Sensitivity of forward-modeled bending angles to vertical interpolation of refractivity for radio occultation data assimilation

Assimilation of radio occultation (RO) observations into numerical weather prediction (NWP) models has improved forecasts, where RO is typically one of the top five observational systems contributing to forecast accuracy. By measuring the phase delay of radio waves traversing Earth's atmosphere between global positioning system (GPS) and low-Earth orbiting satellites, RO obtains quasi-vertical profiles of bending angles (BA) of the radio waves' trajectories. BA are the RO observation most often assimilated into NWP models, but since they are not computed or analyzed in the models, they must be computed from model data using a forward model. First, model refractivity N is computed from variables specified on the model's vertical levels, then using the Abel integral, BA are computed from N. The forward model requires vertical differentiation of N, and accurate differentiation requires vertical interpolation of N between model levels. The interpolation results in errors, which then propagate through the forward model to produce BA errors. In this study, we investigate the sensitivity of forward-modeled BA to five different methods of vertical interpolation of N between model levels to determine a method that minimizes interpolation errors. We use RO-observed N to isolate the interpolation errors and determine an accurate method that can be applied to any NWP model. Of the five methods investigated, the log-spline interpolation reduces N and BA errors the most, regardless of the vertical resolution of the model grid.