Accelerated relative sea-level rise and rapid coastal erosion:

Marine Geology 140 ( 1997) 347–365

Accelerated relative sea-level rise and rapid coastal erosion: testing a causal relationship for the Louisiana barrier islands Je
rey H. List a,*, Asbury H. Sallenger, Jr.b, Mark E. Hansen b, Bruce E. Ja
e c a U.S. Geological Survey, 384 Woods Hole Rd., Woods Hole, MA 02543, USA b U.S. Geological Survey, 600 4th St. S., St. Petersburg, FL 33701, USA c U.S. Geological Survey, 345 Middlefield Rd., Menlo Park, CA 94025, USA Received 25 November 1996; received in revised form 24 March 1997; accepted 24 March 1997

Abstract The role of relative sea-level rise as a cause for the rapid erosion of Louisiana’s barrier island coast is investigated through a numerical implementation of a modified Bruun rule that accounts for the low percentage of sand-sized sediment in the eroding Louisiana shoreface. Shore-normal profiles from 150 km of coastline west of the Mississippi delta are derived from bathymetric surveys conducted during the 1880s, 1930s and 1980s. An RMS di
erence criterion is employed to test whether an equilibrium profile form is maintained between survey years. Only about half the studied profiles meet the equilibrium criterion; this represents a significant limitation on the potential applicability of the Bruun rule. The profiles meeting the equilibrium criterion, along with measured rates of relative sea-level rise, are used to hindcast shoreline retreat rates at 37 locations within the study area. Modeled and observed shoreline retreat rates show no significant correlation. Thus, in terms of the Bruun approach, relative sea-level rise has no power for hindcasting (and presumably forecasting) rates of coastal erosion for the Louisiana barrier islands. © 1997 Elsevier Science B.V. Keywords: sea-level rise; Bruun rule; shoreline change; erosion; equilibrium profile; Louisiana

1. Introduction 1.1. Sea-level rise as a predictor of coastal erosion Predictions of global warming and attendant acceleration of the eustatic sea-level rise rate (e.g. Warrick and Oerlemans, 1990) have stimulated much recent interest in the influence of sea-level rise on coastal erosion (e.g. Nicholls and * Corresponding author. Fax: +1 508 457-2310, E-mail: [email protected] 0025-3227/97/$17.00 © 1997 Elsevier Science B.V. All rights reserved. PII S0 02 5- 3 22 7 ( 9 7 ) 00 03 5- 2

Leatherman, 1994). Although great uncertainty exists in predictions of future sea-level rise rates, with recent estimates downgrading the threat somewhat ( Warrick et al., 1995), a widely-accepted paradigm holds that the generally erosional state of the world’s shorelines (Bird, 1985) is largely due to eustatic sea-level rise, and that any acceleration in the sea-level rise rate will accentuate the problem (e.g. Vellinga and Leatherman, 1989 ). This has provided the impetus for many local, regional, and global studies to assess the impact of current and future sea-level rise rates on shoreline erosion.

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However, in addition to major uncertainties with estimates of future sea-level rise, no unambiguous methodologies exist for relating sea-level rise to coastal erosion using first principles of hydrodynamics and sediment transport. Although some recent models of shoreface evolution incorporate parameterizations of sediment transport rates that are sea-level sensitive (Stive and De Vriend, 1995; Niedoroda et al., 1995), the link between sea-level rise, changes in processes, and shoreline retreat is still far from clear. This deficiency in processes-based approaches has led to the widespread use of conceptual models that assume sea-level rise merely represents a landward translation in processes that are otherwise constant (and therefore do not need to be known). Perhaps the most widely used such model assumes a constant or equilibrium profile form that is translated upwards and landwards in response to a rise in sea level. This simple model, generally known as the Bruun rule (Bruun, 1962, 1983; Schwartz, 1967 ) has been applied to erosion problems in many variations (see SCOR Working Group 89, 1991, for a review). In its simplest form, shoreline retreat, s, is given by s=

al h

( 1)

where a is the sea-level rise, and l and h represent the distance and depth o
shore, respectively, at which changes in the profile are assumed to be negligible over the time period of interest (also known as the closure depth). Although an equilibrium profile is often assumed in the form z=bx2/3

