Engineering Data

GLOBAL WARMING AND COASTAL EROSION

KEQI ZHANG *, 2, BRUCE C. DOUGLAS 1 and STEPHEN P. LEATHERMAN 1

* ********** *** ******* ******** and International Hurricane Research Center,

Florida International University, Miami, FL 33199, U.S.A.

E-mail: zhangk@ u.edu, abpmt9@r.postjobfree.com, leatherm@ u.edu

2 Department of Environmental Studies, Florida International University, Miami, FL 33199, U.S.A.

Abstract. One of the most certain consequences of global warming is an increase of global (eustatic)

sea level. The resulting inundation from rising seas will heavily impact low-lying areas; at least 100

million persons live within one meter of mean sea level and are at increased risk in the coming

decades. The very existence of some island states and deltaic coasts is threatened by sea level rise.

An additional threat affecting some of the most heavily developed and economically valuable real

estate will come from an exacerbation of sandy beach erosion. As the beach is lost, xed structures

nearby are increasingly exposed to the direct impact of storm waves, and will ultimately be damaged

or destroyed unless expensive protective measures are taken. It has long been speculated that the

underlying rate of long-term sandy beach erosion is two orders of magnitude greater than the rate of

rise of sea level, so that any signi cant increase of sea level has dire consequences for coastal inhab-

itants. We present in this paper an analytical treatment that indicates there is a highly multiplicative

association between long-term sandy beach erosion and sea level rise, and use a large and consistent

data base of shoreline position eld data to show that there is reasonable quantitative agreement

with observations of 19th and 20th century sea levels and coastal erosion. This result means that the

already-severe coastal erosion problems witnessed in the 20th century will be exacerbated in the 21st

century under plausible global warming scenarios.

1. Introduction

Coastal erosion is a global problem; at least 70% of sandy beaches around the

world are recessional (Bird, 1985). Domestically, approximately 86% of U.S. East

Coast barrier beaches (excluding evolving spit areas) have experienced erosion

during the past 100 years (Galgano et al., 2004). Widespread erosion is also well

documented in California (Moore et al., 1999) and in the Gulf of Mexico (Morton

and McKenna, 1999). There must be a worldwide cause for such ubiquitous beach

erosion. The three possible candidates are sea level rise (SLR), change of storm

climate, and human interference. But there is no indication of a signi cant increase

in storminess in this century (Zhang et al., 1997; WASA Group, 1998; Zhang et al.,

2000), and human interference is neither worldwide in extent nor uniform region-

ally. Therefore, SLR remains as the plausible candidate (Leatherman, 1991), and

determining whether or not the rate of global SLR is increasing is of the utmost

importance. However, the rate of 20th century global sea level (GSL) rise is the

subject of much controversy; the Third Assessment Report of the Intergovernmen-

Climatic Change 64: 41 58, 2004.

2004 Kluwer Academic Publishers. Printed in the Netherlands.

42 KEQI ZHANG ET AL.

tal Panel on Climate Change (IPCC; see www.ipcc.ch) was unable to provide more

than a broad range (about 1 2 mm per year) for 20th century GSL rise, and the

extreme bounds given for the total 21st century rise are 10 90 cm. If the lower

bound is correct, little effect will be felt. If the upper bound occurs, the results will

be calamitous, since more than 100 million persons today live within one meter of

mean sea level. The economic scale involved is equally vast.

When discussing impacts of sea level rise, it is very important to distinguish

inundation from erosion. Concerning the former, as sea level rises, the high water

line will migrate landward in proportion to the slope of the coastal area. In some

areas the slope is very gradual, and the impact from sea level rise can be severe. For

example, for low-lying regions such as salt marshes, an increase in the rate of sea

level rise much beyond a few mm per year can result in marsh destruction because

the plants there cannot respond rapidly enough to the increasing water level and

drown.

