ABSTRACT 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, that is, 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.