Morphological variation in Upper Erligang II pottery li tripods: An elliptic Fourier and linear discriminant analysis

Pottery li tripods are among the most diagnostic ceramic vessel forms of the early Shang dynasty (c. 1600–1400 BCE). Despite their cultural significance, morphological comparisons between sites have relied predominantly on qualitative typological descriptions, limiting reproducibility and cross-site comparability. This study applies elliptic Fourier analysis (EFA) combined with linear discriminant analysis (LDA) to quantify and compare the profile outlines of 141 pottery li tripods from three Upper Erligang II sites, Xiaoshuangqiao, Yanshi Shang city and Zhengzhou Shang city, and supplements the outline analysis with measured rim diameters and vessel heights for 138 specimens. EFA decomposed each closed outline into 160 Fourier coefficients. An LDA classifier trained under pipeline-integrated cross-validation achieved an overall accuracy of 77.3 %, statistically significantly above chance, although the site signal accounts for only a small share of total shape variation. The principal finding concerns the comparison of size and shape standardisation. Zhengzhou Shang city is simultaneously the most size-standardised assemblage, and the most shape-dispersed, so that the two standardisation axes point in opposite directions at the same site. Xiaoshuangqiao and Yanshi Shang city are less dispersed in shape, though the pairwise contrasts with Zhengzhou are only marginal, and cannot be distinguished from one another on this measure. These patterns are compatible with production by multiple groups, although they do not uniquely identify either production organisation or the subsequent distribution of finished vessels. The framework demonstrated here offers a reproducible approach to quantifying morphological variation in ceramic assemblages that is readily transferable to other periods, vessel types and regions.