A two-dimensional Stockwell transform for gravity wave analysis of AIRS measurements

Abstract

Abstract. Gravity waves (GWs) play a crucial role in the dynamics of the earth's atmosphere. These waves couple lower, middle and upper atmospheric layers by transporting and depositing energy and momentum from their sources to great heights. The accurate parameterisation of GW momentum flux is of key importance to general circulation models but requires accurate measurement of GW properties, which has proved challenging. For more than a decade, the nadir-viewing Atmospheric Infrared Sounder (AIRS) aboard NASA's Aqua satellite has made global, two-dimensional (2-D) measurements of stratospheric radiances in which GWs can be detected. However, one problem with current one-dimensional methods for GW analysis of these data is that they can introduce significant unwanted biases. Here, we present a new analysis method that resolves this problem. Our method uses a 2-D Stockwell transform (2DST) to measure GW amplitudes, horizontal wavelengths and directions of propagation using both the along-track and cross-track dimensions simultaneously. We first test our new method and demonstrate that it can accurately measure GW properties in a specified wave field. We then show that by using a new elliptical spectral window in the 2DST, in place of the traditional Gaussian, we can dramatically improve the recovery of wave amplitude over the standard approach. We then use our improved method to measure GW properties and momentum fluxes in AIRS measurements over two regions known to be intense hotspots of GW activity: (i) the Drake Passage/Antarctic Peninsula and (ii) the isolated mountainous island of South Georgia. The significance of our new 2DST method is that it provides more accurate, unbiased and better localised measurements of key GW properties compared to most current methods. The added flexibility offered by the scaling parameter and our new spectral window presented here extend the usefulness of our 2DST method to other areas of geophysical data analysis and beyond.

Exploring gravity wave characteristics in 3-D using a novel S-transform technique: AIRS/Aqua measurements over the Southern Andes and Drake Passage

“…Eckermann and Preusse, 1999;Jiang, 2002;Alexander and Teitelbaum, 2011) and nadir sounders (e.g. Alexander and Barnet, 2007;Hindley et al, 2016;Hoffmann et al, 2016). These results strongly suggest that the region is the most significant GW source worldwide, with peak GW amplitudes (Yan et al, 2010) and MFs (Geller et al, 2013) at least a factor of 2 and potentially an order of magnitude greater than any other known source.…”

“…Alexander et al, 2008;Fritts et al, 2010;Hertzog et al, 2012;. More recently, the 2-D extension of the ST has been similarly applied to atmospheric datasets including single-altitude stratospheric AIRS retrievals (Hindley et al, 2016) and mesospheric airglow measurements (Stockwell et al, 2011). Here, we introduce a new three-dimensional implementation of the ST for full 3-D GW analysis of our AIRS measurements, which we generalise to N dimensions for future use in other contexts.…”

“…Here, c is a scaling parameter which is usually set to 1, but which can be adjusted to improve temporal localisation at the expense of frequency localisation or vice versa (Mansinha et al, 1997;Fritts et al, 1998;Pinnegar and Mansinha, 2003;Hindley et al, 2016). Equation (1) uses as an apodising function a Gaussian window whose standard deviation is scaled as the inverse of frequency, although we note for completeness that any suitable such function may be used as long as it has a spatial integral equal to unity (Hindley et al, 2016).…”

“…., x N directions, and f denotes the transpose of f . The scaling parameter c n is a scalar quantity in each dimension n that can be adjusted in order to spatially/spectrally tune the localisation capabilities of the N-dimensional ST for each dimension independently (Fritts et al, 1998;Hindley et al, 2016), and hence represents a tunable parameter set which could be used in future work to emphasise different wave properties.…”

“…Our technique is based around a generalised multidimensional extension of the existing 1-D and 2-D Stransforms (STs; Stockwell et al, 1996;Hindley et al, 2016). The use of an ST allows us to systematically analyse the data across the full range of length scales within the AIRS-resolvable wavelength spectrum, while simultaneously estimating wave amplitudes as they vary across individual wavepackets.…”