Both things are true: The climate system is vastly complex, and we’re certain about what we are doing to it. How can we be so confident in a hundred-year projection when we can’t predict the weather with any reliability more than a week out?

“How can it be that both are true?” said Nadir Jeevanjee, an atmospheric physicist at NOAA’s Geophysical Fluid Dynamics Laboratory, a leading institution for cutting-edge simulations of the atmosphere. “It’s a huge tension that’s lurking behind the whole conversation.”

It turns out that complexity can be a veil concealing more basic truths. An enormously complicated system can yield simple answers. You just have to ask a simple enough question.

Complexity Rises

In 1961, Edward Lorenz, a meteorologist at Massachusetts Institute of Technology, was running and rerunning his computer simulation of an atmosphere when something surprised him. What seemed like minute differences in the simulation’s initial states ballooned, until the weather outcomes of different runs bore zero resemblance to one another. In subsequent years, he formulated what would become gospel truth in the Earth modeling community: No matter how much weather prediction advances, it has little value beyond two weeks.

“You need to get the initial conditions right, then you need to get your model right to propagate them forward in time, and very quickly you run into chaos,” said Isla Simpson, an atmospheric scientist at the National Center for Atmospheric Research.

Weather prediction takes a snapshot of the atmosphere today and projects its motion forward, through the theoretical universe of all possible forecasts. Imagine dropping a rubber duck into a raging river. You can have a sense of where it might go, but it’s increasingly impossible to predict precisely where the duck will be the farther downriver it travels. Even if you had flawless equations to describe how the river is moving, you’d never get an exact answer. Turbulent waters vary so dramatically that a slight shift in the duck’s initial position, or a slight error in our knowledge of the starting conditions, would lead to a totally different outcome. As the duck progresses downstream, any tiny deviation will multiply.

The same is true of Earth’s atmosphere. Even with 21st-century technology, no snapshot can perfectly capture the locations and paths of all the gas molecules. Those starting errors — the proverbial flaps of a butterfly’s wings, a metaphor that emerged from Lorenz’s work — grow over time, as will the difference between prediction and reality.

But the trajectory of a river is not defined by the turbulence of the water in it. The river’s bends are driven by larger-scale, longer-term phenomena — the shifting of tectonic plates, the erosion of the riverbank by plant roots, the volume of water flowing through the atmosphere and landscape, and more. A meteorologist is concerned with predicting where the duck will go; a climatologist is concerned with predicting where the river will go.

“We’re not asking what will the weather be on July 7 of 2047 in San Francisco,” said one of those climatologists, Daniel Swain at University of California Agriculture and Natural Resources. “We’re describing the envelope of those variations, not which specific path we’ll take.”

In other words, we can’t possibly know where the duck will end up. But from here, we can clearly see that the river’s course is changing. “We’re giving the system such an enormous and sudden kick — that is actually what gives us the predictability,” Swain added. “Two to four degrees centigrade is like a quarter to half of an ice age, but in the opposite direction.”

Simplicity Emerges

Syukuro Manabe was already intimately familiar with the perils of weather forecasting when, in 1965, as a scientist at the Geophysical Fluid Dynamics Laboratory, he was tasked with building a mathematical model of the Earth’s climate. He had trained as a meteorologist in Japan, but instead of making local forecasts, his new job was to sketch out the universe of possible weather, given the atmosphere’s content and interactions. He was not following the duck, but rather working on a basic simulation of the river.

Decades of indifference had followed Arrhenius’ initial calculation of warming due to carbon dioxide. More than half a century later, Manabe thought his model could help bring some rigor to the idea of a “greenhouse effect.” He used it to simulate the atmosphere at a single location on Earth. He started in equilibrium, with the same amount of energy entering from the sun and escaping to space.

Most radiation from the sun cruises right through the atmosphere to warm Earth’s surface. But the return route of that energy — Earth’s radiation back to space — takes the form of infrared light. Infrared light has longer wavelengths and, crucially, can interact with some gas molecules. So instead of escaping straight to space, it gets absorbed and released many times on its path up through the atmosphere.

Manabe’s model held information about the gas of the atmosphere, including its water content and equilibrium temperature, at various altitudes. Manabe then doubled the amount of carbon dioxide in his artificial atmosphere. Carbon dioxide, one of the gases that absorbs infrared light, is called a “greenhouse gas” for its heat-absorbing effect. More carbon dioxide molecules means more chances for that light to be absorbed and released before it exits to space, lengthening its time within our atmosphere.

Over time, Manabe’s simulated Earth system settled into a new equilibrium. The same amount of the sun’s energy was coming in, and the same total was escaping to space. But more infrared light stayed in residence in the atmosphere — flying around at every height and being exchanged between gas molecules. This made the temperature at every altitude just a little bit hotter, all the way down to the Earth’s surface.

