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This paper investigates the characteristics of the shallow water acoustic channel as a medium for digital communications. Experimental measurements are presented for such channels exhibiting depths of up to 50 m and ranges between to 500 m and 10 km. Results include measured impulse responses extracted via channel soundings using chirp-based pilot signals. Time dispersion and frequency selectivity measures such as the rms delay spread and the coherence bandwidth of the multipath channel are used to characterize the channels under investigation. Additionally, analysis of the temporal variability using the Doppler spectrum of the distinct spectral components present in the received signal is presented. Furthermore, a simulator for a stochastic channel model is proposed based on autoregressive type filters for capturing the temporal dynamics of the channel. Results demonstrate that the proposed simulator may be utilized effectively in simulations of shallow-water channels.