We investigate two methods for estimating the matched signal transformations caused by time-varying underwater acoustic channels in orthogonal frequency division multiplexing (OFDM) communication systems. The underwater acoustic channel for this 12-20 kHz medium frequency range OFDM system is best modeled using multipath and wideband Doppler scale changes on the transmitted signal. As a result, our first channel estimation method is based on discretizing the wideband spreading function time-scale representation of the channel output using the Mellin transform. The second method is based on extracting the time-scale features of distinct ray paths in the received signal using a modified matching pursuit decomposition algorithm. We validate and discuss both methods using data from the recent Kauai Acomms MURI 2008 (KAM08) underwater acoustic communication experiment.