How to Process Radio Occultation Data: 2. From Time Series of Two-Way, Single-Frequency Frequency Residuals to Vertical Profiles of Ionospheric Properties

The MAVEN Radio Occultation Science Experiment (ROSE) generates vertical profiles of electron density in the ionosphere of Mars from two-way, single-frequency radio occultation observations. Here we develop methods for generating vertical profiles of ionospheric electron density from frequency residuals obtained from such observations. We show that the relevant set of equations can be closed for ionospheric observations if the uplink bending angle is equal to the product of the downlink bending angle and the square of the turn-around ratio. This is consistent with the dispersion relation for radio waves in plasma. Four angles, each being the angle between the asymptote of a portion of a refracted ray path and the corresponding idealized unrefracted ray path, provide a natural framework for development of these methods. We also present forms of these methods appropriate to one-way radio occultation experiments. These methods have been validated using a simulated occultation representative for the ionosphere of Mars. Errors are found to be on the order of a few percent.