Miche [1951] suggested that the nearshore wave field is composed of a reflected component, whose amplitude cannot exceed some maximum value dependent on beach slope and wave period, and an independent progressive component that is dissipated across a surf zone to zero amplitude at the shoreline. Accordingly, runup represents flow components that are standing at the shoreline; runup measurements can presumably be used to quantify the cross-shore structure of those fluid motions.
Miche's predictions of functional dependencies for wave runup and reflection were confirmed by careful field observations of incoming and outgoing wave energy made at Duck, North Carolina [ Elgar, et al., 1994]. Changes in foreshore beach slope caused by tide elevation changes over the concave profile were associated with changes in incident band reflectivity measured at 13 m depth. Reflectivity was also found to increase with decreasing frequency, in agreement with Miche's predictions.
Linear theory fails at the shoreline since any finite amplitude swash will cause motion landward of the shoreline (in fact, it is this finite amplitude movement that is the swash). Over the last thirty-five years, the original nonlinear solution for a finite amplitude runup of a single swash with no dissipation proposed by Carrier and Greenspan [1958] has been extended to include dissipation, bottom friction and random wave input. Model results have compared well with laboratory data for a variety of conditions [ Kobayashi, et al., 1990; Cox and Kobayashi, 1992].
In recent field experiments on 1:25 sloping natural beaches, a set of five resistance wire runup sensors stacked at 5 cm intervals above the bed and coupled with video observations, have allowed a detailed examination of swash kinematics in close proximity to the bed [ Holland, et al., in review; Raubenheimer, et al., in review]. Mean and variance of the swash exceed predictions of a simple mapping of linear theory onto the beach face. However, the above nonlinear models showed excellent agreement over a broad range of predicted statistics [ Raubenheimer, et al., in review]. Model behavior on different beach slopes is being explored.