Atmospheric rivers (ARs) are extreme weather events that can alleviate drought or cause billions of dollars in flood damage. By transporting significant amounts of latent energy towards the poles, they are crucial to maintaining the climate system’s energy balance. Since there is no first-principles definition of an AR grounded in geophysical fluid mechanics, AR identification is currently performed by a multitude of expert-defined, threshold-based algorithms. The variety of AR detection algorithms has introduced uncertainty into the study of ARs, and the algorithms' thresholds may not generalize to new climate datasets and resolutions. We train convolutional neural networks (CNNs) to detect ARs while representing this uncertainty; we name these models ARCNNs. To detect ARs without requiring new labeled data and labor-intensive AR detection campaigns, we present a semi-supervised learning framework based on image style transfer. This framework generalizes ARCNNs across climate datasets and input fields. Using idealized and realistic numerical models, together with observations, we assess the performance of the ARCNNs. We test the ARCNNs in an idealized simulation of a shallow water fluid, in which nearly all the tracer transport can be attributed to AR-like filamentary structures. In reanalysis and a high-resolution climate model, we use ARCNNs to calculate the contribution of ARs to meridional latent heat transport, and we demonstrate that this quantity varies considerably due to AR detection uncertainty.