tropospheric biennial oscillation

A door lock with two different keys: one turns easily, the other demands noticeable effort. That is how two layers of hexagonal boron nitride behave when twisted relative to each other. This material consists of boron and nitrogen atoms arranged in a hexagonal lattice, and its layers can sit in different registries, like two identical grids shifted by different angles.

Every year, as December approaches, the water off the coast of Peru becomes anomalously warm or anomalously cold. This is El Niño and La Niña, two phases of the same climate pendulum that swings in the equatorial Pacific. The pendulum is not a simple one: it remembers what happened to it several months earlier, and this memory determines which way it will swing next.

A translator in a conference hall tries to convey the speaker's words, but the hall is noisy: someone coughs, chairs creak, and the street outside is loud. If the speaker lowers their voice, the translator still keeps translating, but their voice drowns in the noise.

Two pendulums suspended from a single invisible spring swing in a shared air current. One always lags the other by exactly half a period: when the first swings left, the second is already returning from the right. By watching the first, you can tell where the second will be half a period later.

In 1991, Mount Pinatubo erupted with such force that it blanketed the planet in a thin veil of ash and gases for years. That veil, like a blanket on a hot night, trapped heat and cooled the ocean surface, causing tropical sea surface temperatures to dip. This event marks the start of a detective story about why some oceans are spawning ever more ferocious hurricanes while others remain calm.

An orchestra plays in a dark hall, and the listener hears only a hum: hundreds of instruments blend into a dense noise in which no melody can be discerned. That is roughly what spectra extracted from climate data by methods like the Koopman operator look like: hundreds of components, each with its own frequency, and it is unclear which ones are true musicians and which are the rattling of chairs.

During a thunderstorm, the sky acts like a giant battery: charge builds up in the cloud, and a lightning bolt discharges it. That charge is invisible, but cosmic particles (muons, which constantly rain down on Earth from space) can sense it. As a muon flies through a charged cloud, it speeds up or slows down slightly, and these changes reveal the voltage inside the cloud.

Over the warm waters of the Indian Ocean, every six to eight weeks, a vast wave of moist air gathers. It moves eastward at a pedestrian pace—about five meters per second—and takes forty to ninety days to circle half the planet.

Ahead of the bow shock that Earth creates in the solar wind, giant bubbles of rarefied gas sometimes appear. Inside them, particle density drops by factors, and electric fields start to tremble like a plucked string.

The bronze plates of a gamelan do not sound according to a single tuning standard: each orchestra on Java keeps its own tuning, and two neighboring ensembles may play the same melody in slightly different intervals.

The Sun is not a calm sphere but a boiling cauldron that follows its own rhythms. Roughly every 11 years, its activity peaks: more dark spots appear on its surface, and streams of charged particles fly into space. But hidden within this grand cycle is a shorter one — about 1.7 years.

The same explosion can sound different: it all depends on which way the wind is blowing. In 2024, researchers set off charges equivalent to ten tons of TNT twice and recorded the sound with a network of 31 microphones spread over a radius of 23 kilometers. The source was identical, but the acoustic pictures turned out to be quite different.

Bacteria in a drop of water jostle and swim: each on its own, but together they create patterns. With weak motion, the fluid churns like soup on a high flame: vortices collide, and the flow direction changes every second. This is called bacterial turbulence.

Glaciers don't just darken from soot. Their surfaces host tiny algae that, as temperatures rise, bloom and turn the ice dark. Dark ice absorbs more sunlight, melts faster, and further warms the planet. It's like how a black t-shirt in the sun gets hotter than a white one. The second player in overheating is forests.

Tuning an old radio receiver requires patience: you slowly turn the dial, catch a crackle, turn it again, until a voice emerges through the static. In much the same way, a reinforcement learning agent searched the ocean for two patches whose temperature difference best predicts rains in Thailand.

The Tibetan Plateau is a giant sponge that soaks up rain and snow, then releases water to Asia's rivers. Since 2000, the sponge has been getting wetter. Scientists decided to check: does this moisture make the sponge stronger, or does it soften it? They used a measure of disorder — entropy.

Every day, about 40,000 thunderstorms flash across the planet. In that moment, the atmosphere resembles an orchestra without sheet music: warm air rises like a bow stroke, winds aloft carry the melody, and lightning punctuates the finale. But who conducts this orchestra?

The orchestra assembled, the instruments were tuned, but there was barely any music: that's what the 2025 Atlantic hurricane season looked like. The ocean was the fifth warmest on record, and a weak La Niña usually adds strength to storms. But instead of a continuous concert, we got isolated thunderous chords: three Category 5 hurricanes, with silence in between. Why was the orchestra silent?

