### Modified Rel Model and Proposed Piecewise Approach
\(p\) and \(\alpha\) parameters are given as follows:  
\[p=\frac{2}{\sqrt{3}}\sqrt{a_{e}(h_{t}+h_{r})+\frac{G^{2}}{4}},\quad\alpha=\cos ^{-1}\!\left(\frac{2a_{e}(h_{t}-h_{r})G}{p^{3}}\right) \tag{4}\]  
The \(S\) parameter reflects the shadowing effects of the signal, which becomes important, especially in environments with obstacles and surface roughness, compared to the wavelength, and is expressed as:  
\[S=\frac{1-0.5\mathrm{erfc}\!\left(\frac{\cot\theta_{i}}{\sqrt{2}\phi_{0}} \right)}{1+\Lambda(\theta_{i},\beta_{0})},\quad\Lambda(\theta_{i},\beta_{0})= \frac{1}{2}\Bigg{[}\frac{\sqrt{2}\beta_{0}}{\sqrt{\pi}\cot\theta_{i}}\exp\! \left(-\frac{\cot^{2}\theta_{i}}{2\beta_{0}^{2}}\right)-\mathrm{erfc}\!\left( \frac{\cot\theta_{i}}{\sqrt{2}\beta_{0}}\right)\Bigg{]} \tag{5}\]  
where \(\theta_{i}\) represents the incidence angle (90-\(\psi\)), and \(\beta_{0}\) represents the RMS surface slope values. The model obtained by adding the Div (divergence) parameter and \(L_{Diff}\) (diffraction loss) to the free-space and 2-ray path loss models, which are generally accepted as PEL in the literature, and considering the curvature of the earth, is called the REL model [1]. However, in the existing studies, the assumptions \(G_{ref}\cong G_{dir}\) and \(D\cong R\) (\(\Delta d\
eq 0\)) were generally made using the REL model in (1), and were simplified as \(F_{REL}\):  
\[F_{REL}=\left|1+\Gamma_{eff}\cdot Div\cdot S\cdot e^{-jk\Delta d}\right| \tag{6}\]  
Although the simplified REL model generally provides better results than other models in shore-to-ship communication environments, it may be insufficient to represent some effects that occur due to the marine environment's nature. Therefore, instead of \(F_{REL}\), which is widely used in the literature for a simplified REL model, a Modified REL model was proposed based on generalized \(F\). Here, in addition to the roughness parameters, the total gains in the direct wave direction and reflected wave direction at the Tx and Rx (\(G_{ref}\
eq G_{dir}\)) and the path taken by the direct wave and the path taken by the reflected wave (\(D\
eq R\)) were not considered as equal, unlike \(F_{REL}\). Consequently, the gain values that vary as a function of the antenna pattern which depends on the antenna height and grazing angle were also taken into account in calculations. In addition, instead of using a fixed \(h_{r}\) value, the best \(h_{r}\) value estimated for each measurement scenario was considered, \(F_{modifiedREL}\) was developed, and a Modified REL model was obtained. Because rapid changes cannot be observed enough in the radio channel in an open-sea environment, one of the most important effects in this environment is the change in the sea wave height. When the propagation environment is considered, \(h_{r}\) will be variable during the communication period depending on the changes in the ship movements caused by the sea wave [2]. These changes in antenna heights cause a horizontal shifting of the loss spikes of the RSSI signal obtained at the Rx [17]. Therefore, an examination was performed at the fixed Rx antenna height (\(h_{r}\) = 3.5 m) determined in still water within the port relative to the sea surface and the change in the RSSI value at the Rx was observed. Because the Tx antenna assembly was on land and fixed, an evaluation was performed only for the Rx antenna height. To reveal the effect of the antenna change on the RSSI at the Rx and to increase the performance, the most suitable Rx antenna height value (\(h_{rbest}\)) corresponding to the lowest RMSE was calculated. Here, \(h_{r}\) was optimized to increase the accuracy of the model. The \(h_{rbest}\) value was determined for each scenario based on various tests and measurements. Optimizing \(h_{r}\) minimizes signal loss and maximizes the power of the reflected signal. Thus, the antenna gains and reflection effects were calculated most accurately. Therefore, the model obtained by adding the \(h_{rbest}\) parameter provided higher accuracy, particularly for highly reflective environments.