In recent years, diffusion models have emerged as powerful tools for generating ensemble members in meteorology. In this work, we demonstrate how 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.

翻译：近年来，扩散模型已成为气象学中生成集合成员的有力工具。本研究展示了去噪扩散隐式模型（DDIM）如何通过调整扩散步数有效控制集合方差。我们建立了一个理论框架，将扩散步数与反向扩散过程表达的方差相关联。聚焦于再分析降尺度任务，我们提出了面向完整ERA5至CERRA区域的集合扩散模型，以全时空分辨率生成方差校准的风速集合成员。该方法使全局平均方差与参考集合数据集保持一致，并确保空间方差分布符合观测到的气象变异性。此外，我们针对CARRA数据集缺乏集合信息的问题，展示了本方法在高效生成高分辨率集合方面的应用价值。