountain road near current-day Oslo along with a couple of friends, when he described the following scene:

“the Sun went down … it was as if a flaming sword of blood slashed open the vault of heaven — the atmosphere turned to blood — with glaring tongues of fire […] I felt something like a great scream — and truly I heard a great scream.”

In another account, he wrote,

“My friends went on, and I stood alone, trembling with anxiety. I felt a great, unending scream piercing through nature.”

The painter was Edvard Munch, and some scholars argue that the scene he witnessed was a consequence of Krakatoa’s eruption. Years later, inspired by this incident, Munch went on to paint ‘The Scream’, one of the most iconic images of western art.

Figure on cliffside walkway holding head with hands
The Scream by Edvard Munch. Wikimedia (Public Domain)

I find it interesting that the language these artists used to describe Krakatoa’s sunsets was often one of being struck by horror. It shows them grappling and trying to come to terms with the strangeness in the everyday.

In a way, Edvard Munch’s ‘Scream’ is the late nineteenth century analog of ‘This Is Fine’ — a meme that has come to symbolize our modern sense of anxiety, unease, and helplessness, as the very threads that tie ecosystems together unravel before our eyes. You hear a similar metaphor when Greta Thunberg says, “our house in on fire”.

From Munch’s Scream to the burning house meme, from Ascroft’s countless sunset drawings to the many social media posts on Jambi’s red skies, these outpourings of human expression chronicle our increasing discomfort and unease with a world that both is and isn’t familiar. They capture our enduring existential scream, our sense of no longer feeling at home in our only home.

The difference, however, is that while Krakatoa was an unavoidable natural catastrophe, the climate crisis is an accelerating problem of our own making, one where we have the benefit of knowing what we need to do to prevent the worst possible outcomes.

So scream, even panic. But also act.

Climate Feedbacks Explained, with Pie

The Rate of Change: September 23, 2019

A Pie Puzzle

Here’s a puzzle that might not seem like it has anything to do with the climate. But it’s at the heart of reasoning about how climate feedbacks work.

Say someone gave you an entire pie. Then they gave you half a pie. And then a quarter of a pie, and then an eighth of a pie, and so on, to infinity. At every step, you get half as much pie as you got before. How much pie would you end up with in the end?

At the heart of this puzzle is the remarkable realization that you can add up an infinite number of diminishing pieces and yet end up with a finite whole. It turns that all those infinitely many slices will add up to two full pies.

Mathematically, we can sum up this pie puzzle like this:

In math-speak, we’d say that this infinite series converges to a finite sum.

What does this have to do with Earth’s climate?

Earth’s temperature arises from a balance between the energy that we absorb and the energy that we radiate into space as heat. Because carbon dioxide is a heat-trapping gas, every unit of carbon dioxide that we emit tips the scales of Earth’s energy balance.

Adding CO2 tips the scales of Earth’s energy balance.

We’re currently out of balance, and are still tipping the scales further. This means that the Earth absorbs more energy than it can radiate away to space. This forces the Earth to warm up.

As the Earth warms, it’ll gradually start to radiate more heat into space. In the future, the Earth will find itself in a new energy balance, one where it has settled in to a warmer temperature.

Over time, the Earth will settle into a new, warmer energy balance.

Here’s a simple way to visualize this process, using Nicky Case’s feedback loop simulator.

You can press play and experiment with this for yourself. Pushing the up arrow emits carbon dioxide. Pushing the down arrow is equivalent to sucking CO₂ back from the air, either through natural or technological processes. The key takeaway is that the level of carbon dioxide in the air determines our eventual temperature rise.

In the previous newsletter and accompanying interactive, we came up with a number for this temperature rise. This is called the climate sensitivity, and it’s the answer to the question: how much does the temperature rise when you double CO₂ levels?

By balancing Earth’s energy budget, we estimated that a CO₂ doubling would cause a temperature shift of 1.1°C (about 2°F). However, climate scientists predict a much larger temperature shift of somewhere between 1.5 to 4.5°C (roughly 3-8°F).

