## 3 Results and Discussion
In the M2 environment, both models showed significant improvements over the REL model, which had the best performance compared to the other models. The Modified REL model provided an R\({}^{2}\) of 0.95 and an RMSE of 2.26, whereas the Proposed Piecewise model maintained the same R\({}^{2}\) value and reduced the RMSE to 1.92. This implies a 15% error reduction and shows that the Proposed Piecewise model provides significant superiority in this scenario. In the M3 environment, the R\({}^{2}\) value of the Modified REL model was 0.97, and the RMSE value was 3.87, which shows considerably high accuracy compared to the other models. However, the R\({}^{2}\) value of the Proposed Piecewise model decreased slightly compared with that of the Modified REL and decreased to 0.93. However, the RMSE value decreased to 2.42, indicating a 37% error reduction. However, it has a similar R\({}^{2}\) value compared to the REL model and again improves the error by 39%. These results clearly show that the Proposed Piecewise model offers a significant advantage in reducing error rates in the M3 environment. These improvements provide superior overall performance despite some small decreases in R\({}^{2}\) values. Finally, in the M4 environment, the R\({}^{2}\) value of the Modified REL model is 0.95, and the RMSE value is 2.54. The Proposed Piecewise model provided a similar R\({}^{2}\) value (0.95) but reduced the RMSE value to 1.65, providing an improvement of approximately 35% over Modified REL and 37% over REL. This also implies that the Proposed Piecewise model provides a significant fitting performance with a low error rate in the M4 environment. Considering all the results, the piecewise modeling approach showed better performance than the other evaluated methods, because, according to the Rayleigh roughness criterion, it is stated that the roughness is a dominant effect at close distances to the Tx antenna and should be taken into account, while its effect can be neglected at longer distances [27]. Therefore, considering the data in a piecewise manner was a more accurate modeling approach. If a qualitative evaluation is performed, the visual results presented in Figure 3 clearly demonstrate the performance superiority of the proposed models. It is observed that the REL model represents the data in each scenario better than the other models. However, owing to the parameters added to the Modified REL model, this model showed a higher fit to the measured data. Figure 3a (left side) indicates the fit of various existing models (free-space, log-distance, dual-slope, 2-ray, 3-ray, and REL) to the measured data for the M1 scenario and their comparison with the Modified REL model. In Figure 3a (right side), the Modified REL and the Proposed Piecewise model, which is based on a piecewise approach, are compared, and it is observed that the piecewise approach provides a superior fit to the entire data. The graphs in Figure 3b-d for the M2, M3, and M4 environments, respectively, make the improvements provided by the Proposed Piecewise model even more apparent. In the graph given for the M2 environment (Figure 3b), the Proposed Piecewise model, represented by the red line, shows the closest fit to the measured data and has a lower RMSE value than all other models. In the M3 and M4 environments, it was determined that this model successfully represented the data at short and long distances, significantly reduced the error rates in particular, and significantly increased the accuracy rate at both short and long distances. As a result, both numerical and visual evaluations show that the proposed Modified REL and Proposed Piecewise models provide significant advantages compared to other models used in shore-to-ship communication scenarios and offer high accuracy with lower error rates. In particular, the Proposed Piecewise model offers a more suitable solution for environments, such as shore-to-ship communication. Figure 3: Comparison of Modified REL model with existing models (**left column**), with proposed piecewise model (**right column**).