Radio occultations are commonly used to determine vertical profiles of ionospheric electron density from measurements of frequency. “Frequency residuals” are important intermediate data products in radio occultation experiments. Frequency residuals are defined as the difference between observed and predicted values of the received frequency, where the predicted frequency includes all effects except refraction at the target object. However, relationships between properties of a vertical profile of ionospheric electron density and properties of time series of frequency residuals are not widely known by the broad community of scientists who may work with frequency residuals. Here we illustrate and explain how properties of a vertical profile of ionospheric electron density affect time series of frequency residuals. We also develop four quantitative relationships between electron density values and frequency residuals. These provide predictions for the topside plasma scale height, topside electron densities, peak altitude, and peak electron density that can be generated directly from a set of frequency residuals without the need to implement the full Abel transform analysis that is usually required to determine electron densities from frequency residuals. They can also be generated prior to the implementation of a high-quality baseline correction, to which the Abel transform analysis is sensitive. The development of these predictions assumed that the ionosphere has an exponential topside and a Chapman-like peak. These predictions are successfully tested on two-way radio occultation observations from the MAVEN Radio Occultation Science Experiment (ROSE) at Mars.

无线电掩星通常用于通过频率测量来确定电离层电子密度的垂直剖面。“频率残差”是无线电掩星实验中重要的中间数据产品。频率残差定义为接收频率的观测值和预测值之间的差值，其中预测频率包括目标对象处的折射以外的所有影响。然而，电离层电子密度垂直剖面的特性与频率残差时间序列的特性之间的关系并没有被可能与频率残差工作的广大科学家群体广泛了解。在这里，我们说明并解释了电离层电子密度垂直剖面的特性如何影响频率残差的时间序列。我们还开发了电子密度值和频率残差之间的四种定量关系。这些提供了对顶部等离子体标度高度、顶部电子密度、峰值高度和峰值电子密度的预测，这些预测可以直接从一组频率残差中生成，而无需实施通常需要确定电子密度的完整 Abel 变换分析从频率残差。它们也可以在实施高质量基线校正之前生成，Abel 变换分析对此很敏感。这些预测的发展假设电离层具有指数顶部和类似查普曼的峰值。