# Scaling of Rain Attenuation Models: A Survey
## 3 Existing Scaling Techniques
### The Clear-Sky-Based Scaling  
Clear air attenuation can be calculated by subtracting the clear air reference level \(S_{CA}\) from the instantaneous signal \(S\) in the dB scale. If we assume \(S_{CA}\) is the signal that would be received if the propagation medium is clear air, it includes scintillation, rain, and cloud effects, but excludes gaseous absorption, and then, their relationship can be expressed as [17]:  
\[A_{CA}=S-S_{CA}(dB) \tag{1}\]  
where \(A_{CA}\) follows directly from attenuation with respect to free space \(A_{FS}\) by removing gaseous attenuation \((A_{GA})\); it can be written as [17]:  
\[A_{CA}=A_{FS}-A_{GA}(dB) \tag{2}\]  
This definition of \(A_{CA}\) is directly applicable to most satellite system designs and can be used for the carrier-to-noise ratio \((C/N)\), which assumes clear air conditions; in many satellite system designs, gaseous absorption losses are included in the power budget as a loss, which is generally within 0.2 dB for \(A_{CA}\) and \(A_{FA}\)[17]. The nonrain frequency scaling is crucial because, most of the time (e.g., more than 95% of the time), the climate is nonrainy in temperate regions. In addition, attenuation at different frequencies occurs at different levels since it results from distinct physical processes, namely oxygen, water vapor, and clouds. This influence of oxygen, water vapor, and clouds makes it possible to estimate frequency scaling. Due to the very high air attenuation produced by oxygen absorption, the 60 GHz band is unsuitable for clear air frequency scaling (see Figure 2). Attenuation due to gases is calculated using a layer-by-layer approach of ITU-R at each atmospheric layer [18]. The liquid water level is approximated using the method of [19], through the measured data. The attenuation of the cloud is estimated with the ITU-R model [20], which is a solid  
Figure 1: Rain attenuation scaling taxonomy. Note: [4] CCIR: Comité Consultatif International des Radiocommunications, [3] DSD: (rain) raindrop size distribution, [5] SAM: simple atmospheric model, [4] ITU-R: International Telecommunication Union-Radiocommunication Sector. physical basis for both computations of attenuation. The attenuation of the zenithal path can be computed as the total of the gas and cloud attenuation contributions, \(A_{g}\) and \(A_{c}\) of every atmospheric (\(i\) index) layer, as seen in (3):  
\[A_{L}=\sum(A_{g}(i)+A_{c}(i)) \tag{3}\]  
To determine the gaseous attenuation, first, the specific attenuation of gases at each layer needs to be calculated, and later, the total number of layer thicknesses using the ITU-R technique needs to be multiplied [18]. The special attenuation, as shown in (4), comprises contributions from the oxygen and water vapor absorption layers that feature \((S_{j})\) for strength and the \((F_{j})\) shape factor, plus the dry continuum \(N_{\mathrm{D}}\arcsec(f)\)[21]. \[\gamma_{g}=0.1820f\cdot\Big{[}\sum_{j}S_{j}F_{j}+N_{D}^{\prime\prime}(f)\Big{]} \quad(\mathrm{dB/km}) \tag{4}\]  
Cloud attenuation can be calculated by the exact attenuation and thickness of the layer as specified in (5), and the specific attenuation in the cloud layer can be computed by the ITU-R [20] technique. The complete computation procedure is shown in Algorithm 1. \[A_{c}(i)=\gamma_{c}(i)\cdot\Delta h(i) \tag{5}\]  
```
Data: Radiosounding data Temperature \(T(i)\) in C, pressure \(P(i)\) in hPa, and relative humidity \(RH(i)\) in % at different layer heights \(h(i)\) in \(m\). // Due to gas, fog, and cloud
1 Compute specific gas attenuation /* Equation (4) */
2 Compute liquid water content by the [19] method
3 Compute cloud attenuation by the ITU-R [20]
4 Compute gas attenuation for a layer \(\triangle h\)
5 Compute cloud attenuation for a layer \(\triangle h\)
6 Compute total attenuation /* Equation (3) */ // Inonrainy conditions
7 Compute \(A_{L}\) /* Equation (3) */
8 Compute frequency-scaled attenuation \(A_{H}\) /* Equation (6) */
```  
**Algorithm 1**Clear sky frequency scaling [21].