The availability of high-resolution weather radar images underpins effective forecasting and decision-making. In regions beyond traditional radar coverage, generative models have emerged as an important synthetic capability, fusing more ubiquitous data sources, such as satellite imagery and numerical weather models, into accurate radar-like products. Here, we demonstrate methods to augment conventional convolutional neural networks with quantum-assisted models for generative tasks in global synthetic weather radar. We show that quantum kernels can, in principle, perform fundamentally more complex tasks than classical learning machines on the relevant underlying data. Our results establish synthetic weather radar as an effective heuristic benchmark for quantum computing capabilities and set the stage for detailed quantum advantage benchmarking on a high-impact operationally relevant problem.