
Wave overtopping is the time-averaged amount of water that is discharged (in liters per second) per structure length (in meters) by
waves
United States Naval Reserve (Women's Reserve), better known as the WAVES (for Women Accepted for Volunteer Emergency Service), was the women's branch of the United States Naval Reserve during World War II. It was established on July 21, 1942, ...
over a structure such as a
breakwater
Breakwater may refer to:
* Breakwater (structure), a structure for protecting a beach or harbour
Places
* Breakwater, Victoria, a suburb of Geelong, Victoria, Australia
* Breakwater Island, Antarctica
* Breakwater Islands, Nunavut, Canada
* ...
,
revetment
A revetment in stream restoration, river engineering or coastal engineering is a facing of impact-resistant material (such as stone, concrete, sandbags, or wooden piles) applied to a bank or wall in order to absorb the energy of incoming water an ...
or
dike which has a crest height above still water level.
When waves break over a dike, it causes water to flow onto the land behind it. Excessive overtopping is undesirable because it can compromise the integrity of the structure or result in a safety hazard, particularly when the structure is in an area where people,
infrastructure
Infrastructure is the set of facilities and systems that serve a country, city, or other area, and encompasses the services and facilities necessary for its economy, households and firms to function. Infrastructure is composed of public and pri ...
or vehicles are present, such as in the case of a dike fronting an
esplanade
An esplanade or promenade is a long, open, level area, usually next to a river or large body of water, where people may walk. The historical definition of ''esplanade'' was a large, open, level area outside fortress or city walls to provide cle ...
or densely populated area.
Wave overtopping typically transpires during extreme weather events, such as intense storms, which often elevate water levels beyond average due to
wind setup
Wind setup, also known as ''wind effect'' or ''storm effect'', refers to the rise in water level in seas, lakes, or other large bodies of water caused by winds pushing the water in a specific direction. As the wind moves across the water’s surf ...
. These effects may be further intensified when the storm coincides with a high spring
tide
Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another.
Tide tables ...
.
Excessive overtopping may cause damage to the inner slope of the dike, potentially leading to
failure
Failure is the social concept of not meeting a desirable or intended objective, and is usually viewed as the opposite of success. The criteria for failure depends on context, and may be relative to a particular observer or belief system. On ...
and inundation of the land behind the dike, or create water-related issues on the inside of the dike due to excess
water pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and ev ...
and inadequate
drainage
Drainage is the natural or artificial removal of a surface's water and sub-surface water from an area with excess water. The internal drainage of most agricultural soils can prevent severe waterlogging (anaerobic conditions that harm root gro ...
. The process is highly
stochastic Stochastic (; ) is the property of being well-described by a random probability distribution. ''Stochasticity'' and ''randomness'' are technically distinct concepts: the former refers to a modeling approach, while the latter describes phenomena; i ...
, and the amount of overtopping depends on factors including the freeboard,
wave height
In fluid dynamics, the wave height of a surface wave is the difference between the elevations of a crest and a neighboring trough. ''Wave height'' is a term used by mariners, as well as in coastal, ocean and naval engineering.
At sea, the ...
,
wave period
Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...
, the geometry of the structure, and slope of the dike.
Overtopping factors and influences
Overtopping can transpire through various combinations of water levels and wave heights, wherein a low water level accompanied by high waves may yield an equivalent overtopping outcome to that of a higher water level with lower waves. This phenomenon is inconsequential when water levels and wave heights exhibit correlation; however, it poses difficulties in river systems where these factors are uncorrelated. In such instances, a
probabilistic
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...
calculation is necessary.
The ''freeboard'' is the height of the dike's crest above the still water level, which usually corresponds to the determining
storm surge
A storm surge, storm flood, tidal surge, or storm tide is a coastal flood or tsunami-like phenomenon of rising water commonly associated with low-pressure weather systems, such as cyclones. It is measured as the rise in water level above the ...
level or river water level. Overtopping is typically expressed in litres per second per metre of dike length (L/s/m), as an average value. Overtopping follows the cyclical nature of waves, resulting in a large amount of water flowing over a structure, followed by a period with no water. The official website of the ''EurOtop Manual'', which is widely used in the design of coastal engineering structures, features a number of visualisations of wave overtopping.
In the case of overtopping at ''rubble-mound'' breakwaters, recent research using
numerical model
Computer simulation is the running of a mathematical model on a computer, the model being designed to represent the behaviour of, or the outcome of, a real-world or physical system. The reliability of some mathematical models can be determin ...
s indicates that overtopping is strongly dependent on the slope angle.
