Wave runup
Definition of Wave runup:
Landward incursion of a wave. Wave runup is usually expressed as the maximum onshore elevation reached by a wave, relative to the waveaveraged shoreline position.
This is the common definition for Wave runup, other definitions can be discussed in the article

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 storm 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 in first approach with the formula of Hunt (1959) ^{[1]},
[math]R = H \xi ,[/math]
where [math]H[/math] is the offshore wave height and [math]\xi[/math] is the wave similarity parameter,
[math]\xi = \Large\frac{S}{\sqrt{H/L}}\normalsize = S \, T \Large\sqrt{\frac{g}{4\pi H}}\normalsize , [/math]
where [math]L = g T^2/(2 \pi)[/math] is the offshore wave length, [math]S[/math] is the beach slope and [math]T[/math] is the wave period. The horizontal wave incursion is approximately given by [math] R / S[/math].
For more precise estimates of wave runup see:
References
 ↑ Hunt, I.A. 1959. Design of seawalls and breakwaters. J. Waterw. Harbors Division ASCE 85: 123–152