Erosion of sandy beaches is an entirely different physical process from inun-

dation. It involves a redistribution of sand from the beach face to offshore. It is

most commonly realized during coastal storms. These storms are accompanied by

a temporary increase of local sea level (the storm-generated surge above the normal

astronomical tide) so that energetic storm waves are able to attack higher elevations

of the beach and dune. Sediment there is extracted and put into suspension by the

waves and carried offshore. Much of the sand is returned to the beach after the

storm by long-period swell waves during normal water level. This phenomenon

suggests that water level plays an important role in beach erosion; a quantitative

demonstration of the relationship of storm erosion magnitude on the U.S. East

Coast from nor easters and their accompanying storm tide amplitude and duration

has been given by Zhang et al. (2001). The issue for global warming scenarios

concerning erosion is related, but takes this form what is the effect on long-

term erosion if water levels are secularly increasing, rather than only temporarily

as is the case of coastal storms? The crucial role in erosion played by elevated

water level during coastal storms clearly makes it plausible that long-term enduring

increases of sea level will monotonically increase long-term erosion rates.

2. Beach Erosion and Relative Sea Level Rise (RSL)

2.1. THE 2- DIMENSIONAL SANDY BEACH EROSION MODEL

Bruun (1954, 1962) rst constructed a simple 2-dimensional (cross-shore) model

based on the equilibrium beach pro le concept to estimate the erosion of sandy

beaches in response to rising sea level. His model is based on the following

assumptions:

1. The active beach pro le perpendicular to the shoreline tends toward an equi-

librium form for a given wave regime, and extends out to the so-called depth

43

GLOBAL WARMING AND COASTAL EROSION

Figure 1. Active cross-shore beach pro le geometry for derivation of the two-dimensional Bruun rule

of beach erosion.

of closure (DOC). The DOC is the water depth (typically 10 m) at which

ocean surface waves no longer signi cantly transport bottom sediments. The

equilibrium active beach pro le is thus de ned as an idealized statistical av-

erage pro le over seasonal and storm-induced uctuations, and includes an

underwater part that makes up most of the pro le.

2. If other conditions remain unchanged and sea level rises, the active beach

pro le will achieve equilibrium with the new sea level by shifting landward

and upward. This will result in erosion of the upper shoreface, with sediment

deposition on the lower (mostly underwater) part of the pro le (Figure 1).

3. Sediment eroded from the upper beach is equal to that sediment deposited on

the nearshore bottom. In addition, there is no net sediment exchange between

the active beach pro le and the outer shoreface (i.e., beyond the DOC).

4. The increase in elevation of the nearshore bottom resulting from deposition of

sediments from the beach face and dune is equal to the rise of sea level.

Given these conditions, a two-dimensional formula for shoreline movement due

to a rise of sea level is given by inspection of Figure 1:

(DB + DC )

s(DB + DC ) = al or a = s = (active pro le slope) s, (1)

l

44 KEQI ZHANG ET AL.

where s is shoreline recession, DB is the elevation of the shore above sea level, DC

is the depth of closure, a is the rise of sea level, and l is distance from the shore

to the closure point . The active pro le slope, (DB + DC )/ l, of the total beach

pro le (which includes the active portion that is underwater) is about 0.01 0.02 at

most sandy coasts. The Bruun equation thus produces s/a = 50 to 100 in terms of

the range of average slopes. This ratio range of s/a is commonly used as a rule of

thumb to estimate shoreline retreat due to sea level rise (SCOR, 1991).

Bruun did not present a rigorous mathematical derivation of Equation (1) in

his papers (Bruun, 1962, 1983), which has caused some confusion in the coastal

research community. For example, Rosen (1978) argued that l in Equation (1)

should be replaced by the distance from the cross point (x3 in Figure 1) to the

closure depth. Allison and Schwartz (1981) gave another analysis of the Bruun

model, and argued that it only holds if beach pro les follow certain curves. Dean

and Maurmeyer (1983) derived the Bruun model by balancing the volume of sand

eroded by shoreline retreat to that deposited by elevating the active pro le. We

present here an alternative mathematical derivation of Equation (1), and show that

even though very simple, the Bruun model has considerable generality.

