“…Those include ionospheric correction in combination with statistical optimization of bending angles (Gobiet & Kirchengast, 2004; Gorbunov, 2002), optimal filtering or smoothing of the L1 and L2 bending angle difference (Hajj et al., 2002; Kuo et al., 2004; Schwarz et al., 2018; Sokolovskiy et al., 2009; Steiner et al., 1999), reduction of fluctuations in the corrected bending angle via comparative discrimination or back propagation (Sokolovskiy et al., 2014), and ionospheric correction in the troposphere via extrapolation when one of the two GNSS signals is unavailable due to tracking limitations (Rocken et al., 1997; Zeng et al., 2016). Nor do we address residual errors in derived refractivity or temperature using the Abel transform and hydrostatic integration (Danzer et al., 2020, 2021; Kursinski et al., 1997; Rieder & Kirchengast, 2001; Schwarz et al., 2017). The residual errors in these variables are linked to the error in bending angle, but the details depend on the particular approach of statistical optimization and upper altitude initialization, and is therefore more difficult to describe in a general sense.…”