( 2)

where z is the water depth, x is the distance o
shore, and b is a constant commonly related to the sediment grain size (Dean and Maurmeyer, 1983), Allison (1980 ) demonstrated that Eq. ( 1) holds for any profile form, as long as the form is invariant over time. Studies employing Eq. (1 ), as well as many variations on Eq. ( 1), have had mixed success in terms of their ability to hindcast past erosional rates. For a comprehensive review, see SCOR

Working Group 89 (1991). Although many studies have demonstrated a landward/upward shift of the profile in response to sea-level rise at least qualitatively in accord with the Bruun rule, the Bruun rule has been largely ine
ective at hindcasting shoreline retreat at specific locations. Most studies have been hindered by a lack of long-term profile data, preventing a site-specific determination of controlling parameters such as l and h in Eq. (1 ), and preventing an adequate assessment of the equilibrium profile assumption. Also, recent work has highlighted the need for a better understanding of the underlying geological framework and its control on the form of the nearshore profile (Riggs et al., 1995; Thieler et al., 1995). Another general problem in the application of the Bruun rule has been a lack of sediment budget information permitting an assessment of net gains or losses to the profile (e.g. through longshore transport). Recent studies ( Everts, 1985; Cowell et al., 1995 ) have shown that the profile response (following variations of Eq. (1 )) is highly sensitive to variations in the net sediment import or export to the profile. In an e
ort to improve hindcasts of shoreline change, Everts ( 1985) extracted a 100-year record of profile change from historical bathymetric surveys and extended Eq. (1 ) in a sand-conservation approach that incorporated estimates of net longshore losses to the profile derived from sediment budget considerations. Hindcast shoreline retreat rates at two locations resulted in near agreement with observations at one location and a 21% overprediction at another. However, this apparent hindcasting success is tempered by the large error that was likely to be present in the sediment budget information (though not reported), and because a statistically significant correlation between observed and predicted shoreline retreat rates cannot be established with only two datum points. Here we test the applicability of a Bruun-type model for hindcasting shoreline retreat at multiple locations along a coast with variable rates of shoreline erosion. The Louisiana barrier islands were chosen as the test location because of the area’s rapid rate of relative sea-level rise, the availability of historical bathymetric and shoreline

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Fig. 1. Map of the study area showing place names referred to in the text and the longshore distance scale, L , constituting the dist horizontal axes in Figs. 4, 5, 7 and 8.

change information, and extensive background knowledge of the region’s geological framework. 1.2. Louisiana barrier islands The Louisiana barrier island coast (Fig. 1 ) consists of a series of headlands and flanking barrier islands formed by the re-working of abandoned Mississippi river delta complexes (Penland et al., 1988). Headland areas, such as the central part of the Isles Dernieres, the Caminada–Moreau headland and the Plaquemines shoreline, consist of deltaic sequences of clays to fine sands representing prodelta, delta front, beach ridge and distributary deposits. Flanking barrier islands, such as the eastern and western islands of the Isles Dernieres chain, Timbalier and East Timbalier islands, Grand Isle and Grand Terre island, consist of concentrated deposits of fine sands. The phenomenal rates of shoreline retreat along most of the Louisiana barrier island coast have been well documented; over 100 years of shoreline position data indicate long-term shoreline retreat rates exceeding 10 m/yr in many areas (McBride et al., 1992). However, the processes responsible for this erosion are not well understood. In 1986,

the U.S. Geological Survey initiated a series of cooperative studies with the Louisiana State University to document rates of historical shoreline and bathymetric change, to provide geological framework information, and to make measurements of storm-induced sediment transport processes on the shoreface and over the barrier islands. The range of investigations carried out in support of this study is described by Sallenger et al. (1987, 1991). One of the fundamental questions raised at the start of these investigations concerned the role of relative sea-level rise in forcing the region’s rapid rates of coastal erosion. As documented by Penland and Ramsey (1990), the region experiences a subsidence-induced relative sea-level rise of approximately 1 cm/yr, or five to ten times greater than the eustatic rate of sea-level rise (Douglas, 1991 ). A seemingly self-evident assumption was that this rapid rate of relative sea-level rise must be a principal agent of coastal erosion (Sallenger et al., 1987 ). However, the processes through which relative sea-level rise contributes to coastal erosion in Louisiana were poorly defined. In addition, subsequent examination of long-term bathymetric changes revealed striking patterns of

