# Evaluation of Forward Models for GNSS Radio Occultation Data Processing and Assimilation
## 3 Results
### Experiment 1: Algorithm Comparison
#### 3.1.3 Analysis to exp_T  
Herein, we discuss the RD and difference between the exp and the revised exp algorithm (exp_T). The RD is two orders of magnitude lower than the difference between exp and direct. Hence, the RD and difference are plotted in separate graphs as shown in Figure 5, the BA of the exp_T algorithm is slightly larger than that of the exp algorithm. According to [24], this difference is due to the temperature term in the new polynomial, which corrects the error of the exp algorithm. However, the corrected amount is limited. Since the exp_T algorithm introduced temperature operator, it requires considerably more computation and time resources. Thus, the exp algorithm is superior operationally. Figure 4: RD of the BAs of FY3D (T) and EC4 Dvar (E) based on the direct and exp Abel integral algorithms, with log-linear and log-cubic interpolation methods. (**a–c**) (\(\mathrm{E-T}\))/T, where E can be calculated by either the exp or direct algorithm, with both interpolation methods; (**d–f**) (\(\mathrm{E_{1}-E_{2}}\))/\(\mathrm{E_{2}}\), where 1, 2 indicate two different FMs. Finally, we list the RD between the true value and all experimental values in Table 1. The above analysis identified that the exp algorithm with log-cubic is the most accurate FM; therefore, the quantity of each FM'error is written as exp's RD plus the left error of the FM for clarity. First, the RD of the exp_lin algorithm is the same as that of the exp algorithm below a height of 55 km; however, it becomes 3% and 20% larger than that of the exp algorithm within 55-60 km and 70-80 km, respectively. Second, the RD of the direct algorithm is approximately 0.3% larger than that of the exp algorithm within 8-45 km, which becomes \(-10\%\) and \(-80\%\) less than that of the exp algorithm within 60-70 km and 70-80 km, respectively. Third, the improvement of the exp_T algorithm is limited (approximately 0.002%) compared to that of the exp algorithm. It should be noted within heights of 55-60 km, the error of the exp_lin algorithm is less than that of the exp algorithm, which is due to errors contributed by refractivity. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**H (km)** & **exp (\%)** & **exp\_lin(\%)** & **direct(\%)** & **direct\_lin(\%)** & **exp\_T(\%)** & **exp\_T\_lin(\%)** \\ \hline
8–15 & & \((-0.3,0.5)\) & exp + 0.3 & & & \\
15–20 & & \((0.5,1)\) & exp + 0.3 & & & \\
20–45 & & \((-0.3,0.5)\) & exp + 0.2 & & & \\
45–55 & & \((-0.5,1.5)\) & exp + 0.1 & exp \(\pm\) 0.002 & exp\_lin \(\pm\) 0.002 \\ \cline{2-6}
55–60 & \((0,5)\) & \((0,4)\) & \((0,3.8)\) & & & \\
60–70 & \((-1,2.5)\) & \((-4,2.3)\) & \((-10,1.8)\) & & & \\
70–80 & \((-1,5)\) & \((-20,-5)\) & \((-80,-10)\) & direct + 4\% & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Relative difference, (E\(-\)T)/T \(\times\) 100%, between the FY3D BA (T) and the forward-modeled BA (E), in which E can be the exp and direct algorithm, and each algorithm has two interpolation methods: log linear (denoted by lin) and cubic spline (no label). Figure 5: Difference (first row) and RD (second row) between the exp_T and exp algorithms. The exp algorithm with log-cubic is the most accurate FM; therefore, the quantity of each FM'error is written as exp's RD plus the left error of the FM for clarity. It is important to note that when E was refractivity, there are already been errors in E\({}_{\text{ref}}\) (ref is refractivity). This error was then passed to BA's (E\(-\)T)/T. Therefore, what we got in experimentone is the which FM is better, rather than how much error exactly one FM causes. This issue will be tested in experiment two. Since analysis above identified that the exp algorithm with log-cubic interpolation is the most accurate FM, in next experiment we will figure out how much exactly the error of exp algorithm is on three fixed model levels. It is important to note that when E is refractivity, errors exist in E\({}_{\text{ref}}\) (where ref denotes refractivity), which are then passed to the (E\(-\)T)/T value of the BA.