We offer a statistical model for the acoustic transmission loss calculated for a wide band of frequencies. The model incorporates the physical laws of acoustic propagation (frequency-dependent attenuation, bottom/surface reflection), as well as the effects of inevitable random local displacements. We focus on two types of phenomena: (1) small-scale effects, such as scattering, that are responsible for fast variations of the instantaneous signal strength, (2) large-scale phenomena (with minute-long coherence time) that affect locally-averaged received power and occur due to slow surface variations and system displacements. We note that variations of yet a higher time-scale (hour-long) are observed in actual UWA systems which are due to very slow changes of the environmental conditions (such as water temperature which affects the sound speed profile and may cause the receivers to slowly move into shadow zones). We propose a log-normal large-scale model, whose mean follows a quasi-stationary log-distance dependence with a frequency-dependent path loss exponent, and whose variance depends on the signal bandwidth. Assuming a Gauss-Markov auto-regressive (AR) model for the path length variation, we also investigate the possibility to model the large-scale transmission loss as an AR process itself. We argue that the small-scale effects, modeled by complex Gaussian multiplicative distortion, average out over time intervals of a few seconds. The auto-regressive nature of the channel with a coherence time of longer than the round-trip transmission delay allows for the applicability of feedback based power control for underwater acoustic channels which makes possible substantial savings in the transmit power.