The underwater acoustic channel is one of the most challenging communication channels. Due to periodical tidal and daily climatic variation, underwater noise is periodically fluctuating, which result in the periodical changing of acoustic channel quality in long-term. Also, time-variant channel quality leads to routing failure. Routing protocols with acoustic channel estimation, namely underwater channel-aware routing protocols are recently proposed to maintain the routing performance. However, channel estimation algorithms for these routing protocols are mostly linear and rarely consider periodicity of acoustic channels. In this paper, we introduce acoustic channel estimation based on nearest neighbor regression for underwater acoustic networks. We extend nearest neighbor regression for SNR (Signal-to-Noise Ratio) time series prediction, providing an outstanding prediction accuracy for intricately periodical and fluctuating received SNR time series. Moreover, we propose a quick search algorithm and use statistical storage compression to optimize the time and space complexity of the algorithm. In contrast with linear methods, this algorithm significantly improves channel prediction accuracy (over three times at most) on both simulation and sea trial data sets. With this channel estimation method, we then propose a Depth-Based Channel-Aware Routing protocol (DBCAR). Taking advantage of depth-greedy forwarding and channel-aware reliable communication, DBCAR has an outstanding network performance on packet delivery ratio, average energy consumption and average transmission delay which is validated through extensive simulations.