Fig. 4: The three-dimensional discrete element model for mélange composed of cubic icebergs with a power-law size distribution and confined within real fjord geometries.

a–c For Helheim glacier, d–f for Kangerlussuaq glacier. The real fjord geometry is scaled down by four times for the discrete element model. a The mélange elevation above mean sea level from ArcticDEM strip, overlain on satellite images acquired around the same date. The ArcticDEM acquisition date is shown in the top right corner. White line across the fjord indicates glacier front location. The images are in polar stereographic projection (EPSG: 3413). Black dots along fjords are adopted in the model to construct boundary walls that resemble fjord geometries. b, c are side and top view for iceberg positions and velocities after 16 days into simulations with steady terminus advance and no calving. The glacier terminus moves at a constant velocity, V_ter = 30 m/day. We calculate the 2-day averaged velocity of each iceberg element by dividing the iceberg’s displacement between 14 and 16 days of terminus motion by the time interval (2 days), which is indicated by filled color in (c). d–f follow captions of (a–c). g, h The comparison of the mélange thickness profile between ArcticDEM (black lines) and discrete element model (red lines) for Helheim and Kangerlussuaq glacier, respectively. i The mélange thickness profile from three ArcticDEM strips and corresponding discrete element models collapse onto the exponential analytical solution (Eq. (7), red dashed line). See supplementary videos for the full temporal evolution of the mélange behaviors.