Assuming the initial and subsequent beach pro les in response to sea level

rise are f (x) and f (x) (see Figure 1), an equation can be written according to

statement (3), above:

x2 x3

[g (x) f (x)dx + [f (x) f (x)]dx =

x1 x2

(2)

x4 x5

= [f (x) f (x)]dx + [g(x) f (x)]dx .

x3 x4

In terms of statement 1, 2 and 4, we have

f (x) = f (x + s) + a . (3)

Assuming that g(x) and g (x) follow the same function, it follows that

g (x) = g(x + l) + (DB + DC ). (4)

Substituting Equations (3) and (4) into Equation (2), we have

x2 x5

g(x + l)dx + f (x)dx + (DB + DC )(x2 x1 ) =

x1 x2

(5)

x4 x5

= f (x + s)dx + g(x)dx + a(x4 x1 ).

x1 x4

Considering x4 x1 = x5 x2 = l and x1 x1 = x5 x4 = s, nally we obtain a

result identical to that given in Equation (1) from very simple arguments:

(DB + DC ) = al . (6)

45

GLOBAL WARMING AND COASTAL EROSION

This derivation shows that the conjecture by Bruun is not dependent on the shape of

the pro le, nor the point of intersection of the new and old pro le, nor the position

of or seaward slope angle of the offshore bar.

There is one assumption in the derivation of Equation (6) that does not come

from the statements 1 4 of the Bruun rule. We assumed that g(x) and g (x) follow

the same function, but this assumption might not be true. However, even in the

extreme condition

g (x) = h+a

(7)

g (x) = h + (DB + DC )

(i.e., the ramps are vertical, a highly unlikely outcome), the maximum error due to

the difference of g (x) and g(x) is equal to sa. This area is insigni cant compared

to (DB + DC )s when a/(DB + DC ) 1. For example, sea level rose 20 40 cm

(Douglas, 1991) in the past century on the U.S. East Coast, and the value there

of (DB + DC ) is normally 8 12 m (Bruun, 1983), giving sa/(DB + DC )s

1/20 1/60. Therefore, it is appropriate mathematically to use the Bruun model

to compute the underlying long-term beach response to sea level rise when the rise

is small compared to the active beach pro le height (DB + DC ).

2.2. METHODS TO EXAMINE BEACH CHANGES IN RESPONSE TO SEA LEVEL

RISE

There are two basic ways to test the Bruun rule: (1) comparing beach pro les

before and after water level rise (Hands, 1983; Schwartz, 1965, 1967; Mimura and

Nobuoka, 1995) and (2) comparing long-term shoreline change rates with sea level

rise rates spatially to test whether sea level rise is correlated with beach erosion

(Rosen, 1978). In the rst case, it is required that there is no net lateral (longshore)

sediment transport because the Bruun formula is for two-dimensional cross-shore

beach pro le change in response to sea level rise. Schwartz (1965, 1967) veri ed

Bruun s hypothesis under controlled conditions in a small wave tank, and Hands

(1980, 1983) further substantiated the potential of the Bruun model using Lake

Michigan as a full-scale natural laboratory using the rst method. It is not surpris-

ing that the Bruun formula is applicable in wave tanks and the U.S. Great Lakes

because the model is a reasonable rst approximation to the actual physical situa-

tion in which no signi cant longshore sediment transport exits. Bruun s result came

to be called the Bruun rule later in the literature, and has been used extensively to

predict the impact of sea level rise on beaches (Leatherman, 1991; Nicholls et al.,

1995).

Results of the application of the Bruun rule to open-ocean coasts are con icting.

Some work seems to verify it (Mimura and Nobuoka, 1995), while others allege

that the Bruun rule does not work (Pilkey and Davis, 1987). A review of the Bruun

rule and other extended models concerning the response of beaches to sea level

rise has been presented by SCOR (1991). There is considerable controversy and

46 KEQI ZHANG ET AL.

debate in the literature about the Bruun rule (SCOR, 1991; Leatherman et al.,

2000a,b; Pilkey et al., 2000). This is not surprising because much more complicated

conditions exist in open-ocean coasts than those in wave tanks and the Great Lakes.

