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Process-based numerical simulation, includ- ing for climate modeling applications, is compute- and resource-intensive, requiring extensive customization and hand-engineering for encoding governing equations and other domain knowledge. On the other hand, modern deep learning employs a much simplified and efficient computational workflow, and has been showing impres- sive results across myriad applications in computational sciences. In this work, we investigate the potential of deep generative learning models, specifically conditional Gen- erative Adversarial Networks (cGANs), to simulate the output of a physics-based model of the spatial distribution of the water content of mountain snowpack, or snow water equivalent (SWE). We show preliminary results indicating that the cGANs model is able to learn map- pings between meteorological forcing (e.g., minimum and maximum temperature, wind speed, net radiation, and precipitation) and SWE output. Moreover, informing the model with simple domain-inspired physical constraints results in higher model accuracy, and lower training time. Thus Physics-Informed cGANs provide a means for fast and accurate SWE modeling that can have significant impact in a variety of applications (e.g., hydropower forecasting, agriculture, and water supply management). 

Abstract—Numerical simulation of weather is resolution-constrained due to the high computational cost of integrating the coupled PDEs that govern atmospheric motion. For example, the most highly-resolved numerical weather prediction models are limited to approximately 3 km. However many weather and climate impacts occur over much finer scales, especially in urban areas and regions with high topographic complexity like mountains or coastal regions. Thus several statistical methods have been developed in the climate community to downscale numerical model output to finer resolutions. This is conceptually similar to image super-resolution (SR) [1] and in this work we report the results of applying SR methods to the downscaling problem. In particular we test the extent to which a SR method based on a Generative Adversarial Network (GAN) can recover a grid of wind speed from an artificially downsampled version, compared against a standard bicubic upsampling approach and another machine learning based approach, SR-CNN [1]. We use ESRGAN ([2]) to learn to downscale wind speeds by a factor of 4 from a coarse grid. We find that we can recover spatial details with higher fidelity than bicubic upsampling or SR-CNN. The bicubic and SR-CNN methods perform better than ESRGAN on coarse metrics such as MSE. However, the high frequency power spectrum is captured remarkably well by the ESRGAN, virtually identical to the real data, while bicubic and SR-CNN fidelity drops significantly at high frequency. This indicates that SR is considerably better at matching the higher-order statistics of the dataset, consistent with the observation that the generated images are of superior visual quality compared with SR-CNN.