Planteamiento del problema

There is concern as to how shorelines of reef islands will respond to future sea-level rise. A conceptual model developed by Bruun (1954) has provided a foundation for many contemporary shoreline management applications (Figure 3.6). The model represents how shorelines may respond to rising sea level, proposing that they react by maintaining an equilibrium profile (Bruun, 1962). This concept was initially tested on shorelines in Denmark and California. The concave equilibrium shape of the profile is explained using a parabolic equation outlined in Equation 1:

65 Where h = water depth, x is the horizontal distance between the shoreline and the offshore area; A represents the sediment characteristics and 2/3 is an exponent.

The rule implies that when sea level rises; shorelines maintain equilibrium by retreating uniformly causing the upper part of the profile to be eroded away and the sand deposited on the lower part of the profile (Figure 3.6). This is illustrated in Equation 2:

R= S (L/ (B+ h)) = (S) 1/ tan Ø……….…Equation 2

L is the length of the profile, Ø is the profile angle, B is berm height and h is the

closure depth. Simply the equation means that when sea level rises by an amount S, the profile will be displaced landward by an amount R (Bruun, 1988). In other words, when sea level rises by a certain amount, the shore profile responds by eroding the upper part of the profile, which ends up on the nearshore to maintain equilibrium. Erosion rates differ depending on the slope of the profile. Low gentle sloped profiles will have low erosion rates; whereas steep ones will have high erosion rates.

Figure 3.6. Schematic diagram illustrating the Bruun Rule of shoreline erosion (source Abuodha and Woodroffe,(2010).

As with all models, the Bruun Rule is based on several assumptions of which the three principal ones are: (1) the profile is a closed two-dimensional system, between the beach and closure depth, depth beyond which waves do not move sediment (Cooper and Pilkey, 2004); (2) the profile maintains equilibrium over a long-term

66 under rising sea level conditions; and, (3) it is unaffected by other constraints, for example rock outcrops (Bruun, 1988).

The Bruun Rule has been widely criticised (Cooper and Pilkey, (2004); Komar, 1988). The criticism is that the assumptions are too restrictive, disregarding many important variables that determine the movement of sediment grain. Another point raised is that the Bruun Rule is considered to be inappropriate to all shorefaces. In nature, the nearshore is more complex and can rarely be considered a closed system (Cooper and Pilkey, 2004). In addition, studies have shown that during stormy conditions, new materials get moved onshore or lost offshore beyond the closure depth. For it to be considered as a closed system requires cell boundaries with consideration of sediment transport pathways and sediment budget approaches (Cowell, et.al., 2006). Additionally other variables such as geology and bathymetry have impacts on shoreface responses to sea-level rise which need to be considered as well. Overall, the Bruun Rule does not work in sedimentary environments that are highly complex, where factors such as sediment supply, wave conditions, coastal erosion rates and geology vary (Cooper and Pilkey, 2004).

The Bruun Rule is also considered inappropriate for reef islands of Kiribati. This was indicated by the results of a study carried out in several reef islands of Tarawa Atoll and atolls of Kiribati. The study applied the Common Methodology developed by IPCC which involved the application of the Bruun Rule to assess the coastal vulnerability to sea-level rise. The shore-normal profiles of reef islands generally end abruptly at the point where the sand meets the hard reef-flat surface (Figure 3.7). Under conditions of sea-level rise, beaches on reef islands undergo erosion, but not all the material is lost as some is deposited to build up the beach ridge (Woodroffe and McLean, 1992). However, with rapid sea-level rise and abnormal storm surges, Woodroffe and McLean (1992) propose that the reef islands may be overwashed and severely eroded as the beaches may not have time to equilibrate.

Figure 3.7. Ocean reef flat and beach appropriateness of the Bruun

profile is marked by A.

between the beach and the hard reef surface. C shows the extent of the beach profile which does not continue onto the non

erodible reef flat on atolls

deposited on the lower part of the profile as proposed under the Bruun Rule. Note hardly any sand is present on the reef flat.

Figure 3.8. A cross-section of applicability of Bruun Rule the shoreface is marked by A.

where sand can be deposited can continue out beyond B up to 30 m which may be a number of kilometres offshore.

sand can be removed from A under conditions of

Another study under following the IPCC

Rule. This study also

shoreline has been accreting in solid reef flat on reef islands do

A

Ocean reef flat and beach on Tarawa Atoll demonstrating the appropriateness of the Bruun Rule for use on atolls. The upper limit of the beach profile is marked by A. B shows the abrupt break in beach profile due to the contact and the hard reef surface. C shows the extent of the beach profile does not continue onto the non-erodible reef flat as marked by D. The non erodible reef flat on atolls does not allow eroded sand from the beach

deposited on the lower part of the profile as proposed under the Bruun Rule. Note hardly any sand is present on the reef flat.

section of North Wollongong beach in Wollongong showing the applicability of Bruun Rule for areas with true continental shelves.

the shoreface is marked by A. B shows the lower profile area and nearshore region deposited can continue out beyond B up to 30 m which may be a number of kilometres offshore. C indicates the possible extent of the profile where

can be removed from A under conditions of sea-level rise.

undertaken to assess the vulnerability of Betio

following the IPCC Common Methodology involved the application of the

also found that it was inappropriate to apply the Bruun Rule as the shoreline has been accreting in response to past sea-level rise (Solomon, 1997) solid reef flat on reef islands does not allow for the lower beach profile to adjust

C B C D A B 67

on Tarawa Atoll demonstrating the in- The upper limit of the beach

profile due to the contact and the hard reef surface. C shows the extent of the beach profile erodible reef flat as marked by D. The non-

eroded sand from the beach (A) to be deposited on the lower part of the profile as proposed under the Bruun Rule. Note that

in Wollongong showing the s. The upper limit of and nearshore region deposited can continue out beyond B up to 30 m which may be a C indicates the possible extent of the profile where

taken to assess the vulnerability of Betio to sea-level rise,

involved the application of the Bruun

found that it was inappropriate to apply the Bruun Rule as the (Solomon, 1997). The

68 therefore identification of a closure depth is inappropriate or impossible (Woodroffe, 2008) (Figure 3.7). This is in contrast to other areas with a true continental shelf such as those in Denmark and California (Figure 3.8). According to the Bruun Rule, sediments would be displaced and appear on the reef flat, however, this is unlikely as reef flats are generally observed to be “clean” or have only a thin veneer of sediment as waves effectively transport sand from the reef flat onto the beaches (Richmond, 1993; Kench and Brander, 2006). Eroded sediments from the upper part of the profile may be transported longshore or offshore into the ocean (Harper, 1989; Forbes and Hosoi, 1995; Solomon and Forbes, 1999) whilst some may be deposited on the reef island to build up the beach ridge (Woodroffe and McLean, 1992).