Global Positioning System (GPS) radio occultation (RO) and radiosonde (RS) observations are two major types of observations assimilated in numerical weather prediction (NWP) systems. Observation error variances are required input that determines the weightings given to observations in data assimilation. This study estimates the error variances of global GPS RO refractivity and bending angle and RS temperature and humidity observations at 521 selected RS stations using the three-cornered hat method with additional ERA-Interim reanalysis and Global Forecast System forecast data available from 1 January 2016 to 31 August 2019. The global distributions, of both RO and RS observation error variances, are analyzed in terms of vertical and latitudinal variations. Error variances of RO refractivity and bending angle and RS specific humidity in the lower troposphere, such as at 850 hPa (3.5 km impact height for the bending angle), all increase with decreasing latitude. The error variances of RO refractivity and bending angle and RS specific humidity can reach about 30 N-unit2, 3 × 10−6 rad2, and 2 (g kg−1)2, respectively. There is also a good symmetry of the error variances of both RO refractivity and bending angle with respect to the equator between the Northern and Southern Hemispheres at all vertical levels. In this study, we provide the mean error variances of refractivity and bending angle in every 5°-latitude band between the equator and 60°N, as well as every interval of 10 hPa pressure or 0.2 km impact height. The RS temperature error variance distribution differs from those of refractivity, bending angle, and humidity, which, at low latitudes, are smaller (less than 1 K2) than those in the midlatitudes (more than 3 K2). In the midlatitudes, the RS temperature error variances in North America are larger than those in East Asia and Europe, which may arise from different radiosonde types among the above three regions.
Numerical discretization causing error variance loss and the need for inflation