## 1 Introduction  
Underwater Wireless Communication Networks (UWCNs) are formed by sensors and Autonomous Underwater Vehicles (AUVs) interacting together to perform specific underwater applications such as collaborative monitoring or surveillance [1]. Communication quality in Underwater Wireless Sensor Networks (UWSNs) is very challenging due to the harsh characteristics of the underwater channel, such as high and variable propagation delays, limited bandwidth, high bit error rates, multipath phenomena and multipath fading [1]. In the extreme case, the spatially-variant underwater channel can cause the formation of shadow zones, which are time-variant areas where there is little signal propagation energy due to the refraction of signals by the sound speed fluctuation [2]. When the sound speed has a negative gradient just beneath the surface [3], a shadow zone is formed because the acoustic rays are refracted downward. Refraction produces shadow zones that sound waves do not penetrate because of their curvature. The sea bottom can produce a shadow zone as well, when the rays are refracted upward. Shadow zones [3] can also appear beneath the mixed layer for a source located near the ocean surface because the acoustic energy is trapped in the surface duct (see Figure 1). The shadow zone is usually bounded by the lower boundary of the surface duct and the limiting ray. Shadow zones can also appear between convergence zones. If the source is located at the same depth of the underwater sound channel axis, the shadow zone will disappear [4]. We distinguish between shallow (depth up to 100 m) and deep water. In shallow water (order of 100 meters depth) and at ranges of 3 kms shadow zones appear [2]. In deep water (order of 1,000s of meters depth) and at ranges of 10s of kms shadow zones are formed [2]. Shadow zones cause high bit error rates, losses of connectivity and dramatically impact communications performance. Some experiments show that for high frequencies signal levels are typically at least 40 dB less than those at the edges of the shadow zone [5]. For low frequencies the signal loss in the shadow zone is less severe; however, variations in received signal-to-noise ratios (SNRs) by as much as 10 dB have been observed on time scales of several hours [6]. Therefore, many authors recommend devising solutions to handle their effects [7, 8]. For these reasons, in this paper we focus on communication reliability in the presence of shadow zones. We propose a distributed adaptive topology reorganization scheme that alleviates the effects of energy limitations and is able to maintain connectivity between sensor nodes in multi-hop three-dimensional UWSNs in the presence of shadow zones. Besides, it is able to estimate when the shadow zones have disappeared using double sensor units to restablish communication very quickly through the original acoustic wireless links. We study the effects of the proposed scheme in shallow (depth up to 100 m) and deep water. A two-path Rayleigh fading channel model and different  
Figure 1: Shadow zone formation beneath the mixed layer when sound velocity monotically decreases with depth. propagation phenomena are considered: shallow water, deep water with convergence zones, deep water with deep sound channel and shallow or deep water with shadow zones. According to the number of links in the three-dimensional UWSN affected by the shadow zone, three different cases have been introduced. In this paper we have extended our work in [9], where only one case was discussed. A mathematical model has been developed for each case to find the optimal placement for the sensor nodes whose ongoing communications are being disturbed. The two major objectives of the proposed mathematical model are: the minimization of the transmission loss and the maintenance of network connectivity. To the best of our knowledge this is the first paper that finds the optimal location for underwater sensor nodes affected by a shadow zone under different propagation phenomena.