Imaging gravity waves in lower stratospheric AMSU-A radiances, Part 1: Simple forward model
Using a simplified model of in-orbit radiance acquisition by the Advanced Microwave Sounding Unit (AMSU-A), we derive three-dimensional temperature weighting functions for Channel 9 measurements (peaking at ~60–90 hPa) at all 30 cross-track beam positions and use them to investigate the sensitivity of these radiances to gravity waves. The vertical widths of the weighting functions limit detection to waves with vertical wavelengths of ≳10 km, with slightly better vertical wavelength sensitivity at the outermost scan angles due to the limb effect. Fourier Transforms of two-dimensional cross-track weighting functions reveal optimal sensitivity to cross-track wavelengths at the near-nadir scan angles, where horizontal measurement footprints are smallest. This sensitivity is greater for the AMSU-A on the Aqua satellite than for the identical instruments on the NOAA meteorological satellites, due to a lower orbit altitude and thus smaller horizontal footprints from antenna spreading. Small cross-track asymmetries in the radiance response to gravity waves are found that peak at the mid-range scan angles, with more symmetric responses at near-nadir and far off-nadir scan angles. Three-dimensional simulations show gravity wave oscillations imaged in horizontal AMSU-A radiance maps swept out by the scan pattern and satellite motion. A distorting curvature is added to imaged wave phase lines due to vertical variations in weighting function peaks with cross-track scan angle. This wave distortion is analogous to the well-known "limb darkening" and "limb brightening" of microwave radiances acquired from purely vertical background temperature profiles by cross-track scanners. Waves propagating along track are more visible in these images at the outermost scan angles than those propagating cross track, due to oversampling and narrower widths of the horizontal measurement footprints in the along track direction. Based on nominal noise floors and representative lower stratospheric wave temperature amplitudes, our modeling indicates that Channel 9 AMSU-A radiances can resolve and horizontally image gravity waves with horizontal wavelengths of ≳150 km and vertical wavelengths of ≳10 km.