Open ocean beaches at speci c sites exhibit complex behavior (for example,

rapid erosion downdrift of tidal inlets, or from antecedent geological factors) that

departs from a simple linear relation of shoreline position to sea level. Thus the

model cannot be used to predict future shoreline position for an arbitrarily selected

beach location. Nevertheless, the model does reveal many interesting facets of the

larger question, which is how large regions of coastline comprised of sandy beaches

can be expected on average to respond to increases of sea level that will result from

global warming. In essence, we will examine whether the Bruun rule is useful to

investigate what will happen in an average sense to sandy beaches, rather than to

predict the behavior at any particular beachfront property. This approach is very

much in the spirit of using approximate climate models to determine the sensitivity

of the overall climate system to variations of one parameter or another. The main

objective of this study is to test if the Bruun rule shows a relation to the rates of

sea level rise and sandy beach erosion along the U.S. East Coast using long-term

historical shoreline position and sea level data.

There are several possible problems when historical shoreline data are used to

test the Bruun rule, which involve: (1) using poor quality data (Dean, 1990); (2)

using short-term data (Galvin, 1983); and (3) failing to remove or minimize the

in uence of inlets and human interference on sediment supply (Pilkey and Davis,

1987). For example, Dean (1990) utilized available data on a state-wide basis to

compare shoreline change rates to average sea level rise rates. His results showed

considerable scatter and no apparent relationship to sea level rise. In fact, New

York and Delaware beaches were mistakenly thought to be accretional on average

because a poor quality data set from May et al. (1983) was utilized; these areas

are clearly erosional on average (Zhang, 1998). There are two problems with the

May et al. (1983) historical shoreline change database. The data were collected

from various sources, and there was no quality control nor error estimation for

these heterogeneous data. The other problem involves employing a low accuracy

technique of using uncorrected aerial photography to determine shoreline changes

(Leatherman, 1983). These problems can be addressed by selecting study sites

where long-term and high quality historical shoreline position data exist.

The U.S. East Coast is a nearly ideal location for testing the Bruun rule since

both shoreline position and sea level histories are available there for the last 100+

years. Sea level rose by varying amounts ( 20 40 cm) along the U.S. East Coast

during the 20th century. The variation observed is due primarily to on-going glacial

isostatic adjustment (GIA) (Peltier, 2001). With the disappearance of the great

ice sheets that advanced as far south as Long Island about 21,000 years ago, the

elevated forebulge region adjacent to the ice load adjusted by sinking while the

formerly ice covered region rose. GIA occurs on a very large scale, and con-

tinues today even though the ice was gone by 5000 6000 years BP. This can

47

GLOBAL WARMING AND COASTAL EROSION

Figure 2. Relative sea level rise rates from Hudson Bay, Canada to Key West, Florida.

clearly be seen in Figure 2. What is shown are 20th century trends of sea level

(see www.pol.ac.uk/psmsl) from long tide gauge records approximately ( 10 deg)

along a meridian from Hudson Bay (the center of the great Laurentide ice sheet

load 21,000 yrs BP) to Key West, Florida. Note that sea level is still falling today

about 10 mm per year at the Churchill tide gauge site on Hudson Bay due to the

ongoing viscoelastic rebound. Coming south, sea level rise increases to a maximum

of about 4 mm per year in the mid-Atlantic, and then recedes to near a background

value of about 2 mm per year at Key West, Florida. This large geographic scale of

sea level variation and the excellent coverage of the U.S. East Coast by long tide

gauge records means that it is possible to compute by interpolation accurate values

of relative sea level rise for beaches whose erosion rates are known.

2.3. SHORELINE POSITION DATA SOURCES

Existing shoreline position data available for this investigation consist of National

Ocean Survey (NOS) T-sheets, aerial photographs, and kinematic GPS surveys.

The earliest data in this collection reaches back to the mid-19th century. The high

water line (HWL) is used as the shoreline indicator in this study because it can be

identi ed in the eld as a dry/wet boundary, interpreted on aerial photographs, and

is the shoreline indicator used in historical NOS T-sheets.

