Runup variability due to time dependence and stochasticity in the beach profiles: two extreme cases of the Spanish coast

Equations for extreme runup worked out from several experimental studies are compared. Infragraviatory oscillations dominate the swash in a dissipative state but not in intermediate - reflective states. Therefore two kinds of equation depending on either significant wave height, H-0, or the Iribarren number, xi(0), should be used. Through a sand bed physical model with a uniform sand bed slope, equations are proposed for both beach states, and results are compared with precedent field and physical model experiments. Once the equations are chosen, the time-longshore variability in a medium - long term time scale of the foreshore slope is evaluated in two extreme cases relating to the Spanish coast. The Salinas beach on the North coast (Bay of Biscay) displayed a permanent dissipative beach state with small variations in the beach foreshore slope both along the shore and in time, so foreshore slope deviations in a medium-long term period were irrelevant and extreme runup is predicted with the wave height worked out from the design return period. Peniscola beach on the East coast (Mediterranean sea) displayed an intermediate state. If only time variations are analysed, variations in determining extreme runup are irrelevant. In contrast, significant differences were found when the longshore variations were studied in this Mediterranean beach.