# Impact of Weather Factors on Unmanned Aerial Vehicles' Wireless Communications
## 2 Methodology
### Mathematical Models  
In the context of UAV communications, slant path propagation represents a more generalized case of signal propagation. The variability in temperature, pressure, and water vapor concentration due to altitude/height changes necessitates that for slant path propagation, attenuation must be computed over multiple path segments such that each segment can be assumed to have constant values for these variables. Both linear and nonlinear path segmentation methodologies may be used for this investigation. While linear path segmentation approach is adequately suitable for communications associated with short distances (<2 km), as applicable in this case, the nonlinear path segmentation  
Figure 1: Atmospheric phenomena on the path of signal propagation. approach described in [6] is more appropriate for very long-distance communications, primarily involving satellites. Figure 2 depicts linearly and non-linearly segmented path models for the computation of attenuation resulting from atmospheric weather conditions. Figure 2a shows the linear model where the UAV height is split into \(N\) uniformly distributed equal length segments. Figure 2b illustrates the non-linear model. In this model, the height is split into \(M\) segments of non-linear lengths, per [6]. Both models follow the approach of piecewise computation of attenuation for the associated propagation path segments over distance \(d\). Effective attenuation for the entire path of propagation is obtained by summation of piecewise computed attenuations. Accordingly, the generic expression for the total attenuation along the slant path is given by  
\[A_{\text{slant}}\ =\frac{1}{\sin(\beta)}\sum_{i=1}^{i=N,M}\delta_{i} \tag{1}\]  
where \(\beta\) is the angle of elevation, \(\delta_{i}\) is the path length corresponding to the \(i_{th}\) height segment, \(\gamma_{i}\) is the corresponding attenuation, and \(N\), and \(M\) correspond to the highest values of the path segment index for linearly and non-linearly segmented path models, respectively. We validated our decision to select the simpler linearly segmented path model by comparing the attenuation results obtained from the two models and finding a negligible difference between the two. Figure 3 illustrates the comparison of atmospheric attenuation between a linear and a non-linear atmospheric model for a propagation distance of 2000 m (6500 ft), UAV height of 400 m, and carrier frequencies of 1, 5, and 10 GHz, at standard atmospheric conditions. Figure 3: Comparison of atmospheric attenuation for linear and nonlinear path segmentations: (**a**) represents the attenuation corresponding to the linear model, and (**b**) illustrates the attenuation corresponding to the non-linear model, operating at standard atmospheric conditions: elevation at mean-sea level, \(T=25\) °C, \(p=1\) Atm, liquid water density \(=7.5\) g/m\({}^{3}\). Figure 2: Illustration of path segmentation approaches: (**a**) demonstrates linear segmentation with \(N\) path segments of equal lengths, and (**b**) illustrates nonlinear segments with \(M\) path segments of nonlinearly increasing lengths. Figure 3a represents the attenuation resulting from a linearly segmented model, whereas Figure 3b depicts the results obtained from the non-linear model. A very small difference of 0.0027 dB at the highest points of attenuation between the two models suggests that the use of the linear model is closely matched with the non-linear model over small distances. The attenuation \(\gamma_{i}\) is scaled according to the specific attenuation, which represents the attenuation for a path length of 1 km. Further, the specific attenuation is defined by different equations for gases, clouds/fog, and rain due to the variations in their attenuation characteristics [6; 7; 8]. Additionally, atmospheric parameters, such as temperature, pressure and humidity, which vary due to variations in height, affect the attenuation.