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We propose forwarding-function () based routing protocol for underwater sensor networks (UWSNs): improved adaptive mobility of courier nodes in threshold-optimized depth-based-routing (iAMCTD). Unlike existing depth-based acoustic protocols, the proposed protocol exploits network density for time-critical applications. In order to tackle flooding, path loss, and propagation latency, we calculate optimal holding time () and use routing metrics: localization-free signal-to-noise ratio (LSNR), signal quality index (SQI), energy cost function (ECF), and depth-dependent function (DDF). Our proposal provides on-demand routing by formulating hard threshold (), soft threshold (), and prime energy limit (). Simulation results verify effectiveness and efficiency of the proposed iAMCTD.