Ad Hoc Expert Meeting on

Climate Change Impacts and Adaptation: A Challenge for

Global Ports

29 – 30 September 2011

Sea Level Rise and the Increase in Rubble Mound Breakwater Damage

By

M. Esteban, H. Takagi, and T. Shibayama

This expert paper is reproduced by the UNCTAD secretariat in the form and language in which it has been received. The views expressed are those of the author and do not necessarily reflect the views of the UNCTAD.

SEA LEVEL RISE AND THE INCREASE IN RUBBLE MOUND

BREAKWATER DAMAGE

Miguel Esteban1 Hiroshi Takagi

2 and Tomoya Shibayama

3

Sea level rise could threaten the stability of rubble mound breakwaters in the future, as greater water

depth will allow larger waves to reach these structures. Particularly worrying, however, is the

prospect of an acceleration in the pace of sea level rise as a result of climate change, especially after

2050. This could lead to a change in the philosophy behind the design of breakwaters and ports,

leading to substantial increases in the cost to build and maintain these costly structures. Particularly

there would have to be a shift in the main parameter used to calculate breakwater sections from the

significant wave height (Hs) to the limiting breaker height (Hb), due to future uncertainties in wave

climate. The likely increases in breakwater costs due to this shift in design philosophy were

evaluated for 4 different rates of sea level rise showing that for the more extreme cases of sea level

rise (for a sea level rise of 1.3m over 50 years) a breakwater designed in 2050 would be between

around 8% and 66% more expensive than one designed in the 20th century not taking into account

sea level rise.

INTRODUCTION

As a consequence of global warming due to increasing concentrations of

greenhouse gases in the atmosphere sea level rise is expected to accelerate in the

course of the 21st century. During the 20

th century global average sea level rose

by an average of around 1.7mm per year, with satellite observations showing

increases of 3mm since 1993, according to the Fourth Assessment Report of the

Intergovernmental Panel on Climate Change, or IPCC 4AR. Future IPCC

projections show that by the end of the 21st century sea level could be between

0.18 and 0.59m higher than at present. More extreme scenarios, such as those by

Vermeer and Rahmstorf (2009), argue that sea level rise could be in the range of

0.81 to 1.79m by 2100.

Sea level rise and other effects of climate change, such as an increase in tropical

cyclone intensity (Knutson and Tuleya, 2004, Elsner et al., 2008, Landsea et al.,

2006, Webster and Holland, 2005) could alter future wave patterns (Mori et al,

2010) and this could lead to increased damage to coastal structures. Generally, it

has been proven that the damage due to winds increases exponentially with

regards to the maximum wind speed, though a number of variables complicate

the assessment of economic damages (Hallegate, 2007, Pielke, 2007)

Typically nowadays the effect of climate change is ignored when designing

breakwaters, which could lead to them being under-designed towards the end of

1Dept of Civil and Environmental Engineering, Waseda University, Ookubo, Shinjuku-ku, Tokyo 169-8555,

Japan 2 Japan International Cooperation Agency, Disaster Management Division 1, Nibancho Center Building 5-25,

Niban-cho, Chiyoda-ku, Tokyo 102-8012, Japan 3 Dept of Civil and Environmental Engineering, Waseda University, Ookubo, Shinjuku-ku, Tokyo 169-8555,

Japan

their life for the cases of rapid increases in sea levels. The effect of sea level rise

on caisson breakwaters was investigated by Okayasu and Sakai (2006), who

found that the probability of sliding failure could increase by up to 50% in the

period ranging from 2000 to 2050 (assuming a design life of 50 years), and that

the adaptation cost could correspond to between 0.5 and 2.3% of the sectional

area of the caisson. Takagi et al. (2010) used a SWAN-based model to show

how a 10% potential increase in the future wind speed of typhoons resulting

from the warming of surface sea temperatures can lead to a 21% increase in the

significant wave height generated by these winds. This effect, together with the

rise in sea level detailed in the IPCC 4AR could make the expected sliding

distances for the breakwaters at Shibushi Ports in Japan up to three times greater

than at present.

However, to the authors’ knowledge, no research has been carried out on the

effect that climate change induced acceleration in sea level rise can have on the

design of rubble mound breakwaters. To do so, the present paper will introduce

a variety of sea level scenarios, which will be assumed to take place during the

design life of the structure (50 years).