Reliable vertical aerial photography only dates back to the early 1940s, but

NOS T-sheets extend the record to the mid 1800s. The available digitized shoreline

position data covers the open-ocean coasts from Long Island, New York to South

Carolina except for the southern part of North Carolina. GPS-surveyed shoreline

positions in 1993 and 1997 along the south shore of Long Island, New York,

48 KEQI ZHANG ET AL.

Delaware, and North Carolina are also incorporated into the existing data set.

This data set of eld and aerial photography measurements has been extensively

evaluated for suitability for long-term shoreline position analysis by Crowell et al.

(1991), Galgano (1998), Zhang (1998), Galgano et al. (1998), Douglas and Crowell

(2000) and others, and the data quality has been found to be accurate enough to be

useful for investigating the underlying trend of shoreline position.

2.4. THE OBSERVED RELATIONSHIP BETWEEN SEA LEVEL RISE AND BEACH

EROSION

The Bruun rule, as noted earlier, has been veri ed experimentally by comparing

beach pro le positions to water levels in wave tanks and lakes. However, for open-

ocean beaches, conclusive tests are much more dif cult because the model is two

dimensional, which describes beach erosion due to sea level rise only if other

factors hold constant. Unfortunately, other in uencing factors are spatially and

temporally variable in most natural conditions. Further, shoreline changes induced

by variability of sediment supply can be much larger than those resulting from sea

level rise on some coasts. Thus the real oceanic beach situation can range widely

from the ideal situation of wave tanks or lakes.

The key to testing the Bruun rule along open-ocean coasts is to remove or

minimize regions of shoreline change induced by gradients in longshore sediment

transport and variations in the active beach pro le slope. To do so, we should

seek shoreline sections where no longshore sediment transport occurs, or more

realistically, where longshore sediment transport is in equilibrium (i.e., there is no

gradient). However, it is dif cult to nd many such beaches. The solution is to com-

pare sea level rise rates with shoreline change rates for geomorphic units in uenced

by similar factors except for the rate of sea level rise. These units are the coastal

compartments recognized by Fisher (1967). He divided the U.S. mid-Atlantic

coast into four coastal compartments displaying similar geomorphic behavior. The

sediment exchange between these compartments is negligible because they are sep-

arated from each other by deep river entrances and bays. The four compartments

include Long Island, New York, New Jersey, Delmarva (Delaware, Maryland, and

Virginia), and North Carolina (Figure 3). South Carolina exhibits similar behavior,

and therefore was included in our study as a fth coastal compartment.

Each coastal compartment consists of four distinct units: (1) terminal north spit,

(2) low, eroding headland, (3) long barrier islands with only a few inlets backed by

open lagoons, and (4) short-stubby barrier islands with marsh- lled embayments

separated by many inlets (Stauble, 1989; Leatherman, 1993). For example, Cape

Henlopen is the north spit of the Delmarva coastal compartment. The shore section

between Rehoboth Beach and Fenwick Island constitutes the eroding headland

which provides the sediment source for the barrier islands to the south. The long

barrier unit is composed of Fenwick Island (actually a sand spit) to Ocean City

Inlet and Assateague Island. Finally, a barrier island chain with more than ten short

49

GLOBAL WARMING AND COASTAL EROSION

Figure 3. Location of coastal compartments, mid-Atlantic bight, U.S.A. The South Carolina unit is

not a de ned coastal compartment, but the long arcuate shore spanning the northern part served our

purpose for this analysis.

members (the Virginia barrier islands) forms the southern unit of the Delmarva

compartment (Figure 4). The southernmost portions of a compartment, with their

large number of inlets, are not usable to study the beach response to sea level

rise because the in uence on sand supply of the multitude of inlets obscures the

underlying erosion rates.

We have seen (Figure 2) that relative sea level trends change along the U.S.

East Coast on a large geographic scale because of glacial isostatic adjustment on-

going since the last deglaciation that began about 21,000 years ago. Sea level rise is

thus consistent on a scale of several hundred kilometers, and the value of sea level

rise at a location on the East Coast can be interpolated accurately from Figure 2.

