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Deep Learning (DL) methods have been transforming computer vision with innovative adaptations to other domains including climate change. For DL to pervade Science and Engineering (S&EE) applications where risk management is a core component, well-characterized uncertainty estimates must accompany predictions. However, S&E observations and model-simulations often follow heavily skewed distributions and are not well modeled with DL approaches, since they usually optimize a Gaussian, or Euclidean, likelihood loss. Recent developments in Bayesian Deep Learning (BDL), which attempts to capture uncertainties from noisy observations, aleatoric, and from unknown model parameters, epistemic, provide us a foundation. Here we present a discrete-continuous BDL model with Gaussian and lognormal likelihoods for uncertainty quantification (UQ). We demonstrate the approach by developing UQ estimates on “DeepSD’‘, a super-resolution based DL model for Statistical Downscaling (SD) in climate applied to precipitation, which follows an extremely skewed distribution. We find that the discrete-continuous models outperform a basic Gaussian distribution in terms of predictive accuracy and uncertainty calibration. Furthermore, we find that the lognormal distribution, which can handle skewed distributions, produces quality uncertainty estimates at the extremes. Such results may be important across S&E, as well as other domains such as finance and economics, where extremes are often of significant interest. Furthermore, to our knowledge, this is the first UQ model in SD where both aleatoric and epistemic uncertainties are characterized. 

The impacts of climate change are felt by most critical systems, such as infrastructure, ecological systems, and power-plants. However, contemporary Earth System Models (ESM) are run at spatial resolutions too coarse for assessing effects this localized. Local scale projections can be obtained using statistical downscaling, a technique which uses historical climate observations to learn a low-resolution to high-resolution mapping. The spatio-temporal nature of the climate system motivates the adaptation of super-resolution image processing techniques to statistical downscaling. In our work, we present DeepSD, a generalized stacked super resolution convolutional neural network (SRCNN) framework with multi-scale input channels for statistical downscaling of climate variables. A comparison of DeepSD to four state-of-the-art methods downscaling daily precipitation from 1 degree (~100km) to 1/8 degrees (~12.5km) over the Continental United States. Furthermore, a framework using the NASA Earth Exchange (NEX) platform is discussed for downscaling more than 20 ESM models with multiple emission scenarios.