# LESS: Link Estimation with Sparse Sampling in Intertidal WSNs
## 3 Problem Overview and Motivation
### Network Dynamics in Intertidal WSN Systems  
Network dynamics such as link quality, topology and routing path changes are revealed in many WSN systems including GreenOrbs [34], SoilScape [35], OASIS [36], etc. To have a deep understanding of the dynamic characteristics in intertidal WSNs, we deployed two WSN systems in Zhoushan, China (\(29^{\circ}56^{\prime}43^{\prime\prime}\) N, \(122^{\circ}5^{\prime}10^{\prime\prime}\) E, Figure 1a) and in George Town, US (\(33^{\circ}22^{\prime}37^{\prime\prime}\) N, \(79^{\circ}17^{\prime}40^{\prime\prime}\) W, Figure 1b) to monitor the intertidal areas. The system details are presented in Section 6. The link qualities in those two systems are heavily impacted by the environments, i.e., the tide movement. The sensors are submerged in the water at a high-tide, and emerged from the water at a low-tide. In addition, sensor nodes are often suddenly lapped by waves. The intertidal environment causes link qualities to change frequently and imposes severe challenges. We quantify the dynamics of the two systems with two 24-h datasets in Figure 2 from three metrics. * **Link quality change ratio:** Nodes evaluate link quality between neighbors in each cycle, and we compare the link quality change between two continuous cycles. The link quality change ratio is defined as: \[\textit{Link quality change ratio}=\frac{|link\textit{ quality}_{ab}(t+1)-link\textit{quality}_{ab}(t)|}{link\textit{quality}_{ab}(t)}*100\%\] (1) where \(link\textit{quality}_{ab}(t)\) and \(link\textit{quality}_{ab}(t+1)\) represent the link quality between node \(a\) and node \(b\) at cycle \(t\), and cycle \(t+1\). * **Topology change ratio:** During one cycle, any occurrence of new links or disappearance of existing links is defined as a topology change. The topology change ratio is calculated as: \[\textit{Topology change ratio}=\frac{\#\textit{of cycles with topology changes}}{\#\textit{of total cycles}}*100\%\] (2)
* **Routing path change ratio:** Similarly, any hop change along a routing path from a source to a destination is called a routing path change in one cycle. The routing path change ratio can be represented as: \[\textit{Routing path change ratio}=\frac{\#\textit{of cycles with routing path changes}}{\#\textit{of total cycles}}*100\%\] (3)  
Figure 1: Wireless sensor networks in intertidal zones. We deploy 27 nodes in Zhoushan system and seven in George Town system. Figure 2b illustrates the topology and routing path changes ratio in George Town system and Figure 2c demonstrates the case in Zhoushan system, and CTP [37] is utilized as the routing protocol. Figure 2a reveals the link quality change of both George Town system and Zhoushan system. When all sensors nodes are completely submerged under water, no links exist and the change ratio is 0. Therefore, we only take the above-water case into consideration and have the following important findings in Figure 2.  
First, the link quality change ratio in the George Town system is higher than that in the Zhoushan system which is shown in Figure 2a. The link quality change ratios of over 60% links in the Zhoushan system are smaller than 20%, while this value is 29.6% in the George Town system. The reason is that the deployment environments in George Town and Zhoushan are different. For example, the tide level in George Town grows with fierce sea waves while the tide level in Zhoushan growing gradually and peacefully. We also find the routing and topology changes in George Town are more remarkable than that in Zhoushan, which implies that link quality change has fundamental impact upon both topology and routing paths. Second, for both systems, the topology change is more significant than the routing path change. For example, in George Town system, the topology has an average change ratio of 35% while the routing path is only 15% in average. This indicates that topology changes do not necessarily cause routing path changes, which allows us to use partial or sparse topology information yet still obtain accurate routing paths (Section 4).