AI 中文总结
本研究采用储备池计算评估多模型集合预报的有效性，发现多模型算术平均预报更接近真实值，加权平均可进一步提升性能，同时指出其与理论行为的偏差源于随机储备池计算的误差分布尾部。
AI 中文摘要
天气预报和气候预测频繁使用多模型集合（MME），通过对不同模型的结果取平均来改进短期预报，但这种做法往往缺乏充分的依据或验证。本研究采用储备池计算（RC）作为替代大规模物理模型的高效计算方法，评估MME方法在混沌时间序列中的有效性。通过在同一数据集上训练多个随机构建的RC，构建一个多模型集合，其中每个模型具有独特的误差。这些模型误差导致预报性能差异显著，预报误差分布呈现重尾特征。对于同一目标，多个模型预报结果的算术平均值通常比大多数单个预报更接近真实值；若基于各模型的测试集性能构建权重，采用加权算术平均还可进一步提升性能。研究表明，多步迭代预报会沿目标点的不稳定流形向两个方向偏离真实值，若预报误差相互独立且均值为零，算术平均预报应按1/√Nens的速度趋近真实目标，其中Nens为多模型集合的规模。但研究观察到与该理论行为的偏差，将其归因于随机RC的误差分布尾部。
英文摘要
Weather forecasting and climate projection frequently use multi-model ensembles (MMEs) to improve short-term forecasts by averaging across models. However, this practice is often not well justified or validated. Using reservoir computing (RC) as a computationally efficient alternative to large-scale physical models, we assess the validity of the MME approach for chaotic time series. By training multiple randomly constructed RCs on the same dataset, we create a multi-model ensemble in which each model has its own unique error. These model errors lead to very different forecasting performances, with forecast error distributions that exhibit heavy tails. The arithmetic mean across forecasts from multiple models for the same target is usually closer to the ground truth than most individual forecasts, and further improvement is achieved by weighted arithmetic means where the weights are constructed based on each model's test-set performance. We show that iterated forecasts over many time steps deviate from the ground truth along the unstable manifold of the target point, in both directions, so that, if forecast errors were independent and had zero mean, the arithmetic mean forecast should approach the true target like $1/\sqrt{\nens}$ where $\nens$ is the size of the multi-model ensemble. We observe deviations from this behavior, which we attribute to the tails of the error distribution of random RCs.
