Accurate weather forecasting is critical for science and society. Yet, existing methods have not managed to simultaneously have the properties of high accuracy, low uncertainty, and high computational efficiency. On one hand, to quantify the uncertainty in weather predictions, the strategy of ensemble forecast (i.e., generating a set of diverse predictions) is often employed. However, traditional ensemble numerical weather prediction (NWP) is computationally intensive. On the other hand, most existing machine learning-based weather prediction (MLWP) approaches are efficient and accurate. Nevertheless, they are deterministic and cannot capture the uncertainty of weather forecasting. In this work, we propose CoDiCast, a conditional diffusion model to generate accurate global weather prediction, while achieving uncertainty quantification with ensemble forecasts and modest computational cost. The key idea is to simulate a conditional version of the reverse denoising process in diffusion models, which starts from pure Gaussian noise to generate realistic weather scenarios for a future time point. Each denoising step is conditioned on observations from the recent past. Ensemble forecasts are achieved by repeatedly sampling from stochastic Gaussian noise to represent uncertainty quantification. CoDiCast is trained on a decade of ERA5 reanalysis data from the European Centre for Medium-Range Weather Forecasts (ECMWF). Experimental results demonstrate that our approach outperforms several existing data-driven methods in accuracy. Our conditional diffusion model, CoDiCast, can generate 3-day global weather forecasts, at 6-hour steps and $5.625^\circ$ latitude-longitude resolution, for over 5 variables, in about 12 minutes on a commodity A100 GPU machine with 80GB memory. The open-souced code is provided at \url{https://github.com/JimengShi/CoDiCast}.

本研究针对现有天气预测方法在准确性、不确定性和计算效率之间的矛盾提出了CoDiCast模型。该模型通过条件扩散过程，结合来自过去的观测数据，生成高精度的天气预报，并在保持合理计算成本的同时实现不确定性量化。实验结果表明，CoDiCast在准确性方面超过了多种现有数据驱动的方法，对天气预测领域具有重要影响。

CoDiCast：一种用于天气预测的条件扩散模型及其不确定性量化