## 1 Introduction  
Lately, underwater wireless sensor networks (UWSNs) have attracted many researchers due to their various applications in different fields such as environmental, scientific, military, and commercial [1; 2; 3]. In UWSNs, the radio and optical signals affect the network performance, particularly in radio signals, which require large antennas and tremendous transmission energy as they propagate at low frequencies (30-300) and long-distance [4; 5; 6]. On the other hand, optical signals need high accuracy in aiming the small laser beams and are influenced by scattering [7; 8; 9]. Therefore, acoustic signals can be used with UWSNs as a communication medium as acoustic signals can overcome these limitations [10; 11; 12]. Nevertheless, using these acoustic signals, the UWSNs have several challenges such as high propagation delay (about 1500 m/s), insufficient bandwidth (less than 100 KHz), and high bit error rate as a result of the intense aspects of the underwater channel [13; 14; 15]. Furthermore, in UWSNs, the sensor nodes have low energy with high battery replacement because of the harsh environment [16; 17; 18]. Consequently, it is necessary to increase the overall network lifetime in UWSNs [19; 20; 21]. Regarding the challenges mentioned previously, routing protocols in the terrestrial sensor network are not appropriate for underwater areas; instead, numerous algorithms have been suggested for UWSNs [22; 23]. The UWSN routing protocols are categorized into localization-based and non-localization protocols, where the localization-based ones need full positioning information using the Global Positioning System (GPS). However, the harshness of the underwater areas decreases the appropriateness of localization-based algorithms in UWSNs. Accordingly, non-localization routing protocols have attracted researchers to investigate UWSNs [24; 25; 26]. Furthermore, the non-localization protocols undergo an efficient aggregate of metrics, resulting in unstable links and high energy consumption forwarder nodes. The depth-based routing only uses the depth information, which leads to choosing high power consumer nodes as a next-hop forwarder [27; 28; 29]. energy efficient depth based routing (EEDBR) uses the depth metric and remaining power without link quality, leading to wastage of power in various paths provoked by unbalanced link choice [30]. In related literature, a vector-based forwarding protocol (VBF) strategy has been suggested requiring position information of all nodes in the network [31; 32]. Furthermore, it was improved as Hop-by-Hop (HH) VBF, considering the pipelining of positioning information of the forwarding path in the network [33]. Another improvement, vector based void avoidance (VBVA) utilizes the 3D flooding approach for detecting empty areas in the network [34]. A cross layer focused beam routing (FBR) has been suggested as a beaconing centric improvement relying on request to send and clear to send overhead packets [35; 36]. Similarly, location free approaches [37; 38; 39; 40] have utilized expected transmission cost (ETX) as major network monitoring parameters, which are not practically suitable in most underwater networking applications [41]. Therefore, considering green computing concepts in underwater wireless sensor networks, it is necessary to design and develop an efficient algorithm that handles the problems above-mentioned effectively to reduce energy consumption, improve the packet delivery ratio, and further maximize the network lifetime. In this paper, we introduce a non-localization routing protocol for UWSNs, called the triangle metric based multi-layered routing protocol for UWSNs (TM2 RP). Moreover, we employed an energy balancing technique to improve the network lifetime. The main aim of the proposed TM2 RP is to utilize a set of supernodes as a leading part of the forwarding process. We want to clarify that our depth based underwater networking architecture is computationally novel and capable of saving more energy than the literature architecture presented in MRP [42].