## 3 Results and Discussion  
In this study, propagation modeling was performed for shore-to-ship communication in the Black Sea, an inland sea in Turkiye, and as a result, a Modified REL and Piecewise path loss model was proposed. First, for the four different scenarios, shore-to-ship communication channel measurements were performed at 5.6 GHz along the Black Sea coast in Trabzon, Turkiye. These measurements were performed in four different scenarios, M1, M2, M3, and M4, according to the sea roughness, weather conditions, and Tx heights. While the M1, M2, and M3 scenarios represent changes in various weather and sea conditions, the M4 measurement was performed at different Tx heights under similar weather and sea conditions to the M3 measurement, focusing on the effect of this change on path loss. The maximum measurement distances vary in scenarios M1, M2, and M3 due to differences in weather and sea conditions, and in scenario M4 due to different transmitter antenna height. In this context, first, the performances of the well-known free-space, log-distance, dual-slope, 2-ray, 3-ray, and REL models, which are frequently used in the literature for shore-to-ship communication, are presented comparatively for four different measurement scenarios, as shown qualitatively in Figure 3 and quantitatively in Table 4. R2 and RMSE metrics were used to evaluate the fit of the models to the measured data. It can be seen that the proposed Modified REL and Piecewise models offer significant improvements compared to the existing models; in particular, the Proposed Piecewise model significantly reduced the error rates (RMSE) and increased the overall accuracy. The main contribution of this study is the development of a Modified REL model by adding the estimated best Rx height and the varying paths and gains of the direct and reflected waves as additional parameters according to the data to the calculation of the classical REL model, which provides more successful results than other models and a more realistic approach. Then, it was determined that the Modified REL represented the data well up to a certain distance (\(d_{break}\) distance), but after this distance, it was in the log-distance pattern rather than the characteristic \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**M1**} & \multicolumn{2}{c}{**M2**} & \multicolumn{2}{c}{**M3**} & \multicolumn{2}{c}{**M4**} \\ \cline{2-7}
**Models** & **R2** & **RMSE** & **R2** & **RMSE** & **R2** & **RMSE** & **R2** & **RMSE** \\ \hline Free Space & 0.88 & 3.11 & 0.90 & 3.50 & 0.88 & 5.72 & 0.82 & 5.72 \\ Log-Distance & 0.89 & 3.09 & 0.90 & 2.45 & 0.88 & 2.60 & 0.82 & 3.01 \\ Dual-Slope & 0.88 & 3.11 & 0.91 & 2.36 & 0.89 & 2.59 & 0.81 & 2.95 \\
2-Ray & 0.62 & 6.43 & 0.76 & 4.24 & 0.89 & 4.32 & 0.86 & 3.31 \\
3-Ray & 0.88 & 7.37 & 0.89 & 4.51 & 0.88 & 2.93 & 0.82 & 3.90 \\ REL & 0.91 & 2.79 & 0.95 & 2.34 & 0.94 & 3.97 & 0.93 & 2.62 \\ Modified REL & 0.92 & 2.72 & 0.95 & 2.26 & 0.97 & 3.87 & 0.95 & 2.54 \\ Proposed Piecewise & 0.92 & 2.68 & 0.95 & 1.92 & 0.93 & 2.42 & 0.95 & 1.65 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance comparisons of proposed model with existing models, RMSE in dB. of this model. For this reason, a piecewise model based on a piecewise analysis of the data was proposed, and a performance comparison was made with other models for each scenario. In this study, the performance results of our proposed Modified REL and Proposed Piecewise models were examined in detail, and both visual and numerical evaluations demonstrated the superiority and effectiveness of the proposed approaches. In scenario M1, the Modified REL and Proposed Piecewise models performed better than the other models. The Modified REL model provided a good fit to the measured data with an R\({}^{2}\) of 0.92 and an RMSE of 2.72. However, the Proposed Piecewise model exhibited the best performance with a lower RMSE value (2.68), despite achieving a similar R\({}^{2}\) value (0.92).