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Quality of service (QoS)-aware data gathering in static-channel based underwater wireless sensor networks (UWSNs) is severely limited due to location and time-dependent acoustic channel communication characteristics. This paper proposes a novel cross-layer QoS-aware multichannel routing protocol called QoSRP for the internet of UWSNs-based time-critical marine monitoring applications. The proposed QoSRP scheme considers the unique characteristics of the acoustic communication in highly dynamic network topology during gathering and relaying events data towards the sink. The proposed QoSRP scheme during the time-critical events data-gathering process employs three basic mechanisms, namely underwater channel detection (UWCD), underwater channel assignment (UWCA) and underwater packets forwarding (UWPF). The UWCD mechanism finds the vacant channels with a high probability of detection and low probability of missed detection and false alarms. The UWCA scheme assigns high data rates channels to acoustic sensor nodes (ASNs) with longer idle probability in a robust manner. Lastly, the UWPF mechanism during conveying information avoids congestion, data path loops and balances the data traffic load in UWSNs. The QoSRP scheme is validated through extensive simulations conducted by NS2 and AquaSim 2.0 in underwater environments (UWEs). The simulation results reveal that the QoSRP protocol performs better compared to existing routing schemes in UWSNs.