Downward looking (DL) GPS receivers from platforms within Earth's atmosphere (e.g. from a mountain top) can observe GPS satellites and produce an estimate of atmospheric refractivity profiles through the radio occultation technique. The main observations are the radio wave bending angles as a function of the impact parameter. The DL technique provides bending angles at both negative and positive elevation angles. Either a least-squares ray tracing method or the Abel inversion technique can be used for the retrieval of the refractivity from the bending angles. A least-squares method (LS) can be applied directly to the set of positive and negative elevation angles. It allows the retrieval of the refractivity to about 2 km above the receiver height. The Abel inversion operates on a profile of partial bending angles found by subtracting the positive elevation measurement from the negative ones with the same impact parameter.
This paper summarizes the promises and limitations of the two inversion techniques using simulated data. The analysis uses both dry and wet atmospheres from a climatological model and real radiosonde data. The results show that both LS and Abel techniques are capable of retrieving the refractivity. The paper also highlights the differences between the two algorithms and the limitations.