Effect of the assumption of circular satellite orbit on the derivation of earthʹs atmospheric parameters from GPS radio occultation data

An analytic expression for the angle of refraction in GPS radio occultation in the general case is presented. The angle of refraction without assuming a circular orbit is calculated iteratively starting with the value from the circular assumption. The atmospheric parameters are then calculated by inversion with and without the circular assumption. It is shown that the bias caused by the circular assumption is up to about 1 mbar in the pressure and up to about one degree Celsius in the temperature. On one hand, this result supports the practice of using the circular assumption in qualitative error analyses; on the other hand, it shows the necessity of foregoing the circular assumption when the highest accuracy is required of the atmospheric parameters.