The purpose of the present work, however, is not to evaluate the potential

increase in damage to a single breakwater, as this would require an in-depth

assessment of the wave conditions present at that particular breakwater. Rather,

the authors argue that an increase in water depth could result in an increase in

the future damage potential to breakwaters in general, and the objective of the

present paper is to provide a general idea of the magnitude of the increase in

cost (in terms of the cross sectional area of breakwater required) to adapt to this

specific problem of climate change. Currently, the wave depth in front of a

breakwater limits the height of the waves that can reach it, and thus an increase

in future water depth could result in higher potential damage to breakwaters,

provided that the wind speed is enough to generate the required waves. Although

this might not apply to all areas in the world, expected increases in tropical

intensity (see Knutson and Tuleya, 2004) make it likely that this will be the case

in areas affected by tropical cyclones. Furthermore, the patterns of wave action

in different parts of the world are likely to change in the future (Mori et al,

2010). The authors will thus conclude how it will be necessary to shift the

current design methodology from one which focuses on the significant wave

height (Hs) to the limiting breaker height (Hb).

METHODOLOGY

Breakwater Design according to Van der Meer Formula

Rubble mound breakwaters consist of several layers of stones, with the centre of

them typically made of quarry run and the outer layer consisting or armour units.

The present study uses the Van der Meer formula (1987) for the design of a

variety of breakwater sections. This formula uses the significant wave height

(Hs) as the main design parameter and derives two different expressions

according to the type of breaker. For plunging breakers

(1)

For surging breakers

(2)

Where Ns is a parameter knows as the stability number, a is the relative

underwater density of the armour, Da is the nominal armour unit diameter, Pb is

the overall porosity of the breakwater, Nw is the number of waves acting on the

breakwater, is the angle of the front slope of the structure with respect to the

horizontal and Sa is the armour damage, defined as

(3)

where Ae is the erosion area of the breakwater profile between the still water and

plus/minus one wave height. For Sa=0 an infinite Da would be required, and

hence Van der Meer recommends using Sa=2 as an equivalent for zero damage.

Limiting Breaker Height

This parameter will have a crucial influence on the behaviour of a rubble mound

breakwaters in the event of rapidly rising seas, as it will increase the height of

the waves that will be able to reach the structure. In the present study, the

following equation proposed by Goda [1985] is used for evaluating the limit

wave height that is possible in front of the breakwater Hb.

(4)

in which h is the water depth at the breakwater, L0 is the deep water wave length

and is the slope of the sea bottom.

Estimation of Run-Up

In order to adequately compute the required size of a breakwater it is necessary

to calculate the estimated run-up of the waves. It is important to note that sea

level rise will cause an increase in Hb, and hence the heights of the wave

reaching the breakwater could also be increased. Hence, the potential run-up on

the breakwater will also increase and will require engineers to design the

structures with higher crests that at present so that there is not significant

overtopping towards the end of their working lives. Van der Meer (1993)

provides a relatively simple estimate of run-up, for ξp<2:

(5)

Or for ξp≥2:

(6)

Where r2% is the runup exceeded by 2% of the waves, rf is the factor which takes

into account friction, any horizontal berm sections in the front face, the angle of

approach and whether the waves are short crested (for simple rock breakwater

with waves coming normal to the face rf=0.5). The surf similarity parameter, ξp,

is based on the peak period of the wave spectrum.

Breakwater Sections Considered

The effects that sea level rise will have on rubble mound breakwaters will vary

greatly depending on factor such as the geometry of the breakwater, the

bathymetry in front of it or the wave climate. A total of 12 breakwaters sections

were calculated, in water depths ranging from 3 to 25m. Each section was then

calculated for a variety of significant wave heights (Hs), ranging from 3 to 15m.

Each Hs was calculated for a total of 5 wave periods (from 6 to 14 sec).

Furthermore, all breakwater sections were calculated for 4 different bottoms

slopes in front of the breakwater (). Other parameters, such as the slopes of the

seaside and portside of the structure, the breadth of the top section, or the storm

duration were not changed, in order to simplify the results. Another crucial

parameter that was not changed was the type of armour used. Again, for the sake

of simplicity and ease of comparison only rock armour was used, though for the

case of the deeper sections it is normally very difficult to find rock of adequate

size to fulfil the requirements of Van der Meer (1987) and hence concrete units

such as tetrapods or accropods are used. These units also have better

interlocking capabilities and can contribute to a decrease in the required armour

weight. However, these units also have other associated costs, such as the

formwork and labour to make them. The current approach of only using rock is

simplistic, but allows for an intuitive understanding of the problem, by providing

an insight into the increase in armour requirements according to the Van der

Meer formula (1987). Nevertheless, all the combinations summarised in Table 1

resulted in a total of 5440 breakwater section calculations.

Sea Level Rise Scenarios

Future patterns in sea level rise are highly uncertain due to a lack of

understanding of the precise working of global climate and its interaction with

the physical environment. A lot of this is down to uncertainty in the response of

the big ice sheets of Greenland and Antarctica (Allison et al., 2009). In fact, it is

currently believed that sea level in the 21st century is likely to rise much more

than the range of 0.18-0.59m given in the IPCC 4AR. In this report, the coupled

models used for the 21st century sea level projections did not include

representations of dynamic ice sheets, only including simple mass balance

estimates of the contributions from Greenland and the Arctic ice sheets. In fact

the IPCC 4AR assumed that ice was accumulating over the Antarctic ice sheet,

though it is currently losing mass as a consequence of dynamical processes, as

shown in Allison et al., (2009). Recent research such as that by Vermeer and

Rahmstorf (2009) show how sea level rise for the period 1990-2100 could be in

the 0.75 to 1.9m range.