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sediment redistribution in the longshore direction (Ja
e et al., 1989, 1997; Sallenger et al., 1992; List et al., 1994). Cross-shore, not longshore, transport is a fundamental requirement of the Bruun rule model for shoreline translation in response to sealevel rise. Testing the Bruun concept for the most erosive stretch of shoreline, the Caminada–Moreau Headland (Fig. 1 ), List et al. ( 1991) found that the 10–20 m/yr of observed shoreline retreat could only be accounted for by including the removal of approximately 54 m3/m/yr of sediment from the profile. Sallenger et al. (1992 ) further showed that longshore transport, both in the nearshore and at shoreface depths, could largely account for the volume of sediment lost from eroding segments of shoreline. These results suggested that processes associated with the longshore transport of sediments, not sea-level rise, may have played the dominant role in the region’s accentuated rates of shoreline retreat. Still, an overall evaluation of the role of relative sea-level rise in forcing the region’s shoreline change was lacking. This study represents a comprehensive attempt to evaluate the ability of a Bruun-type model to hindcast shoreline retreat throughout the 150 km of coast in the study area. The Louisiana barrier islands would appear to be an ideal site for this test, with high rates of shoreline retreat and relative sea-level rise, a geological framework consisting of largely unconsolidated sediments (i.e. no bedrock controls on profile form or migration), and at least some profiles that have maintained an invariant form over the last 100 years (List et al., 1991 ). We obtained profiles from historical and recent bathymetric surveys and tested them for profile similarity between di
erent survey years. Should a profile maintain its form as it erodes, we conclude that it has maintained an equilibrium configuration. Profiles meeting the criterion for equilibrium provide the basis for a numerical implementation of the Bruun rule adopted to account for the small fraction of sand-size sediment in the eroding shoreface sediments (similar to Everts, 1985). The paper’s main result is a comparison between model-predicted and observed shoreline retreat rates, providing an evaluation of the Bruun rule’s predictive capability for the study area.

2. Data and methods 2.1. Profile data We obtained profile data from surface grids generated from the 1880s, 1930s and 1980s bathymetric surveys, covering 150 km of coastline west of the modern Mississippi delta ( Fig. 1). The bathymetric data sources, processing methods, vertical datum correction and error assessment are described by Ja
e et al. (1991), Hopkins et al. (1991) and List et al. (1994). List et al. (1994 ) assigned a no-significant-change zone of ±0.5 m for bathymetric change between di
erent year’s surveys, based on many potential sources of error, including sounding measurement error, tidal correction problems, vertical and horizontal datum inconsistencies and computer griding errors. This error level will be incorporated below in a criterion for assessment of each profile’s stability or tendency to maintain an equilibrium form. The overall objective in extracting profiles for this study was to obtain as many profile samples as possible, while ensuring that each profile is as independent of adjacent ones as possible. For example, two profiles separated by an along-coast distance of 100 m are clearly not independent, especially considering that the original spacing of bathymetric survey lines was generally greater than 500 m (List et al., 1994 ). The following describes the procedures used to generate the profile samples that constitute the data for this study. The 1880s to 1930s and 1930s to 1980s change periods (hereafter referred to as the 1880s–1930s and 1930s–1980s), are considered independent for the purposes of identifying segments of coast for extracting profiles. This means that profile comparisons for both change periods can be extracted from the same location and treated as independent samples. In some cases this assumption is clearly invalid: where a section of shoreline maintains a constant erosion rate over the entire 100 years spanning the study period, breaking the data into two 50-year time spans creates an artificial bias for that location’s data. However, rapid changes in bathymetry and shoreline physiography resulted in many areas of great dissimilarity between the 1880s–1930s and 1930s–1980s. The formation of

