Daniel Getter

Daniel Getter, Julie Bessac, Johann Rudi et al.

Machine learning models have been employed to perform either physics-free data-driven or hybrid dynamical downscaling of climate data. Most of these implementations operate over relatively small downscaling factors because of the challenge of recovering fine-scale information from coarse data. This limits their compatibility with many global climate model outputs, often available between $\sim$50--100 km resolution, to scales of interest such as cloud resolving or urban scales. This study systematically examines the capability of convolutional neural networks (CNNs) to downscale surface wind speed data over land surface from different coarse resolutions (25 km, 48 km, and 100 km resolution) to 3 km. For each downscaling factor, we consider three CNN configurations that generate super-resolved predictions of fine-scale wind speed, which take between 1 to 3 input fields: coarse wind speed, fine-scale topography, and diurnal cycle. In addition to fine-scale wind speeds, probability density function parameters are generated, through which sample wind speeds can be generated accounting for the intrinsic stochasticity of wind speed. For generalizability assessment, CNN models are tested on regions with different topography and climate that are unseen during training. The evaluation of super-resolved predictions focuses on subgrid-scale variability and the recovery of extremes. Models with coarse wind and fine topography as inputs exhibit the best performance compared with other model configurations, operating across the same downscaling factor. Our diurnal cycle encoding results in lower out-of-sample generalizability compared with other input configurations.

Harrison J. Goldwyn, Mitchell Krock, Johann Rudi et al.

Accurate quantification of uncertainty in neural network predictions remains a central challenge for scientific applications involving high-dimensional, correlated data. While existing methods capture either aleatoric or epistemic uncertainty, few offer closed-form, multidimensional distributions that preserve spatial correlation while remaining computationally tractable. In this work, we present a framework for training neural networks with a multidimensional Gaussian loss, generating closed-form predictive distributions over outputs with non-identically distributed and heteroscedastic structure. Our approach captures aleatoric uncertainty by iteratively estimating the means and covariance matrices, and is demonstrated on a super-resolution example. We leverage a Fourier representation of the covariance matrix to stabilize network training and preserve spatial correlation. We introduce a novel regularization strategy -- referred to as information sharing -- that interpolates between image-specific and global covariance estimates, enabling convergence of the super-resolution downscaling network trained on image-specific distributional loss functions. This framework allows for efficient sampling, explicit correlation modeling, and extensions to more complex distribution families all without disrupting prediction performance. We demonstrate the method on a surface wind speed downscaling task and discuss its broader applicability to uncertainty-aware prediction in scientific models.