## 5 Simulation Results  
We use the real ocean temperature data provided by NASA ([[https://www.nasa.gov/specials/ocean-worlds](https://www.nasa.gov/specials/ocean-worlds)]([https://www.nasa.gov/specials/ocean-worlds](https://www.nasa.gov/specials/ocean-worlds))) to test our algorithm against the two cutting-edge methods. Note that the sensor network they deploy to monitor the environment is huge and we only choose 1000 nodes from this network which are deployed in a 3-D undersea region divided into \(10\times 10\times 10\) grids. The size of the area is 18.5 km \(\times\) 14.5 km \(\times\) 0.8 km. We compare our method with other two cutting edge method which also applies CS into routing. The method introduced in [31] for 3D UWSN is named as \"DRMCS\" which is the abbreviation of \"distributed random multi-hop compressive sensing\". The other method is called \"ICCS\" following its name in [29] and later on in [30]. We extend it to 3D scenario by changing the clustering and routing methods to 3D protocol through replacing the 2D distance \((x,y)\) to 3D distance \((x,y,z)\). The parameters we set for the energy consumption model in Section 4.1 are listed in Table 1 according to [43]. Before the whole simulations, we firstly select the appropriate value of parameter \(\epsilon\). It is impossible for us to obtain the signal \(\mathbf{z}\) before the algorithm is run. To solve this problem, we do some preparatory experiments to decide an appropriate \(\epsilon\). In the first five rounds, we set \(\epsilon=0.9\), run the experiments once, and then we obtain the reconstructed signal \(\hat{\mathbf{z}}\). The reconstructed signal \(\hat{\mathbf{z}}\) is regarded as the approximation of the original signal \(\mathbf{z}\) in order to compute the reconstruction error in the following simulations. That is, afterwards we ran the first five rounds with different \(\epsilon\) ranging from 0.2 to 0.8, respectively. The average consuming energy and the reconstruction error are compared. For example, the results of round 1, 3 and 5 are shown in Table 2. Considering the reconstruction error and energy consumption state integrally, we found that in our algorithm \(\epsilon=0.4\) is the most suitable. As a result, for the rest rounds, \(\epsilon\) is set to be 0.4. All experiments were performed on MATLAB 2018b and a computer with intel(R) Core(TM) i7-8700K 2.50 GHz CPU, 16.00 GB RAM and the Windows 10 system. \begin{table}
\begin{tabular}{c c} \hline \hline
**Energy Consumption Parameter** & **Values** \\ \hline \(\eta\) & 0.5 \\ \(\alpha\) (\(\text{bps}/\text{Hz}\)) & 0.5 \\ \(k\) & 1.5 \\ \(SNR_{tgt}\) (dB) & 8 \\ \(P_{r}\) (W) & 2 \\ \(b\) (dB re kHz) & 14.39 \\ \(\beta\) (dB re kHz/km) & \(-0.55\) \\ \(R_{c}\) (km) & 3.5 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Energy Consumption Parameters. The more balanced condition and less energy-consuming phenomenon of our scheme can also be proved in Figure 9, which shows the remaining living nodes of the network in each round. From Figure 9, we can observe that by our algorithm, the first dead node appears much later. The proposed algorithm has its first dead node at round more than 100 while the other algorithms has its first dead node at about round 70. Such a fact indicates that the proposed two-tier protocol consumes less energy each round as well as consumes energy more equally for each node of the whole network. The improvement attributes to the fact that in order to better balance the whole network, we add a factor named \"network-balancing\" in the particles' fitness value calculation. Considering that the nodes closer to the sink burden heavier transmission load and hence are easier to die, we put energy consumption ratios of inner and outer layers into consideration. Reducing the ratio can avoid repeatedly choosing inner layer nodes and balance the network energy consumption better. In order to observe the impact of node density on the network performance, we fix the total node number as 1000 and vary the volume of the area where these nodes are deployed.