## 5 Results  
Now we study the performance of the proposed scheme under the presence of shadow zones via numerical evaluations. We distinguish between shallow and deep water. The five different channel models considered appear in Section 4. The parameters used in our evaluation are listed in Table 1. They follow the architecture of the commercial off-the-shelf underwater acoustic modem (LinkQuest) UWM3000 for shallow and UWM10000 for deep water [22].  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline
**Sea depth \(H\)** & Shallow water: 100 m \\  & Deep water: 5,000 m \\  & Shallow water: 16,000 x 16,000 \(\times\) 100 m\({}^{3}\) \\
**Volume** & Deep water: \\  & 40,000 \(\times\) 40,000 \(\times\) 5,000 m\({}^{3}\) \\
**Number of sensors** & 25 \\
**Packet size** & 238 bytes \\
**Data rate** & 6 Kbps \\ \(T\) & 15 \({}^{\circ}\)C \\ \(pH\) & 8 \\ \(S\) & 35 ppt \\
**Transmission power \(P_{t}\)** & Shallow water: 12 W \\  & Deep water: 40 W \\
**Noise level** & 47.69 dB \\
**Speed of sound** & 1500 m/s \\
**Sensor speed** & 0.5 m/s \\
**Movement power \(P_{Bw}\)** & 10 W \\ \(\Lambda\) & 0.01 \\  & Shallow water: 5,000 m \\ \(R_{MAX}\) & Deep water: 11,000 m \\ \(E_{n}\) & 1,500 J \\ \(TL_{n}\) & Shallow water: 112.5 dB \\  & Deep water: 129 dB \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameter Values.  
The whole seab is divided into a 2D square grid of equal sizes \(r\) = 4,000m for shallow water and \(r\) = 10,000 m for deep water as shown in Figure 6. The sensor nodes are located in a square grid floating at different depths. 25 sensor nodes are deployed in a 3D volume of 16,000 \(\times\) 16,000 \(\times\) 100 m\({}^{3}\) for shallow water and of 40,000 \(\times\) 40,000 \(\times\) 5,000 m\({}^{3}\) for deep water. In shallow water, sensor nodes are located following a hierarchical structure at the depth levels of 25, 50, 75 and 90 m. In deep water, we study the communication between sensor nodes located following a hierarchical structure at the depth levels of 300, 350, 400 and 450 m.  
We consider realistic cases where shadow zones can influence the propagation of sensors. Figures 7, 8 and 9 show examples of the propagation paths for the sensor nodes in shallow water. The sound speed profile is based on the measurements conducted at the coast of Kauai, Hawaii [6], with a water depth of 100 m and a frequency of 1 kHz. The rays shown are for launch angles between -20\({}^{\circ}\) and 20\({}^{\circ}\) with a 1\({}^{\circ}\) increment. The corresponding ray traces in Figure 7 for a source depth of 90 m and a receiver depth of 75 m, in Figure 8 for a source depth of 75 m and a receiver depth of 50 m and in Figure 9 for a source depth of 50 m and a receiver depth of 25 m are plotted. Shadow zones appear at ranges around 3 Kms. In our simulations we consider a 2D square grid of equal sizes \(r\) = 4,000 m because at these ranges it is possible to appreciate the shadow zone effects.  
Figure 6: 2D Square grid.  
Figure 8: Corresponding ray trace for a source depth of 75 m.  
Figure 7: Corresponding ray trace for a source depth of 90 m.  
Figure 9: Corresponding ray trace for a source depth of 50 m.