AI 中文总结
本研究提出基于1-Wasserstein距离的新指标，用于量化大集合气候数据的内部变率，经验证其稳定性优于现有指标，可清晰呈现内部变率随强迫增强而降低的规律。
AI 中文摘要
量化气候数据中的强迫变率与内部变率是检测气候变化信号、评估气候预估不确定性的基础。我们提出一种可量化单模式初始条件大集合（SMILEs）中内部变率相对大小的度量指标。我们采用两种1-Wasserstein距离（一种最优传输代价形式）分别测量强迫变率与内部变率，所提指标为内部变率对应的距离除以两种距离之和。计算该比值仅需对样本排序并对所得分位数求差，无需额外参数。该指标可反映完整分布形态，适用于非高斯变量，因为1-Wasserstein距离可量化任意两个概率分布间的差异。我们采用来自高斯、均匀和对数正态分布的合成气候数据验证该指标。与现有两种指标不同，只要集合成员数约为40个或更多，所提指标无论分布形态及是否存在异常值，均可给出稳定估计。随后，我们将所提指标与现有指标应用于两种不同强迫情景下的社区地球系统模型大集合（CESM-LE）的2米气温和总降水数据。所有指标均表明，内部变率的相对贡献随强迫强度增加而降低，但所提指标能最清晰地呈现该响应。因此，1-Wasserstein距离为分析大集合数据集提供了一种简单实用的工具。
英文摘要
Quantifying forced and internal variability in climate data is fundamental to detecting the climate change signal and assessing uncertainty in climate projections. We propose a metric that quantifies the relative magnitude of internal variability in single-model initial-condition large ensembles (SMILEs). We measure forced and internal variability by two 1-Wasserstein distances, a form of optimal transport cost. The proposed metric is the distance for internal variability divided by the sum of the two. Computing this ratio requires only sorting the samples and differencing the resulting quantiles, with no additional parameters. The metric reflects the entire distribution shape and applies to non-Gaussian variables, because the 1-Wasserstein distance quantifies the difference between any two probability distributions. We validate the metric with synthetic climate data from Gaussian, uniform, and lognormal distributions. Unlike the two existing metrics, the proposed metric gives stable estimates irrespective of the distribution shape and the presence of outliers, provided that the ensemble has about 40 members or more. We then apply the proposed and existing metrics to the 2 m air temperature and total precipitation of the Community Earth System Model Large Ensemble (CESM-LE) under two different forcing scenarios. All the metrics indicate that the relative contribution of internal variability decreases as the forcing increases, but the proposed metric shows this response most clearly. The 1-Wasserstein distance thus provides a simple and useful tool for analyzing large-ensemble datasets.
