Accurate real-time forecasts of atmospheric plume behavior are crucial for effective management of environmental release incidents. However, the computational demands of weather simulations and particle transport codes limit their applicability during emergencies. In this study, we employ a U-Net enhanced Fourier Neural Operator (U-FNO) to statistically emulate the calculations of the WSPEEDI dose forecasting numerical simulator, using pre-calculated ensemble simulations. The developed emulator is capable of effectively simulating any radioactive-release scenario and generating the time series of dose distribution in the environment 4000 times faster than the numerical simulator, while still maintaining high accuracy. It predicts the plume direction, extent, and dose-rate magnitudes using initial- and boundary-condition meteorological data as input. The speed and efficiency of this framework offers a powerful tool for swift decision-making during emergencies, facilitating risk-informed protective actions, evacuation execution, and zone delineation. Its application extends to various contaminant release and transport problems, and can be instrumental in engineering tasks requiring uncertainty quantification (UQ) for environmental risk assessment.