So where did we go wrong?

Going around in circles

The reason our answer was too small is that we neglected all of the feedback loops in Earth’s climate system. For example, here’s a climate model that includes a process known as the water vapor feedback. (Interactive version here.)

Notice that adding a single unit of CO₂ now has a larger effect than before.

For every direct increase in temperature due to carbon dioxide’s greenhouse effect, there’s also an indirect increase from the cycle shown above. It works like this. As the temperature rises, more water evaporates. Water vapor is a greenhouse gas, so this extra water vapor traps more heat, and so the temperature rises further, which adds even more water vapor in the air, and so the cycle continues. This spiraling cycle is an amplifying feedback loop.

It’s worth remembering that even though water vapor is a greenhouse gas, turning on your lawn sprinkler won’t warm the planet. That’s because each drop of water that evaporates in your lawn will fall back down as rain in 9 to 10 days. The amount of water vapor in the air is limited by Earth’s average temperature, so any more that we try to add will eventually just fall back out as rain.

But as carbon dioxide warms the planet, evaporation ramps up. Unlike with your lawn sprinkler, in a warmer world there really is more water vapor in the air, and this water vapor further amplifies the initial warming.

So water vapor is a temperature multiplier.

Through the water vapor feedback cycle, the warming effect of carbon dioxide is roughly doubled. It’s as if every time that you raised the temperature on your thermostat by one degree, someone walked in to the room and set it a degree higher.

This is why feedbacks matter. They amplify change. They multiply the warming effect of carbon dioxide, and thereby shift climate change from being a cause for concern into becoming an all out emergency.

Climate Jargon: Things that directly alter Earth’s temperature by creating an energy imbalance are known as ‘forcings’. For example, an increase in the Sun’s brightness, or a volcano spewing sunlight-dimming ash are both possible types of forcings. In contrast, feedbacks act indirectly, by amplifying or diminishing the effect of a forcing. So water vapor is a feedback and not a forcing.

A Hidden Puzzle

But there’s a puzzle lurking within these loops.

If you think about it, doesn’t it seem like there’s no end to this feedback cycle? What prevents this process from spiraling out of control? And if this feedback loop will loop forever, doesn’t that mean that there’s no end to the warming?


OK, deep breaths. <inhale> <exhale>

To solve this puzzle, we need to take a closer look at how feedback loops work.

Say that we eventually double the carbon dioxide in Earth’s atmosphere. Climate scientists tell us that this will add 3.7 W/m² to Earth’s energy imbalance. Last week, we discovered that this will directly lead to about 1.1°C of warming.

So every time we add an energy imbalance to the pile on the left, we can multiply it by 0.3 to get a temperature increase on the right.

But the warming is just getting started. For every degree that the temperature rises, climate scientists tell us that the water vapor feedback cycle will add 1.8 W/m² to our energy imbalance. So we can multiply the pile on the right by 1.8, and get the additional energy imbalance caused by one loop of the water vapor feedback cycle.

But wait! This additional energy imbalance will now cause its own rise in temperature. So once again, we multiply the blue box on top by 0.3.

And once again, this new temperature rise will add a little more to our energy imbalance. So we multiply the red box on top by 1.8.

Which, in turn, causes a further temperature rise. Maybe you see where this is going…

The cycle continues, repeating forever. With every loop, the red and blue piles grow a little bit taller.

As the feedback loop keeps looping, it looks a little like this:

The feedback factor tells you the effect of going around a feedback loop once. As the animation above shows, each loop contributes a factor of 1.8 times 0.3 (= 0.54, or about half) to the overall temperature change. In other words, every loop contributes about half the temperature change of the previous loop. Or, in the cartoon picture above, each new red block is about half the size of the block below it.

