The British landscape painter John Constable is considered foundational for the Realist movement in 19th-century European painting. Constable's painted skies, in particular, were seen as remarkably accurate by his contemporaries, an impression shared by many viewers today. Yet, assessing the accuracy of realist paintings like Constable's is subjective or intuitive, even for professional art historians, making it difficult to say with certainty what set Constable's skies apart from those of his contemporaries. Our goal is to contribute to a more objective understanding of Constable's realism. We propose a new machine-learning-based paradigm for studying pictorial realism in an explainable way. Our framework assesses realism by measuring the similarity between clouds painted by artists noted for their skies, like Constable, and photographs of clouds. The experimental results of cloud classification show that Constable approximates more consistently than his contemporaries the formal features of actual clouds in his paintings. The study, as a novel interdisciplinary approach that combines computer vision and machine learning, meteorology, and art history, is a springboard for broader and deeper analyses of pictorial realism.