Since present
design guidelines for non-breaking waves do not include the effect of the slope angle, modified guidelines have also been proposed. Whilst these observed slope effects are too large to be ignored, they still need to be verified by tests using
physical models
A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , .
Models can be divided int ...
.
Overtopping behaviour is also influenced by the geometry and layout of different coastal structures. For example,
seawall
A seawall (or sea wall) is a form of coastal defense constructed where the sea, and associated coastal processes, impact directly upon the landforms of the coast. The purpose of a seawall is to protect areas of human habitation, conservation, ...
s (which are typically vertical, or near-vertical, as opposed to sloping breakwaters or revetments), are often situated behind natural
beach
A beach is a landform alongside a body of water which consists of loose particles. The particles composing a beach are typically made from Rock (geology), rock, such as sand, gravel, shingle beach, shingle, pebbles, etc., or biological s ...
es.
Scour
Scour may refer to:
Hydrodynamic processes
* Hydrodynamic scour, the removal of sediment such as sand and silt from around an object by water flow
** Bridge scour, erosion of soil around at the base of a bridge pier or abutments via the flow ...
at the base of these structures during storms can have a direct impact on wave energy dissipation along their frontage, thus influencing wave overtopping. This phenomenon assumes critical importance when storms occur in such quick succession that the beach doesn't have sufficient time for
sediment
Sediment is a solid material that is transported to a new location where it is deposited. It occurs naturally and, through the processes of weathering and erosion, is broken down and subsequently sediment transport, transported by the action of ...
s removed by the storm to be re-established. Experimental results show that, for near-vertical structures at the back of a beach, there is an increase in wave overtopping volume for a storm that starts from an eroded beach configuration, rather than a simple slope.
Calculation of overtopping

Wave overtopping predominantly depends on the respective heights of individual waves compared to the crest level of the coastal structure involved. This overtopping doesn't occur continuously; rather, it's a sporadic event that takes place when particularly high waves within a storm impact the structure.
The extent of wave overtopping is quantified by the volume of water that overflows onto the adjacent land. This can be measured either as the volume of water per wave for each unit length of the seawall, or as the average rate of overtopped water volume per unit length during the storm wave period.
Much research into overtopping has been carried out, ranging from laboratory experiments to full-scale testing and the use of simulators. In 1971,
Jurjen Battjes
Jurjen Anno Battjes (born 22 February 1939) is a Dutch civil engineer. He was a professor of fluid dynamics at Delft University of Technology until his retirement in 2004.
Battjes was elected an international member of the National Academy of Eng ...
developed a theoretically accurate equation for determining the average overtopping. However, the formula's complexity, involving
error function
In mathematics, the error function (also called the Gauss error function), often denoted by , is a function \mathrm: \mathbb \to \mathbb defined as:
\operatorname z = \frac\int_0^z e^\,\mathrm dt.
The integral here is a complex Contour integrat ...
s, has limited its widespread adoption in practical applications. Consequently, an alternative empirical relationship has been established:
:
in which
is the dimensionless overtopping, and
is the dimensionless freeboard:
:
in which:
:
is the water depth
:
is the freeboard
:
is the overtopping discharge (in m³/s)
:
is the significant wave height at the toe of the structure
:
is the deep water wavelength
:
is the inclination of the slope (of e.g. the breakwater or revetment)
:
is the
Iribarren number
In fluid dynamics, the Iribarren number or Iribarren parameter – also known as the surf similarity parameter and breaker parameter – is a dimensionless parameter used to model several effects of (breaking) surface gravity waves on beaches an ...
:
is a resistance term.
The values of
and
depend on the type of
breaking wave
In fluid dynamics and nautical terminology, a breaking wave or breaker is a wave with enough energy to "break" at its peak, reaching a critical level at which linear energy transforms into wave turbulence energy with a distinct forward curve. ...
, as shown in the table below:
:

The resistance term
has a value between approximately 0.5 (for two layers of loosely dumped
armourstone) and 1.0 (for a smooth slope). The effect of a berm and obliquely incident waves is also taken into account through the resistance term. This is determined in the same way as when calculating wave run-up. Special revetment blocks that reduce wave run-up (e.g., Hillblock, Quattroblock) also reduce wave overtopping. Since the governing overtopping is the boundary condition, this means that the use of such elements allows for a slightly lower flood barrier.
Research for the EurOtop manual has provided much additional data, and based on this, the formula has been slightly modified to:
: