Internal solitary waves (ISWs) in the northern South China Sea are among the most energetic worldwide, and ISWs can cause severe impacts on offshore platforms and underwater operations; rapid forecasting of the propagation process of ISWs is therefore a practical need in ocean engineering. In the actual ocean, the leading-crestline morphology at the ocean surface often provides a general indication of the propagation and evolution of the underlying internal wave. This study develops a parametric representation of surface-expressed leading-crestline morphology for the east-of-Dongsha segment of the Luzon Strait–Dongsha corridor. Specifically, leading crestlines are extracted from sea-surface-height-gradient (SSHG) fields of nonhydrostatic MITgcm simulations forced by World Ocean Atlas 2018 monthly stratification, using Canny edge detection and density-based clustering. The analysis results indicate that, under the assumption of monthly climatological stratification, the crestlines binned by their along-corridor location cluster around a common, location-dependent propagation morphology that is represented by cubic polynomial curves and summarized in monthly coefficient tables. Evaluated against independent satellite-derived crestlines, the representative curves achieve a mean root-mean-square error (RMSE) of approximately 0.01° in longitude and a mean of 0.870. Consequently, by analyzing the monthly average climate-state leading-crestline morphology across different months of the year, we can identify the key characteristics of internal wave propagation in the northeastern South China Sea.