293 h 2w < θ < h w (2) Here, the mixed layer depth h around the Galápagos Islands during the cold season was assumed to be 10 m based on previous reports (Warms & Karnauskas, 2025). Ocean circulation data were obtained from the GLORYS12 global ocean reanalysis product, which provides threedimensional current fields with a horizontal resolution of 1/12° and daily temporal resolution. Horizontal velocity fields at a depth of 9.57 m were extracted for the simulations, corresponding to the closest model level to the assumed mixed-layer depth. This depth was therefore selected as a representative value for near-surface advection. Within the mixed layer, active turbulent mixing driven by wind stress and surface buoyancy fluxes tends to homogenize the vertical distribution of momentum, resulting in a relatively uniform velocity profile compared to the sharp shear typically observed at the pycnocline (Price et al., 1986). Particle tracking simulations were performed for particles with diameters of 10 μm and 30 μm. The maximum residence time derived from the above formulation was adopted as the simulation period. Particle positions (latitude and longitude) were recorded at different temporal intervals depending on particle size: 10 μm particles were output every 3 hours, whereas 30 μm particles were output every 1 hour. 2.6 Digital twin construction and geospatial integration The time-series position data obtained from the Lagrangian particle tracking model were integrated into a three-dimensional geospatial information system (GIS) to construct a digital twin of the quarry–coastal system. The digital twin supports interactive visualisation of spatiotemporal dispersion pathways by combining particle trajectories with topography and bathymetry layers, enabling rapid interpretation of likely transport corridors and potential receptor areas under the cold-season scenario. 3. RESULTS 3.1 Seasonal characteristics of transport direction Figure 1 summarizes the distribution of daily mean transport directions for the warm season (February–May) during the period from 2020 to 2024. Transport direction is defined as the direction the wind blows toward. During the warm season, directions are widely dispersed (approximately ±75° around the mean), indicating strong day-to-day variability. This variability complicates the definition of representative offshore deposition zones; therefore, marine particle tracking is not presented for the warm season in this study.
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