## 2 Background Study
### Rain Type  
In total, two types of rain, known as stratiform and convective precipitation, exist. The convective rain is heavy; thus, the propagated radio waves attenuated by convective rain are heavily attenuated. Conversely, stratiform rain is comparatively light and comparatively less attenuated. Therefore considering the effects of different rain types can yield better-predicted attenuation. For example, the rain attenuation model in [62] considers stratiform and convective rainfall to predict rain attenuation. The convective type is heavy rain that corresponds to a high rainfall rate and stratiform rain corresponds to light rain and hence low rainfall rate. The structure of the rain cell is also incorporated with the rainfall rate, which is shown in Figure 1.  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Ref.** & **Conversion Techniques** \\ \hline \hline \multirow{3}{*}{[49]} & Using the Rain rate \(\Gamma_{\tau}(R)\), where \(\Gamma_{\tau}(R)=P_{1-\min}(R)/P_{\tau-\min}(R)\), the model can convert rain between 1- and \(\tau\)-min, where \(P_{1-\min}\) is the probability that the mean rainfall rate is exceeded for a 1 min accumulation time, and \(P_{\tau-\min}\) is the probability that the mean rainfall rate is exceeded for \(\tau\) min accumulation time. \\ \hline \hline \multirow{3}{*}{[50]} & Using cumulative rainfall distributions, the model can convert rain between 1- and \(\tau\)-min. \\ \cline{2-3}  & Using the conversion factor \(R_{1}(P)/R_{60}(P)=CF_{60}\), where \((CF_{60}=aP^{b}+ce^{(d,P)})\) the model can convert 60 min to a 1 min integration time rain rate, where \(CF_{60}\) is the conversion factor, \(a\), \(b\), \(c\), \(d\) are constants, and \(P\) is the probability of rainfall rate exceedance within 0.001\% \(\leq P\leq\) 1%. It can also be used to convert between different rain rates [52]. \\ \hline \hline \multirow{3}{*}{[53]} & Using the equation \((P_{1}=1.71\cdot P_{\tau}\cdot 10^{(-0.242\cdot\exp(\tau/2428))})\), \(\tau\) min to 1 min conversion. \\ \hline \hline \multirow{3}{*}{[54]} & Using the equation \(R_{1-\min}=(R_{\tau-\min})^{d}\), where \(d=0.987(\tau)^{0.061}\) the model can convert the rain rate from \(\tau\) min to 1 min. \\ \cline{2-3}  & Using the equation, \(log[R_{1-\min}(P)]=\alpha_{r}\cdot log[R_{r-\min}(P)]\), where \(\alpha_{r}\): regression component determined statistically, and \(5.0\%\leq P\leq 0.01\%\). \\ \hline \hline \multirow{3}{*}{[56]} & In the absence of accurate long-term rainfall data, this method takes the percent of time exceedance, latitude, and longitude as input to generate a 1 min integration time rain rate. \\ \cline{2-3}  & The model simply calculates the rain rate \(R=60\cdot TR_{T}/T\), where \(TR_{T}\): maximum rainfall in mm for time interval \(T\) min. \\ \hline \multirow{3}{*}{[58]} & \(P_{1}(R)=(a_{1}/a_{t})R^{(b-h_{t})}\exp[(u_{t}-u_{1})R]P_{t}(R)\), \(R\): rain rate, \(u\): empirical constant, \(a\), \(b\): depending on the location and integration time of the rain gauge. \\ \cline{2-3}  & \(R_{0.01\%}=\frac{\ln(0.036\frac{\mu}{\mu})}{0.05}\) where \(M\) is the average annual rainfall (mm), and \(T\) is the number of hours in the year during which rain rates exceed \(R\) (mm/h). \\ \hline \multirow{3}{*}{[60]} & \(R_{p}=a_{p}M^{b_{p}}\beta^{c_{p}}\) where \(p\) is the percentage of the time, \(M\) is the total annual rainfall accumulation, \(a_{p}\), \(b_{p}\) and \(c_{p}\) are constants, which can be derived from \(x=log(P)\), and \(\beta\) is the thunderstorm ratio (\(\beta=M_{1}/M_{1}+M_{2}\)), where \(M_{1}\) is the rain rate due to a thunderstorm and \(M_{2}\) is the rain rate without a thunderstorm. \\ \hline \multirow{3}{*}{[61]} & \(R_{0.001\text{ initial }}=23.50390R^{0.27896}\) and \(\beta^{0.34162}\)\(R_{0.01\text{ initial }}=3.69786R^{0.46613}\beta^{0.43482}\) where \(R\) is the rain rate in mm/h and \(\beta\) is the regional climatic parameter. \\ \hline \hline \end{tabular}
\end{table}
Table 5: Rain rate conversion techniques.