A method for constructing directional surface wave spectra from ICESat-2 altimetry

On its margins, waves heavily impact sea ice. Routine and repeat observations of waves in sea ice are currently lacking, and therefore a comprehensive understanding of how waves interact with sea ice and are attenuated by it is elusive.In this paper, we develop methods to separate the two-dimensional (2D) surface wave spectra from sea-ice height observations made by the ICESat-2 (IS2) laser altimeter, a polar-orbiting satellite.

A combination of a linear inverse method, called generalized Fourier transform (GFT), to estimate the wave spectra along each beam and a Metropolis-Hastings (MH) algorithm to estimate the dominant wave's incident angle was developed. It allows us to estimate the 2D wave signal and its uncertainty from the high-density, unstructured ATL03 ICESat-2 photon retrievals. The GFT is applied to re-binned photon retrievals on 25 km segments for all six beams and outperforms a discrete Fourier transform (DFT) in accuracy while having fewer constraints on the data structure.The MH algorithm infers wave direction from beam pairs every 25 km using coherent crests of the most energetic waves.