# Atmospheric GNSS RO 1D-Var in Use at UCAR: Description and Validation
## 3 Results
### Comparison to High Vertical Resolution Radiosondes
The specific humidity standard deviations increase toward the surface, and NEW displays persistently smaller standard deviations than OLD at heights below 6 km. The 1D-Var specific humidities are negatively biased with respect to radiosondes, which is consistent with the well-known negative bias of RO observation in the lower troposphere. NEW is cooler than radiosonde in the lower troposphere, although we expect a warm bias from the negative observation bias. While the cause is uncertain, itcould be a warm radiosonde or cold background bias. Nevertheless, the temperature bias is minor, with a minimum value of \(-0.25\)\({}^{\circ}\)C at about 2.5 km. In the light of the Hollingsworth-Lonnberg method described in Section 2.2.4, the difference between a nearby RO-radiosonde pair depends on the separation in space and time as well as the errors of RO and radiosonde. When all contributors to the difference are uncorrelated, the RO- radiosonde standard deviation \(\sigma_{t}\) can be approximated as:  
\[\sigma_{t}=\left(\sigma_{RO}^{2}+\sigma_{RS}^{2}+\sigma_{d}^{2}\right)^{1/2}, \tag{30}\]  
where \(\sigma_{RS}\) is radiosonde observation error, \(\sigma_{RO}\) is RO retrieval error, and \(\sigma_{d}\) is atmospheric variation across the separation. At zero separation \(\sigma_{d}\) vanishes, leading to \(\sigma_{t}~{}=~{}\left(\sigma_{RO}^{2}+\sigma_{RS}^{2}\right)^{1/2}\). Figure 15 shows NEW-radiosonde standard deviations for different collocation thresholds. The difference in the mean, which is insensitive to the separation, is not shown here. The collocation is pursued on a level-by-level basis (rather than profile-by-profile) to consider the horizontal drifts of RO tangent points and the balloon. Therefore, a NEW-radiosonde pair is partially excluded from the comparison when the separation on each height level exceeds the threshold. Figure 15 reveals that the standard deviation decreases rapidly as the separation narrows. We can estimate the hypothetical \(\sigma_{t}\) obtainable at zero separation by extrapolating the standard deviation profiles of different thresholds. The \(\sigma_{t}\) at zero separation comprises observation errors of RO and radiosonde, containing the representativeness error, which  
Figure 14: COSMIC retrievals compared to collocated high vertical resolution RS92 observations in temperature (**left panels**; \({}^{\circ}\)C), pressure (**middle**; %), and specific humidity (**right**; g kg\({}^{-1}\)) for the period from May 2006 to August 2015. **Upper panels** are standard deviations and **lower panels** are mean differences. is shared by the observation errors in an unknown ratio. The representativeness error in this RO-radiosonde comparison may be large because the two high-vertical-resolution data sets describe small-vertical-scale atmospheric structures very differently. Hence, the \(\sigma_{t}\) extrapolated to zero separation is still a conservative upper bound of the error of NEW. Considering all these factors, we find that the agreement between NEW and radiosonde is excellent and that the 1D-Var provides accurate and precise RO-based profiles.