## 1 Introduction  
In total, 71% of the Earth's surface is covered by oceans, which are extremely rich in resources. With the curiosity of human beings for the unknown space and the growing demand for natural resources, the scientific exploration of the ocean has attracted more and more attention from researchers. Among them, the underwater wireless sensor network (UWSN) has great potential in the scientific exploration of the ocean through wireless sensing, collection, and real-time transmission of data [1]. Therefore, in recent years, UWSNs have been used to collect various underwater data to achieve many goals (such as pollution monitoring, disaster prevention, flood monitoring, oceanographic research, oil pipeline monitoring, mineral exploration, military surveillance, etc.) [2, 3]. However, due to the particularity of the underwater environment, the underwater communication paradigm is different from the terrestrial communication paradigm. For instance, the radio frequency (RF) has a large attenuation in cases employed for underwater transmission. The RF can only be transmitted over short distances underwater and is, therefore, not suitable for underwater transmission [4], even though there has been some research on this [5, 6, 7, 8]. As an alternative, the sound wave is commonly used to assist underwater communication. Therefore, UWSN technologies are implemented and deployed deep underwater with sensors using acoustic signals to perform communication [9]. Nevertheless, due to the narrow available bandwidth and high channel noise of underwater acoustic channels, underwater inter-sensor communication still requires significant power consumption [10; 11]. Meanwhile, since the underwater acoustic sensors are energy-limited, the substantial communication energy consumption contributes to their service lifetime reduction [12]. Therefore, how to improve underwater acoustic sensors' communication energy efficiency and extend the service life of sensor nodes are urgent challenges for UWSMs. Some researchers effectively reduce the energy consumption of UWSNs by using an autonomous underwater vehicle (AUV) to assist data acquisition [13; 14]. Yet, the delay for this data acquisition and processing scheme is excessive for some data with heightened importance. For transmission tasks that have requirements on transmission and the processing delay, they can only be transmitted to the BS through sensor nodes or sinking nodes. Therefore, other researchers have proposed some effective underwater data compression schemes, as well as energy-efficient UWSN routing protocols [15; 16; 17]. These reduce the energy consumption of underwater nodes to a certain extent and extend the service life of the UWSN. Existing studies have improved the energy efficiency of nodes in UWSN to some extent. To the best of our knowledge, few existing studies, however, considered an essential concern, i.e., the communication energy consumption of nodes located in different water depths varies in UWSNs. This is because transmission energy consumption is different due to the different transmission paths of various nodes to ensure the quality of service (QoS). Therefore, if the influence of water depth is not considered, the existing research can reduce the overall energy consumption of underwater sensor networks. Yet, some sensors are potentially more energy-hungry. As a result, nodes need to be replaced frequently in different time periods, resulting in long-term service interruption. This paper thus aims to improve the energy consumption efficiency of underwater node communication, while trading off the energy consumption of each node's fairness. The main contributions of this paper are as follows:  
1. We first propose a novel hierarchical underwater wireless sensor transmission (HUWST) framework. In the presented HUWST framework, sensor nodes are managed in clusters. The sink node (SN) acts as the cluster head; it converges the data collected by the whole cluster sensor nodes.