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new inlets, land losses due to erosion, and the generation of new shoreline through spit growth resulted in di
erent shoreline configurations or erosion rates between the two comparison periods in most areas. Thus, although some data bias results from considering the two change periods as independent, this problem is minimal and we judge it to have little influence on the results of this study. With the assumption that the two change periods are independent, we extracted profiles with a maximum spacing of 1 km along the coast and a cross-shore data interval of 50 m (resulting in a 50 m resolution in the numerical application of the Bruun rule, as described below). We then averaged adjacent profiles, where possible, to create sets of profiles representing independent samples of distinct segments of coast. We followed several criteria for determining the length of coast for profile averaging. First, and most obviously, the segment of barrier shoreline must be present for both years defining the change period. Second, the segment of coast to be averaged must have a relatively uniform rate of shoreline change, arbitrarily taken as no more than a 50% di
erence in erosion rate between individual profiles. Third, the segment of coast must be contained within one geomorphic feature, i.e. within the same island (not spanning inlets). Following these criteria, we generated 70 averaged profiles, representing segments of coast ranging in length from 0.5 km to 11.0 km. Fig. 2 gives examples of these averaged profiles for the 1930s–1980s at four di
erent locations along the coast. 2.2. Shoreline change data For each segment of coast represented by an averaged profile, we obtained an averaged shoreline position change from historical and recent shoreline position surveys. The sources, processing methods and error assessment for these data are described in detail by McBride et al. ( 1992). McBride et al. (1992) determined a maximum long-term error in shoreline change position of ±0.5 m/yr, or about ±25 m for the 50 year time periods considered here. Considering the high shoreline change rates prevalent throughout the

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study area, this error is negligible and is not considered further. 2.3. Equilibrium assessment As described above, a critical requirement for application of the Bruun rule is that the profile maintain the same form over the period of study, the assumption being that the profile is in some sort of ‘equilibrium’ with conditions (e.g. wave climate, sediment properties, etc.) that are not changing significantly over the given time period. Thus we adopted the following criterion to measure objectively the degree to which the 70 averaged profiles conform to this equilibrium concept. Dean (1977 ) tested the fit of Eq. (2 ) to 502 East Coast and Gulf of Mexico beach profiles using a root-mean-square (RMS) di
erence test between the best-fit Eq. (2 ) profile and observations. Here we are not concerned with the fit of Eq. (2) to the measured profiles, but only with the fit between profiles in succeeding years; the Bruun rule assumes only that the profile form is invariant over time, not that it conforms to any particular model. For each profile pair we found an RMS di
erence as

C

D

n ∑ (P1 −P2 )2 1/2 i i D = i=1 rms n

(3 )

where P1 and P2 represent the averaged profiles at times 1 and 2 with the cross-shore distance shifted such that the shorelines for both profiles are coincident, i represents the discrete profile points at the digitized interval, and n is the most seaward profile point considered. Based on ±0.5 m as the threshold for significant sea-floor change (List et al., 1994), profile pairs with D <0.5 m rms are considered to be in equilibrium and are used in Bruun rule calculations, while those with D >0.5 m are discarded from further rms consideration. An important free variable in Eq. (3 ) is n, representing the maximum profile distance and associated depth o
shore for calculation of D . rms

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We determined this location for each segment of coast as the point at which the unaveraged, unshifted profiles converge to within ±0.5 m, the no significant change level for bathymetric comparisons. For most locations, once the profiles converged to within ±0.5 m, they remained converged to the o
shore limit of data. The convergence depth represents a profile closure depth controlled by the accuracy of the bathymetric data and the time interval between profiles, in this case 50 years. Clearly, sediment transport could have occurred at depths greater than this purely geometrical closure depth; the resulting bathymetric changes, however, were undetectable in this study. 2.4. Application of the Bruun rule The approach for implementing the Bruun rule follows Everts ( 1985), with adaptations for the Louisiana case. The profile response to sea-level rise can be found through a sediment budget approach in which volumes of sediment eroded or accreted are balanced as

k(Ve +Ve )+(Va +Va )+V =0 ( 4) 1 2 1 2 0 where V represents the net import or export of 0 sediment to the profile through longshore transport and other processes, k represents the fraction of sand-sized material in eroding shoreface sediments, and volumes per unit shoreline distance Ve , Ve , 1 2 Va and Va represent erosional or accretional 1 2 areas of the profile as shown in Fig. 3. Multiplication of the eroding areas by the factor 0
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Fig. 3. Definition diagram for Bruun rule calculations using model result for 1930s-1980s at 13
tions to Eq. (4 ). First, the volume Ve , represent1 ing a thin veneer of littoral and low dune sands overlying transgressed marsh deposits (Dingler and Reiss, 1990), is assumed to be redeposited in area Va through overwash and eolian processes 1 as the coast retreats (Ritchie and Penland, 1988). The bulk of deposition in volume Va , however, 1 represents the vertical accretion of marsh deposits composed of fine sediments and organics not accounted for in Eq. (4 ) (Dingler and Reiss, 1990). Therefore, the sand-sized material in Ve is 1 assumed to be conserved as it is redeposited in Va ; both volumes can then be disregarded in 1 Eq. (4 ). Although the assumptions behind this simplification are not fully tested, potential errors are small due to the small volume of Ve relative 1 to Ve . 2 Eq. (4 ) is further simplified by the elimination of V , representing the net sediment gain or loss 0 to the profile through longshore transport or other processes such as cross-shore transport beyond the identified active zone of the profile. V is not 0

