An Abel transform for deriving line‐of‐sight wind profiles from LEO‐LEO infrared laser occultation measurements

Abstract

AbstractWe have developed a formula for the retrieval of the line‐of‐sight (l.o.s.) wind speed from future low Earth orbit (LEO) satellite‐to‐satellite infrared laser occultation measurements. The formula involves an Abelian integral transform akin to the Abel transform widely used for deriving refractive index from bending angle in Global Navigation Satellite System radio occultation measurements. Besides the Abelian integral transform, the formula is derived from a truncated series expansion of the volume absorption coefficient as a function of frequency and includes a simple absorption‐line‐asymmetry correction term. A first‐order formulation (referred to as the standard formula) is complemented by higher‐order terms that can be used for high‐accuracy computations. Under the assumptions of spherical symmetry and perfect knowledge of spectroscopy, the residual l.o.s. wind error from using the standard formula rather than the high‐accuracy formula is assessed to be small compared to that anticipated from measurement errors in a real experiment. Applying the new formula just in standard form to future infrared laser transmission profiles would therefore enable the retrieval of l.o.s. stratospheric wind profiles with an accuracy limited mainly by measurement errors, residual spectroscopic errors, and deviations from spherical symmetry.