A probabilistic coral rubble mechanical instability model applied with field observations from the Great Barrier reef

Unstable coral rubble hinders coral recruitment and recovery of coral reefs after damage from cyclones and bleaching events. If coral rubble remains unstable under typical everyday environmental conditions, areas of coral rubble will not be able to recover. Evaluating the probability of rubble instability over regional scale reef systems can assist the optimization of coral reef restoration efforts. Currently, robust and verified models for such applications do not exist. This paper presents a comprehensive assessment method to predict the probability of coral rubble instability, which combines a fluid-structural interaction approach with a statistical regional wave climate model. The hydrodynamic model employs non-linear wave theory to determine near-bed velocity, pressure gradients, and the corresponding drag and inertia forces acting on the coral rubble. The instability model assesses when overturning or sliding forces exceed resisting forces, considering thousands of combinations of different coral sizes and densities to calculate the proportion of instability under a given wave forcing. The model was calibrated and validated using prior laboratory experiments as reported by Kenyon et al. (2023b). The hydrodynamic and instability models use an extensive dataset of non-cyclonic wave climates (hindcast from over 30 years of wind measurements) specific to the region around Heron Reef, Great Barrier Reef, Australia, enabling a comprehensive evaluation of the probability of rubble instability in this area. Results indicate that the overall probability of rubble instability $\left({\mathrm{Pr}}_3\right)$ reaches 0.74 in water depths less than 2 m (typical of reef crests or reef flats), while it declines to below 0.21 at a depth of 12 m (typical deeper parts of the fore reef). Coral rubble on reef crests near Heron Reef, which are sheltered by surrounding formations, demonstrates low probability of instability. Thus, coral rubble instability is influenced by both its specific location within the reef and the position of the reef relative to other nearby reefs. By integrating the rubble instability model with non-cyclonic wave climate data, a map of the probability of rubble instability was generated for eight reefs in the Capricorn and Bunker Group (CBG). This map provides valuable guidance for coral reef restoration efforts, significantly reducing the need for extensive field-based data.