Fig. 2. Examples of D values determined from averaged profiles with horizontal datum arbitrarily shifted so that depth=0 m at rms x=0 m, with the vertical datum uncorrected for relative sea-level rise. Closure depth was determined from individual unaveraged profiles with a relative sea-level rise correction and no horizontal datum shift. The shoreline retreat, s, is given as an average for the section of coast over which the profiles are averaged. The range of alongshore distances, L in Fig. 1, for profile averaging is ( A) dist 13-16 km, (B) 66-70 km, (C) 75-86 km and (D) 116-118 km.

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eliminated on the argument that it is negligible; on the contrary bathymetric change comparisons suggest that longshore transport plays a central role in the coast’s evolution (Ja
e et al., 1989, 1997; Sallenger et al., 1992; List et al., 1994). Rather, V is eliminated to focus on the Bruun 0 rule’s ability to hindcast shoreline retreat, and because of an assertion that sediment budget information is unlikely to be accurate enough to make the approach of incorporating a V estimate at 0 each profile location meaningful. The rational for neglecting V is explained further in the discus0 sion section. The simplified version of Eq. (4 ), kVe +Va =0 2 2 is solved as

CP

( 5)

x1 [P(x−s)+a]dx x0 x + 2 {[P(x−s)+a]−P(x)}dx x1 x + n+s {[P(x−s)+a]−P(x)}dx x2 x + n {r(x)−P(x)}dx=0 ( 6) xn+s where the integral limits are defined in Fig. 3, x is the distance o
shore, P(x) represents the original profile before sea-level rise, P(x−s)+a represents the profile after sea-level rise, and r(x) represents the ‘ramp’ (Everts, 1985 ), a geometrically constrained line controlled by the rates of sea-level rise and shoreline retreat and given by k

P P P

r(x)=

D

a s

(x−x )+h n n

(Penland and Ramsey, 1990), relative sea-level rise, a, is about 1 cm/yr or 0.5 m for both 50-year time periods and all profile locations examined here. Thus it is assumed that this rate of relative sea-level rise, measured at one central location in the study area, is valid throughout the spatial and temporal range of the study. This assumption cannot be rigorously tested with the available data. However, Penland and Ramsey (1990) provide evidence that the rates of relative sea-level rise are directly related to the Holocene sequence thicknesses for the Mississippi river delta and chenier plains. As the study area falls within a region of delta sediments of relatively uniform thickness (150–200 m), it is likely the rates of relative sealevel rise are fairly uniform as well. Still, localized deviations from a=1 cm/yr may exist, adding additional undetermined error to our results. The variable k is problematic due to both the diculty of its estimation and the sensitivity of shoreline retreat estimates to errors in k ( Everts, 1985). Based on an examination of cores logs from the vicinity of the Caminada–Moreau headland (Fig. 1 ), List et al. (1991) estimated that k=0.31. As most of the cores represent non-reworked sediments from the Bayou Lafourche lobe of the Mississippi river ( Penland et al., 1988), this value for k may represent a minimum value since other sections of coast formed through spit growth (e.g. Timbalier Island, Grand Isle, etc.) have a much higher concentration of sand (Penland et al., 1988). However, the core information is not extensive enough to make individual k determinations for all averaged profiles. Therefore, in this study we primarily used k=0.31, with some tests using k=1.00 for sections of shoreline formed through spit growth.

( 7)

where h and x are the depth and distance to the n n closure depth on P(x). Shoreline retreat, s, is found for each 50-year time period at each profile location through the numerical integration of Eq. ( 6). The resolution of s is 50 m, resulting from the 50 m spacing of profile points extracted from the bathymetry. Based on 45 years of tide records at Grand Isle

3. Results In this section, results are first presented for the determination of closure depth and the test of the equilibrium profile assumption. Using site-specific closure depth and restricting the analysis to profile locations meeting the equilibrium criterion, the regional variability of shoreline change rates are then compared to Bruun rule hindcasts.

