For the local diagnosis of wave properties, we develop, validate, and apply a novel method which is based on the Hilbert transform. It is called Unified Wave Diagnostics (UWaDi). It provides the wave amplitude and three-dimensional wave number at any grid point for gridded three-dimensional data. UWaDi is validated for a synthetic test case comprising two different wave packets. In comparison with other methods, the performance of UWaDi is very good with respect to wave properties and their location. For a first practical application of UWaDi, a minor sudden stratospheric warming on 30 January 2016 is chosen. Specifying the diagnostics for hydrostatic inertia–gravity waves in analyses from the European Centre for Medium-Range Weather Forecasts, we detect the local occurrence of gravity waves throughout the middle atmosphere. The local wave characteristics are discussed in terms of vertical propagation using the diagnosed local amplitudes and wave numbers. We also note some hints on local inertia–gravity wave generation by the stratospheric jet from the detection of shallow slow waves in the vicinity of its exit region.
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