Imagine a pendulum that is pushed in time with the seasons: harder in winter, softer in summer. But this pendulum has a quirk: a switch that operates with a delay. When the pendulum passes through zero, the switch clicks and changes the direction of the push. That is exactly how the simplified El Niño model built by mathematicians works.

A warm patch off the coast of Peru does not appear every year, but when it does, deserts are drenched with rain and Australia is plagued by wildfires. This is El Niño, a phenomenon that climate models struggle to reproduce. Simple models do well at estimating how often it occurs but lose spatial details.

In 2015, downpours in Chennai turned streets into rivers overnight. The city was caught unprepared: seasonal models offered only a vague warning. Yet the monsoon is not a whim of the sky; it is the pulse of a vast machine linking oceans and continents.

Over warm ocean waters, air rises, spins, and turns into a giant vortex that carries winds faster than a race car. For such a vortex to form, several conditions must align: rotation, heat, moisture, and calm winds aloft. Previously, meteorologists combined these conditions into complex indices, like a kitchen recipe with a dozen ingredients.

Every year, the same drama unfolds over West Africa: from June to September, the sky fills with moisture and releases rains that determine the harvests of millet, sorghum, and maize. This rainy season is driven by the West African monsoon, a giant atmospheric pump that pulls moist air from the ocean deep into the continent.

Seventy-five years of weather observations in India, when plotted on a graph, resemble the cardiogram of a vast organism. Instead of a single steady pulse, there are fifteen different lines, each with its own rhythm. Somewhere the heartbeat is as steady as a sleeping person's, while elsewhere it falters, as if after a quick run.

Sumatra's mountain range works like a stamping press: easterly winds hitting the slopes leave a chain of rotating imprints in the air behind the island. These vortices, like blanks on an assembly line, detach from the land and drift over the ocean, where some of them grow into tropical cyclones.

In the vast concert hall of the atmosphere, ozone plays a part that changes from tier to tier. Near the surface, its notes sound alarming, for there it is a pollutant that irritates lungs and leaves. At 25 kilometers up, the same gas becomes a protective shield that absorbs harsh ultraviolet radiation.

In 1884, British meteorologist Henry Blanford built the first model for forecasting the Indian monsoon. Nearly a century and a half later, seasonal forecast skill has barely improved.

Every year, farmers in southern India wait for the same thing: the sky to open up and the monsoon to arrive. Whether rice sprouts and whether there is enough water for the whole season depends on it. So the monsoon forecast is not abstract science but a matter of survival for hundreds of millions of people.

In 1984, the Ethiopian sky stayed silent for months. Fields cracked, livestock died, and roads were clogged with people fleeing hunger. Droughts in this country have killed hundreds of thousands, but warning of them in advance was impossible: too many threads pull the weather in different directions. The Pacific Ocean works like an invisible conductor.

Imagine a house of cards where each card supports the others. One wobbles, and the neighbors start to lean. Earth's climate system works similarly: ice sheets, ocean currents, tropical forests, all are connected. If one element crosses a threshold, it can drag the rest down with it.

Every few years, the Pacific Ocean rearranges itself: warm water from the east flows toward the coasts of South America, and weather goes haywire for six months. This is El Niño, and its arrivals cannot be predicted precisely, even though there is a rhythm to them. A model with 930 variables shows that noise is to blame—random gusts of wind acting like an invisible conductor.

The orchestra has been playing in the Pacific Ocean for over a century. Some instruments carry a fast melody, others draw out a slow bass line, and together they create a pattern of warm and cold patches on the water's surface.

On a playground, two swings stand side by side. One child pumps on their own, while the other barely moves until the first gives a push with their foot. Something similar happens in the tropical Pacific and Indian Oceans, except instead of children, there are warm and cold masses of water.

Every summer, the same performance unfolds over the Indian Ocean: moist air rushes from the sea onto the scorched land, bringing rains that billions of people depend on.

In 1972, anchovies vanished off the coast of Peru. Fishermen were left empty-handed, and the world learned the word El Niño. Since then, scientists have been searching for ways to predict when that warm current will once again upend the planet's weather.

An orchestra without a conductor: the instruments set their own rhythm. That is how one might describe the climate system of the Indo-Pacific region, where sea surface temperatures oscillate across many time scales, from seasonal to multi-decadal. Previously, to hear a single instrument, you had to pre-tune filters, cutting off everything else.

For thirty years, climatologists have been gathering the shards of a broken vase. Each climate model is its own shard, and they all promise different warming by 2100, from 1.5 to nearly 6 degrees. The spread does not shrink no matter how much the models are improved.