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Fig. 4. Along-coast plot of (A ) closure depth, h , and (B) RMS di
erence between profiles, D ( Eq. ( 3)), for the 1880s to 1930s n rms change period. Bar widths indicate the length of coast used for profile averaging. In ( A), the dashed line is the closure depth, d , l found using Hallermeier (1981) and in ( B) the dashed line is the cuto
criterion for determining equilibrium.

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Fig. 5. Same as Fig. 4 for the 1930s to 1980s change period.

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3.1. Closure depth Figs. 4a and 5a give the regional pattern of closure depths, h , determined for the 1880s–1930s n and 1930s–1980s change periods. The patterns are similar in both change periods, with deep closure along headland areas and more shallow closure along the islands fronting the adjacent embayments. An exception to this pattern is in the Isles Dernieres, a headland area where closure depths are very shallow, most likely due to the sheltering e
ect of Ship Shoal, a large sand shoal which lies about 20 km seaward of the Isles Dernieres (Penland et al., 1986). Another exception to the general closure depth pattern is in the area of Grand Terre Is. (109
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also highly variable through the study area, as shown in Figs. 4b and 5b. Here the trend is for low values in headland areas, especially along the Isles Dernieres and the Caminada–Moreau Headland, and for mixed high and low values elsewhere. Also shown in Figs. 4b and 5b is the D cuto
criterion discussed earlier, with profiles rms considered to be in equilibrium falling below this D level. rms Examination of averaged profile pairs, such as those in Fig. 2, support, in general, the D cuto
rms criterion. Fig. 2a,c from headland areas, show a close match in profile form with a corresponding D below the 0.5 m criterion. Fig. 2b,d show rms major changes in profiles form and corresponding high D values. Many of the profile pairs with rms high D values can be explained as areas where rms local coastal processes changed during the 50-year time period. For example, in Fig. 2b the construction of a massive breakwater system arrested the shoreline recession, resulting in a much steeper profile as the shoreface continued to erode. In Fig. 2d, the growth of an adjacent ebb-tidal delta (List et al., 1994) resulted in a less steep profile. In these cases, it is clear that the profiles do not maintain an equilibrium form and the Bruun rule cannot be applied. Many of the D values in Figs. 4b and 5b are rms much closer to the cuto
criterion than the examples in Fig. 2; for these profiles the classification as equilibrium or non-equilibrium is less clear. However, the overall distribution of D values, rms given in Fig. 6, shows a break in the distribution at D =0.5 m. This suggests a natural division rms between profiles with small D , for which prorms cesses have remained constant over the 50-year period and for which D reflects the error inherent rms in the bathymetric change data, and profiles with large D , for which processes have changed over rms the 50-year period and for which D reflects a rms true change in the profile form. Nevertheless, a D =0.5 m cuto
criterion remains an essentially rms arbitrary, though conservative, division between equilibrium and non-equilibrium profiles. Using the above criterion, only about half the profiles examined have maintained an equilibrium form over the study period. This result is important in that many previous applications of the Bruun

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Fig. 6. Distribution of D showing the cuto
criterion for rms determination of profile equilibrium.

rule have assumed an equilibrium profile without either a quantitative or a qualitative test of this assumption. Clearly, these results demonstrate that the Bruun rule cannot be applied blindly without historical profile information to validate the equilibrium assumption. Below, only profiles with D <0.5 m are used for Bruun rule calculations. rms 3.3. Shoreline change predictions Figs. 7 and 8 compare the along-coast pattern of observed and modeled shoreline change for the 1880s–1930s and 1930s–1980s change periods. Model predictions were found using Eq. ( 6) with k=0.31, and are given only for profile locations meeting the equilibrium criterion. Although model results match observations at some locations, an overall comparison of model hindcast versus observed shoreline retreat for both change periods, given in Fig. 9, reveals that this form of the Bruun rule has no power for hindcasting shoreline change (r2=0.05 not significant at 95% C.I.). The locations where the Bruun rule closely hindcasts the measured shoreline change (Figs. 7 and 8 ) deserve some consideration. It would be tempting to assume that these represent locations where other processes, such as those causing longshore transport losses or gains to the profile, are less active, permitting the isolated e
ect of sea level-