What does this remind you of? We started off with about one degree of warming. The water vapor feedback loop tacks on another half a degree of warming. Then it adds half of that. And half of that, and so on…

The water vapor feedback loop is the pie puzzle in disguise!

Just as we ended up with two pies, this feedback process amplifies one degree of warming into two degrees.

We can do a bit better than this. The gain of a feedback loop is the overall amount by which it multiplies the original effect. It turns out there’s a simple relationship between the feedback factor of a loop (its effect after one cycle) and its gain (its cumulative effect after all the cycles).

Here’s a chart that shows how the gain depends on the feedback factor.

A graph of the gain of a feedback loop (its cumulative effect after all the cycles) plotted versus its feedback factor (its effect after one cycle). Notice that as the feedback factor approaches 1, the gain blows up. This graph is from Gerard Roe’s paper Feedbacks, Timescales,and Seeing Red.

And here’s the formula for this graph.

Since the feedback factor of the water vapor loop was 1.8 ⨉ 0.3 = 0.54, plugging this into the formula tells us that its gain is 2.17. The water vapor feedback loop converts 1 degree of warming into ~2.2 degrees of warming.

In the pie puzzle, each slice of pie was smaller than the last, and this is what allowed us to reach a finite sum. Similarly, each loop of the feedback cycle makes a diminishing contribution to the overall temperature gain.

This is the solution to the loop puzzle — it’s the reason why we don’t end up with a runaway process that spirals out of control every time we have a feedback loop. An infinite series can converge to a finite sum.

The numberphiles among you may recognize the gain formula as the formula for the sum of a geometric series. If f represents the feedback factor due to one loop, then the gain due to all cycles of a feedback loop is given by the infinite sum 1 + f + f² + f³ + …, where each term in the series represents one more cycle of the feedback loop. Just like in the pie puzzle, each additional term contributes a diminishing amount to the overall sum. So this is a convergent sum (so long as the feedback factor f is less than 1), and the solution is that the total gain is 1 / (1 - f).


There are essentially two kinds of feedback loops. Those with a positive feedback factor amplify changes, just like the water vapor cycle. Let’s call these amplifying feedback loops. (You can see from the graph above that a positive feedback factor implies a gain that’s bigger than 1.)

And then there are those with a negative feedback factor. Let’s call these regulating feedback loops, because they diminish the original change. (The graph above shows us that a negative feedback factor implies a gain that’s less than 1.) A classic example of a regulating feedback loop is a thermostat — when the room gets too hot, the thermostat switches off the heat, which cools the room back down.

Earth’s climate system is a complicated mix of amplifying and regulating feedback loops. So the picture looks more like this.

That’s quite a mess! (And even this is a massive simplification.)

It turns out that there’s one really nice feature of these complicated feedback loops. You can simply add together the feedback factors for each loop to get the feedback factor for their combined effect. And climate scientists have painstakingly estimated the feedback factors for each of these different loops.

The graph below shows a summary of these estimates. The column to the right is the sum of all the factors — that’s the number we’re after.

A graph from Gerard Roe’s paper Feedbacks, Timescales, and Seeing Red, compiling together different estimates of various climate feedback factors.

While the water vapor and lapse rate feedback cycles (the first two columns) individually have large uncertainties, it turns out if you consider them together (the third column) you can estimate them more accurately. Most of the uncertainty comes from estimating the feedback factor for clouds (the fifth column), which are notoriously difficult to model.

Adding all this together, you end up with a total feedback factor of about 0.6, with a considerable margin of error around that value.

Plugging 0.6 into our formula for the gain, this tells us that all these feedback loops together have a combined amplification effect (i.e. gain) of 1 / (1 - 0.6) = 2.5

So we can finally revise our estimate of the climate sensitivity. At first, we calculated that a doubling of carbon dioxide would lead to 1.1°C of warming. By taking these feedbacks into account, this number gets multiplied by 2.5, putting our revised prediction for Earth’s climate sensitivity at 2.75°C (which is within the range of accepted answers, if a bit on the low side).

