Topological Tools for Finding Vortex Rings in Cloud Formation

Prediction and modelling of climate enhance our understanding of atmospheric phenomena, climate, and daily weather. These are key in forming our understanding of the long-term climate trends and the likely impacts of climate change. Clouds play a crucial role in climate models, and can either cool or warm the Earth's surface, depending on their altitude and composition. Factors affecting cloud development include atmospheric conditions at different altitudes such as temperature, pressure, and humidity, with better predictions typically requiring more variables.
Computer simulations of cloud formation can examine the effects of different hypotheses by changing specific parameters. One hypothesis currently of interest is the role of structures known as ring vortices. Like the mundane example of a smoke ring, these structures occur when parcels of air moving at different speeds interact, generating ring shapes which can travel a significant distance before dissipating. In cloud formation, vortex rings can cause the cloud tops to rise to higher altitudes where temperatures are colder and cloud formation is easier. But including vortex rings in numerical cloud formation models requires developing hypotheses about the nature and source of vortex rings.
While vorticity is well understood in fluid dynamics, detecting vortex rings in simulations is not easy, and a number of approaches have been developed, such as the Q-criterion, a secondary computation which indicates how vortex-like a region of space is. In 3-D, this makes the task of spotting vortices visually easier for the human, using visualisation tools to present the data on a screen. Although this is a powerful approach, it is human-intensive and breaks down on larger data sets. A reliable way to detect vortex rings automatically is therefore important for studying cloud formation.
Fortunately, the mathematics has tools that can be adapted for this task. In particular, we can look at the "genus" of an object - i.e. the number of handles it has, and a ring always has one handle, as can be seen on a coffee cup. This "genus" is one of the fundamental properties studied in the branch of mathematics known as topology, and can be computed automatically.
However, using this in meteorology is not easy, as there are several parameters that must be chosen correctly. This project will therefore study the parameters that can be used to detect vortex rings automatically using topology in order to build reliable tools for analysis of cloud formation.