induced changes to be evident. However, two points argue against this interpretation. First, no statistical statements can be made about the Bruun rule’s ability to hindcast shoreline change at specific locations. Unlike the overall results in Fig. 9, no measure of variability is available for individual locations and, therefore, no statistical test can substantiate them. Second, assuming an idealized case where a coast’s evolution is dominated by longshore transport, there will always be nodes between erosional zones and depositional zones where the transport gradient, and shoreline change rate, are zero. Similarly, there will always be points where the Bruun rule exactly predicts the shoreline change even if this model of shoreline retreat were entirely invalid. Thus, we view the close association between Bruun rule hindcast and observed shoreline change at several locations as fortuitous. As described above, k=0.31 probably represents a significant underestimate of the percentage of sand in eroding shoreface sediments fronting spitbuilt barrier islands. Thus some measure of the influence of variable k values on the above results is warranted. Fig. 10 compares hindcast shoreline change using k=0.31 and k=1.00 for all profile locations, showing that overall the di
erence between hindcast change assuming 31% sand and 100% sand is small. However, the possibility still exists that the association shown in Fig. 9 could be significantly improved if individual locations were assigned correct k values. This is tested to the degree possible by assigning k=1.00 to all profile locations fronting spit-built barriers and k=0.31 elsewhere. Fig. 11 shows that this does improve the relationship between observed and predicted shoreline change slightly; r2 is increased 0.12, marginally significant at the 95% C.I. While this does leave open the possibility that improved knowledge of k would further improve the relationship, this marginally significant r2 and the small di
erence between k=0.31 and k=1.00 predictions (Fig. 10), makes it unlikely that much of the variability in observed shoreline change could be explained even with the perfect assignment of k. Several previous studies have attempted to correlate regionally-averaged rates of shoreline change with Bruun rule predictions or regional sea-level

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Fig. 7. Along-coast plot of 1880s to 1930s ( A) observed shoreline change and (B) modeled shoreline change, s, using k=0.31. Bar widths indicate the length of coast used for profile averaging. Negative numbers indicate erosion, positive numbers indicate accretion.

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Fig. 8. Same as Fig. 7 for 1930s to 1980s change period.

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Fig. 9. Observed vs. modeled shoreline change, s, using k=0.31. The line symbolizing predicted = observed is shown for reference (dotted line).

Fig. 10. Relation between modeled shoreline change using k=1.00 and modeled shoreline change using k=0.31. The line symbolizing predicted = observed is shown for reference (dotted line).

change information ( Rosen, 1978; Dean, 1990). Conceptually, this procedure should remove local variations in profile response due to local variations in the sediment budget. If shoreline change

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Fig. 11. Observed vs. modeled shoreline change using k=0.31 for headland areas and k=1.00 for spit-formed barrier islands. The line symbolizing predicted = observed is shown for reference (dotted line).

data are comprehensive enough to cover a closed littoral cell containing a balanced sediment budget with negligible o
shore losses or gains, this method should result in an improved ability to hindcast shoreline change using the Bruun rule. Sallenger et al. (1992) provide evidence, from sediment budget considerations, that the study area encompasses several complete cells of transport. We compare averaged hindcast (with 31% sand ) and measured shoreline retreat rates, using the locations meeting the equilibrium profile test criterion, and weighting each profile sample for the length of coastline that it represents (shown by the bar widths in Figs. 4, 5, 7 and 8 ). For the 1880s to 1930s the average observed change was −425 m while the average hindcast change was −305 m, or 72% of the observed. For the 1930s to 1980s the average observed change was −597 m while the average hindcast change was −348 m, or 58% of the observed. Using associated standard deviations, and an approximate t-test for samples with unequal variances (Zar, 1984, p. 131), it can be shown that at the 95% confidence level the observed shoreline change is not significantly di
erent from the hindcast for the

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1880s–1930s period (although marginal ), while for the 1930s–1980s period the di
erence is significant. This negative result must be tempered by the fact that only profile locations determined to be in equilibrium were used in along-coast averaging; it cannot be assumed that the entire littoral cell, including a balance of erosion and accretion, was included in the averaging. Previous studies, including that of Rosen (1978), did not have gaps in alongshore coverage, but also made no attempt to assess comprehensively the validity of the equilibrium assumption inherent to the Bruun rule. Because it requires a stretch of coast that satisfies the equilibrium assumption everywhere and, at the same time, encompasses a complete littoral cell, the averaging technique for improving Bruun rule hindcasts is unlikely to be a useful approach for many study areas.

