Wave Runup


Wave runup is the maximum vertical extent of wave uprush on a beach or structure above the still water level (SWL) (Sorensen, 1997).  This definition is depicted in the figure below.















Wave runup is an important process in causing and or promoting bluff erosion.  Wave runup may cause erosion by directly impacting the bluff, dislodging material, and redistributing it to the foreshore and nearshore.  Wave runup promotes bluff erosion by carrying failed bluff material away from the toe of the bluff, regardless of what caused failure and erosion of the bluff.  For example, a small slump due to elevated groundwater levels may carry material to the bluff toe.  If this material remained at the toe, it would act to stabilize the bluff.  However, if wave runup removes the material, then the bluff is less stable and more prone to direct wave attack. 

Two different wave runup values were investigated in this study: mean and two percent wave runup.  Mean runup is simply the average runup (R) of all waves observed.  The two percent wave runup (R2%) is the runup that only two percent of the wave runup values observed will reach or exceed.  


Wave Runup Prediction Formulas

Five different formulas for predicting wave runup were investigated in this study.  The following table provides the wave runup equations used in this study with some comments on the different formulas. 

General equations and variables defined for wave runup formulas.









Hunt, 1959; Battjes, 1974

Smooth, impermeable, continuous



0.1 < x < 0.3


CERC Shore Protection Manual, 1984

Smooth, impermeable, continuous



Chart solution, see figure below


Mase, 1989

Smooth, impermeable, continuous, gentle:  q = 1.9 - 11.3



Nielsen and Hanslow

Nielsen and Hanslow, 1991

Natural sand beaches with      

q = 1.5 - 10.8  


Mean grain size = 0.18 - 0.8 mm



for tan bF > 0.10

for tan bF < 0.10


Ahrens and Seelig

Ahrens and Seelig, 1996

Sand and gravel beaches


 Laboratory and Field


d in mm, wsr in cm/s


wsr for fresh water and 0.15 < dsr < 0.85 mm












WR predictinon equations investigated for this study






































CERC wave runup chart solution, reproduced from Sorensen (1997).

Deep water wave data

Each of the wave runup formulas requires input wave data.  For this study deep water wave data from three different sources was used.  NOAA's Nation Buoy Data Center (NDBC) has a wave buoy (station 45006) in the western half of Lake Superior that records wave data for nearly 75% of the year (see figure below).  USACE wave Information Study (WIS) data stations, which are locations at which a computer model was used to hindcast deep water wave data, are another source of deep water wave data.  The final method was to use wind data hindcast deep water wave data from measurements of fetch, time of duration, and wind speed.




















NOAA NDBC buoy 45006 (www.noaa.org, 2003).





Field Measurements of Wave Runup

Wave runup was measured in the field to determine the appropriate wave runup equations to be used for the study sites. 

Video cameras were used to record 60 minute segments of wave runup at most of the study sites.  For calm conditions a line of stakes was set up at a known interval (see figure below).  The slope of the beach was measured using an inclinometer.  Wave runup videos were manually digitized to record the peak wave runup of each wave.  Wave runup was calculated knowing the hypotenuse length of runup (WRL) and the angle of the beach (b):

Ri = (WRL)i sin b

where i denotes an individual wave













Example of field wave runup recording setup (calm conditions).  Camera is on tripod in back; orange stakes mark 0.3 m intervals


















Storm conditions were also measured to determine which formulas were best suited for predicting wave runup during storms.  The same procedure was used, except for storms the scale for measuring WRL was recorded during calm conditions overlaid on the storm data image for digitization.


Determination of Appropriate Wave Runup Equation

The wave runup measured in the field is compared to the R and R2% formulas discussed above.  The most suitable equation was chosen as the equation yielding the lowest errors overall.  Mean wave runup values were calculated for the wave runup data, and two percent wave runup values were determined from cumulative frequency distributions of wave runup.    


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Wave Runup    Wave Impact Height    Analysis and Results    Conclusions    References