This paper addresses the problem of underwater acoustic channel estimation for communications in time-varying environments. In the case of a rapidly time-varying environment, the channel needs to be estimated and tracked continuously. In this case, prior information on the channel can be used to improve channel estimation performance. In this paper, a-priori statistics on the channel time-variations are used in order to obtain a maximum a-posteriori estimator for channel tap-coefficients. It is also shown that in a shallow water waveguide, typical channel time-variations span a small subspace of channel tap-coefficients variations. This fact is used to reduce the number of parameters to be estimated and improve the channel estimation performance. The results demonstrate a performance gain of 5-10 dB in terms of the signal-to-noise ratio in decision-feedback equalizer mean-squared error, compared to the least-squares method which ignores the a-priori statistics on the channel time-variations.