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An AI solution to climate models’ gravity wave problem

Stanford scientists are among a growing number of researchers harnessing artificial intelligence techniques to bring more realistic representations of ubiquitous atmospheric ripples into global climate models.

Raindrops over field
For many regions, it’s unclear how the frequency of storms and dry spells, intensity of downpours, or amount of snowfall will change as the planet warms. More realistic estimates of atmospheric gravity waves could help.

Global climate models agree on a litany of consequences from the buildup of heat-trapping gasses in Earth’s atmosphere, from higher average surface temperatures and rising sea levels to more extreme heat waves.

Cloud bands over Lake Superior
Gravity waves are ubiquitous atmospheric ripples that emerge when air is forced upward by wind blowing over, for instance, a thunderstorm or mountain. (Image credit: NASA)

But there are other aspects of our climate for which the outlook remains murkier than scientists would like. Models disagree on how rainfall patterns will change as the planet warms, and for many regions, it’s unclear how different the frequency of storms and dry spells, intensity of downpours, or amount of snowfall will be in 50 years. “That’s the sort of thing we would ultimately like to be able to have a lot more confidence in,” said Aditi Sheshadri, an assistant professor of Earth system science at Stanford University, because the uncertainty hinders efforts to safeguard water supplies, food production, infrastructure, and people against future climate impacts. 

Research published recently by Sheshadri and her former graduate student Zachary Espinosa in the journal Geophysical Research Letters may help to build that confidence by providing more realistic estimates of ubiquitous atmospheric ripples called gravity waves. “Including a more physical representation of gravity waves in climate models should ultimately lead to more accurate climate projections, particularly at a regional scale,” Sheshadri said.

Unlike gravitational waves, which distort the fabric of space-time, gravity waves emerge when air is forced upward by wind blowing over, for instance, a thunderstorm or mountain. Launched into a higher, thinner layer of atmosphere, the air falls back down under the force of gravity – then rises again like a cork bobbing up from underwater. Any given air parcel may rise and fall for a few minutes or many hours, transporting momentum as it goes. Eventually, the wave spreads up and out until it breaks in the middle and upper atmosphere like an ocean wave crashing on the beach.

Atmospheric scientists have long understood gravity waves help to drive the overall circulation of the atmosphere, and influence storm tracks and the polar vortex – the swirl of bitter cold air near Earth’s poles that occasionally wobbles and brings extreme winter weather to parts of the United States, Europe, and Asia.

“We understand the physics of how gravity waves propagate and break, but their effects cannot be explicitly represented in climate models due to computational constraints,” Sheshadri said.

Global temperature projection
Including a more physical representation of gravity waves in climate models should ultimately lead to more accurate climate projections, particularly at a regional scale.  — Aditi Sheshadri, Assistant Professor of Earth System Science and Center Fellow (by courtesy) at Stanford Woods Institute for the Environment

Small waves, big impact

Summit supercomputer
Global climate models require large amounts of computing power, such as that of the Summit supercomputer at the Department of Energy’s Oak Ridge National Laboratory. (Image credit: Oak Ridge National Laboratory)

Gravity waves are simply too small and short lived to appear in models designed to cover the whole planet, much the way fine details are absent from low resolution photographs. Higher resolution models can provide more detailed information but are computationally expensive to run at the global scale for predictions covering more than a couple weeks.

To account for smaller scale processes like gravity waves without bogging down computation, scientists use simplified equations known as “parameterizations,” which are informed by physics but don’t calculate the oscillations and interactions of individual waves or incorporate even the limited available observational data. “We put in a guess as to what we think gravity waves are doing to the mean flow based on variables that the model can resolve,” Sheshadri said.

Even small changes in the approximations built into gravity wave parameterizations can lead to very different regional climate projections. As a result, climate modelers “tune” parameterizations so the results overall resemble the observed climate today – leaving a cloud of uncertainty around how circulation will respond as people and industry add more carbon dioxide to the atmosphere.

Accounting for gravity waves through AI

Sheshadri and Espinosa are among a growing number of researchers looking to machine learning and artificial intelligence techniques for a possible solution. “Parameterizations are a large computational sink for climate models, so if we can accelerate them, that means we can bump up the resolution of all sorts of things,” Espinosa said.

The researchers have developed an AI-driven model, dubbed WaveNet, that can accurately emulate how dissipating gravity waves accelerate and decelerate atmospheric winds. The work involved building and training a set of artificial neural networks in the widely used programming language Python, and then coupling them to a typical global climate model built decades ago in a language from the 1950s, called Fortran.

Loon balloon in flight
Superpressure balloons designed to provide internet service incidentally also collected data that researchers have been able to use to calculate gravity wave motions. (Image credit: Loon)

The model has passed two important tests. Trained on only one year of data, its predictions of how gravity waves would respond to extremely high CO2 concentrations over 800 years were similar to those produced by conventional parameterizations. And, based on only one phase of data, it accurately simulated a full two-phase cycle of the quasi-biennial oscillation, a regular reversal of winds racing high above the equator that affects surface weather and ozone depletion – and is driven by breaking gravity waves.

“WaveNet is not really telling us anything new about gravity waves’ response to the CO2. It’s just doing what the conventional gravity wave parameterization would have done as a response to CO2 – at least, for now,” Sheshadri said.

The results are a promising first step towards developing fully data-driven gravity wave parameterizations, the focus of an international project Sheshadri leads called DataWave. These parameterizations could be optimized for speed and trained with data from high resolution regional simulations, high resolution but short-term global climate simulations, and a growing trove of atmospheric measurements from internet-beaming superpressure balloons. “Hopefully, that will give us computationally feasible ways of representing gravity waves in climate models that are physically meaningful as well as observationally constrained,” she said. “That’s the ultimate goal with this project.”

Espinosa is now a PhD student at University of Washington. Stanford coauthors include Gerald R. Cain, a senior lecturer in the Department of Computer Science. Additional coauthors are affiliated with New York University, NASA Goddard Institute for Space Studies, and Universities Space Research Association.

 This research was supported by the National Science Foundation, the NASA Postdoctoral Program at the Goddard Institute for Space Studies, and Eric and Wendy Schmidt by recommendation of the Schmidt Futures program.


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Media Contacts

Aditi Sheshadri
School of Earth, Energy & Environmental Sciences

Zachary Espinosa
School of Earth, Energy & Environmental Sciences

Josie Garthwaite
School of Earth, Energy & Environmental Sciences
(650) 497-0947,

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