# Rainfall Estimation from Tropospheric Attenuation Affecting Satellite Links
## 6 Performance Evaluation
### Comparison with Other Rain Rate Estimation Models: Accuracy Assessment  
This Section presents the comparison of the prediction accuracy that was achieved by the methods described in Section 6.1 and by the proposed model. The following notation will be used to name the methods taken into consideration to simplify the discussion:  
* _NF_, which refers to the NEFOCAST system;
* _CM_, defining the centralized method for real-time rainfall estimation [8]. More specifically, the first solution (described by (21)) is labelled as _CM_1, while the alternative one (described by (23)) is denominated as _CM_2; and,
* _BM_, associated to the method developed by the BME-HVT.  
Figure 16 shows the \(P(R)\) obtained by using the abovementioned techniques, along with the two curves that were obtained from the measurements and the proposed model, respectively. In addition, the corresponding statistical indicators are reported in Table 6.  
The results indicate that the proposed model shows the highest accuracy. A critical aspect that is common to all of the models listed above is the limitation in estimating high rain rates: all the curves diverge significantly from the reference one (red line), as the rain rate increases. This issue is significantly lower for the proposed model, which introduces a more complex and accurate method for estimating the equivalent rain height. The lower accuracy of the other models is likely due to the following reasons:  
* _NF_ does not consider any path reduction factors, which, on the contrary, are included in the prediction model in [19], and are intended to model the spatial inhomogeneity of rainfall along the path.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & \(\mathbf{E[e_{r}(P)]}\) & \(RMS[\mathbf{e_{r}(P)]}\) \\ \hline Proposed Model & 0.62 mm/h & 1.19 mm/h \\ _NF_ & 3.82 mm/h & 4.79 mm/h \\ _CM_1 & 0.14 mm/h & 2.03 mm/h \\ _CM_2 & \(-\)0.29 mm/h & 4.24 mm/h \\ _BM_ & 0.70 mm/h & 1.57 mm/h \\ \hline \hline \end{tabular}
\end{table}
Table 6: Mean and RMS values corresponding to the comparison between the measurement and the estimated curves reported in Figure 16.  
Figure 16: Yearly \(P(R)\): comparison of different models.  
Notwithstanding the very good results achieved, it is worth mentioning that the proposed model was calibrated and tested on the same reference dataset: additional data, not yet currently available to the authors, are required for corroborating the model applicability and performance in other sites.  
Conceptualization, L.L. and C.G.R.; methodology, R.A.G., L.L. and C.G.R.; software, R.A.G., L.L. and C.G.R.; validation, R.A.G. and L.L.; formal analysis, R.A.G. and L.L.; investigation, L.L. and C.G.R.; writing--original draft preparation, R.A.G.; writing--review and editing, R.A.G., L.L. and C.G.R.; visualization, R.A.G.; supervision, L.L. and C.G.R.; project administration, L.L. and C.G.R. All authors have read and agreed to the published version of the manuscript.  
This work was partially supported by the Air Force Office of Scientific Research, Air Force Material Command, United States Air Force, European Office of Aerospace Research and Development under Grant FA9550-17-1-0335.  
The Authors want to thank NASA for making the propagation data available.  
The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.