Bioengineered reefs seed fast-growing coral fragments onto engineered substrate. As colonies grow, the reef surface becomes rougher (higher "rugosity"), and that roughness drags energy out of passing waves through bottom friction and wave breaking — the same mechanism natural fringing reefs use to protect coastlines.
Colony height follows a logistic growth curve, and wave height decays exponentially as it crosses the reef flat, with the decay rate set by live coral coverage and structural rugosity:
H(t) = Hmax / (1 + e^(-k(t - t0))) // colony height, logistic growth
β = β0 · (coverage/100) · rugosity // attenuation coefficient (1/m)
H(x) = H0 · e^(-β·x) // wave height across reef width x
- Offshore wave height — incoming significant wave height H0 before it meets the reef.
- Coral coverage — fraction of the reef flat colonized; scales instance count and β.
- Colony age — years since outplanting; drives logistic growth of colony height H(t).
- Growth form — branching colonies (high rugosity ≈2.2) vs massive/boulder colonies (lower rugosity ≈1.3, but sturdier).
Reef restoration projects use exactly this trade-off: branching corals attenuate waves faster but are more storm-fragile, while massive corals grow slower yet form a more resilient long-term barrier.