Time Series Analysis of Post-Tsunami Coastal Recovery on the Sendai Coastline Using Dynamic Time Warping and Persistent Homology

This study presents a computational framework combining Dynamic Time Warping (DTW) and Persistent Homology to quantify the long-term morphological evolution of the Sendai coastline following the 2011 Tōhoku tsunami. Using multispectral satellite imagery from Landsat 5 TM, Landsat 8 OLI, and Sentinel-2 MSI (2010–2024), instantaneous shorelines were extracted via the Modified Normalized Difference Water Index (MNDWI) and reconstructed with parametric B-spline curves. DTW analysis indicated severe initial deformation, with a 90,927 m difference between pre- and post-tsunami instantaneous shorelines, followed by gradual stabilization as distances declined to 59,584 m by 2024. Persistent Homology revealed a more complex topological trajectory, with the number of 1-dimensional features (H1) rising sharply after the tsunami, consolidating by 2015, and expanding again to over 8000 by 2020–2024. The Stable Distance of Persistent Homology (SDPH) identified 2015–2020 as the key phase of transformation (38,088 m), marking a shift toward higher morphological complexity. A weak negative correlation (r = −0.362) between DTW and SDPH confirmed their complementarity in describing geometric and topological change. Overall, the results suggest that post-tsunami recovery followed a non-linear path toward a new dynamic equilibrium characterized by increased structural complexity and resilience.