Internal climate variability arises from the climate system's inherently chaotic dynamics. Quantifying it is essential for climate science, as it enables risk-based decision-making and differentiates between externally forced change and internal fluctuations. In statistical terms, natural variability corresponds to aleatoric uncertainty, i.e., irreducible stochastic variability. Despite this close conceptual alignment, the link between internal climate variability and aleatoric uncertainty has not yet been formalized. We establish a theoretical link by showing that member-to-member differences in single-model large ensembles provide a direct representation of aleatoric uncertainty. To quantify the spatio-temporal structure of aleatoric uncertainty, we employ generalized additive models. The proposed framework is validated through comparison with ERA5-Land reanalysis data, demonstrating that ensemble-derived estimates reproduce key spatial and temporal patterns of real-world variability. Applied to the water balance over the Iberian Peninsula, our approach reveals coherent variability structures and pronounced regional heterogeneity. We find a decline in variability in drought-prone regions and seasons, a pattern that strengthens under +3 °C global warming, implying an increased risk of persistent summer drought conditions. Beyond this application, the framework is climate-model agnostic and transferable to other variables and spatial scales, providing a statistical basis for quantifying internal climate variability as aleatoric uncertainty.

翻译：气候内部变异性源于气候系统固有的混沌动力学。对其进行量化对气候科学至关重要，因为这能够支持基于风险的决策，并区分外部强迫变化与内部波动。从统计学的角度来看，自然变异性对应于偶然不确定性，即不可约的随机变异性。尽管在概念上高度一致，但气候内部变异性与偶然不确定性之间的联系尚未被正式化。我们通过证明单一模型大集合中成员间差异直接体现了偶然不确定性，从而建立了这一理论联系。为了量化偶然不确定性的时空结构，我们采用了广义加性模型。通过与ERA5-陆面再分析数据的对比验证，该框架证明集合估计能够再现现实世界变异性的关键空间和时间模式。应用于伊比利亚半岛的水平衡分析，我们的方法揭示了相干变异性结构和显著的区域异质性。我们发现在易发生干旱的区域和季节，变异性呈下降趋势，在全球变暖3°C的情景下这一模式会加剧，意味着持续夏季干旱条件的风险增加。除该应用外，该框架对气候模型具有普适性，并可迁移至其他变量和空间尺度，为将气候内部变异性量化为偶然不确定性提供了统计基础。