The design of hydraulic structures in the Arctic is complicated by shallow relief, which cause unique runoff processes that promote snow-damming and refreeze of runoff. We discuss the challenges encountered in modeling snowmelt runoff into two coastal freshwater lagoons in Utqiaġvik, Alaska. Stage-frequency curves with quantified uncertainty were required to design two new discharge gates that would allow snowmelt runoff flows through a proposed coastal revetment. To estimate runoff hydrographs arriving at the lagoons, we modeled snowpack accumulation and ablation using SnowModel which in turn was used to force a physically-based hydraulic runoff model (HEC-RAS). Our results demonstrate the successful development of stage-frequency curves by incorporating a Monte Carlo simulation approach that quantifies the variability in runoff timing and volume. Our process highlights the complexities of Arctic hydrology by incorporating significant delays in runoff onset due to localized snow accumulation and melting processes. This methodology not only addresses the uncertainty in snow-damming and refreeze processes which affect the arrival time of snowmelt inflow peaks, but is also adaptable for application in other challenging environments where secondary runoff processes are predominant.