## 2 Related Work  
In the underwater environment, the batteries of underwater sensor nodes cannot be replaced regularly. Therefore, one of the most important factors in underwater routing protocols is energy limitation. Clustering is a common and effective technique for saving energy. Many cluster-based underwater routing protocols have been proposed for energy conservation. These protocols can be divided into two categories based on the application scenarios, i.e., two-dimensional (2D) and three-dimensional (3D) UASN protocols. Two-dimensional UASNs primarily operate in horizontal planes and are typically used in shallower waters, such as offshore areas, lakes, or rivers. Two-dimensional UASN protocols focus on efficient routing and communication within the horizontal plane. The multi-layer cluster-based energy-efficient (MLCEE) protocol addressed load imbalance and energy consumption in 2D UASN by layering the network and using Bayesian probability for cluster head selection [9]. The quality-of-service (QoS)-aware evolutionary cluster-based routing protocol (QERP) optimized the relay node selection based on traffic and energy consumption [10]. Another 2D UASN protocol, Q-learning and data-priority-based routing protocol with dynamic computing cluster head (QD-DCR), used Q-learning and data prioritization to dynamically select cluster heads and balance energy distribution [11]. However, these protocols often do not fully consider the unique challenges of underwater environments, such as acoustic attenuation and multipath propagation. Three-dimensional UASNs suitable for deep-water applications cover all three dimensions and must contend with issues such as node localization, dynamic topology, and varying depth. The joint clustering and routing protocol (JCRP) for 3D UASN selects cluster heads based on residual energy and the weighted cost of network connectivity [12]. The cellular-clustering-based interference-aware data transmission protocol (CIDP) for 3D undersea exploration uses TDMA scheduling and hierarchical routing to reduce interference and improve data transmission [13]. In [14], a multi-hop energy-efficient routing protocol was proposed to improve the energy efficiency of data distribution, especially for nodes far from surface sinks. However, these protocols do not adequately address the challenges of 3D underwater communication, particularly in terms of energy-efficient data transmission. The LEACH protocol, which is one of the most classical cluster-based 2D protocols, randomly selects sensor nodes as cluster heads to aggregate and transmit data to a base station in order to optimize energy consumption and extend the network lifetime. The LEACH protocol was first applied to underwater sensor networks in [15]. Since then, many modified LEACH protocols have been proposed for 2D UASNs. In [16], a modified LEACH protocol was proposed to optimize network energy consumption by finding the ideal number of clusters. But its underwater energy propagation model was too simple and ignored factors like acoustic attenuation and multipath propagation effects. In [17], an adaptation of LEACH was proposed, which employed an absorption-losses-related underwater energy propagation model but overlooked some critical factors in underwater communication, such as transmission loss and excess loss. In [18], a novel solution named underwater modified LEACH (UMOD_LEACH) was proposed to improve the transmission phase in clustering. However, it omits propagation delay and an underwater energy model, which are crucial for underwater communication. In [19], an underwater energy model was applied to the LEACH protocol to calculate the network power consumption and update the node energy. But the transmission loss was not considered in this protocol. These existing modifications to the LEACH protocol, while targeting energy optimization in 2D UASNs, often oversimplify the underwater energy propagation model and overlook crucial aspects of underwater communications such as transmission loss and excess loss.