# Applications of GNSS-RO to Numerical Weather Prediction and Tropical Cyclone Forecast
## 3 Research and Applications of RO to TC Forecast
### Effect of RO Assimilation Operator on TC Forecasts  
To further improve the accuracy of TC forecast using RO measurements, the forecast model should consider the assimilation approaches and associated operators in the assimilation system. The popular assimilation approaches include 3D-Var, 4D-Var, and ensemble Kalman filter [64]. In terms of the assimilation operator, as listed in Table 2, the RO provides two measurements: the refractivity and the bending angle. These two can be used to derive several assimilation operators. The refractivity includes the local refractivity, non-local refractivity [65], and non-local excess phase; the bending angle includes the 2D/3D ray tracer [66] and local bending angle [67]. On the one hand, the first operator of the bending angle, i.e., the ray tracer, is computationally expensive. The local bending operator of the bending angle is theoretically equivalent to the local refractivity operator because the bending angle can be transformed to a refractive index via Abel transformation. However, the local bending angle is more accurate and has a wider range [67]. On the other hand, the local refractivity used to be the most popular operator for avoiding complex computations [68]. In the assimilation system for TCs, a better choice is the non-local excess phase operator (EPH), as the high moisture environment in the inner regions of a TC results in strong local-refractivity horizontal gradients, which break the spherically symmetric atmosphere assumption, resulting in multipath effects [69]. In such circumstances, the local refractivity would induce significant representativeness errors. Nevertheless, the EPH can avoid this issue, as proven in many papers [68; 70; 71; 72; 73]. Here, the non-local value represents a more accurate value estimated under the mathematical assumption. The EPH is a virtual value obtained by integrating the refractivity along an arbitrary trajectory, which passes the tangent point closer to the actual ray path [74]. Based on ten tropical cyclones that occurred during 2008-2010, the authors of [75] investigated the impact of RO measurements on the tropical cyclogenesis using the WRF data assimilation system. The study demonstrated that the EPH can help improve the probability of successful TC predictions from 30% to 70%, whereas the local refractivity operator (LOC) improved this value by only 10%. A case study on the typhoon Nutri revealed that the experiment using the EPH shows a higher moisture content near the ocean surface and vertical motion, as indicated by the red circle in Figure 14a. Additionally, the dashes in Figure 14b indicate a stronger mid-level vorticity development in the EPH experiment against the LOC experiment. Therefore, the non-local excess phase operator is a better assimilation operator. \begin{table}
\begin{tabular}{c c} \hline \hline
**Observation** & **Assimilation Operator** \\ \hline \multirow{3}{*}{Refractivity} & Local refractivity \\  & Non-local refractivity \\  & Non-local excess phase \\ \hline \multirow{2}{*}{Bending angle} & Local bending angle \\  & 2D/3D Ray tracer \\ \hline \hline \end{tabular}
\end{table} 
Table 2: RO operator in data assimilation. All the above studies prove that assimilating the RO data can promote the accuracy of TC forecast. RO data below 6 km are essential as they play an important role in the initial stages of TC genesis. The RO data in the UTLS region have a positive influence on the forecast over three days owing to their high vertical resolution. Through the vertical studies of TC, RO data provide a more accurate initial field above the sea surface, including sufficient water vapor, which restores the dynamic structures of TCs such as the eyewall and rain bands. Therefore, the TC forecast is improved significantly owing to the RO measurement. However, the current number of RO measurements is insufficient. The planned missions, such as COSMIC-2, MetOp, and FY-3, are expected to increase the daily number of RO soundings in the future. This will bring remarkable improvements for TC prediction [76].