High-Resolution Climate Projections Using Diffusion-Based Downscaling of a Lightweight Climate Emulator

Technical Summary: High-Resolution Downscaling of a Lightweight Climate Emulator Using Diffusion-Based Super-Resolution

Problem Statement
High-resolution climate data is critical for assessing regional risks, such as localized convective precipitation, heatwaves, and orographic gradients, which coarse global climate models (GCMs) cannot resolve. While machine learning (ML) offers a computationally efficient route for climate emulation, existing lightweight emulators like the Lightweight Uncoupled ClImate Emulator (LUCIE) operate at coarse resolutions (approx. 300 km, T30 grid) to ensure long-term stability and computational efficiency. This coarse resolution limits their utility for local impact assessments. Furthermore, applying super-resolution (SR) models trained on "perfect" reanalysis data to inputs from independent, imperfect emulators presents a challenge: the "imperfect input" setting can degrade spatial consistency and underestimate extremes if the emulator's biases differ statistically from the training data.

Methodology
The authors propose a two-stage framework that couples the coarse-grained LUCIE emulator with data-driven super-resolution models to generate high-resolution (approx. 28 km, 0.25°) climate fields. The SR models are trained exclusively on 6-hourly ERA5 reanalysis data (2000–2009) and evaluated on out-of-sample LUCIE predictions (2010–2018). The study compares four approaches:

1. Deterministic Baselines:
   • Bicubic Interpolation: A standard baseline.
   • SFNO-SR: A Spherical Fourier Neural Operator super-resolution model sharing the same operator backbone as LUCIE, designed to respect spherical geometry.
   • UNet-SR: A standard convolutional U-Net architecture.
2. Probabilistic Diffusion Formulations:
   • Conditional Elucidated Diffusion Model (EDM): A model trained to directly learn the conditional distribution $p(x_{high} | y_{low})$ by concatenating upsampled low-resolution inputs with noisy high-resolution states.
   • Diffusion Posterior Sampling (DPS): A test-time approach using an unconditional prior $p(x_{high})$ and a learned likelihood term to guide sampling toward the coarse observation $y_{low}$ without retraining.

The evaluation utilizes a comprehensive suite of diagnostics including latitude-weighted Root-Mean-Squared-Error (RMSE), temporal standard deviation, power spectra, probability density functions (PDFs), and Empirical Orthogonal Function (EOF) analysis of zonal wind. Crucially, the study includes a "perfect-prognosis" (PP) setting where models downscale coarsened ERA5 inputs to isolate downscaler bias from emulator bias.

Key Results

• Climatological Accuracy: Deterministic baselines (UNet-SR, SFNO-SR) produce oversmoothed fields that fail to resolve fine-scale features like sharp thermal gradients in the Rocky Mountains or orographic precipitation bands in the Himalayas. In contrast, diffusion-based models (Conditional EDM and DPS) successfully recover these mesoscale structures.
• Bias Attribution: In the imperfect-input setting (LUCIE outputs), the Conditional EDM inherits the coarse emulator's biases but introduces minimal additional bias of its own. Conversely, DPS exhibits non-trivial residuals even in the perfect-prognosis setting, suggesting it relies more heavily on its learned prior than on the coarse conditioning, leading to weaker conditioning fidelity.
• Spectral and Distributional Fidelity: Diffusion models restore realistic high-wavenumber variance and heavy tails in PDFs, which deterministic models and bicubic interpolation fail to capture. SFNO-SR, while sharing LUCIE's backbone, introduces high-wavenumber spectral artifacts (wavy oscillations).
• Ensemble Calibration: A significant limitation identified is that neither diffusion ensemble is well-calibrated. Spread-skill ratios (SSR) are well below unity (ranging from 0.1 to 0.7), indicating that the ensembles are under-dispersed and systematically underestimate the true error.
• Performance Comparison: In the perfect-prognosis setting, the Conditional EDM outperforms DPS in RMSE for all variables, demonstrating that a dedicated conditional model is more accurate when the training and inference distributions align. However, under LUCIE inputs, the performance gap narrows, and DPS occasionally achieves lower RMSE for specific variables (temperature, zonal wind) despite its weaker conditioning.

Significance and Claims
The paper claims that this framework serves as a "promising step toward, rather than a finished tool for," high-resolution climate planning. The primary contribution is demonstrating that a data-driven super-resolution framework can bridge the gap between computationally efficient, stable climate emulators and the high-resolution data required for regional impact assessment.

The authors emphasize that the downscaler acts as a spatial post-processing step that adds fine-scale detail implied by the coarse state without altering the large-scale dynamics. They explicitly state that the framework is not intended to correct the physical biases of the underlying emulator (LUCIE); rather, it propagates the emulator's coarse-scale biases while reconstructing plausible fine-scale structures.

The study concludes that while the Conditional EDM is the more practical choice for scaling due to its accuracy and lower inference cost, the DPS approach offers distinct flexibility for future applications involving observation-constrained downscaling without retraining. The work highlights the need for future research to address ensemble calibration (under-dispersion) and to improve the conditioning fidelity of posterior sampling methods.