His simulation was no ambiguous, unreliable weather forecast. It was the greenhouse effect, clear as the air after a summer rain.

“The fundamental physics is very well established,” said Joanna Haigh, an emeritus atmospheric physicist at Imperial College London. “We can say without any shadow of doubt that more greenhouse gases means higher surface temperature.”

In Manabe’s simple simulation, the complexities of weather didn’t matter to the long-term outcome. The state in which those complexities played out — the course of the metaphorical river — had shifted.

The model also told Manabe something new: Water vapor is a much larger component of Earth’s atmosphere than carbon dioxide (up to 4% versus 0.04%), and traps more heat per molecule. The model made it clear that a warmer atmosphere can hold more water, which in turn doubles the total warming and therefore draws even more water molecules into the air. This was the first and most significant calculation of a climatic “feedback loop,” or an additional, indirect impact of carbon dioxide on temperature.

In the decades since Manabe’s groundbreaking work, study after study has stacked evidence to confirm the startling accuracy of his prediction. His model is playing out on Earth’s surface right now, escaping from simulations into the realm of human experience. Today, the global mean temperature has risen at least 1.2 degrees Celsius from preindustrial levels, according to the World Meteorological Organization — almost exactly as much as Manabe’s simple model predicted for the amount of carbon dioxide we’ve pumped into the air. Anthropogenic carbon dioxide has shifted the course of the river, the envelope of uncertainties that constrain our chaotic weather patterns.

Chaos Lingers

Manabe’s model has been confirmed by vast reams of data from a wide range of sources. But it was hardly complete. Changing the temperature changes lots about the Earth, from the reflectivity of sea ice to the stability of permafrost. The oceans are their own swirling mess, deeply interwoven with climate and weather alike. We’ve since begun to understand how these downstream, often chaotic forces may further shape the river. As scientists decipher them, there’s one particular feedback loop that has come to dominate the conversation.

“Clouds are certainly the greatest current source of uncertainty,” said Kerry Emanuel, an emeritus atmospheric scientist at the Massachusetts Institute of Technology. “We’re flying almost blind on clouds.” These familiar, turbulent morasses of swirling droplets continue to stymie scientists. Water vapor is a greenhouse gas, and the liquid droplets and ice in clouds can also trap heat. But at the same time they reflect some of the sun’s ultraviolet and visible light back to space. The cloud droplets form around natural and human-made aerosol particulates in the air according to microscopic physics that are not fully understood.

“We’re pretty sure we have a good sense what the baseline is,” said Robin Wordsworth, a climate scientist at Harvard University. “The question is, are clouds going to make things worse by a small amount or a lot?”

Clouds are chaos’s revenge. In the decades since Manabe’s work, the uncertainty present in climate models due to clouds has barely improved, and remains consequential. “Clouds will make the difference between climate change being kind of tolerable for humanity and catastrophic for humanity,” said Timothy Palmer, a climate physicist at the University of Oxford.

Chaos complicates the picture in other ways, too. The atmosphere’s “memory” of its beginning state (that is, today) is a matter of weeks. After that, today’s conditions cease to matter, which is why weather prediction has a hard limit. But as models have improved to include more feedback loops, researchers have started to incorporate the longer “memories” of other parts of the climate system. The upper ocean takes a few years to “forget” its initial conditions; the deep ocean takes centuries. Ice sheets can “remember” for millennia. In 2100, the state of these systems will depend intricately on their state today, and will partly determine the global climate of that increasingly less distant time. We know the planet will keep getting hotter, but by exactly how much will be determined by these subtle factors scientists are still trying to understand.

Subtle, but consequential. Several distinct measurements have recently suggested that more energy is entering the Earth system than leaving it — more than our best climate change models predicted. “It’s quite worrying. We really need to figure out exactly why this happened,” Emanuel said. The answer could be clouds, or aerosols, or possibly an unknown ocean cycle that will dissipate in 10 years and put us back on the predicted track. But something significant is clearly missing from our picture of the system.

The simple question — What happens when you double atmospheric carbon dioxide? — has indeed yielded a relatively simple answer: The Earth will get a few degrees hotter. From that baseline, we can now ask, if not answer, ever more specific questions in the space between weather and climate. The answers to these questions have less to do with the fate of the climate than with how we are going to deal with it.

“If you’re building a bridge in North Carolina, you need to know what’s the maximum rainfall in the year 2100,” said R. Saravanan, an atmospheric scientist at Texas A&M University. “The global average temperature is not very useful for that.”

So much sophistication has already been layered upon the simple models of Arrhenius, Lorenz and Manabe. Day by day, we are recharting the river of our climate and all its possible futures. We study the loops and update our map, hoping it will help us navigate the torrent. And we’re doing it from the perspective of the duck, trying to make that critical guess where we will be in 100 years when we can hardly tell where we will be tomorrow.