Hungjui Yu | Search arXiv

arXiv2026

Taylor Diagram and Wasserstein Distance for Model Evaluation

The Taylor diagram is used to evaluate and compare predictive models with observed data and has many applications in climate and environmental sciences. Three statistics of interest--the centered root-mean-squared error, standard deviation, and the product-moment correlation coefficient--are related by the law of cosines; Taylor diagrams leverage this fact to allow visualization of all three statistics in a two-dimensional plot without any loss of information. In this work, we present a novel model evaluation tool--the Wasserstein-Taylor diagram--formed from integrating the Wasserstein distance from optimal transport into a Taylor diagram framework. This tool is built upon the fact that the law of cosines still holds in the Taylor diagram if the centered root-mean-squared error and product-moment correlation coefficient are replaced by the centered 2-Wasserstein distance and quantile correlation coefficient, respectively. The advantage of this Wasserstein-Taylor diagram is that one can use the distribution perspective afforded by the Wasserstein distance to compare observed and predicted data sets of different sizes and even to compare statistical models with only observed data. We further show that the quantile correlation coefficient on empirical measures converges to the quantile correlation coefficient on the sampled measures.

stat.ME↗

arXiv2025

Using machine learning to downscale coarse-resolution environmental variables for understanding the spatial frequency of convective storms

Global climate models (GCMs), typically run at ~100-km resolution, capture large-scale environmental conditions but cannot resolve convection and cloud processes at kilometer scales. Convection-permitting models offer higher-resolution simulations that explicitly simulate convection but are computationally expensive and impractical for large ensemble runs. This study explores machine learning (ML) as a bridge between these approaches. We train simple, pixel-based neural networks to predict convective storm frequency from environmental variables produced by a regional convection-permitting model. The ML models achieve promising results, with structural similarity index measure (SSIM) values exceeding 0.8, capturing the diurnal cycle and orographic convection without explicit temporal or spatial coordinates as input. Model performance declines when fewer input features are used or specific regions are excluded, underscoring the role of diverse physical mechanisms in convective activity. These findings highlight ML potential as a computationally efficient tool for representing convection and as a means of scientific discovery, offering insights into convective processes. Unlike convolutional neural networks, which depend on spatial structure and grid size, the pixel-based model treats each grid point independently, enabling value-to-value prediction without spatial context. This design enhances adaptability to resolution changes and supports generalization to unseen environmental regimes, making it particularly suited for linking environmental conditions to convective features and for application across diverse model grids or climate scenarios.

physics.ao-ph↗