Elsevier

Advances in Space Research

Volume 66, Issue 10, 15 November 2020, Pages 2466-2475
Advances in Space Research

Revised predictions of uncertainties in atmospheric properties measured by radio occultation experiments

https://doi.org/10.1016/j.asr.2020.07.049Get rights and content

Abstract

Radio occultations are commonly used to determine vertical profiles of ionospheric electron density and neutral atmospheric density from measurements of frequency. Previous work has developed expressions for how uncertainties in electron density and neutral density depend on uncertainty in frequency. However, these expressions assume that the relevant density decreases exponentially with increasing altitude, which limits their applicability. Here we develop alternative expressions for uncertainties in radio occultation experiments. We find that uncertainties depend on the vertical resolution. We validate these expressions on radio occultation observations by Mars Global Surveyor and MAVEN. These expressions can be used to perform preliminary design studies of future radio occultation experiments.

Introduction

Radio occultations are a common method for making remote sensing measurements of vertical profiles of ionospheric electron density and neutral atmospheric density, pressure, and temperature of solar system objects (e.g. Phinney and Anderson, 1968, Fjeldbo et al., 1971, Yakovlev, 2002, Kliore et al., 2004, Withers, 2010). In such observations, a radio signal is sent from a transmitter to a receiver at a time when the ray path between transmitter and receiver passes through the ionosphere and atmosphere of a target object. The transmitter is often on a spacecraft and the receiver is often an antenna of the NASA Deep Space Network (DSN) on Earth.

In a radio occultation observation, the uncertainty in an electron density or neutral density measurement depends on the uncertainty in the radio frequency. Lipa and Tyler (1979) developed a sophisticated description of how uncertainties in derived ionospheric and neutral atmospheric properties depend on uncertainties in measured properties of the radio signal. However, it is not straight-forward to apply the description developed by Lipa and Tyler (1979). Withers (2010) found simple expressions for how the electron density and neutral density uncertainties depend on the frequency uncertainty. However, these expressions assumed that the relevant density decreased exponentially with increasing altitude, which limited their applicability. For example, they cannot be used to predict experimental performance at a target object if the relevant scale height is not known a priori. This suggests that the results of Withers (2010) provide an incomplete description of how electron density uncertainties and neutral atmospheric density uncertainties are related to frequency uncertainties.

The aim of the present work is to develop expressions for how electron density uncertainties and neutral atmospheric density uncertainties are related to frequency uncertainties, where these expressions do not rely on exponential behavior with a known scale height.

The structure of this article is as follows. Section 2 presents background on radio occultation observations and the relevant results of Withers (2010). Section 3 uses a case study of a one-way occultation of Mars to introduce relationships between uncertainties in frequency and uncertainties in ionospheric electron density and neutral atmospheric density. Section 4 develops generalized expressions for these relationships. Section 5 tests these expressions using observations by Mars Global Surveyor (MGS) (Hinson et al., 1999, Hinson et al., 2000, Tyler et al., 2001) and MAVEN (Withers et al., 2018, Withers et al., 2020b, Withers et al., 2020a, Withers and Moore, 2020). Section 6 compares the predictive expressions developed in this work to those of Withers (2010). Section 7 presents the conclusions of this work.

Section snippets

Background

The value of the received radio frequency, f, is affected by refraction in the ionosphere and atmosphere of the target object. The “frequency residual” is 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.

Two sign conventions exist for the angle α by which the ray path is bent by refraction. Following Ahmad and Tyler, 1998, Withers, 2010, Withers and Moore, 2020,

Case study

For illustration, we explore a case study of a one-way egress occultation of Mars. We assume that ionospheric plasma and neutral atmospheric gases are absent. The planetary radius is 3400 km. The occultation covers 100 km to 300 km altitude with vertical resolution of 1 km, typical of ionospheric occultations at Mars. The radio frequency is 8.4 GHz, a typical X-band frequency. The rate of change of the altitude of closest approach of the ray path is 2 km s−1. Hence the implied time resolution

Generalization

In order to develop a method to predict uncertainties σν,σNe, and σn from σΔf, it is necessary to generalize beyond the case study outlined in Section 3.

We begin with Eq. (13). As in Section 3, we assume there is no refraction along the highest ray path such that lnμp=νp=αp=0. As refractivities are small, we replace lnμ by ν. We also replace ai by aj+i-jdz, where dz is the vertical separation between the closest approach distances of adjacent ray paths. That is, dz is the vertical resolution of

Validation

We test the prediction set forth in Eq. (31) using two occultations at Mars. The first is a one-way X-band occultation acquired by MGS on 27 December 1998 (identifier 8361M48A). This occultation was used by Withers et al. (2014) to demonstrate the development of methods to process data from one-way radio occultation observations. The second is a two-way X-band occultation acquired by MAVEN on 20 September 2016. This occultation was used by Withers et al., 2020b, Withers et al., 2020a to

Discussion

The prediction of Eq. (31) for how the uncertainty in refractivity of a radio occultation observation depends on the uncertainty in the frequency residual can be compared against the prediction of Withers (2010) that is given in Eq. (9). The two functional forms are very similar. There only two differences. First, dz appears in Eq. (31), but H appears in the prediction of Withers (2010). Second, numerical factors.

It is not surprising that dz replaces H. The factor cσΔf/vf must be common to all

Conclusions

This work presents expressions that can be used to predict uncertainties in refractivity, ionospheric electron density, and neutral atmospheric density for radio occultation experiments. Unlike the related work of Withers (2010), these expressions do not depend upon the scale height of the refractive medium. We recommend use of the expressions presented herein over those presented by Withers (2010) for two reasons. First, in planning of future observations, uncertainties in these quantities can

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported, in part, by the MAVEN project, which is supported by NASA through the Mars Exploration Program, and by NASA award NNX15AI87G. PW thanks colleagues associated with the MAVEN ROSE investigation for useful conversations regarding radio occultations, two anonymous reviewers for valuable comments, and Dave Hinson for MGS frequency residuals.

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