4. Discussion The influence of the sediment budget, whereby sections of coast alternate between a net sediment deficit and a net sediment surplus, may be one of the primary factors explaining the inability of the Bruun rule to hindcast shoreline change for our study area. As shown by Sallenger et al. ( 1992), List et al. (1994 ) and Ja
e et al. (1997 ), the regional patterns of long-term bathymetric change clearly indicate a massive longshore redistribution of sediment, both at nearshore and shoreface depths. Everts (1985 ) incorporated sediment budget estimates in the sediment balance approach to the Bruun rule ( Eq. (4 )), computing hindcast estimates of shoreline retreat that were in better agreement with observations. However, although a sensitivity analysis demonstrated that large uncertainties in sediment budget estimates may translate to similarly large uncertainties in the hindcast shoreline change, Everts ( 1985) did not provide an error assessment with his sediment budget estimates, which were based on regional patterns of erosion and accretion. These errors are generally unavailable for even the most detailed regional sediment budget studies (cf. Kana, 1995).

Following the approach of Everts ( 1985), List et al. (1991 ) included a regionally-based sediment budget estimate in a hindcast of shoreline retreat along the Caminada–Moreau headland ( 72
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barriers in Louisiana cannot maintain their subaerial expression as they retreat. The available sandsized sediment takes the form of shoals or feeds ebb-tidal deltas (Penland et al., 1988; List et al., 1991) which are growing due to increases in tidal prism (also a direct result of relative sea-level rise and marsh disintegration). Many areas within the Louisiana barrier islands, in particular the Isles Dernieres and the Plaquemines shoreline (Fig. 1 ), seem poised for a conversion to open water through these processes related to sea-level rise.

5. Conclusions This paper presents a comprehensive test of the Bruun rule’s ability to hindcast shoreline retreat in the Louisiana barrier islands, where a wealth of bathymetric and shoreline change data are available and the rate of relative sea-level rise is extreme. Unlike most previous studies, we were able to make a detailed determination of a geometricallydefined closure depth parameter and test the critical assumption that profiles maintain an equilibrium form. We find that closure depth is highly variable throughout the study area, with deeper closure, most commonly, along more exposed parts of the coast. We conclude that the specification of a constant closure depth for the entire study area is not acceptable. The degree to which profiles maintained an equilibrium form is also highly variable through the study area, with headlands generally maintaining equilibrium and mixed results in other areas depending on the influence of changing processes (i.e. the placement of coastal structures or the growth of ebb-tidal deltas associated with adjacent inlets). Overall, only about 50% of the profiles examined could be classified as having maintained an equilibrium form; this is an important limitation in applying the Bruun rule that could not have been determined without a detailed examination of historical bathymetric data. For the 37 profile locations meeting the equilibrium criterion, we apply the Bruun rule in a numerical form accounting for a limited percent sand in the eroding shoreface sediments but disregarding sediment budget terms. Although hindcast

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values of shoreline retreat match observations at some individual profile locations, as a whole the 37 locations show no significant correlation between hindcast and observed change. Tests varying the percent sand in the model formulation, as well as a regional averaging of the results, make little improvement in the relationship. It is argued that the results at locations where hindcast values match observations should be viewed as fortuitous. In terms of a Bruun rule-type readjustment of the coastal profile, we conclude that relative sealevel rise is not the primary factor forcing the region’s shoreline change, and that the Bruun rule should not be used for predicting future rates of change in the region. Considering the area’s extreme rate of relative sea-level rise and the wealth of shoreline and bathymetric change data constraining the problem, this casts considerable doubt on the applicability of the Bruun rule to most other coasts, where sea-level rise rates are typically much lower and detailed long-term information is generally lacking. Without historical data to verify the equilibrium assumption, to determine the appropriate closure depth, and to verify Bruun rule hindcasts of observed shoreline changes, future predictions should be viewed as having little value.

Acknowledgements This work was conducted as part of the Louisiana Barrier Island Erosion Project, a cooperative study between the U.S. Geological Survey, Marine and Coastal Program and the Louisiana State University. We thank Shea Penland, Randy McBride and others at the Louisiana State University for providing shoreline position data. The bathymetric data were collected and processed though the e
orts of numerous people, including Greg Gabel, Thang Phi, Graig McKendrie, Rob Wertz, Todd Holland, Carolyn Degnan, Clint Steel, Tracy Logue, Dorothy Hopkins and Keith Dalziel. Karen Morgan is thanked for contributions to the figures.

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