Implementation of a Multiresolution Analysis Method to Characterize Multi-Scale Wave Structures in Lidar Data

Extracting gravity wave (GW) perturbations from atmospheric observations relies on background removal techniques whose results may differ depending on the observational type and the spectral characteristics of the chosen method. This variability complicates the intercomparison of GW properties across instruments, sites, and studies. Nighttime averaging provides a simple estimate of the background but may smooth out smaller-scale structures. Spectral filtering enables targeted wavelength extraction, though it can be sensitive to noise and edge effects. Sliding polynomial fit offers flexibility but may suppress relevant signals depending on the polynomial degree. To address this issue, we implement and evaluate a processing method based on multiresolution analysis (MRA), designed to better extract and characterize the background and the multi-scale structures of GWs in lidar temperature and wind profiles. The MRA approach is then evaluated in comparison to these techniques and applied to lidar temperature and wind measurements collected on the night of 20 November 2023 at La R & eacute;union. By decomposing the signal into dyadic vertical wavelength bands and an appropriate choice of corresponding details, the MRA can improve the detection of GW-induced perturbations in the spectral range of 0.8 to 12.8 km vertical wavelength by simultaneous background removal and denoising. We use the variance method as a benchmark for determining gravity waves potential energy (GWPE) and ask the question: "How well do the different filtering techniques compare with the variance method?" Given an overall agreement between our developped MRA and the variance method, we conclude that the MRA can also be used to determine reliable gravity wave kinetic energy (GWKE).Beyond energy estimation, MRA provides a unique capability to compute kinetic and potential energy profiles for tunable vertical wavelength bands, enabling the characterization of vertical and temporal evolution and interactions between different GW scales. These results establish MRA as a robust and complementary tool for improving GW analyses from lidar measurements, with promising applications to long-term climatologies and multi-instrument observational strategies.