Prof. Dr. Nedjeljka Žagar (U Hamburg): Modal interactions on the sphere

Understanding the complex, multiscale nature of atmospheric variability, both in space and time, necessitates simplifications of the governing equations. Linearisation of the equations of motion on the sphere reveals two main dynamical regimes of horizontally propagating waves, characterised as eastward- and westward-propagating inertia-gravity (IG) waves (fast regime) and Rossby waves (slow regime). In addition, there are special wave solutions - the Kelvin waves and mixed Rossby-gravity (MRG) waves - that complicate the time-scale separation between slow and fast dynamics, as well as the separation between waves and coherent flows in observations and models. Physical processes, especially convection, and their interactions with wave motions further escalate the challenge of providing causal explanations for simulated variability in weather and climate models.
While linear wave theory provides a foundation for conceptual models of atmospheric variability, understanding wave-wave and wave-mean interactions requires numerical simulations and diagnostic tools. This is achieved through a hierarchy of models with varying levels of complexity. Among them, spectral modelling using Hough harmonics as basis functions describes the atmosphere as a superposition of non-linearly interacting IG, Rossby, Kelvin, and MRG waves, which are fully separable at the linear level. This framework offers an attractive means of disentangling the dynamics of temperature and wind variability on the sphere and motivated the development of TIGAR - the Transient Inertia-Gravity And Rossby wave dynamics model, by the Atmospheric Dynamics and Predictability Group at the University of Hamburg. In TIGAR, each wave mode is treated as a prognostic variable, similar to how the stream function represents Rossby waves in quasi-geostrophic models.
In this seminar, I will discuss recent advances in understanding large-scale atmospheric dynamics by combining linear analysis of observed circulation with numerical simulations of modal interactions using TIGAR.
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