Prediction of uncertainties in atmospheric properties measured by radio occultation experiments

Refraction due to gradients in ionospheric electron density, NeNe, and neutral number density, nnnn, can shift the frequency of radio signals propagating through a planetary atmosphere. Radio occultation experiments measure time series of these frequency shifts, from which NeNe and nnnn can be determined. Major contributors to uncertainties in frequency shift are phase noise, which is controlled by the Allan Deviation of the experiment, and thermal noise, which is controlled by the signal-to-noise ratio of the experiment. We derive expressions relating uncertainties in atmospheric properties to uncertainties in frequency shift. Uncertainty in NeNe is approximately (4πσΔffcmeϵ0/Ve2)2πHp/R where σΔfσΔf is uncertainty in frequency shift, f is the carrier frequency, c   is the speed of light, meme is the electron mass, ϵ0ϵ0 is the permittivity of free space, V is speed, e   is the elementary charge, HpHp is a plasma scale height and R   is planetary radius. Uncertainty in nnnn is approximately (σΔfc/Vfκ)Hn/2πR where κκ and HnHn are the refractive volume and scale height of the neutral atmosphere. Predictions from these expressions are consistent with the uncertainties of the radio occultation experiment on Mars Global Surveyor. These expressions can be used to interpret results from past radio occultation experiments and to perform preliminary design studies of future radio occultation experiments.