Empirical analysis and modeling of errors of atmospheric profiles from GPS radio occultation

The utilization of radio occultation (RO) data in atmospheric studies requires precise knowledge of error characteristics. We present results of an empirical error analysis of GPS RO bending angle, refractivity, dry pressure, dry geopotential height, and dry temperature. We find very good agreement between data characteristics of different missions (CHAMP, GRACE-A, and Formosat-3/COSMIC (F3C)). In the global mean, observational errors (standard deviation from "true" profiles at mean tangent point location) agree within 0.3% in bending angle, 0.1% in refractivity, and 0.2 K in dry temperature at all altitude levels between 4 km and 35 km. Above 35 km the increase of the CHAMP raw bending angle observational error is more pronounced than that of GRACE-A and F3C leading to a larger observational error of about 1% at 42 km. Above ≈20 km, the observational errors show a strong seasonal dependence at high latitudes. Larger errors occur in hemispheric wintertime and are associated mainly with background data used in the retrieval process particularly under conditions when ionospheric residual is large. The comparison between UCAR and WEGC results (both data centers have independent inversion processing chains) reveals different magnitudes of observational errors in atmospheric parameters, which are attributable to different background fields used. Based on the empirical error estimates, we provide a simple analytical error model for GPS RO atmospheric parameters for the altitude range of 4 km to 35 km and up to 50 km for UCAR raw bending angle and refractivity. In the model, which accounts for vertical, latitudinal, and seasonal variations, a constant error is adopted around the tropopause region amounting to 0.8% for bending angle, 0.35% for refractivity, 0.15% for dry pressure, 10 m for dry geopotential height, and 0.7 K for dry temperature. Below this region the observational error increases following an inverse height power-law and above it increases exponentially. For bending angle and refractivity we also include formulations for error correlations in order to enable modeling of full error covariance matrices for these primary data assimilation variables. The observational error model is the same for UCAR and WEGC data but due to somewhat different error characteristics below about 10 km and above about 20 km some parameters have to be adjusted. Overall, the observational error model is easily applicable and adjustable to individual error characteristics.