We develop a new physical model for the rain effect and show that the well-known atmosphere scattering model (ASM) for the haze effect naturally emerges as its homogeneous continuous limit. Via depth-aware fusion of multi-layer rain streaks according to the camera imaging mechanism, the new model can better capture the sophisticated non-deterministic degradation patterns commonly seen in real rainy images. We also propose a Densely Scale-Connected Attentive Network (DSCAN) that is suitable for both deraining and dehazing tasks. Our design alleviates the bottleneck issue existent in conventional multi-scale networks and enables more effective information exchange and aggregation. Extensive experimental results demonstrate that the proposed DSCAN is able to deliver superior derained/dehazed results on both synthetic and real images as compared to the state-of-the-art. Moreover, it is shown that for our DSCAN, the synthetic dataset built using the new physical model yields better generalization performance on real images in comparison with the existing datasets based on over-simplified models.