### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Ensemble Design and Simulations
- 3. Phase and Doppler Observables
- 4. Retrieval of Atmospheric Profiles
- 5. Analysis Results and Discussion
- 6. Error Covariance Matrices for Refractivity and Other Data Products
- 7. Summary, Conclusions, and Outlook
- Acknowledgments
- References

[1] Radio occultation (RO) observations using the Global Navigation Satellite System (GNSS) globally provide high quality atmospheric data which can support the advancement of climate monitoring and modeling as well as the improvement of numerical weather prediction. In order to make optimal use of the data, e.g., via data assimilation systems, the characterization of measurement errors is of importance. Within this context we present results of an empirical error analysis based on quasi-realistically simulated GNSS RO data. The study is based on an end-to-end forward-inverse simulation involving (1) modeling of the neutral atmosphere and ionosphere, (2) simulation of RO observations, (3) forward modeling of excess phase observables including realistic observation system error modeling, and (4) retrieval of atmospheric parameters. Occultation observations were simulated for one day from which an ensemble of 300 occultation events was chosen, with 100 events in each of three latitude bands (low, middle, high). Phase path profiles were computed showing a realistic rms error of the ionosphere corrected phase paths of 2–3 mm at mesospheric and stratospheric heights at 10 Hz sampling rate. Atmospheric profiles were retrieved by applying a dry air retrieval in the stratosphere and an optimal estimation retrieval in the troposphere. The retrieved profiles were referenced to the “true” co-located ones of the analysis field of the European Centre for Medium-range Weather Forecasts (ECMWF). We empirically estimated bias profiles and covariance matrices (standard deviations and correlation functions) for the retrieval products such as bending angle, refractivity, pressure, geopotential height, temperature, and specific humidity. Results include the refractivity error showing a relative standard deviation of 0.1–0.75% and a relative bias of <0.1% at 5–40 km height. Temperature exhibits a standard deviation of 0.2–1 K at 3–31 km height and a bias of <0.1–0.5 K below 33 km and of <0.1 K below 20 km. Simple analytical error covariance formulations are presented for refractivity, as deduced from the empirically estimated covariance matrices. The reasonably realistic error estimates presented are a good basis for further retrieval algorithm improvements and for proper specification of observational errors in data assimilation systems.