Wave runup
Definition of Wave runup:
Wave runup is the maximum onshore elevation reached by waves, relative to the shoreline position in the absence of waves.
This is the common definition for Wave runup, other definitions can be discussed in the article

Notes
Wave runup is an important parameter for assessing the safety of sea dikes or coastal settlements. Wave runup is the sum of wave setup and swash uprush (see Swash zone dynamics) and must be added to the water level reached as a result of tides and wind setup.
By waves is meant: waves generated by wind (locally or on the ocean) or waves generated by incidental disturbances of the sea surface such as tsunamis, seiches or ship waves. Wave runup is often indicated with the sympol [math] R [/math].
For waves collapsing on the beach, the wave runup can be estimated to first approximation with the formula of Hunt (1959) ^{[1]},
[math]R = \eta_u + H \xi ,[/math]
where [math]\eta_u[/math] is the wave setup, [math]H[/math] is the offshore wave height and [math]\xi[/math] is the wave similarity parameter,
[math]\xi = \Large\frac{\tan \beta}{\sqrt{H/L}}\normalsize = T \tan \beta \Large\sqrt{\frac{g}{4\pi H}}\normalsize , [/math]
where [math]L = g T^2/(2 \pi)[/math] is the offshore wave length, [math]\beta[/math] is the beach slope and [math]T[/math] is the wave period. The horizontal wave incursion is approximately given by [math] R / \tan \beta[/math].
Related articles
References
 ↑ Hunt, I.A. 1959. Design of seawalls and breakwaters. J. Waterw. Harbors Division ASCE 85: 123–152