So we’ve just seen how climate feedback loops amplify Earth’s climate sensitivity, and magnify climate change into a much bigger problem. In a coming newsletter, we’ll take a look at how these feedbacks also amplify uncertainty, and make it harder for us to predict the future.


This post was largely inspired by the article Feedbacks, Timescales, and Seeing Red by Gerard Roe, which was very helpful for me in understanding how feedback loops work. Any errors in understanding are entirely my fault.

This is the fourth part in a series of explainers on climate science. Part 1 and part 2 explore the idea of Earth’s energy balance, and part 3 builds on this idea to predict Earth’s climate sensitivity. This essay improves the climate sensitivity estimate from part 3 by incorporating climate feedbacks.

If you’re interested in learning more about the basics of climate science, I recommend David Archer's online lectures and textbook (he also has a Coursera course that covers similar material).

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The email header image is based on the Warning Stripes illustration by Alexander Radtke. The pie image is modified from Vecteezy.

How Sensitive is Earth's Climate?

The Rate of Change: September 14, 2019

This is the third part in a series breaking down the fundamentals of climate science. Here’s Part 1 and Part 2.

To predict how much the world is going to warm in the future, one of the key numbers to understand is Earth’s climate sensitivity. This is the answer to the question: how much will Earth’s temperature rise if we double carbon dioxide levels?

It turns out that this question is as old as the field of climate science. In 1896, the Nobel Prize winning Swedish chemist Svante Arrhenius took a creative approach to solving this problem. By cleverly reinterpreting data on the intensity of moonlight, Arrhenius was able to make the first modern prediction of Earth’s climate sensitivity. (If you’re interested in how he did this, here’s an in-depth video.)

Arrhenius’s answer — 5 to 6 ℃ — is on the high end, compared to our current understanding. Today climate scientists predict this number to be between 1.5 and 4.5 ℃. But the fact that Arrhenius was even in the right ballpark is impressive, given that he was working with indirect data, had to fill in many gaps in the theory, and spent an entire year crunching the numbers by hand!

By the time Arrhenius carried out his calculation, it was well known that carbon dioxide was a greenhouse gas (a fact that we owe to Eunice Newton Foote, although typically credited to John Tyndall). This was the basis for his work, which he combined with the then brand-new theory of heat.

However, Arrhenius wasn’t particularly concerned about global warming. His main motivation was to understand why the ice ages happened. By extrapolating forwards from 1896, Arrhenius worked out that it would take thousands of years for humans to double carbon dioxide levels.

Which was a perfectly reasonable prediction to make in 1896, unless of course humans somehow managed to exponentially increase their carbon emissions.

Well… we all know how that turned out.

Today, we’re in the process of actually conducting Arrhenius’s alarming thought experiment. We’re nearly halfway to a CO₂ doubling compared to pre-industrial levels, and our carbon emissions are accelerating.

So it’s easy to see why Earth’s climate sensitivity is an important number to understand. It helps us understand the future.

We don’t really know where our carbon dioxide levels will end up, that depends on the extent to which climate action succeeds. But Earth’s climate sensitivity lets us predict how much warming we can expect to see in different possible climate futures.

A First Attempt at Calculating Earth’s Climate Sensitivity

So let’s take a stab at cooking up Earth’s climate sensitivity. To do this, we’re going to need a few ingredients.

Take One Part Sunlight

First, we need to know how much sunlight a patch of Earth receives. We’ve encountered this number in previous newsletters — it’s approximately 240 Watts per square meter. We can call this number our incoming energy flow.

The standard term for this quantity is ‘energy flux’. Energy flux = energy / area / time, or the amount of energy absorbed or radiated by 1 square meter of a planet’s surface in 1 second.

This means that one square meter of our planet receives 240 Watts of solar power, on average. I say on average because, of course, day is brighter than night, sunlight is more intense at the equator than at the poles, days are longer in summer than in winter, and so on. This number averages over all these variations.

