  The availability of reliable, high-resolution climate and weather data is
important to inform long-term decisions on climate adaptation and mitigation
and to guide rapid responses to extreme events. Forecasting models are limited
by computational costs and, therefore, often generate coarse-resolution
predictions. Statistical downscaling, including super-resolution methods from
deep learning, can provide an efficient method of upsampling low-resolution
data. However, despite achieving visually compelling results in some cases,
such models frequently violate conservation laws when predicting physical
variables. In order to conserve physical quantities, here we introduce methods
that guarantee statistical constraints are satisfied by a deep learning
downscaling model, while also improving their performance according to
traditional metrics. We compare different constraining approaches and
demonstrate their applicability across different neural architectures as well
as a variety of climate and weather data sets. Besides enabling faster and more
accurate climate predictions through downscaling, we also show that our novel
methodologies can improve super-resolution for satellite data and natural
images data sets.
