Ageostrophic corrections for power spectra and wave-vortex decomposition

We present a method to incorporate weakly nonlinear ageostrophic corrections into a previously developed wave-vortex decomposition algorithm for one-dimensional data obtained along horizontal flight, ship or remote-sensing tracks in the atmosphere or ocean. A new statistical omega equation is derived that links the power spectra of a quasi-geostrophic stream function to the power spectra of the ageostrophic correction. This step assumes mutually independent Fourier components for the quasi-geostrophic stream function. Then this equation is used to estimate the ageostrophic correction from one-dimensional track data under the additional assumptions of horizontal isotropy and the dominance of a single vertical wavenumber scale. A robust and accurate numerical method is designed, tested successfully against synthetic data and then applied to atmospheric flight track data near the tropopause. This probes the robustness of the previous linear wave-vortex decomposition method under the ageostrophic corrections. Preliminary findings indicate that the lower stratospheric flight tracks are very robust whilst the upper tropospheric ones showed some sensitivity to the correction.