Also, nearly a third of Earth’s incoming sunlight reflects off stuff like clouds and glaciers — this is known as our albedo (Latin for ‘whiteness’). The number above also takes this into account.

Take An Equal Part Heat

The higher the temperature of any object, the more energy it radiates in the form of heat. In an earlier post, we saw how you can work out a planet’s temperature by balancing the solar energy it receives with the heat that it radiates.

Through this simple balance, we were able to get surprisingly good predictions for the temperature of Mercury and Mars. However, this model falls short for Earth and Venus, because it doesn’t account for the greenhouse effect.

Stick in a Thermometer

To account for the greenhouse effect, we’ll need to know the actual temperature of our planet. Our average temperature is about 15 ℃ (59 ℉), or 288 Kelvin. Once again, this is averaged over the globe, over the seasons, and over day and night.

Yes, we’re leaving out a lot of detail here, but you have to start somewhere. When building a scientific model, there’s always a trade-off between simplicity and detail, and we’re aiming for extreme simplicity here.

The technical term for this type of climate model is a zero-dimensional energy balance model — zero dimensional because we’re only considering global averages, and ignoring the variation at different points on the Earth. The next step up in complexity is a one-dimensional energy balance model, which considers how sunlight, temperature, and ice cover varies with latitude.

Mix in a bunch of CO₂

Finally, we want to understand what happens when we double CO₂. In previous posts, we’ve seen how adding carbon dioxide to the atmosphere increases Earth’s energy imbalance.

Let’s make this quantitative. The IPCC tells us that doubling carbon dioxide will increase Earth’s energy imbalance by 3.7 W/m². This number comes from detailed calculations of how a CO₂ molecule absorbs heat.

You can think of this number as simply being added to our incoming energy flow. To understand what this number means, notice that 3.7 W/m² is about 1.6% of our incoming solar energy flow. So doubling carbon dioxide would have a similar effect on Earth’s temperature as instead making the Sun 1.6 percent brighter.

The technical jargon for this additional energy imbalance is radiative forcing. So climate scientists might say something like “the radiative forcing due to a doubling of CO2 is 3.7 W/m²”.

Now that we have all the ingredients, let’s get cooking.

Set to 288 Kelvin and Bake

Now that we’ve gathered all the pieces that we need, let’s put them together.

Rather than just telling you how this works, I think it’ll be more interesting for you to do it yourself. So I’ve put together an interactive essay that walks you through building a simplified climate model.

It’s called Climate Toy. I hope you find it interesting!

Climate Sensitivity

Feel free to drop me a line with your feedback. Did you find this helpful or instructive? Was it confusing? Would you like to see more stuff like this in future? I’d love to hear what you think.

Recent Climate News

You might have heard that Jonathan Franzen published a piece in the New Yorker arguing that a climate apocalypse is inevitable, and that we should stop pretending that we can avert it, and instead focus on taking more local actions.

Here are my 3 favorite responses to this piece:

  • Ula Chrobak at Popular Science wrote an excellent critique of what the piece gets wrong on climate science and policy.

  • Mary Heglar wrote a powerful, thoughtful, and poetic response: Home is always worth it.

  • Kate Marvel wrote an excellent piece on how understanding climate change changes it from a foregone conclusion to a choice.

Trevor Noah asked Greta Thunberg what people can do to act on climate change. Here’s her brilliant response:

“If I were to choose one thing everyone would do, it would be to inform yourself, and to try to understand the situation, and to try to push for a political movement that doesn’t exist. Because the politics needed to “fix this” doesn’t exist today. I think what we should do as individuals is to use the power of democracy to make our voices heard, and to make sure that the people in power actually can not continue to ignore this.”

NYT put together a phenomenal visual explainer showing the extent of the flooding along in the US Midwest and South.

Visualizing the world’s addiction to plastic bottles. This page opens with a gut punch of an animation. The image below, from the article, visualized a years worth of plastic bottles sold next to the tallest building in the world.

