## 5 Rain Attenuation in Slant Paths to Geostationary Satellites: The Synthetic Storm Technique
### Application of the SST to All Sites  
We applied the SST twice: first, by using as input the experimental 1 min rain rate time series, namely, \(R_{1}(t)\), and second, by using the simulated \(R(t)\). Figure 19 shows the annual average rain attenuation probability distributions obtained with \(R_{1}(t)\) and with \(R(t)\). There are no appreciable differences that can impact the satellite system design.  
Figures 20-26 show the annual average rain attenuation probability distributions obtained with \(R_{1}(t)\) and with \(R(t)\) for the other sites. Also, in these cases, we can see that there are no appreciable differences that can impact the satellite system design.  
Figure 19: Average annual probability distribution \(P(A)\)—namely, the fraction of time of a year—that the rain attenuation \(A\) (dB) in abscissa is exceeded, estimated with the SST. Cyan line: experimental \(R_{1}(t)\); magenta line: simulated \(R(t)\).  
Figure 20: **Gera Lario.** Average annual probability distribution \(P(A)\) that the rain attenuation \(A\) (dB) in abscissa is exceeded, estimated with the SST; blue line: experimental \(R_{1}(t)\), black line: simulated \(R(t)\). **Left panel**: \(P(A)\) is obtained by using local values of the conditional rain rate PDFs. **Right panel**: \(P(A)\) is obtained by using Spino d’Adda conditional PDFs (Table 2).  
Figure 21: **Fucino.** Average annual probability distribution \(P(A)\) that the rain attenuation \(A\) (dB) in abscissa is exceeded, estimated with the SST; blue line: experimental \(R_{1}(t)\), black line: simulated \(R(t)\). **Left panel:**\(P(A)\) is obtained by using local values of the conditional rain rate PDFs. **Right panel:**\(P(A)\) is obtained by using Spino d’Adda conditional PDFs (Table 2).  
Figure 22: **Madrid.** Average annual probability distribution \(P(A)\) that the rain attenuation \(A\) (dB) in abscissa is exceeded, estimated with the SST; blue line: experimental \(R_{1}(t)\), black line: simulated \(R(t)\). **Left panel**: \(P(A)\) is obtained by using local values of the conditional rain rate PDFs. **Right panel:**\(P(A)\) is obtained by using Spino d’Adda conditional PDFs (Table 2).  
Figure 23: **Prague.** Average annual probability distribution \(P(A)\) that the rain attenuation \(A\) (dB) in abscissa is exceeded, estimated with the SST; blue line: experimental \(R_{1}(t)\), black line: simulated \(R(t)\). **Left panel**: \(P(A)\) is obtained by using local values of the conditional rain rate PDFs. **Right panel**: \(P(A)\) is obtained by using Spino d’Adda conditional PDFs (Table 2).  
Figure 24: **Tampa.** Average annual probability distribution \(P(A)\) that the rain attenuation \(A\) (dB) in abscissa is exceeded, estimated with the SST; blue line: experimental \(R_{1}(t)\), black line: simulated \(R(t)\). **Left panel**: \(P(A)\) is obtained by using local values of the conditional rain rate PDFs. **Right panel**: \(P(A)\) is obtained by using Spino d’Adda conditional PDFs (Table 2).  
Figure 25: **White Sands.** Average annual probability distribution \(P(A)\) that the rain attenuation \(A\) (dB) in abscissa is exceeded, estimated with the SST; blue line: experimental \(R_{1}(t)\), black line: simulated \(R(t)\). **Left panel**: \(P(A)\) is obtained by using local values of the conditional rain rate PDFs. **Right panel**: \(P(A)\) is obtained by using Spino d’Adda conditional PDFs (Table 2).  
Now, since for satellite communications, the tolerated outage probability due to rain attenuation, i.e., \(P(A)\), is in the range of \(10^{-1}-10^{-2}\) (%) (i.e., annual average outage time from 525 to 52.5 min, respectively), from these figures, it turns out that for most probability ranges, there are no significant differences between the rain attenuation \(A\) estimated with local and with Spino d'Adda parameters.