Modeling ice clouds as nonlinear oscillators

Clouds have a tremendous impact on Earth’s climate. They can reflect sunlight back into space, cooling the planet, but they can also trap heat near the surface, warming the atmosphere. Climate models must account for both of these effects when incorporating cloud coverage.

Low-altitude water clouds are relatively simple to model and their dynamics are well understood. However, high-altitude ice clouds are more complex and still have a significant effect on climate and weather. Hannah Bergner and Peter Spichtinger developed a model for these types of clouds and analyzed it using the theory of dynamical systems.

Part of what makes ice clouds difficult to study is their extensive vertical movement, which both creates more ice crystals and induces their precipitation.

“Upward motion introduces cooling, and this produces nucleation and ice crystals, which can grow and fall out. This interplay between these different processes makes [modeling] difficult,” said Spichtinger. “On the other hand — and this was the surprising thing — it also makes it very simple because, in the end, we find out that it acts like this weird non-linear oscillator.”

Rather than simulate the dynamics of every ice crystal individually, the authors’ model deals with the mean values of number concentration and mass concentration, along with the saturation ratio. With these three variables, they constructed a system of ordinary differential equations to describe the processes of nucleation, sedimentation, deposition, evaporation, and cooling.

With their model established, the researchers plan to expand it to replicate even more features of high-altitude clouds.

“If we start with this zero-dimensional model and extend it in the horizontal and the vertical directions, can we find pattern formation?” said Spichtinger. “And if so, can this be compared to the patterns we find in nature?”

Source: “Ice clouds as nonlinear oscillators,” by Hannah Bergner and Peter Spichtinger, Chaos (2026). The article can be accessed at https://doi.org/10.1063/5.0297531 .