# Analysis of the Accessibility of the Swinoujscie-Szczecin Fairway for Deep-Draught Ships
## 4 Impact of \(\Delta\)h on Vessel Waiting--Analysis in Swinoujscie  
In this study, two modelling approaches were used to assess vessel accessibility: deterministic and probabilistic. The deterministic model evaluates each situation based on fixed parameters: vessel draught, dynamic vertical margin (\(\Delta\)h), and observed water level. A vessel is considered to experience a delay if the water level drop \(\Delta\)h(t) exceeds the allowable threshold \(\Delta\)h.  
The probabilistic model applies a Monte Carlo simulation to estimate the probability of delays under variable hydrological conditions. The simulation involves:  
* Random sampling of vessel entry times from a uniform distribution;
* Use of hourly water level data to calculate \(\Delta\)h(t) for each vessel;
* Comparing each sampled \(\Delta\)h(t) with the fixed threshold \(\Delta\)h;
* Repeating the process for 1000 vessels (\(n\) = 1000);
* Computing the proportion of vessels that must wait as the estimated probability of delay. This approach allows for quantification of navigational risk due to water level variability. To assess the impact of the permissible reduction in water level (\(\Delta\)h) on the accessibility of the Swinoujscie-Szczecin fairway for deep-draught ships, an analysis was conducted based on hourly data from the water gauge station in Swinoujscie from 2008 to 2022. The fairway depth was assumed to be 12.5 m, the ship's draught 11.5 m, and the reference level in Amsterdam 500 cm. Variable \(\Delta\)h values of 15, 20, 25, 30, and 35 cm were used in the calculations. The critical water level was considered to be the level at which the under-keel clearance (UKC) falls below the permissible \(\Delta\)h value--in such cases, the ship \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Water State** & \multicolumn{2}{c}{**465**} & \multicolumn{2}{c}{**470**} & \multicolumn{2}{c}{**475**} \\ \hline  & **Avg.** & **Duation** & **Expected** & **Avg.** & **Avg.** & **Duation** & **Expected** & **Avg.** & **Avg.** & **Duation** & **Expected** \\  & **Drops/Year** & **Duation** & **Number/Year** & **Drops/Year** & **Duation** & **[h]** & **Number/Year** & **Drops/Year** & **Duation** & **Number/Year** \\ \hline Swinoujscie & 26.13 & 7.31 & 2.18 & 37.47 & 7.98 & 3.41 & 55.67 & 8.30 & 5.28 \\ \hline Trzbeüz & 4.47 & 10.15 & 0.52 & 10.20 & 10.13 & 1.18 & 13.40 & 14.65 & 2.24 \\ \hline Szczecin & 1.6 & 13.79 & 0.00 & 2.60 & 18.64 & 0.00 & 5.67 & 17.96 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the water level verification study in the Swinoujscie–Szczecin fairway. cannot continue its movement along the fairway and must wait for conditions to improve. Figures 15-17 show the frequency and duration of water level drops below 475, 470, and 465 cm. Deterministic calculations showed that the average number of waiting events per year (PdH) increases non-linearly with increasing \(\Delta\)h--from about 0.05 for \(\Delta\)h = 15 cm to 0.16 for \(\Delta\)h = 35 cm. Although these values are low, the trend confirms that a reduction in the reserve under the keel results in a higher risk of reduced track availability. A complementary Monte Carlo simulation was carried out, generating 1000 vessels with a random draught between 11.00 and 12.00 m and random moments of entry into the  
Figure 16: Duration of water level falls below 470 cm. Figure 17: Duration of water level falls below 465 cm. Figure 15: Duration of water level falls below 475 cm. track during the study period. The results showed that, at \(\Delta\)h = 25 cm, only single vessels (e.g., 1-2 out of 1000) encountered water levels that prevented passage. This is consistent with the histogram of water levels, which shows that values below the critical threshold (e.g., 425 cm) are relatively rare, confirming the correctness of selecting \(\Delta\)h = 25 cm as a compromise value. The reliability of model-based estimation of water levels in data-sparse or uncertain measurement conditions is crucial for robust planning of fairway accessibility.