## 1 Introduction
Furthermore, the communication energy consumption still has ample room for improvement. Therefore, we proposed a node depth adjustment deployment algorithm based on two-dimensional (2D) convex hull and spanning tree (NDACS). A sink node is fixed at the center of the monitored water surface, and all of the nodes are scattered on the monitored water surface uniformly and randomly and are in a sleep state. First, the sink node sends control information to activate three nodes according to the node ID from small to large and forms a very simple 2D convex hull (triangle). Thereafter, it uses the geometric characteristics of the 2D convex hull and empty circle to minimize the 2D plane network coverage overlaps as its optimization goal. The optimal sleep node that needs be activated is found, whereas the 2D coverage efficiency could be greatly improved. When the coverage threshold of the first layer is reached, the algorithm forms the best fully 2D node activation convex hull. At the same time, most of the nodes are in a sleep state to save overall network energy. Thereafter, the sink node acts as a root node of all active nodes on the 2D convex hull and gradually forms a small spanning tree. Eventually, a new spanning forest is formed through the adjustable communication radius model in the 2D water surface. The child nodes closer to the sink node have greater probability of data transmission and relay and have to consume more energy. Therefore, for the network to be able to continuously operate stably, more nodes must be deployed near the sink node, in which more subtrees are found around the sink node, and the size of surrounding subtrees should be smaller. We adopt the time marker to define the 2D network level and make the interlayer neighbor intersection be as close to the parent node of the spanning tree as possible, increasing the node deployment density around the sink node and balancing network energy consumption. Finally, the active node is used as the parent node of its neighbor sleep node, and the depth-adjustment strategy based on the time marker is used to achieve the 3D overall network coverage. The simulation results show that compared to the typical depth-adjustment deployment algorithm (VBDA), the NDACS algorithm can maintain full network connectivity with a high network coverage rate while reducing communication energy consumption with better network reliability during deployment. Compared with existing depth-adjustment deployment algorithms, our proposed algorithm contributes through the following aspects:  
1. The geometric characteristics of the 2D convex hull and empty circle is used to minimize the 2D plane network coverage overlaps, with a minimum number of activated nodes to meet the requirement of the first layer of the network deployment. 2. The activation scheduling mechanism is adopted to reduce the energy consumption of communication between nodes. 3 The adjustable communication radius model is established to ensure that all active nodes have full network connectivity in the first layer. In addition, in the process of depth adjustment, the communication connection is guaranteed between the parent and its child nodes in real time. 4. Depth adjustment is based on the time marker, adjacent time marker neighbor nodes set is dominated by its parent node, and it is a perfect approach to balance the density of node deployment. When the set is empty, the neighbor nodes intersect to execute depth-adjustment assignment, ensuring that the network deployment performance of near water bottom is relatively good and that network operation is more reliable. Overall, our work optimizes network coverage rate under the premise of full network connectivity, reducing the energy consumption of communication. The rest of this paper is organized as follows: in Section 2, the related works about the node deployment problem in three categories algorithm for UWSNs. In Section 3, the models of UWSNs and related definitions are described.