There is a significant need for precise and reliable forecasting of the far-field noise emanating from shipping vessels. Conventional full-order models based on the Navier-Stokes equations are unsuitable, and sophisticated model reduction methods may be ineffective for accurately predicting far-field noise in environments with seamounts and significant variations in bathymetry. Recent advances in reduced-order models, particularly those based on convolutional and recurrent neural networks, offer a faster and more accurate alternative. These models use convolutional neural networks to reduce data dimensions effectively. However, current deep-learning models face challenges in predicting wave propagation over long periods and for remote locations, often relying on auto-regressive prediction and lacking far-field bathymetry information. This research aims to improve the accuracy of deep-learning models for predicting underwater radiated noise in far-field scenarios. We propose a novel range-conditional convolutional neural network that incorporates ocean bathymetry data into the input. By integrating this architecture into a continual learning framework, we aim to generalize the model for varying bathymetry worldwide. To demonstrate the effectiveness of our approach, we analyze our model on several test cases and a benchmark scenario involving far-field prediction over Dickin's seamount in the Northeast Pacific. Our proposed architecture effectively captures transmission loss over a range-dependent, varying bathymetry profile. This architecture can be integrated into an adaptive management system for underwater radiated noise, providing real-time end-to-end mapping between near-field ship noise sources and received noise at the marine mammal's location.