## 4 Review: Slant Links Rain Fade Models
### Physical Models
#### 4.3.4 SCEXCELL Model  
The SCEXCELL model [62] is based on the rain attenuation statistics generated from the Earth-space links. This model uses the synthetic EXCELL cell to obtain a finite value using a lower factor and modifying the rain profile. Furthermore, the model identifies different types of precipitating clouds, such as cumulus- and stratus-type clouds. The lower value of the rainfall rate is used to separate the yearly rain probability into stratiform and convective distribution, where it is assumed that for a stratiform rainfall, a rate of 10 mm/his rarely exceeded. The procedure for assessing attenuation due to rain involves the derivation of the probability of stratiform and convective rainfall from the yearly rainfall rate based on the discrimination method (steps are shown in Algorithm 18) [122].  
The convective and stratiform rain heights were calculated using the local climatological parameters (\(h_{l}\): the monthly mean values of the \(0^{\circ}\) isotherm height; \(\beta_{l}\): the ratio between the convective and the total rain amounts calculated over each successive 6 h period, as estimated by the European Center for Medium-Range Weather Forecasts (ECMWF) forecast process for the ECMWF Re-Analysis-15 (ERA-15) databank; and \(p_{i}\): monthly mean values of the 6 h rainy periods' probability) from the ERA-15 databank and the average equivalent bright-band height (BBH, a layer where maximum radar reflectivity happens), as defined by Equation (48).  
\[BBH(f)=4.58e^{-0.0675f}+0.51\ [\mathrm{km}] \tag{48}\]Equation (48) is valid for the following conditions: initial density of the melting particles (\(d_{0}=0.16\) g/cm\({}^{3}\)); particle size distribution (gamma with \(\mu=0\)); and frequency (\(10\,\mathrm{GHz}<f<50\,\mathrm{GHz}\)). Due to the concept of non-ideal exponentially shaped cells, the model considers the plateau contribution to the attenuation due to stratiform and convective types of rain differently.  
\[A(P)_{str} =A_{C}(P)_{str}+A_{P}(P)_{str} \tag{49}\] \[A(P)_{env} =A_{C}(P)_{env}+A_{P}(P)_{env}\] (50) \[P(A)_{tot} =P(A)_{str}+P(A)_{env} \tag{51}\]  
Although the model does not outperform the existing ITU-R model (it has approximately 2.4% error), it does consider supporting site diversity [123], the conversion of rainfall rate from 1 min to 1 h [124], and interference due to hydrometer scattering [125]. The rain attenuation determination procedure by this model is shown in Algorithm 18.  
```
1 Sample \(\rho_{0}\) /* 20 samples between 0.6-20 km */
2 Solve for \(R_{M}^{*}\)
3 Calculate \(N(R_{M},\rho_{0})\)
4 Calculate \(R_{M,th}\)
5 ifcells with \(R_{M}<R_{M,th}\)then
6 Generate the stratiform P(R)
7 else
8 Produce the convective P(R)
9 Calculate \(BBH(f)\) /* Equation (48) */
10 Calculate \(H_{str}\) and \(H_{env}\)/* \(H_{str}\leftarrow\frac{\sum_{i=1}^{12}\delta_{i}\pi_{i}}{\sum_{i=1}^{12}\delta_ {i}\pi_{i}}\), \(H_{env}\leftarrow\frac{\sum_{i=1}^{12}\delta_{i}\pi_{i}}{\sum_{i=1}^{12}\delta_ {i}\pi_{i}}\) */
11 Compute \(H_{strRain}\) /* \(H_{strRain}\gets H_{str}+BBH(f)\) */
12 Compute \(H_{envRain}\) /* \(H_{max}\gets 1.2h_{max}\) (km) */
13 Compute \(A(P)_{str}\) /* Equation (49) */
14 Compute \(A(P)_{env}\) /* Equation (50) */
15 Find \(P(A)_{tot}\) /* Equation (51) */
16 Estimate \(A\gets P(A)_{tot}\)
17 Return \(A\)
```  
**Algorithm 18** SCEXCELL Model [62]  
Advantages  
The model fuses the benefits of the EXCELL and HYCELL models. It facilitates the simulation of long microwave terrestrial links (and, consequently, extended terrestrial microwave networks) to evaluate site diversity systems.