Table 1. Summary of Parameters of Breakwater Sections Considered

Parameter Symbol

(unit)

Conditions Calculated Notes

Water Depth h (m) 3, 5, 7, 9, 11, 13, 15, 17,

19, 21, 23, 25

Effect of sea level rise for

deeper sections where

h>25 is very small

Significant Hs (m) For h=3, Hs=3. 5

Wave Height

For h=5, Hs=3. 5, 7

For h=7, Hs=3. 5, 7, 9

For h=7, Hs=5, 7, 9, 11,

13

All others, Hs= 5, 7, 9, 11,

13, 15

Wave Period T (s) 6, 8, 10, 12, 14

Slope of sea

bottom 1:10, 1:20, 1:30, 1:40

Sections considered by

Goda (1985)

Run-up friction rf 0.5 for all cases See Van der Meer (1993)

Breadth of top

section B (m) 6m for all cases

Angle seaside

of breakwater 1:3 for all cases

Angle portside

of breakwater Β 1:2 for all cases

Zero-damage

parameter Sa 2 for all cases

See Van der Meer (1988)

Storm Duration Ds

(hours) 2 hours for all cases

See Shimosako and

Takahashi (2000)

Sea level rise hr(m) 0.15, 0.44, 0.9, 1.35 See IPCC 4AR, Vermeer

and Rahmstorf (2009)

The current research employs four different sea lever rise scenarios over a period

of 50 years (the assumed design life of a rubble mound breakwater)

Scenario 1: 0.15m increase, which would correspond to an annual increase

of 3mm, similar to that at the end of the 20th

century

Scenario 2: 0.44m increase, which would be similar to the increase

suggested by the worst IPCC 4AR in the period between 2050 and 2100

Scenario 3: 0.9m increase, around half-way between scenarios 2 and 4.

Scenario 4:1.3m increase, similar to the increase suggested by Vermeer and

Rahmstorf (2009) in the period 2050 to 2100.

RESULTS

Fig. 1 shows the average increase in breakwater cross-section (including the

increase in required breakwater height as a consequence of sea level rise and

increased run-up, and the required increase in armour size) for the various sea

level rise scenarios outlined in the previous section. To produce these figures,

the results at each depth for each of the Hs and T were averaged together. This

would at first appear counter-intuitive, as there are significant differences in the

required armour necessary for different rates of sea level rise, as is shown for

example in Fig. 2. This Fig. shows the required weight of armour rocks for

Scenario 2, compared with a control scenario where these is no sea-level rise.

The figure plots the effect that sea level has on different values of h, for a

θ=1:40 and a Hs=9m, showing how especially for the lower values of h the

requirements in armour will increase substantially, as the Hb parameter will

increase and hence higher waves will reach the breakwater. The effect is far

more severe for Scenario 4, as shown on Fig. 3.

Figure 1. Increase in Breakwater cross section for the different sea level rise

scenarios

Figure 2. Increase in the required weight of armour rocks for Scenario 2, compared

with no sea-level rise

Figure 3. Increase in the required weight of armour rocks for Scenario 4, compared

with no sea-level rise

The effect of an increase in required armour is greater for the case of the sections

with lower h, as an increase in sea level will also increase Hb. On the other hand,

for the deeper sections Hb is less likely to be affected, and hence the armour

requirements will not change substantially or at all, as shown in Figs. 2 and 3.

Thus, for the deeper sections the most important effect is the increase in h,

which will require the breakwaters to increase in size in order to avoid

overtopping.

Nevertheless, averaging the results from various ranges of T and Hs to make Fig.

1 will obviously result in the loss of some degree in accuracy, as can be seen

from Figs 4 and 5. The values shown in both of these Figs. are averaged values

of the increased in armour and cross-sectional area required for a variety of Hs

and h, though in this case each point shown is the average of the 5 computed

values of T for each Hs. Fig. 4 thus shows how for the case of the deeper

breakwaters averaging all the values of Hs does not induce a significant

deviation in the production of Fig. 5, though this deviation from the average will

increase for the shallower sections. For the case of the armour the deviation is

more significant, though in this case it should also be understood that most of

the likely increase in cost will come from increasing the height of the breakwater

as a consequence of greater run-up, and not due to need for larger armour size.

In fact, most of the increase in breakwater cost appears to come from the

enlargement of the cross-sectional area of the core and underlayers of the

breakwater which results from heightening the structure. This typically

represents between 22 and 34% of the area of any one section, as shown in Fig.

