Cooperative communication is considered as a major enabling technique to meet the demanding performance requirements of future underwater acoustic (UWA) communication systems. In this paper, we investigate the information theoretic performance of a cooperative UWA system to provide insight into the fundamental performance limits imposed by underwater acoustic channels. We first propose an approximate statistical model for the non-stationary ambient noise. The proposed model allows mathematical tractability and is a good fit for most operating frequencies in practical systems. Based on this ambient noise model, we investigate the outage performance of a precoded cooperative multicarrier UWA system with amplify-and-forward (AF) relaying. Our numerical results for cooperative UWA systems demonstrate significant performance gains over point-to-point systems. The impact of several system and environmental parameters on the performance is further demonstrated.