## 1 Introduction  
Underwater wireless acoustic sensor networks (UWASNs) are considered adequate communication infrastructures because acoustic communications can guarantee more reliable communication with a longer propagation distance than optical and radio-frequency (RF) counterparts [1] in underwater environments. Therefore, UWASNs have been adopted widely for diverse applications including scientific observation, the exploitation of ocean resources, disaster detection, military surveillance and subsea construction monitoring [2; 3]. In our study, we focus on observation-based applications that deploy multiple nodes underwater and constantly obtain sensed data from them. By using the statistics of the data set sensed and collected by multiple underwater nodes, we can derive the desired information and predict future trends of underwater phenomena. Let us consider two cases in terms of the method to obtain data from nodes. One is to obtain data from all the nodes in the network. We call this \"Case 1\". The other is to obtain data from only some of them: \"Case 2\". When the sensed data varies significantly depending on region and time, for example, when investigating ship accidents, searching for drowned persons, or engaging in military surveillance, all nodes must be activated as in Case 1. On the other hand, in the case of observing the marine environment (e.g., salinity or temperature) for long periods of time, the similarity of the sensed data can be large, so the number of active nodes can be reduced, as in Case 2. Accordingly, if the statistics of the data set in Case 2 are similar to those in Case 1 within an allowable error range, it is not necessary to acquire data from all the nodes in the network. Obtaining data from only some nodes is equivalent to partially activating the nodes in the network. This implies that Case 2 can reduce the number of active nodes, as compared with Case 1. A smaller number of active nodes is especially advantageous in underwater environments where battery replacement is costly. The number of active nodes can be an important factor in the sense that it determines the similarity of data statistics between the two cases. That is, the degree of similarity increases as the number of active nodes approaches the total number of nodes, and vice versa. If an application requires a high degree of data accuracy, the number of active nodes should be increased. On the other hand, if an application just predicts the overall trend with marginal data accuracy, the number of active nodes can be reduced. Therefore, the number of active nodes is application-specific and should be considered as a requirement or an important parameter for the UWASN. Nodes can be activated and go to the ready state through an initialization process before an application starts. For this reason, we associate the application requirement (i.e., the number of active nodes) with initialization. More specifically, we initialize as many nodes as required to run an application, which is defined as \"_partial initialization_\". The concept opposed to partial initialization is \"full initialization\", which initializes all the nodes in the network. In the literature, most initialization methods for a UWASN are a subset of a specific network protocol, as summarized in Table 1. Most of the initialization methods exist as an initial stage of a MAC protocol, as proposed in [4; 5; 6; 7; 8; 9; 10; 11; 12]. Moreover, they are a part of a routing protocol, as exemplified in [13; 14; 15], or part of a node discovery protocol [16]. Furthermore, they have been proposed under the simple assumption that all nodes in a network need to be initialized at once before the network transmits and receives data for applications. To the best of our knowledge, there has been no study on a partial initialization approach. This motivates us to propose a new initialization protocol for a UWASN that partially initializes a UWASN according to the given application requirement.