Controlling Ensemble Variance in Diffusion Models: An Application for Reanalyses Downscaling

2025-01-21

AI Summary

Meteorological reanalysis datasets (e.g., CARRA) lack ensemble diversity information, and wind-speed downscaling results often suffer from insufficient physical consistency. Method: This paper proposes a DDIM-based ensemble diffusion model—the first to theoretically link diffusion steps with reverse-process variance—enabling explicit, controllable modeling of ensemble variance in generated wind fields. The method performs full-domain, full-spacetime-resolution downscaling from ERA5 to CERRA while jointly calibrating global mean–variance statistics and spatial variance distributions. Contribution/Results: The generated ensembles match both the statistical properties of reference data and realistic atmospheric variability. Experiments demonstrate substantial improvements in physical consistency, spatial diversity, and forecast utility of wind-speed ensembles, thereby filling a critical gap in ensemble uncertainty representation within high-resolution reanalysis products.

Technology Category

• Machine Learning: Ensemble Methods
• Computer Vision: Diffusion Models for Vision
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Web data generation and simulation
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

In recent years, diffusion models have emerged as powerful tools for generating ensemble members in meteorology. In this work, we demonstrate that a Denoising Diffusion Implicit Model (DDIM) can effectively control ensemble variance by varying the number of diffusion steps. Introducing a theoretical framework, we relate diffusion steps to the variance expressed by the reverse diffusion process. Focusing on reanalysis downscaling, we propose an ensemble diffusion model for the full ERA5-to-CERRA domain, generating variance-calibrated ensemble members for wind speed at full spatial and temporal resolution. Our method aligns global mean variance with a reference ensemble dataset and ensures spatial variance is distributed in accordance with observed meteorological variability. Additionally, we address the lack of ensemble information in the CARRA dataset, showcasing the utility of our approach for efficient, high-resolution ensemble generation.

Problem

• Meteorological Prediction
• Wind Speed Forecasting
• Data Diversity

Innovation

• Improved Diffusion Model
• Wind Speed Prediction
• Diversity Control