Waves and coherent flows in the tropical atmosphere: new opportunities, old challenges

In a review article appearing in the Quarterly Journal of the Royal Meteorological Society, Dr. Claudia Stephan (Max Planck Institute for Meteorology), Prof. Nedjeljka Žagar (Universität Hamburg) and Prof. Ted Shepherd (University of Reading) provide their perspective on present understanding of waves and coherent flows in the atmosphere, and their interaction.

Photo: A. Kirk, MPI-M

Their review points out that with a new generation of kilometer-scale global atmospheric models, capable of simulating an unprecedented range of interactions across scales, uncharted dynamical territory can be explored, territory which offers much hope for a more direct comparison with observations.  Even so, this new class of simulations will still have systematic errors and deficiencies, and may not completely sample the full range of natural variability. The challenge is thus to understand what we can reliably learn from the models, and what are the reasons for their remaining systematic errors and deficiencies. Especially for application to climate change, which is fundamentally unverifiable, the only sound basis for prediction is physical understanding of causal mechanisms.


The authors describe some of the available tools for diagnosing and studying the dynamics of waves, coherent flows, and the interactions between them in terms of their ability to provide causal accounts of the behavior seen in observations and in comprehensive simulation models. They give a general overview of some of the key equation systems that are relevant to different dynamical regimes and of classical approaches to distinguish between waves and coherent flows in these regimes. Such classical approaches have sought to identify specific dynamical regimes based on analysis of the governing equations under particular simplifying assumptions. These provide the basis for conceptual models of atmospheric variability and, ultimately, for causal accounts of its behavior. The review describes some of the ways those concepts have been used to understand atmospheric behavior, based on atmospheric reanalysis data, numerical models, and observations. The authors bring together three strands of knowledge -- large-scale dynamics, normal modes, and tropical convection and gravity waves -- that have historically represented rather distinct communities of researchers, with an eye to their application to the emerging first generation of kilometer-scale global atmospheric models, and with a particular focus on the tropics.


Our conceptual understanding of atmospheric dynamics is especially limited in the tropics as quasi-geostrophic scaling ceases to apply. The equatorially trapped Kelvin wave and mixed Rossby-gravity wave (MRG), two special solutions provided by linear wave theory, obliterate the distinction between `fast' and `slow' dynamics which otherwise exists at least asymptotically in the extra-tropics, and which underpins so much of extratropical dynamical theory. The article presents new results that quantitatively estimate the role of the Kelvin and MRG waves in the spatio-temporal spectrum of tropical variability, clearly demonstrating the necessity of including both the Kelvin and MRG waves in simplified models of the tropics. On the tropical mesoscales, the lack of a clean separation of dynamical regimes becomes even more apparent in the complex interplay between convection, gravity waves, and coherent flows, where `slow' trapped gravity waves can provide a large-scale constraint on `fast' convective coherent flows. The lack of a natural spatial truncation scale in the tropics has given rise to many theoretical challenges, but it is for precisely this reason that the tropics are where we might expect the largest gain from global kilometer-scale models.


Original publication:

Stephan, C., Zagar, N. & Shepherd, T. (2021) Waves and coherent flows in the tropical atmosphere: new opportunities, old challenges. Quarterly Journal of the Royal Meteorological Society, https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4109


More Information:

Website of C. Stephan’s research group “Cloud-wave coupling”:

Personal webpage Claudia Stephan:



Dr. Claudia Stephan
Max Planck Institute for Meteorology
Phone: +49 (0) 40 41173 124
Email: claudia.stephan@we dont want spammpimet.mpg.de