A stationary compound process has been formulated and investigated as a model for underwater acoustic ambient noise pressure with long-term power fluctuations. The process is represented by

, where

is a non-negative stationary random process, and

is a zero-mean, unit-variance stationary Gaussian process independent of

. The process

, termed the power envelope, has a relaxation time much greater than that of

and the latter determines the bandwidth of the compound process. With a suitable selection of parameters, the compound process conforms to the results of carefully analyzed experiments. The process has been employed to predict the performance of passive sonars operating in a fluctuating acoustical environment.