TIME highlights 15 women leading the fight against climate change

We need systemic changes that will reduce everyone’s carbon footprint, whether or not they care.” Michael Mann on how lifestyle changes aren’t enough.

The Washington Post has a great infographic-rich series on the places that have already warmed by over two degrees Celsius.

The UN rights chief on climate change: “The world has never seen a threat to human rights of this scope

If carbon dioxide hits a new high every year, why isn’t every year hotter than the last?

A map of how every part of the world has warmed – and could continue to warm.

The Trump adviser who tried to create a White House panel to attack climate science is leaving the administration.

“There are 118 elements on the periodic table. An iPhone contains about 75 of them.” I thought this was a fascinating piece by Maddie Stone on the challenges of recycling electronics.

The US is planning to open nearly 200 fossil-fuel power plants. What’s worse, the article concludes that many of these plants will be more expensive than renewable alternatives.

“An analysis by the Rocky Mountain Institute published Monday looked at 88 gas-fired power plants scheduled to begin operation by 2025. They would emit 100 million tons of carbon dioxide a year – equivalent to 5% of current annual emissions from the U.S. power sector. 

The institute calculated the cost of producing a megawatt-hour of electricity of a clean energy portfolio in each state that would provide the same level of power reliability as a gas plant. It determined that building clean energy alternatives would cost less than 90% of the proposed 88 plants.”

Read more.

“The mountain peak known to Swedes as their country’s highest can no longer lay claim to the title due to global heating”

Via Brad Plumer: Why did India’s devastating Cyclone Fani kill only 40 people — not 10,000?

“Democratic presidential candidates recently spoke of the need to address the adverse effects of global warming on poor and marginalized communities.”

Another blow for the future of corals. By Ed Yong in the Atlantic.

Shlesinger and his colleague Yossi Loya have found that three common coral species in the Red Sea have lost their rhythm. Their timing is off; their unison is breaking. Rather than releasing a majestic unified blizzard of eggs and sperm at precise moments, they now spawn in pathetic, erratic drizzles across weeks and months. “It doesn’t look promising for those species,” Shlesinger says.

“This study is heartbreaking,” says Shayle Matsuda of the Hawaii Institute of Marine Biology. “This is something we’ve all worried might be true.”

Read more.

Global heating made Hurricane Dorian bigger, wetter – and more deadly

Here are a number of highly rated organizations providing aid and relief in the aftermath of Hurricane Dorian.

Hurricane Dorian may have caused a critically endangered bird to go extinct.

The increasing concentration of carbon dioxide in our atmosphere is making our food more sugary and less nutritious.

Climate misinformation may be thriving on YouTube, a social scientist warns

Are we overestimating how much trees will help fight climate change?

Global 5G wireless networks threaten weather forecasts

New research reveals the loss of forest elephants damages the carbon-storage capacity of the central African forests in which they live

A deeply reported multi-part series on Baltimore’s Climate Divide — how the impact of heating is being felt disproportionately by its most vulnerable residents.

What 500,000 Americans hit by floods can teach us about fighting climate change

To fight global warming, think more about systems than about what you consume. Bill McKibben reviews Tattiana Schlossberg’s new book in the New York Times.

That’s all for this week. See you next time! If you found this newsletter informative or helpful, consider recommending it to a friend. It really helps get the word out. If someone forwarded this email to you, you can subscribe using the button below.

Amazon Fires & Climate Rage

The Rate of Change: August 26, 2019

Understanding the Amazon Fires

This New York Times piece is the best explainer I’ve read on the extent of the fires currently burning in the Amazon Rainforest. It places this August’s fires in the context of the previous decade.

Image: NYT. Description: A map illustrating the extent of fires burning in August in the Brazilian Amazon.

In the years following 2005, there was a very significant reduction in deforestation in Brazil’s Amazon, as a result of environmental protection policies.

