  Generative adversarial networks (GANs) have been recently adopted for
super-resolution, an application closely related to what is referred to as
"downscaling" in the atmospheric sciences: improving the spatial resolution of
low-resolution images. The ability of conditional GANs to generate an ensemble
of solutions for a given input lends itself naturally to stochastic
downscaling, but the stochastic nature of GANs is not usually considered in
super-resolution applications. Here, we introduce a recurrent, stochastic
super-resolution GAN that can generate ensembles of time-evolving
high-resolution atmospheric fields for an input consisting of a low-resolution
sequence of images of the same field. We test the GAN using two datasets, one
consisting of radar-measured precipitation from Switzerland, the other of cloud
optical thickness derived from the Geostationary Earth Observing Satellite 16
(GOES-16). We find that the GAN can generate realistic, temporally consistent
super-resolution sequences for both datasets. The statistical properties of the
generated ensemble are analyzed using rank statistics, a method adapted from
ensemble weather forecasting; these analyses indicate that the GAN produces
close to the correct amount of variability in its outputs. As the GAN generator
is fully convolutional, it can be applied after training to input images larger
than the images used to train it. It is also able to generate time series much
longer than the training sequences, as demonstrated by applying the generator
to a three-month dataset of the precipitation radar data. The source code to
our GAN is available at https://github.com/jleinonen/downscaling-rnn-gan.
