Improved model for correcting the ionospheric impact on bending angle in radio occultation measurements

The standard approach to remove the effects of the ionosphere from neutral atmosphere GPS radio occultation measurements is to estimate a corrected bending angle from a combination of the L1 and L2 bending angles. This approach is known to result in systematic errors and an extension has been proposed to the standard ionospheric correction that is dependent on the squared L1 inline-formula∕ L2 bending angle difference and a scaling term (inline-formulaκ). The variation of inline-formulaκ with height, time, season, location and solar activity (i.e. the F10.7 flux) has been investigated by applying a 1-D bending angle operator to electron density profiles provided by a monthly median ionospheric climatology model. As expected, the residual bending angle is well correlated (negatively) with the vertical total electron content (TEC). inline-formulaκ is more strongly dependent on the solar zenith angle, indicating that the TEC-dependent component of the residual error is effectively modelled by the squared L1 inline-formula∕ L2 bending angle difference term in the correction. The residual error from the ionospheric correction is likely to be a major contributor to the overall error budget of neutral atmosphere retrievals between 40 and 80 km. Over this height range inline-formulaκ is approximately linear with height. A simple inline-formulaκ model has also been developed. It is independent of ionospheric measurements, but incorporates geophysical dependencies (i.e. solar zenith angle, solar flux, altitude). The global mean error (i.e. bias) and the standard deviation of the residual errors are reduced from inline-formula $M8inlinescrollmathml-\mathrm{normal\; 1.3}\times {\mathrm{normal\; 10}}^{-\mathrm{normal\; 8}}$ 59pt14ptsvg-formulamathimg647598611b25385ce346f76061d6fdcb amt-11-2213-2018-ie00001.svg59pt14ptamt-11-2213-2018-ie00001.png and inline-formula $M9inlinescrollmathml\mathrm{normal\; 2.2}\times {\mathrm{normal\; 10}}^{-\mathrm{normal\; 8}}$ 51pt14ptsvg-formulamathimg865d54b74b26581971b007146a77b91f amt-11-2213-2018-ie00002.svg51pt14ptamt-11-2213-2018-ie00002.png for the uncorrected case to inline-formula $M10inlinescrollmathml-\mathrm{normal\; 2.2}\times {\mathrm{normal\; 10}}^{-\mathrm{normal\; 10}}$ 63pt14ptsvg-formulamathimg0783b29ddad6b7974bb7b63b5f1e2166 amt-11-2213-2018-ie00003.svg63pt14ptamt-11-2213-2018-ie00003.png  rad and inline-formula $M11inlinescrollmathml\mathrm{normal\; 2.0}\times {\mathrm{normal\; 10}}^{-\mathrm{normal\; 9}}$ 51pt14ptsvg-formulamathimgb50f4cfbc43207377f92b8f7f1d45908 amt-11-2213-2018-ie00004.svg51pt14ptamt-11-2213-2018-ie00004.png  rad, respectively, for the corrections using the inline-formulaκ model. Although a fixed scalar inline-formulaκ also reduces bias for the global average, the selected value of inline-formulaκ (14 radinline-formula⁻¹) is only appropriate for a small band of locations around the solar terminator. In the daytime, the scalar inline-formulaκ is consistently too high and this results in an overcorrection of the bending angles and a positive bending angle bias. Similarly, in the nighttime, the scalar inline-formulaκ is too low. However, in this case, the bending angles are already small and the impact of the choice of inline-formulaκ is less pronounced.