## 1 Introduction  
Underwater wireless sensor networks (UWSNs) consist of many underwater wireless sensor nodes distributed within the marine environment, which support a wide variety of applications such as surveillance, navigation, data acquisition, resource exploration, and disaster prevention [1; 2; 3]. Each sensor node of UWSNs is equipped with an acoustic modem because it uses acoustic signals to communicate with each other [4]. These nodes are capable of forming a network without any infrastructure. The responsibility of the sensor nodes is to monitor the underwater environment such as the temperature, and send the collected data to a sink node (SN) through a single hop or multiple hops [5]. The SN, located on the sea surface, has the ability to receive the data from underwater sensor nodes through acoustic signals and send the received data to terrestrial network devices through radio signals [6]. In the underwater environment, the radio signals face the absorption problem and attenuate quickly [7]. Hence, they are not suitable for long-distance underwater communications. The sound wave is adopted during underwater communications because it is less affected by attenuation, scattering, as well as absorption loss [6]. The acoustic signals propagate slowly, which causes the high propagation delay [8]. What is more, there are other drawbacks of the underwater acoustic channel, such as low bandwidth, as well as high error rate [9]. Therefore, it consumes lots of energy to successfully transmit data packets in UWSNs and keep the good performance of UWSNs. Furthermore, the sensor nodes have restrained energy, and it is not easy to recharge or redistribute them [10]. Therefore, the energy consumption and the network lifetime are major concerns in UWSNs [11]. There are some energy-efficient routing approaches in terrestrial wireless sensor networks (TWSNs), which could not be directly adopted by UWSNs because UWSNs employ acoustic signals while TWSNs use radio signals to send data [12]. Moreover, two-dimensional network models are usually employed in TWSNs, whereas UWSNs often use three-dimensional network models, which is very challenging for researchers [13]. As a result, how to choose effective transmission paths for complicated three-dimensional UWSNs becomes crucial. A number of works have shown that clustering routing protocols are effective and efficient in finding optimal routing paths for data transmission, which can save energy and extend the network lifespan [14; 15]. The clustering routing protocols divide the whole network into lots of clusters. Every cluster is composed of a cluster head node (CHN) and some cluster member nodes (CMNs). After completion of the cluster formation, the CHN allocates channel resources for the CMNs in the same cluster, and the CMNs send data to the CHN based on the allocation, thereby decreasing collisions [16]. In every cluster, after the CHN receives the data sent by the CMNs, it fuses the received data, which can eliminate the redundant data and reduce the amount of data to be transmitted to the SN, thus contributing to energy conservation [4]. Moreover, the decreased data size reduces collisions during data transmissions. In addition, clustering routing protocols employ a CHN rotation mechanism and select CHNs in every round, which helps avoid the excessive energy dissipation of the selected CHNs, balance the energy consumption, and prolong the network lifecycle [17]. The data fusion technique [18; 19], which is used by CHNs to fuse data in this paper, is a common and effective way to eliminate the data redundancy, reduce the data size, and decrease the energy consumption. This paper uses an improved back propagation neural network (BPNN) to implement the data fusion. In UWSNs, sensor nodes may collect the data with high redundancy. When the redundant data are sent to the SN, unnecessary energy consumption arises, leading to a premature death of the node and a shortened lifespan of the network.