  Adapting to the changing climate requires accurate local climate information,
a computationally challenging problem. Recent studies have used Generative
Adversarial Networks (GANs), a type of deep learning, to learn complex
distributions and downscale climate variables efficiently. Capturing
variability while downscaling is crucial for estimating uncertainty and
characterising extreme events - critical information for climate adaptation.
Since downscaling is an undetermined problem, many fine-scale states are
physically consistent with the coarse-resolution state. To quantify this
ill-posed problem, downscaling techniques should be stochastic, able to sample
realisations from a high-resolution distribution conditioned on low-resolution
input. Previous stochastic downscaling attempts have found substantial
underdispersion, with models failing to represent the full distribution. We
propose approaches to improve the stochastic calibration of GANs in three ways:
a) injecting noise inside the network, b) adjusting the training process to
explicitly account for the stochasticity, and c) using a probabilistic loss
metric. We tested our models first on a synthetic dataset with known
distributional properties, and then on a realistic downscaling scenario,
predicting high-resolution wind components from low-resolution climate
covariates. Injecting noise, on its own, substantially improved the quality of
conditional and full distributions in tests with synthetic data, but performed
less well for wind field downscaling, where models remained underdispersed. For
wind downscaling, we found that adjusting the training method and including the
probabilistic loss improved calibration. The best model, with all three
changes, showed much improved skill at capturing the full variability of the
high-resolution distribution and thus at characterising extremes.