This enables us to compare observed beach erosion rates to the local rate of SLR

continuously along the barrier beaches and determine if there is a relationship. But

the effects of longshore sediment transport, active pro le slopes (see Equation (1)),

and other local factors within a coastal compartment can result in shoreline changes

50 KEQI ZHANG ET AL.

Figure 4. Long-term shoreline change rates at Delmarva. Shoreline change rate at each transect at

100 m interval is determined by linear regression (excluding storm-in uenced shoreline positions).

Note that large shoreline change rates occur near inlet-in uenced areas, which therefore cannot be

used to examine the relationship between sea level rise and beach erosion.

51

GLOBAL WARMING AND COASTAL EROSION

larger or smaller than the underlying ratio between sea level rise and beach erosion

predicted by the Bruun rule. Shoreline segments in uenced by tidal inlets and

coastal engineering projects (such as seawalls or beach replenishment) obscure the

relation of sea level rise to beach erosion because such segments depart radically

from the assumptions of the model. Inlets play the dominant role in determining

shoreline changes wherever these breaks in the littoral drift system are present.

Opening, closing, and migration of inlets can affect many kilometers of updrift and

downdrift beaches by changing longshore sediment supply. More than 65% of the

shoreline along the U.S. East Coast is in uenced by inlets (Galgano et al., 2004).

As an example of an inlet-in uenced shoreline section, Figure 5 shows the

downdrift arc of erosion and updrift accretion llet at the Indian River Inlet on

the Atlantic coast of Delaware. The arc of erosion is obviously much longer than

the accretionary llet. This situation is true for most inlets because ebb and ood

tidal deltas trap a large volume of sediment. Far more sediment than that deposited

at the updrift side is eroded downdrift of an inlet in order to satisfy the longshore

current. It is clear that shoreline change (erosion and accretion) does not average

out at inlet areas, although the volume of deposited sediment at the updrift side in

combination with the sediment held in ood and ebb tidal deltas may still be equal

to the volume of sediment lost at the downdrift side. Thus, the greater length of

the erosion arc compared to the accretion zone biases the average shoreline change

rate in a compartment toward erosion, and renders meaningless a comparison of sea

level rise to a compartment-wide average erosion rate if inlet-in uenced shorelines

are included. Therefore, the erosion and accretion zones generated by inlets have to

be excluded from the calculation of average shoreline change rates. The prior study

which relied on state-wide shoreline change data failed to nd any correlation with

sea level rise (Dean, 1990).

Lateral growth of spits and coastal engineering projects can also alter shoreline

change processes. These alterations, whose effect is highly variable, create discon-

tinuities in the historical shoreline position record that mask underlying long-term

behavior. To eliminate the bias induced by inlets, spits, and coastal engineering

projects, only the shoreline segments not in uenced by these factors in each coastal

compartment are used in this paper to estimate the average long-term erosion rates.

Shoreline segments in uenced by inlets were identi ed and removed by com-

paring spatial variations of shoreline trends before and after inlet opening or

stabilization (Galgano et al., 2004). This method is very straightforward: Shore-

lines altered by inlets will deviate from previous long-term trends, but will return to

their long-term trend at a point beyond the in uence of the inlet (Galgano, 1998).

The shoreline segments in uenced by coastal engineering projects and lateral spits

can also be identi ed using a similar methodology.

The shoreline change rates used for this study were computed at a spatial inter-

val of 100 meters in ArcView using linear regression (Zhang, 1998). The detailed

procedure to compute shoreline change rates can be found in Leatherman and Clow

(1983). Crowell et al. (1997) and Douglas and Crowell (2000) have demonstrated

52 KEQI ZHANG ET AL.

Figure 5. Shoreline change rates near Indian River Inlet on the Delaware coast. Shoreline change rates

are computed every 200 m using the linear regression (LR) method. Note the length of erosion zone

on downdrift side is about ve times that of updrift shoreline accretion. Therefore, shoreline changes

induced by inlet activities always bias average shoreline change rates greatly toward erosion.

