Jonathan Logan, S&E Editor
Pierre-Simon Laplace, the French scholar and mathematician, engaged in a thought experiment nearly 220 years ago. In this particular thought experiment, he imagined the Earth’s atmosphere as a film of fluid enveloping the planet. You might picture this idea with a phenomenon from a well-known video game: Super Mario Galaxy. In this Nintendo classic, Mario was blown up to ridiculously large sizes with respect to the planets he was exploring. Some of these planets had oceans on them. When Mario stepped in one, the water would displace and splash upward before falling back to the surface. It all seemed otherworldly as you peered around the curvature of the planet and saw ripples disappear over the horizon.
Laplace’s Mario was the Moon. He postulated that our Moon would gravitationally pull on the atmosphere in the same way it pulls on the oceans and create atmospheric tides of high and low pressure. Think of Mario stepping down on the atmosphere and squishing it into regions of high pressure on his side. The opposite side of the planet would bulge outward to compensate, creating a region of high pressure. Now imagine Mario walking around on the atmosphere parallel to the equator, creating a never-ending wave of high and low pressure. Physicists refer to this wave-like behavior as sinusoidal. Laplace envisioned this 220 years ago and now his waves have been discovered. The sole mechanism that drives these pressure waves did not turn out to be the Moon, but a grand combination of solar heating, turbulence, pure chaos in the form of hurricanes and a little bit of assistance from the push and pull of the Moon… or a stomping Mario?
In 2016, the European Center for Medium-Range Forecasts released a data set dubbed ERA5. The data set brought together weather data from ground stations, satellites, and weather balloons. In its final form, the data set reconstructed what a planet-wide weather system would have recorded between 1979 and 2016. ERA5, in the hands of the University of Tokyo’s Takatoshi Sakazaki, proved to be the tool that would tease Laplace’s waves into existence. What made this data set unique was that it took pressure and temperature measurements essentially every ten kilometers. Prior work that attempted to discover the atmospheric waves was limited to a single weather station or a global patchwork of stations separated by great distances.
There is an important fact about waves that must be understood in this context. Atmospheric waves are primarily classified by their spatial and temporal frequency – that is, the distance and time between successive peaks on a wave. Imagine two atmospheric waves oscillating at an identical frequency and riding around the earth side-by-side, shadowing the other’s movements. If these waves decided to overlap, they would be able to look back around the planet and see that they match each other perfectly. This phenomenon creates what are known as normal modes of a wave.
Some normal modes of a wave are less energetic than others, so they “peak” at greater distances. Thus, prior to the ERA5 data set, Hamilton and Rolando Garcia were able discover the lowest-energy normal mode of atmospheric waves since they only looked at data from a single station – separated by half the circumference of Earth. In other words, they could only detect atmospheric waves whose peaks were spaced by distances near half of the Earth’s circumference. Sakazaki and his post-doc research adviser, Kevin Hamilton, realized that they could piece together higher-energy, higher-frequency normal modes of these waves with ERA5 data that looked at smaller distances (ten kilometers) and timescales. They managed to tease out the other modes of atmospheric waves and prove that Laplace had stumbled upon a global orchestra of gaseous oscillations with his thought experiment.
But what does Mario have to say? Imagine that Mario is moping around the Earth creating his low-frequency, low-energy atmospheric wave. Meanwhile, the Sun is heating up different parts of the Earth in its own wavelike fashion as it creates day and night. Suddenly there are two atmospheric waves. Now the wind decides to blow at certain speeds all around the globe. A third wave! Hurricanes spawn in the Atlantic while typhoons spin up in the Pacific adding their own chaotic waves to the global system. At different distances and times all of these waves synchronize to the other’s motion and frequency creating the first mode and traceable atmospheric wave.
Mario gets all worked up when he sees a goomba in his mind’s eye. He starts power walking and stomping like mad on imaginary goombas in his fury. The first wave he created with his mope disappears as the new pressure waves race around the planet. Typhoons and hurricanes get stomped out in favor of Amazon rains and strong winds whip around Patagonia in the Southern Ocean. The whole system is in turmoil! Yet, the individual pressure, temperature, and weather waves synchronize again, forming the second mode and a new class of atmospheric waves. These higher-energy, higher-frequency waves race around the globe faster. They may even hang out over the northern hemisphere more than they do over the southern.
Perhaps Mario needs extra umph in smashing a goomba. Thus, he would start planting both feet on the southern and northern atmosphere to take great bounds around the earth. The atmospheric pressure waves would sync up in the northern and southern hemispheres respectively, creating a high-pressure region over the equator. Now there are northern and southern wave modes racing one another around the globe.
Of course, Mario cannot run and jump infinitely fast and create an infinite number of modes. This would break some of the basic tenets of Physics – namely degrees of freedom. His speed limit is something like “Princess Peach is in danger” revolutions per day. The atmosphere cannot just bend into any shape it wants just as Mario cannot run beyond Princess Peach speed. In other words, the freedom of movement it experiences is limited to three-dimensional space and its constituent molecules.
This is precisely why the discovery of Laplace’s waves is so revolutionary. Sakazaki and Hamilton’s work gives us an additional degree of freedom in predicting weather and Mario’s motivations. They have completed a theory developed 220 years ago. Their work was published in the American Meteorological Society’s Journal of the Atmospheric Sciences and adapted by Charlie Wood of Quanta Magazine in his article, “Global Wave Discovery Ends 220-Year Search”.
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