Radar sensing offers a method of achieving 24-h all-weather drone surveillance, but in order to be maximally effective, systems need to be able to discriminate between birds and drones. This work examines drone-bird classification performance as a function of signal to noise ratio (SNR). Classification at low SNR values is necessary in order to classify drones with a small radar cross-section (RCS), as well as to facilitate reliable classification at longer ranges. To investigate the relationship between classification performance and SNR, Gaussian noise is added to an experimentally obtained dataset of radar spectrograms. Classification is performed by convolutional neural networks (CNNs). It is shown that for the data available classification accuracy drops with falling SNR, as might be expected for any given CNN. The degree to which performance degrades with reduced SNR is presented. It is further shown that simpler network architectures are more robust to noise. Finally, it is demonstrated that data augmentation can be used as a means of enhancing classification accuracy at lower SNR values. Bayesian optimisation is used to find the optimal augmentation hyperparameters and overall, classification accuracies of 92% are achieved at low SNR.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.