Four-dimensional variational (4D-Var) assimilation forecast impact experiments were conducted with CHAMP radio occultation measurements from 1st June to 31st July 2004. The CHAMP bending angles were assimilated with one-dimensional (1D) and two-dimensional (2D) bending angle observation operators, enabling the potential benefits of the latter to be investigated. Two computationally affordable 2D bending angle observation operators were considered. The first can be viewed as a straightforward generalisation of the 1D operator. The second is based on a fourth order Runge–Kutta solution of the differential equations defining the ray-path through the refracting atmosphere.
It is demonstrated that the computational cost of the 2D bending angle operators is not prohibitive and that they improve the root-mean-square of the observed minus background (O-B) bending angle departures by around 5% in the lower-troposphere of the northern and southern hemispheres. The O-B distributions in the tropical lower-troposphere are biased low, but the first-guess departure quality control procedure removes ∼2–3% of the observations and this reduces the bias by around 20%. The assimilation of the CHAMP measurements with both the 1D and 2D operators improves the analysis and forecast fit to radiosonde temperature measurements in the southern hemisphere on the 300, 200, 100 and 50 hPa levels, over the day-1 to day-5 forecast range. The forecast scores in the lower-troposphere for geopotential height and relative humidity are generally neutral, but there is a small improvement in the anomaly correlation of the 500 hPa geopotential height field in the southern hemisphere, over the day-1 to day-2 forecast range. However, there are no clear, statistically significant differences between the 1D and 2D experiments for this two-month period. Copyright © 2007 Royal Meteorological Society