that linear regression is the best estimator of long-term shoreline change rates

which we utilized herein. However, arriving at the best estimate of the long-term

shoreline change rate is complicated by the existence of seasonal and interannual

variations of shoreline position caused by storms that are not modeled by linear

regression. Storms can result in severe beach erosion with subsequent recovery

lasting in some cases several years to as much as a decade (Thom and Hall, 1991;

Morton et al., 1994; Douglas and Crowell, 2000). Thus post-storm shorelines

deviate considerably from the long-term shoreline trend. Including these storm-

in uenced positions in the shoreline change data set distorts the estimate of the

long-term trend, especially when shoreline position records are less than about 80

years long (Galgano et al., 1998). For this reason all shoreline positions in uenced

by large storms were excluded from linear regression analyses performed in this

study.

In addition to eliminating shoreline change rates for areas in uenced by inlets

and coastal engineering projects, the well-known erosion hot spot at Sandbridge,

Virginia was removed in the computation of average shoreline change rate because

large quantities of sand are lost offshore there (Kimball and Wright, 1989) due to

focusing of wave energy.

The percentage of shoreline sections not in uenced by inlet and coastal engi-

neering projects are presented in Table I. These shoreline sections constitute about

53

GLOBAL WARMING AND COASTAL EROSION

Table I

Percentage of shore sections not in uenced by inlets and coastal engineering projects

Location Length (km) (Length of sections not (Length of erosional areas

in uenced by inlets and not in uenced by inlets and

coastal engineering projects)/ coastal engineering

(length of entire projects)/(length of entire

compartment) compartment)

Long Island, NY 134 53% 34%

New Jersey 177 18% 13%

Delmarva 176 39% 29%

North Carolina 145 30% 24%

South Carolina 265 29% 25%

All Areas 898 32% 24%

32% of the entire study area, of which 75% and 25% are erosional and accretional,

respectively. The local effects of accretion and erosion caused by longshore sed-

iment transport are averaged out by using tens of kilometers of shoreline in rate

computations because there are no sediment sinks, such as ood and ebb deltas.

The local geological effects are also minimized by rate averaging at spatially large

scales. Therefore, average change rates of shoreline sections not in uenced by

inlets and coastal engineering projects on a compartment basis are used to test

the Bruun rule.

The rates of sea level rise for each shoreline sector were interpolated based on

the trends from tide gauges along the coast (Figure 2). The nal results were in-

sensitive to the interpolation method employed. We chose to use the most accurate

method, which was to determine the latitude for each shoreline transect and obtain

an estimate of sea level trend for it from trends determined by tide gauges. An

interpolating quadratic polynomial was obtained from a least squares t to the sea

level trends from the coastal tide gauges along the compartments having a record

length of 60 years. Finally, the erosion rate for each transect was divided by its

rate of sea level rise, and the average rate of erosion divided by rate of sea level

rise was computed for each compartment. We nd that the ratio of shoreline change

rate, r, to the rate of SLR, s, varies from about 50 to 120, with an average value of

78 for the ve coastal compartments (Table II). This rate is in good agreement to the

rule of thumb for the Bruun rule. Thus the rate of shore erosion is approximately

two orders of magnitude greater than the rate of sea level rise, and Bruun rule

is validated. But the variability of the results between compartments is large and

needs consideration.

We rst note that the ratio of erosion to SLR rates for Long Island, New York

and Delmarva (e.g., Delaware, Maryland, and Virginia) are relatively low at 50

54 KEQI ZHANG ET AL.

Table II

Ratios of shoreline change rates, r, to rates of SLR, s, for each coastal compartment. Compartment

averages are shown, but the rate of RSL rise for each transect was computed by interpolation from

Figure 2 for the actual latitude of the transect. Negative sign of shoreline change rate indicates that

beaches have experienced erosion

Compartment Long Island, New Jersey Delmarva North South

New York Carolina Carolina

Average latitude (degrees) 40.86 39.92 38.30 35.85 33.76

Average RSL rise rate 2.62 3.17 3.83 4.16 3.81

(a, mm/yr)

