New edition of a classic: Decades-old turbulence theory updated

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Measuring station in the Inn Valley Ivana Stiperski and students of the course ,
Measuring station in the Inn Valley Ivana Stiperski and students of the course ,,Alpinmeteorologisches Geländepraktikum’ setting up the instruments at the i-Box station ,,Hochhäuser’ in the community of Kolsassberg in the Inn Valley. © Tobias Posch

A correct representation of turbulence in the atmosphere is crucial for accurate weather forecasts and climate projections. However, the theory behind this is not only very old, but also not very representative, since it only applies to flat terrain. Innsbruck meteorologist Ivana Stiperski has now extended the theory on turbulence that has been in use since the 1950s. The researcher thus paves the way for the first time to a generally valid turbulence theory over complex terrain.

Turbulence is the most important exchange mechanism between the Earth’s surface and the atmosphere above. However, this mechanism remains one of the last great mysteries of classical physics and mathematics. Ivana Stiperski, head of the Atmospheric Turbulence research group at the Institute of Atmospheric and Cryospheric Sciences at the University of Innsbruck, is dedicated to the study of turbulence over mountains and has been working on this topic with her team since 2020 under an ERC Consolidator Grant. "Turbulence influences different phenomena such as climate, storm systems, air pollution and glacier melt. Accurate weather forecasts and climate predictions therefore require a precise description of turbulence. Over complex terrain of mountainous regions, this is particularly difficult because very little is known about how this terrain alters turbulence. There has not been much progress in advancing the theory over the past 70 years," Stiperski explains. Until now, understanding of atmospheric turbulence and how it is accounted for in weather and climate models has been based on what is known as similarity theory, or more specifically, the "Monin-Obukhov similarity theory" first described in 1954. However, this decades-old turbulence theory assumes that the Earth’s surface is flat and horizontally homogeneous - that is, it has uniform features horizontally, such as infinite fields of grass or corn. It is therefore not representative of most of the Earth’s land surface. "This ultimately incorrect representation of turbulence contributes to inaccuracies in weather forecasts and climate projections," Ivana Stiperski adds.

Theory for complex terrain

The researcher’s goal is to develop a generalized theory that applies to all realistic atmospheric conditions. A first major step in this direction has now been taken. "About 70 percent of the Earth’s surface is characterized by a heterogeneous, mountainous structure, i.e. a complex terrain such as here in Tyrol. In our study, we use a unique ensemble of large measurement datasets and machine learning techniques to develop new similarity relationships," says Ivana Stiperski, describing the approach of the new study, which was published in the journal Physical Review Letters and highlighted as an "Editor’s Suggestion." In her new theory, the meteorologist uses a new key variable in the calculations: "In our novel approach, we include the so-called anisotropy, which is the information about how energy in the turbulence is distributed in different spatial directions. We show that this quantity encodes information about the complexity of the surface and flow conditions that drive the turbulence. This allows us to extend similarity theory to complex terrain and brings us closer to a unified theory of complex atmospheric turbulence." The approach allows for a more correct representation of turbulence effects in weather, climate and air pollution models. "This is particularly important for understanding and predicting weather and climate projections in mountainous and polar regions, where similarity theory regularly fails. These regions are particularly vulnerable and are already experiencing unprecedented warming due to the climate crisis. An accurate description of further developments is therefore of crucial importance," emphasizes Ivana Stiperski.

The research of atmospheric turbulence has a long tradition in Innsbruck, only recently the 100th anniversary was celebrated with international scientists in Innsbruck.

About the person

Ivana Stiperski was born in 1980 in Zagreb, Croatia. She studied atmospheric and oceanic physics at the University of Zagreb and received her PhD there in 2010. A year later, she moved to the University of Innsbruck and worked on mountainous boundary layers in Mathias Rotach’s group. Stiperski has received numerous international awards and fellowships, including a Hertha Firnberg Fellowship from the FWF and the Mountain Meteorology Outstanding Early Career Award from the American Meteorological Society. In March 2019, she was appointed to an Ingeborg Hochmair Women’s Professorship at the Institute of Atmospheric and Cryospheric Sciences at the University of Innsbruck. In 2020, Ivana Stiperski received an ERC Consolidator Grant, one of the most highly endowed science awards. The European Research Council (ERC) supports groundbreaking research by outstanding scientists with up to 2 million euros over five years.

Generalizing Monin-Obukhov Similarity Theory (1954) for Complex Atmospheric Turbulence Ivana Stiperski and Marc Calaf Phys. Rev. Lett. 130, 124001 24 March 2023.
DOI: 10.1103/PhysRevLett.130.124001 ( )