Further developments on estimating inertia-gravity-wave properties: Combining the Riesz transform with machine learning methods

One of the remaining issues in the parameterization of inertia-gravity waves is the estimation of wave characteristics such as wavenumber and intrinsic frequency. In this survey, we explore a new way to estimate the wave characteristics at the launch level. To this end, we retrieve the wavenumber using the Riesz Transform which is the generalized form of the Hilbert Transform applicable in the multi-dimensional analysis. For this purpose, the high-resolution horizontal divergence field has been employed since it filters the background flow and thus provides a reasonable representation of the inertia-gravity wave signal. This is followed by the application of machine learning to reconstruct the retrieved wavenumber using the coarse-grained resolvable variables including the horizontal wind speed, the large scale vertical velocity, the cross-stream ageostrophic wind speed, the frontogenesis function and the latent heat released during condensation as explanatory variables at the launch level.
We have employed the ERA5 dataset in this survey, having observed that the dataset can directly resolve the inertia-gravity waves at its full resolution. In order to avoid mountain waves and focus on non-orographic inertia-gravity waves, two areas far from the significant obstacles over the midlatitude of the Atlantic Ocean and Northern Pacific Ocean are considered from December 2018 to February 2019. The results show a reasonable correlation between the reconstructed wavenumber using low-resolution explanatory variables and the retrieved one using the Riesz Transform so that this method can be utilized to estimate the inertia-gravity wave number at the launch level.