Describing the atmosphere as a two-dimensional fluid can help predict long-term climate effects

What is it about?

Most of the atmosphere is contained in the troposphere, a layer 12km thick, which is extremely thin compared to the size of our planet (12,000km diameter): If the Earth were of the size of a basketball, the troposphere would be about as thick as a sheet of paper (0.2mm). Therefore, a good approximation would be to think of it as a two-dimensional fluid in which the vertical motions are disregarded. Other notable examples of two-dimensional fluids in physics occur in high temperature superconductors, in the quantum Hall effect, or in graphene, where the electronic flow is restricted to two-dimensional planes. These systems are aptly described using a mathematical structure known as the Chern-Simons form, discovered by mathematicians Shiing-Shen Chern and James Harris Simons in topology. Using these mathematical objects as Lagrangians, the resulting dynamical equations describe the evolution of fields in 2D. With some small adjustments to allow for dissipative phenomena, the Earth’s rotation and the exchange of energy with the Sun and outer space, it turns out that the equations that govern the atmosphere are essentially the same as those obtained from the Chern-Simon structures. These equations relate the velocity, density and temperature fields at any time and anywhere on the surface of the Earth. The authors have even produced a freely accessible on-line application that allows exploring the space of solutions by tweaking the parameters.

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Photo by ActionVance on Unsplash

Photo by ActionVance on Unsplash

Why is it important?

Climate is essential for life and several climate models have been developed. The current climate change phenomenon urgently requires reliable models to plan ahead and take action, or to understand the consequences of inaction. This study presents a novel alternative approach to develop a simple climate model. The proposed equations depend on a number of physical parameters –such as the mean density and the emissivity– that allow to obtain the time evolution of the system as a function of those parameters. Thus, the simplified model proposed here has the potential of providing a tool for modelling the atmosphere at large and for long-term phenomena. For instance, one of the predictions of the model is that by a 2.5% reduction in emissivity, the average global temperature could rise by some 7ºC.

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