Wave setup
Definition of Wave setup:
Elevation of the mean water level at the shoreline due to wave breaking in the surf zone.
This is the common definition for Wave setup, other definitions can be discussed in the article

Notes
Wave transformation in shallow water generates changes in the mean water level, called setup for an upward change and setdown for a downward change. The changes in mean sea level are related to the socalled radiation stress. The radiation stress is defined as the excess flow of momentum due to wave orbital motions. Gradients in the radiation stress induce an effective momentum transfer from wave motion to steady motion that takes place when the wave amplitude changes along the direction of propagation. Wave setdown [math]\eta_d[/math] occurs in the shoaling zone where the wave amplitude increases; wave wetup [math]\eta_u[/math] occurs in the surf zone where the wave amplitude decreases. Analytical expressions of the wave setdown at the breakpoint and the wave setup at the shoreline can be derived for a monochromatic wave, see Shallowwater wave theory:
[math]\eta_d \approx \frac{\gamma}{16} H_b , \qquad \eta_u \approx \eta_d +\frac{3 \gamma}{8} H_b \approx \frac{5 \gamma}{16} H_b,[/math]
where [math]\gamma = H_b/h_b[/math] is the breaker index (values in the range 0.61.2), [math]H_b[/math] is the wave height at the breakpoint and [math]h_b[/math] the depth at the breakpoint.
Assumptions are:
 a constant seabed slope [math]m = \tan\beta[/math], i.e. depth [math]h(x) = m \, x[/math];
 shallow water, [math]2kh_b \lt 1[/math] ([math]k[/math] is the wave number);
 depthlimited wave amplitude [math]H/h=\gamma \;[/math] throughout the surf zone (saturated wave breaking).
Observations at different field locations suggest that the wave setup depends on the beach slope [math]m[/math] following the empirical relationship^{[1]}
[math]\eta_u \approx (0.02 + \large\frac{0.003}{m}\normalsize) \, H_b .[/math]
Related articles
References
 ↑ Raubenheimer, B., Elgar, S. and Guza, T. 2001. Field observations of wavedriven setdown and setup. J. Geophys. Res. 106: 46294638