# Opportunistic Weather Sensing by Smart City Wireless Communication Networks
## 2 OISAC of Weather--Current Situation
#### Commercial Microwave and mmWave Links  
The OISAC of the weather using wireless links as sensors is based on the fact that the attenuation levels of each of the links are being logged (usually automatically by the network management systems, for network management purposes), and can be converted into a time series of, e.g., rain-intensity values, as if it was reported via virtual rain gauges, based on the relationship between the rain-induced attenuation and the actual rainfall. In general, the relationship between the channel rain-induced attenuation and the rain intensity is usually modeled by an empirical power law. It is an approximation that gives a reasonably accurate relationship for links of the length of hundreds of meters and above (up to few kilometers) in micro and mmWave frequencies. This power-law is given by [32]  
\[\mathbf{A}=\mathbf{a}\mathbf{R}^{\mathbf{b}} \tag{1}\]  
where \(\mathbf{A}\) is the rain-induced attenuation per kilometer (in dB/km), \(\mathbf{\underline{R}}\) (in mm/h) is the path-averaged instantaneous rain rate along the link, and \(\{\mathbf{a},\mathbf{b}\}\) are coefficients whose values depend on the link's frequency, polarization, and on the local drop size distribution (i.e., the local climatological conditions) of the rain [31]. That is, given the measured attenuation in a CML and the coefficients \(\{\mathbf{a},\mathbf{b}\}\) that were derived for the various areas, \(\mathbf{\underline{R}}\) can be directly extracted and each CML can be transformed into a virtual rain gauge. Moreover, in [33] it was proposed that, given several CMLs in an area, each CML can be transformed into several virtual rain gauges. It is worth noting that the power law of Equation (1) approximates the full physical description of the interaction between water droplets and the signal, which is based mainly on Mie scattering (see [34] for the full development of the formula). The coefficients \(\{\mathbf{a},\mathbf{b}\}\), although set empirically [31], are known to produce accurate CML-based rain estimates in many parts of the world, including Africa [12], Europe (Germany [21; 23], Sweden [35], the Netherlands [22], the Czech Republic [20]), and the Middle East (Israel [30; 33]) among others. In practical use, as several factors can cause attenuation to wireless microwave signals, as illustrated in Figure 2, the first step in this model-driven approach is to isolate the rain-induced attenuation. The total attenuation of the wireless signal at a line-of-sight link of length L (in km) at time t, \(\mathbf{A}_{T}(\mathbf{t},\mathbf{L})\) (_in dB_) can be expressed as follows [36]:  
\[\mathbf{A}_{T}(\mathbf{t},\mathbf{L})=\mathbf{A}_{0}(\mathbf{L})+\mathbf{A}_{m}(\mathbf{t},\mathbf{L})+\mathbf{A} _{p}(\mathbf{t},\mathbf{L})+\mathbf{A}_{w}(\mathbf{t})+\mathbf{A}_{n}(\mathbf{t}) \tag{2}\]  
where \(\mathbf{A}_{0}(L)\) is the link path loss, \(\mathbf{A}_{m}(\mathbf{t},\mathbf{L})\) is the contribution of moisture (water vapor), \(\mathbf{A}_{p}(\mathbf{t},\mathbf{L})\) is a component which represents the contribution of precipitation (if exists), \(\mathbf{A}_{w}(\mathbf{t})\) is the contribution of the wet antenna effect, and \(\mathbf{A}_{n}(\mathbf{t})\) represents all the other sources, defined as \"noise\", such as the obstacles that may be present at the propagation channel (e.g., birds [37]), and the measurement noise. For simplicity, in the sequel, we assume that precipitation is pure rain, so the term \(\mathbf{A}_{p}(\mathbf{t},\mathbf{L})\equiv\mathbf{A}_{L}(\mathbf{t})\) represents the rain induced attenuation. Extracting the rain-induced attenuation from the signal level measurements provided by the cellular operators is far from being trivial. First, \(\mathbf{A}_{T}(\mathbf{t},\mathbf{L})\) in (2) is not directly measured and is to be extracted from the available measurements of the transmitted (Tx) and the received (Rx) signals levels, which are usually quantized and are not synchronized.