Modal-space statistics of Rossby waves during Eurasian heatwaves: implications for circulation dynamics in reanalyses and climate models

This study introduces a new methodology for diagnosing atmospheric circulation associated with surface extremes in modal space. The approach is conceptually similar to spherical harmonics analysis but employs Hough harmonics as basis functions. These harmonics arise from the linearised primitive equations and form an orthogonal basis. Projection onto this basis yields complex Hough expansion coefficients that describe the amplitudes and phases of the modal contributions to the global three-dimensional fields. Each Hough coefficient is indexed by zonal wavenumber, meridional mode, and vertical structure function. The orthogonality of the modes allows a decomposition of the total energy into the energy of the zonal mean flow and the energies of different wave components.

The method is applied to global reanalysis datasets and to a subset of CMIP5 climate model simulations from 1980 onwards. Reconstructed circulation fields, obtained by inverse projection onto wind and geopotential using scale-selective filtering, indicate that Eurasian heatwaves (EHWs) are primarily driven by large-scale anticyclonic systems. This agrees with previous dynamical studies and supports the physical interpretability of the diagnostic. Probability distribution functions of Rossby wave energies are computed separately for the zonal mean, for planetary-scale, and for synoptic-scale zonal wavenumbers, focusing on barotropic structures in the troposphere. The corresponding energy time series are well described by chi-square distributions, and the skewness indicates about a 50% reduction in the effective degrees of freedom of planetary-scale circulation during EHWs.

This reduction is not observed in the CMIP5 simulations, which points to systematic model deficiencies. The models reproduce present-day surface EHW characteristics and associated Rossby wave patterns reasonably well, but struggle to reproduce day-to-day circulation variability observed in reanalyses. This limitation reduces confidence in projections of future changes in heatwaves and their related large-scale circulation. The results suggest that metrics describing intrinsic variability should be included as complementary to existing ones when evaluating simulations of heatwaves and associated circulation.

Overall, the diagnostic provides a holistic dynamical view of the variability spectrum of Rossby waves linked to surface extremes. It enables scale-selective filtering of variability in physical space and reveals statistical properties in modal space, offering a useful tool for model assessment and for studying complex atmospheric dynamics.