## 6 Results  
As a first assessment of the employed training approaches, the vertically averaged RMS error is evaluated comparing \(N\) obtained as output of the different neural network trainings (\(N\)=\(N_{d}\)+\(N_{w}\)), hereafter named as the autotest result, with the corresponding ECMWF profiles. Also, the vertically averaged RMS error of \(N\) computed from Abel transformation, i.e. the input of the networks, and the mean standard deviation of the entire ECMWF database are reported in Table 3 and in Table 4, for desert and vegetation zone respectively. The ECMWF standard deviation can be assumed as an index of the climatological variability of a given atmospheric parameter, than a good accuracy of a retrieval algorithm is obtained when its RMS error is clearly below it. From these tables, we deduce the good performances of the proposed approaches, with the cross validation technique (12.5%) exhibiting the best results. \begin{table}
\begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{**Vegetation zone**} \\ \hline \multicolumn{6}{|c|}{**EARLY STOPPING - PCA**} \\ \hline  & **Input** & **HL1** & **HL2** & **HL3** & **Output** \\ \hline
**N Dry** & 14 & 6 & 6 & 3 & 11 \\ \hline
**N Wet** & 14 & 12 & 8 & - & 11 \\ \hline
**P Dry** & 14 & 10 & 10 & 10 & 7 \\ \hline \multicolumn{6}{|c|}{**EARLY STOPPING – Full Profile**} \\ \hline
**N Dry** & 54 & 15 & 8 & - & 54 \\ \hline
**N Wet** & 54 & 12 & 5 & - & 54 \\ \hline
**P Dry** & 54 & 10 & 10 & 10 & 54 \\ \hline \multicolumn{6}{|c|}{**CROSS VALIDATION (25\%) - PCA**} \\ \hline
**N Dry** & 14 & 10 & 10 & 3 & 11 \\ \hline
**N Wet** & 14 & 4 & - & - & 11 \\ \hline
**P Dry** & 14 & 13 & 13 & 9 & 7 \\ \hline \multicolumn{6}{|c|}{**CROSS VALIDATION (12.5\%) - PCA**} \\ \hline
**N Dry** & 14 & 17 & 9 & - & 11 \\ \hline
**N Wet** & 14 & 12 & 12 & 12 & 11 \\ \hline
**P Dry** & 14 & 13 & 11 & - & 7 \\ \hline \end{tabular}
\end{table} 
Table 2: Best neural network topologies over vegetation zone obtained for each neural network approach: input, HL1, HL2, HL3 and output columns report the number of neurons for the input, hidden layer 1, hidden layer 2, hidden layer 3 and output, respectively. Each approach employs 3 neural networks, named N Dry (for dry refractivity estimation), N Wet (for wet refractivity estimation) and P Dry (for dry pressure estimation). To evaluate performance and generalization capability of each neural network approach, the RMS error profiles for \(N\) (\(N\)=\(N_{d}\)+\(N_{w}\)) employing the independent test set of 10 and 35 occultations for desert and vegetation zones, are shown in Figure 2 and Figure 3, superimposed to the corresponding ECMWF standard deviation profiles. \begin{table}
\begin{tabular}{|c|c|c|c|c|c|} \hline \multicolumn{6}{|c|}{**Desert zone**} \\ \hline \multirow{3}{*}{**Mean standard deviation of \(N\)**} & \multirow{3}{*}{**Vertically averaged RMS**} & \multicolumn{3}{c|}{**Output autotest (88 events):**} \\  & & & **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
**6.20 N-units** & **5.33 N-units** & **4.08 N-units** & **3.80 N-units** & **3.91 N-units** & **2.70 N-units** \\ \hline \end{tabular}
\end{table} 
Table 4: Vegetation 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 (312 events) using the different approaches. E.S. : Early Stopping; C.V.: Cross Validation. The best result is highlighted.