Retrieval of a wind profile from the Galileo Probe telemetry signal

Ultrastable oscillators onboard the Galileo Probe and Orbiter will permit very accurate determinations of the frequency of the Probe's telemetry signal as the Probe descends from a pressure level of several hundred mb to a level of about 20 bars. Analysis of the time-varying frequency can provide, in principle, a unique and important definition of the vertical profile of the zonal wind speed in the Jovian atmosphere. In this paper, we develop a protocol for retrieving the zonal wind profile from the Doppler shift of the measured frequency; assess the impact of a wide range of error sources on the accuracy of the retrieved wind profile; and perform a number of simulations to illustrate our technique and to assess the likely accuracy of the retrieval.Because of unavoidably large uncertainties in the absolute frequencies of the oscillators, we use time-differenced frequencies in our analysis. Nevertheless, it is possible to recover absolute wind speeds as well as wind shears, since the Orbiter/Probe geometry changes significantly during the Probe relay link. We begin with the full relativistic Doppler shift equation. Through the use of power series expansions and a basis function representation of the wind profiles, we reduce the basic equation to a set of linear equations that can be solved with standard linear least-squares techniques.There are a very large number of instrumental and environmental factors that can introduce errors into the measured signal or to the recovery of zonal winds from the data. We provide estimates of the magnitudes of all these error sources and consider the degree to which they may be reduced by a posteriori information as well as the results of calibration tests. The most important error source is the a posteriori uncertainty in the Probe's entry longitude. The accuracy of the retrieved winds is also limited by errors in the Probe's descent velocity, as obtained from atmospheric parameters measured by several Probe experiments, and in the a posteriori knowledge of secular drifts in the oscillators' frequencies during the relay link, due, for example, to aging and radiation damage.Our simulations indicate that zonal winds may be retrieved from the Doppler data to an accuracy of several m s^-1. Therefore, it may be possible to discriminate among alternative models for the basic drive of the zonal winds, since they differ significantly in the implied zonal wind profile.