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Compendium on methods and tools to evaluate impacts of, and vulnerability and adaptation to, climate change

Bruun Rule Description
Description The first and best known model relating shoreline retreat to an increase in local sea level is that proposed by Per Bruun (1962). The IPCC reports that 1 cm rise in sea level erodes beaches about 1 m horizontally. This becomes a large issue for developed beaches that are less than 5 m from the ocean (IPCC, 1998).

The Bruun rule states that a typical concave-upward beach profile erodes sand from the beach face and deposits it offshore to maintain constant water depth. The Bruun rule can be applied to correlate sea-level rise with eroding beaches. The Bruun rule estimates the response of the shoreline profile to sea-level rise. This simple model states that the beach profile is a parabolic function whose parameters are entirely determined by the mean water level and the sand grain size. The analysis by Bruun assumes that with a rise in sea level, the equilibrium profile of the beach and shallow offshore moves upward and landward.

The analysis is two-dimensional and assumes that,

  1. The upper beach is eroded due to the landward translation of the profile;
  2. The material eroded from the upper beach is transported immediately into the offshore and deposited, such that the volume eroded is equal to the volume deposited;
  3. The rise in the nearshore bottom as a result of deposition is equal to the rise in sea level, thus maintaining a constant water depth in the offshore (SCOR, 1991).
Appropriate Use The Bruun rule is only applicable for small scale local sites.
Scope Over long stretches of coast, the Bruun rule and associated cross-shore transport models become complex. There has been a number of critiques e.g. Cooper and Pilkey (2004).
Key Output Shoreline recession (in metres relative to sea-level rise).
Key Input An increase in sea level, (S), cross shore distance (L) to the water depth (h) taken by Bruun as the depth to which nearshore sediments exist (depth of closure), and B is the height of the dune.
Ease of Use Easy to use with numerous assumptions.
Training Required Familiarity with the coastal zone being investigated.
Training Available None
Computer Requirements None, unless it is incorporated into a model.
Documentation Originally proposed by Per Bruun in 1962.
International Studies
Bruun (1962, 1988)
Contacts for Framework, Documentation, Technical Assistance See applications
Cost No cost to use the Bruun rule.
Bruun rule has been applied but caution needs to be exercised where other factors influence sediment budget or control profile.