Global Navigation Satellite System (GNSS) radio occultation climatologies mapped by machine learning and Bayesian interpolation

Global Navigation Satellite System (GNSS) radio occultation (RO) is a space-based remote sensing technique that measures the bending angle of GNSS signals as they traverse the Earth's atmosphere. Profiles of the microwave index of refraction can be calculated from the bending angles. High accuracy, long-term stability, and all-weather capability make this technique attractive to meteorologists and climatologists. Meteorologists routinely assimilate RO observations into numerical weather models. RO-based climatologies, however, are complicated to construct as their sampling densities are highly non-uniform and too sparse to resolve synoptic variability in the atmosphere.In this work, we investigate the potential of machine learning (ML) to construct RO climatologies and compare the results of an ML construction with Bayesian interpolation (BI), a state-of-the-art method to generate maps of RO products. We develop a feed-forward neural network applied to Constellation Observing System for Meteorology, Ionosphere, and Climate-2 (COSMIC-2) RO observations and evaluate the performance of BI and ML by analysis of residuals when applied to test data. We also simulate data taken from the atmospheric analyses produced by the European Centre for Medium-Range Weather Forecasts (ECMWF) in order to test the resolving power of BI and ML. Atmospheric temperature, pressure, and water vapor are used to calculate microwave refractivity at 2, 3, 5, 8, 15, and 20 km in geopotential height, with each level representing a different dynamical regime of the atmosphere. The simulated data are the values of microwave refractivity produced by ECMWF at the geolocations of the COSMIC-2 RO constellation, which fall equatorward of 46 degrees in latitude. The maps of refractivity produced using the neural networks better match the true maps produced by ECMWF than maps using BI. The best results are obtained when fusing BI and ML, specifically when applying ML to the post-fit residuals of BI. At the six iso-heights, we obtain post-fit residuals of 10.9, 9.1, 5.3, 1.6, 0.6, and 0.3 N units for BI and 8.7, 6.6, 3.6, 1.1, 0.3, and 0.2 N units for the fused BI&ML. These results are independent of season.The BI&ML method improves the effective horizontal resolution of the posterior longitude-latitude refractivity maps. By projecting the original and the inferred maps at 2 km in iso-height onto spherical harmonics, we find that the BI-only technique can resolve refractivity in the horizontal up to spherical harmonic degree 8, while BI&ML can resolve maps of refractivity using the same input data up to spherical harmonic degree 14.