6.

Figure 4. Increase in armour size for Scenario 4 for a variety of Hs.

Figure 5. Increase in cross-section size of breakwater for Scenario 4 for a variety of

Hs (note this only includes the core of the breakwater and the filter layers)

Figure 6. Ratio of the area of the armour compared to the total cross section of the

breakwater (armour plus core and filter layers)

DISCUSSION

The analysis carried out previously highlights the problems that might be

brought about by a rapid change in sea levels in the future. Traditionally

breakwaters are designed by looking at the historical records of wave conditions

over an area, which are assumed not to change over time. Also, this traditional

design philosophy does not take into account sea level rise (despite the fact that

sea levels have been increasing over the past century), and assumes that sea level

will be the same at the end of the working life of the breakwater. These

structures have a typical long design life, usually of 50 years, though many

continue to serve their purpose even after that. However the way that these

breakwaters are designed in a future of rapidly changing climate and sea level

will have to change significantly. First of all the potential damage to the

breakwaters built in the shallower waters will increase towards the end of their

life, due to a higher value of Hb. During the course of the 20th

century, annual

increases in 1.7mm would mean relatively small differences in h even after 50

years, which would not result in the expected damage at the end of a

breakwater’s life to increase substantially. In a future where sea level rises

quickly this assumption would no longer hold true, and hence sea level rise will

have to be taken into account by the practicing engineer.

The second part of the problem is that if the climate is expected to change,

engineers will not be able to rely on past records to predict the wave heights at

the middle or end of the life of a breakwater. Mori et al. (2010) analysed the

annual averaged and extreme sea surface winds and waves throughout the world

as a consequence of climate change, and found that there are clear regional

dependences of both annual average and also extreme wave height changes from

present to future climates. The practicing coastal engineer would thus be left in a

situation of uncertainty regarding future wave climate, and would have to design

a breakwater relying on the only measure which would give him some degree of

confidence on the wave heights, Hb. Assuming a rapidly changing climate which

is not completely understood, the most important design parameter will become

Hb rather than the significant wave height (Hs), as it is at present.

Finally, it is worth noting that the present work does not take into account other

possible effects such as the phenomenon of wave setup, associated with the

existence of stress acting on the water due to the presence of wave motion

(called radiation stress), which causes a quasi linear rise in the mean water level

towards the shoreline. The magnitude of the radiation stress may change due to

variations in the wave height as it propagates towards the coastline (due to

shoaling and wave breaking), and hence this may cause changes in the

inclination of the mean water level. This can thus affect the depth of water in

front of the breakwater and hence the damage. Increases in tropical cyclone

intensity (Knutson and Tuleya, 2004, IPCC AR4) are also likely to result in

increased levels of storm surge, and these can also have a negative effect on the

stability of breakwaters. Thus, the effect of climate change on rubble mound

breakwater stability is likely to be far more complex than the simplistic approach

given in this paper. Nevertheless, by only considering one factor (sea level rise)

it is possible to understand the isolated effect that this would have on the future

economic cost involved in building and maintaining these structures.

CONCLUSIONS

A key factor for the future design of breakwaters is the effect that progressively

higher concentrations of greenhouse gases will have on the rate of sea level rise,

which is expected to speed up in the second half of the 21st century (according to

the IPCC 4AR). In the present work, the effect that 4 different rates of sea level

rise will have on the economic costs of building rubble mound breakwaters was

analysed, showing that for the more extreme cases of sea level rise (Vermeer and

Rahmstorf (2009), for a sea level rise of 1.3m) a breakwater designed in 2050

would be between around 8% (for the deeper sections) and 66% more expensive

(for the shallower sections) than one designed in the 20th

century not taking into

account sea level rise.

The future design philosophy will also have to significantly change. First of all,

it will be necessary to take into account sea level rise in the design of a

breakwater. Second, in a future in which the wave climate is changing (Mori et

al., 2010), an engineer will no longer be able to use historical data in order to

calculate the expected significant wave height (Hs) for a given section. Thus, the

design philosophy of breakwaters will have to change to one where the main

parameter is the limiting breaker height (Hb), causing yet more increases in the

cost of the breakwater, as quite often in current design Hs<Hb.

The present work thus highlights yet more problems related to anthropogenic

based rapid climate change, as the lack of certainty in the future will not allow

for economic designs based on past experience.

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KEYWORDS – CSt2011

Abstract acceptance number: p0129

SEA LEVEL RISE AND THE INCREASE IN RUBBLE MOUND

BREAKWATER DAMAGE

1st Author: ESTEBAN, Miguel

2nd

Author: TAKAGI, Hiroshi

3rd

Author: SHIBAYAMA, Tomoya

Breakwaters

Climate Change

Rubble Mound

Sea Level Rise

Limiting Breaker Height