Image: NYT. Description: A graph of annual deforestation in the Brazilian Amazon. The numbers show large spikes up to 10,000 square miles in the 1990s and early 2000s, followed by a significant reduction post 2005.

However, in recent years Brazil’s deforestation numbers are on the rise again. Herton Escobar reports in Science Magazine:

“Recent data have clearly shown that deforestation in Brazil is on the rise. From January through the end of July, 6800 square kilometers [2625 square miles] were cleared, according to INPE [Brazil’s National Institute for Space Research], 50% more than in the same period last year. But Bolsonaro called the data “a lie” and had INPE’s director, physicist Ricardo Galvão, fired in early August.”

Julia Rosen at LA Times covered the consequences of losing rainforest area in the Amazon.

James Temple at MIT Technology Review explores whetherdeforestation will push the world’s largest rainforest to a tipping point, where spiraling feedback effects convert much of the forest into savannah”.

The reasoning behind the rainforest tipping point idea goes like this. Although you may think that clouds from afar bring rain to forests, we now know that the Amazon rainforest produces half of its own rainfall. The way it works is that trees suck up water, which evaporates through leaves, seeding new clouds that rain over the forest. Through this cycle, trees in the Amazon can recycle the water brought in by clouds from the Atlantic five to six times over.

In fact, you can even see this process.

Image: NASA Earth Observatory (Public Domain) Via Wikimedia. Click through for image description.

The picture above shows the Amazon during the dry season. The tiny dew-like white spots are very likely clouds created by the process of ‘evapotranspiration’ — they’re the rain clouds that the forest creates. (You can read more about this remarkable process here and here.)

By deforesting the Amazon, among other things, we reduce the forests ability to create rain. The difference can be as high as nearly 50 centimeters (~19 inches) of rain per year, which is nearly a quarter of the annual rainfall, or about an hour of heavy rain per week.

Some scientists argue that this can lead to a vicious cycle where at a certain level of deforestation, the rainforest can no longer produce enough rain to sustain the habitat, and the land converts from forest to savanna.

Minute Earth did a fantastic job of illustrating and explaining this feedback loop, in a video that also highlights the value of indigenous knowledge.

Here’s a remarkable visualization of the carbon store in the Amazon rainforest, by Greg Fiske at Woods Hole Research Center.

Forests as mountains by @greg.fiske for @WoodsHoleResearchCenter. This map shows aboveground forest carbon located in the Amazon. It presents the biomass as 3D elevation surface, so the higher the "mountain," the more carbon is stored within that area.
The Amazon has lost more than 800,000 square km of forest—an area equivalent to about 1/10th of the lower 48 United States. Much of the deforestation is due to intentional burning to clear land for agriculture. In addition, the hotter and drier conditions brought by climate change are increasing the number of fires in a region that has not experienced them historically.

The Amazon sequesters an enormous amount of carbon—equivalent to 10 years worth of global emissions. Woods Hole Research Center studies the impact of these fires on the local and global climate, and helps government agencies anticipate at-risk areas, in order to more efficiently deploy firefighting resources. Follow @WoodsHoleResearchCenter to see more of their work.
August 22, 2019

The Case for Climate Rage

A lot of climate communication takes a dispassionate look at the problem. Amy Westervelt wrote an excellent piece arguing for the role of emotion and even anger in confronting & communicating climate change.

She also provides an excellent starter reading list:

The story of climate change, both its history and its future, needs to be told by people who have already experienced injustice and disempowerment, people who are justifiably angry at the way the system works. And some of those stories are beginning to be told.

I’d pair that with Maria Bustillos’ piece on the relation between collective and individual responsibility — Pascal’s Climate.

Understanding Climate Sensitivity: What’s up with the error bars?

The Earth’s climate sensitivity is the rise in our planet’s average temperature brought about by doubling carbon dioxide levels. Before the Industrial Revolution, CO₂ levels were at 280 parts per million. This year we hit 415 parts per million, so we’re almost halfway towards a CO₂ doubling compared to pre-industrial times.