Average shoreline change 0.13 0.38 0.20 0.32 0.34

rate (s, m/yr)

s/a 50-120-**-**-**

Average s/a, all 78

compartments

and 52, respectively, compared to the other compartment results. There is evidence

in both cases that beach replenishment is occurring naturally. On-going erosion

of the Montauk bluffs at the eastern end of Long Island is providing sediments

to downdrift (westward) areas. Also, there is strong scienti c evidence that relict

glacial shoreface sand is being fed onto the beach (Schwab et al., 2000). In the case

of Delmarva, there is a relict Pleistocene barrier in Delaware that supplies sand to

the littoral system (Kraft, 1971).

Leatherman et al. (2000b) demonstrated that the shoreline change rate is about

150 times that of the sea level change rate. That result was obtained by remov-

ing the acretional sections from shorelines not in uenced by inlets and coastal

engineering projects. Such accretion can result from local variations in longshore

sediment transport, sand feed from offshore, or the in uence of local geological

factors. Therefore, localized erosion effects caused by longshore sediment trans-

port are not averaged out by removing all accretional sections, and the ratio can be

viewed as the upper bound of the ratio of shoreline change rate versus the rate of

sea level rise. The average ratio of 78 derived herein can be viewed as the lower

bound of the ratio because some shoreline sections may receive a sand feed from

offshore (Kraft, 1971; Schwab et al., 2000).

55

GLOBAL WARMING AND COASTAL EROSION

3. Discussion and Conclusions

The agreement between the simple Bruun rule and observed erosion trends along

the U.S. East Coast suggests that sea level rise induces beach erosion, and further

that the rate of erosion is about two orders of magnitude greater than the rate of sea

level rise. Of course, this does not mean that sea level rise causes long-term erosion

directly; there is too little energy associated with it. In our view, rising sea levels

act as an enabler of erosion because higher water levels allow waves to act further

up the beach pro le and move sediment seaward. The Bruun rule describes how

beach pro les respond to sea level rise if other conditions (e.g., sediment supply)

remain unchanged, and this process will occur as long as there is a rise in sea level.

Some may nd it surprising that we have not considered in this analysis the

possibility of storm activity as an alternative to sea level rise as a determiner of

barrier beach erosion rates. But there is substantial evidence that the effect of

storms on shoreline position is episodic, rather than secular. Morton (1994) in his

study of beach erosion and recovery at Galveston Island, Texas due to Hurricane

Alicia found that recovery after the storm was proportional to the long-term rate of

erosion, and approached 100% after about 10 years for those areas that were stable

before the storm. Galgano (1998) and Douglas and Crowell (2000) also found that

in Long Island, New York and Delaware that beach width appeared to recover to

the long-term trend after severe nor easters.

Zhang et al. (2002) analyzed a more extensive set of shorelines that veri ed the

earlier studies on beach recovery. The fact that barrier beaches along the U.S. East

Coast recover to their long-term trend positions after storms regardless of storm

severity strongly suggests that storms are not responsible for long-term beach ero-

sion. In other words, if long-term erosion were event-driven, one would expect that

larger storms would result in more net shoreline retreat than smaller ones, which is

not supported by the available data. Finally, there is a critical and fundamental fact

that cannot be overlooked; the U.S. East Coast barrier islands have existed in more

or less their present state (albeit in more seaward positions) for at least the last

few thousand years, indicating that they exist in a state of dynamic equilibrium.

If this were not true, great storms would have destroyed the barrier islands long

ago by overwash processes and cutting of inlets. But if left alone, microtidal inlets

eventually close and the shoreline straightens, and dunes are rebuilt by aeolian

processes. At any given time (such as now) we have a snapshot of the long-term

situation blurred by inlet activity. From this perspective, sea level rise is ultimately

responsible for long-term beach erosion on the U.S. East Coast barrier beaches,

and probably for sandy beaches everywhere.

56 KEQI ZHANG ET AL.

Acknowledgements

This research was supported by The Andrew W. Mellon Foundation and the

National Aeronautics and Space Administration.

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(Received 22 March 2002; in revised form 13 August 2003)

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