## 6 Results
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{**Vegetation zone**} \\ \hline \multirow{3}{*}{**Mean standard deviation of \(N\)**} & \multirow{3}{*}{**Vertically averaged RMS**} & \multicolumn{3}{c|}{**Output autotest (312 events):**} \\  & & **averaged RMS** & \multicolumn{3}{c|}{**vertically averaged RMS errors of \(N\) (N-units)**} \\ \cline{3-6}  & & **E.S.** & **E.S.** & **C.V. (25\%)** & **C.V. (12.5\%)** \\ \cline{3-6}  & & **PCA** & **Full Profile** & **PCA** & **PCA** \\ \hline
**7.11 N-units** & **4.76 N-units** & **3.70 N-units** & **4.06 N-units** & **3.80 N-units** & **3.41 N-units** \\ \hline \end{tabular}
\end{table} 
Table 3: Desert zone: mean standard deviation of ECMWF refractivity \(N\), vertically averaged RMS error of refractivity \(N\) from Abel transformation and vertically averaged RMS error of refractivity \(N\) as output of neural network autotest (88 events) using the different approaches. E.S. : Early Stopping; C.V.: Cross Validation. The best result is highlighted. As underlined in the previous sections, choosing to train three networks for each approach enables us to retrieve atmospheric profiles without the constraint of temperature profile availability at each GPS occultation, only using eq. (2). In particular, with the availability of \(N_{d}\), \(N_{w}\) and \(P_{d}\), first we can solve for temperature \(T\) in a straightforward way from the dry refractivity using eq. (3), and then for partial pressure of water vapor \(\mathrm{P_{w}}\) from the wet refractivity using eq. (4). In Figure 4 and Figure 5 the RMS error profiles for \(T\) and in Figure 6 and Figure 7 the RMS error profiles for \(P_{w}\) are shown superimposed to the corresponding ECMWF standard deviation profiles, for desert and vegetation zone respectively. Figure 3: Vegetation zone, neural network independent test (35 occultations): RMS error profiles for \(N\) using the different neural network approaches. Figure 2: Desert zone, neural network independent test (10 occultations): RMS error profiles for \(N\) using the different neural network approaches. In order to summarize the performances of each neural network approach on the ability to reconstruct all the analyzed tropospheric profiles, i.e. \(N_{d}\), \(N_{w}\), \(N\), \(T\), \(P_{w}\) and \(P\) (\(P\)=\(P_{w}\)+\(P_{d}\)), their vertically averaged RMS error values with respect to ECMWF data for the independent test are reported in Table 5 and 6. In the tables, the corresponding ECMWF mean standard deviations of the entire data set are also reported. Analyzing the results, the ability of the neural networks to retrieve the atmospheric parameters is evident. By comparing the proposed approaches, it's noticeable that each one produces good results, the best ones provided by using the early stopping with full profiles but especially by the cross validation with the PCA. Particularly, adequate accuracy is achieved in the lower troposphere over  
Figure 6: Desert zone, neural network independent test (10 occultations): RMS error profiles for \(P_{w}\) using the different neural network approaches. Figure 7: Vegetation zone, neural network independent test (35 occultations): RMS error profiles for \(P_{w}\) using the different neural network approaches. both the desert and vegetation zone, where the presence and the variability of the water vapour is more consistent. However, considering these approaches from the standpoint of the computational cost in terms of time and memory requirements, the cross validation with the PCA is less expensive than the only early stopping but with the full profiles.