In this study, a Level III reliability method for the performance-based design of nature-based solutions (NbS) is developed and applied to mangroves to mitigate wave overtopping. This method was developed incorporating both hydrodynamic and ecological processes and uncertainties. The model was examined with an idealized use case of a coastal embayment, which considered the overtopping of fetch-limited wind waves over a revetment fronted by mangroves. Uncertainties were evaluated using field and laboratory data. The model output was the reliability of the hybrid NbS, determined with the probability of failure, Pf, and encounter probability of failure, PEf, which is the probability of at least one failure occurring over the design life. The model was run for four cases: (1) the baseline case without mangroves, (2) a mangrove forest of moderate (20–100 m) cross-shore width using the drag coefficient parameterized with the Reynolds number, (3) the same mangrove forest as Case 2 using the drag coefficient parameterized with the Keulegan–Carpenter number, and (4) the same as Case 2 with the addition of during-storm mangrove mortality. For the baseline configuration without mangroves, PEf over the 50-year design life was 99.98%. For Case 2, PEf reduced to 37% and 6% for 20 and 100 m of mangroves, respectively, highlighting the role that mangroves can play to improve the reliability of the hybrid system. While Pf was constant for the baseline case, it decreased with time when including mangroves. PEf was approximately 1.5 times larger for Case 3 than for Case 2 for 20 m of mangroves, indicating that the parameterization of the drag coefficient affected the probability of failure. Mangrove mortality also affected the reliability, with PEf increasing from 37% (Case 2) to 66% (Case 4) for the 20 m of mangroves.
Ostrow et al. (Thu,) studied this question.