a$)$ Consider first the two$-$dimensional case of a barrier island that maintains its geometry relative to sea level by overwashing sand and landward migration without cross$-$section change. Suppose that no sand is carried offshore. If the slope on the plane $$base$$ is $1$:$100,$ what distance will the barrier island retreat in one century?

b$)$ Suppose as a second case, that, as the barrier retreats, a portion of the sand is transported offshore, and no additional sand is introduced into the system. What effects will this have on the barrier with time? Now compare the retreat rate with that determined in $($a$)$ if the island is to remain viable.

c$)$ As a third case, suppose that, as the barrier retreats, sand is eroded from the bottom and incorporated into the island. What effects will occur with time? Compare the retreat rate with that computed in $($a$).$