Climate scientists estimate that the warming brought about by a CO₂ doubling — our climate sensitivity — lies between 1.5℃ and 4.5℃. Why does this prediction have such a wide range? How do climate scientists arrive at this number? If you’re interested in these questions, Zeke Hausfather at Carbon Brief has an excellent explainer from last year on how scientists estimate Earth’s climate sensitivity.

More Climate News

This is a remarkable statistic: “By the end of the summer, about 440 billion tons (400 billion metric tons) of ice — maybe more — will have melted or calved off Greenland’s giant ice sheet, scientists estimate. That’s enough water to flood Pennsylvania or the country of Greece about a foot (35 centimeters) deep.

Tree cover can cool down a city block by as much as 10 degrees Fahrenheit

Alie Ward interviews Dr. Samantha Montano about disasters, on the brilliant and funny Ologies podcast

As wildfires get worse, insurers pull back from riskiest areas

How firefighters in California are preparing for future fires

How can we do right by future generations?

A study found that more aggressive spiders were more likely to survive once a hurricane had passed

Fracking boom tied to methane spike in Earth’s atmosphere

Fracking may be a worse problem for climate change than we thought

Iceland mourns loss of a glacier by posting a warning about climate change

Ellen Swallow Richards: MIT’s first female student

Before Rachel Carson was born, Richards wrote and lectured that a direct link could be drawn between the well-being of humans and the safety and cleanliness of the environment in which they lived. At the turn of the 20th century, as if she was anticipating many of the discussions taking place today in the age of the Anthropocene, Richards said, “The quality of life depends on the ability of society to teach its members how to live in harmony with their environment, defined first as the family, then with the community, then with the world and its resources.”

“The world’s biggest ever climate mobilisation was led by children. It’s time adults stepped up.” Find a climate strike happening near you.

The broader importance of #FridaysForFuture

How one billionaire could keep three countries hooked on coal for decades

July was officially the hottest month ever recorded

As Greenland melts, its sand is becoming increasingly valuable

In order to understand the brutality of American capitalism, you have to start on the plantation. That’s the tile of sociologist Matthew Desmond’s piece in the remarkable 1619 project, a New York Times production exploring the history and enduring legacy of slavery in the United States. Read more stories from this project here, or check out the podcast. If you’re an educator, the Pulitzer center has published a school curriculum around this project.

Another excellent and deeply historically researched read on the links between slavery and American capitalism is the book This Half Has Never Been Told.

A history of estimating global CO2 emissions

How people in Phoenix, Arizona are adapting to warming temperatures

The US Government is moving to weaken the Endangered Species Act

The Washington Post has a new series about places that have already warmed by ~2 degrees Celsius, roughly double the global average. Here’s the first piece, on New Jersey & Rhode Island — the two lower 48 states with the highest level of warming so far.

The tweet above shows a screen capture of an FAQ from the Hurricane Research Division of NOAA responding to some of the more creative and outlandish ideas for combating hurricanes.

The Thin Orange Peel

Here’s an interesting fact I learnt this week. The atmosphere is thinner than you might think — and it’s uneven. The part of the atmosphere in which all weather occurs is called the troposphere. This layer contains 99% of water vapor, and makes up 75% of the atmosphere by mass. It turns out that at the poles, the troposphere ends at roughly the same height as Mt Everest, while at the equator, it extends to about twice this height.

The picture below shows us what this layer looks like in practice. The orange layer is the troposphere, the white layer is the stratosphere, and the blue layer is the mesosphere.

Image: NASA / Wikimedia (Public Domain)

Nearly everything we think of as the atmosphere — every cloud that we’ve ever seen — exists in that thin orange peel. If you scaled an orange up to the size of the Earth, it’s skin would be about 30 times thicker than Earth’s troposphere.

That’s all for this week, see you next time!

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