Revised predictions of uncertainties in atmospheric properties measured by 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 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 , and from , 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 . As refractivities are small, we replace by . We also replace by , 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 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.
References (24)
The radio occultation method for the study of planetary atmospheres
Planet. Space Sci.
(1973)- et al.
Statistical and computational uncertainties in atmospheric profiles from radio occultation: Mariner 10 at Venus
Icarus
(1979) Prediction of uncertainties in atmospheric properties measured by radio occultation experiments
Adv. Space Res.
(2010)- et al.
How to process radio occultation data: 1. From time series of frequency residuals to vertical profiles of atmospheric and ionospheric properties
Planet. Space Sci.
(2014) - et al.
The two-dimensional resolution kernel associated with retrieval of ionospheric and atmospheric refractivity profiles by Abelian inversion of radio occultation phase data
Radio Sci.
(1998) - et al.
Spacecraft Doppler tracking: Noise budget and accuracy achievable in precision radio science observations
Radio Sci.
(2005) - et al.
Principles of Optics
(1959) - et al.
Cassini radio occultation observations of Titan’s ionosphere: the complete set of electron density profiles
J. Geophys. Res.
(2019) - et al.
The neutral atmosphere of Venus as studied with the Mariner V radio occultation experiments
Astron. J.
(1971) - et al.
An Introduction to the Theory of Numbers
(1938)
Initial results from radio occultation measurements with Mars Global Surveyor
J. Geophys. Res.
Erratum: Initial results from radio occultation measurements with Mars Global Surveyor
J. Geophys. Res.
Cited by (7)
Determination of uncertainty profiles in neutral atmospheric properties measured by radio occultation experiments
2022, Advances in Space ResearchCitation Excerpt :The derived uncertainty profiles are thus dependent on the scale heights of both ionosphere and neutral atmosphere. In a revised version, Withers (2020) proposed an alternative approach that do not require an a priori knowledge of the scale heights. This revised formulation, based on the Abel transform too, only depends on the vertical resolution.
Cassini Radio Occultation Observations of Saturn's Ionosphere: Electron Density Profiles From 2005 to 2013
2023, Journal of Geophysical Research: Space PhysicsGravity Wave Modulations at the Lower Altitudes of Venus Ionosphere
2023, Geophysical Research LettersGanymede's Ionosphere Observed by a Dual-Frequency Radio Occultation With Juno
2022, Geophysical Research LettersObservations of High Densities at Low Altitudes in the Nightside Ionosphere of Mars by the MAVEN Radio Occultation Science Experiment (ROSE)
2022, Journal of Geophysical Research: Space PhysicsQuantification of Errors in the Planetary Atmospheric Profiles Derived From Radio Occultation Measurements
2022, Earth and Space Science