Coastal ecosystem dynamics affected by climate change ...

IMPERIAL COLLEGE LONDON

Faculty of Engineering

Department of Civil and Environmental Engineering

Coastal ecosystem dynamics affected by climate change feedbacks

Alfie Hewetson

2019-2020

Submitted in fulfilment of the requirements for the MSc and the Diploma of Imperial College London

DECLARATION OF OWN WORK

Declaration:

This submission is my own work. Any quotation from, or description of, the work of others is acknowledged herein by reference to the sources, whether published or

unpublished.

Signature : __Alfie Hewetson_________________________________


Alfie Hewetson 1

Abstract

The purpose of this study is to investigate the effect that mangroves can have on

mitigating coastal flooding. This is attempted by employing theoretical and analytical

models that characterise the flow conditions, the vegetation properties and the

geographic conditions, in order to find the dissipation rate.

To successfully build the model a test area, of 3 tiles 5 degree by 5 degree each is

chosen along the coast of Vietnam.

Within this study, satellite survey databases will be used to build a model where by a

1 in 100-year storm event, caused by storm surge, tide and waves can be measured in

terms of it’s total flood. This will then be compared in situation in which mangrove do

and do not interact with the flow.

This wave attenuation is modelled by investigating individual wave rays which make

up a wave front. The flooding is comprised of the flooding potential of the wave height

of the wave ray. This wave ray, when passing through mangroves will be attenuated

and thus lose some of its flooding potential.

This method of analysis performed well during the validation stage, with the wave

dissipation being in similar regions as found in other papers and field studies within

the area. When applying the full flooding model an error appeared where by the waves

of the wrong angle were selected, causing a reduction in the wave height, due to the

use of fetch limited waves. As such the final results at this stage are inconclusive, with

a single grid now taking 6 hours to complete, this has yet to be run.

.


Alfie Hewetson 2

Acknowledgements

Have to thank my dad for helping with the proof reading and the rest of my family for

putting up with me during the stressful time.

Also thank you to Ali for not only the support through the project but of proposing a

project I have thoroughly enjoyed.


Alfie Hewetson 3

Contents

Abstract ......................................................................................................................... 1

Acknowledgements ........................................................................................................ 2

Contents ........................................................................................................................ 3

1 Introduction ........................................................................................................... 4

2 Background ............................................................................................................ 5

2.1 Literature review of wave attenuation through vegetation .................................... 5 2.2 Paramertization of the drag coefficient ................................................................... 7 2.3 Exploration of the terms within the wave attenuation equation .......................... 10

3 Datasets ............................................................................................................... 13

3.1 Mangrove location ................................................................................................. 13 3.2 Extreme sea-level tide and storm .......................................................................... 15 3.3 MERIT topography ................................................................................................. 16 3.4 Wave data .............................................................................................................. 17

4 Methodology ........................................................................................................ 22

4 Results and Discussion .......................................................................................... 29

4.1 Validation ............................................................................................................... 29 4.2 Limitations ............................................................................................................. 33 4.3 Flooding extent ...................................................................................................... 36

5 Conclusions .......................................................................................................... 40

References ................................................................................................................... 41

Database References .................................................................................................... 48

A Significant wave height with respect to direction ................................................... 49

B Peak frequency with respect to direction .............................................................. 55


Alfie Hewetson 4

1 Introduction

Coastal flooding is predicted to become more severe in the coming decades due to the

onset of climate change [IPCC chapter 4]. This is compounded by the fact that

population densities are 5 times higher than the global mean in low elevation coastal

zones [Neumann et al 2015]. [Mendelsohn et al. 2012] has predicted that the economic

damage from extreme sea levels, ESL, will double as a result of this increased

development, with the onset of climate change causing a further doubling. As such

adequate coastal defences are required to offset the threat from extreme sea levels to

coastal land and communities. However, current hard structures commonly used in

coastal protection do not have the ability to respond to the changing conditions brought

on by a changing climate [Conger and Chang 2019, McGranahan et al., 2007, Borsje

et al., 2011]. This has led to a change in thinking towards natural infrastructure in flood

defences.

These natural ecosystems have proven coastal protection benefits and studies by

[Zhang et al., 2012, Barbier 2016, Narayan et al., 2016, Menendez et al., 2018] show

mangrove ecosystems can cause wave attenuation and shoreline stabilisation. Yet

natural infrastructure also has the ability to self-maintain and repair itself after major

storms [Gedan et al., 2011, Ferrario et al., 2014]. This results in a cost-saving, due to

increased maintenance of hard solutions, but as [Narayan et al., 2016] shows, natural

infrastructure can be several times cheaper than the equivalent breakwater in initial

cost. Natural infrastructure can also keep up with the effects of climate change; either

through horizontal migration, moving over time to higher ground on the landward side,

or through vertical build up from sediment, increasing the height of the mangrove’s

bathymetry/topography [Sasmito et al., 2015, Gholami et al., 2020].

[Giesen et al., 2007] describes mangroves as woody vegetation types occurring in

marine and brackish environments, this study goes onto say they are generally

restricted in habitat from between the lowest low water to the highest high water in the

tidal cycle. As such mangroves are not necessarily a type of plant but a habitat in which

various species of plants can live. Due to their coastal location they interact with

incoming waves and cause a reduction in the wave height, due to the work performed

on the root and trunks [Dalrymple et al., 1984, Mork, 1996].

A number of field observations have already been undertaken to find the wave

attenuation performed by mangroves [Mazda et al., 1997, Mazda et al, 2006, Vo-


Alfie Hewetson 5

Luong and Massel, 2006, Quartel et al., 2007, Bao, 2011]. The number of these studies

are limited by the difficulty and inaccessibility of mangroves [Horstman et al., 2014].

These studies tend to be categorised by finding the wave height reduction at a certain

distance and quantifying it as a ratio of wave height reduction per unit meter,

r=ΔH/(H*Δx). The findings for the value of r vary significantly on the conditions, such

as wave height, period, location and species of mangrove.

This ratio of wave height reduction assumes a linear change with distance. When

experimental and analytical studies [Dalrymple et al., 1984, Kobayashi et al., 1993]

suggests that the wave attenuation is either a parabolic or an exponential decay.

The object of this report is to try and use the results from experimental and analytical

studies, regarding wave attenuation by vegetation, and apply them to real world data

to the find the resultant effect mangroves can have on flooding under a 1 in 100-year

storm event. This will require a coupled model taking into account the

topography/bathymetry, mangrove locations, wave data and tide/storm surge data.

This coupled model will be developed on three, 5degreex5degree, tiles situated along

the coast of Vietnam. Vietnam was chosen as the test case for several reasons. Current

literature has already had a large focus on this country, including both field and

numerical studies [Mazda et al., 1997, Mazda et al., 2006, Vo-Luong and Massel,

2006, Quartel et al., 2007, Bao, 2011, Phan et al., 2019]. Vietnam also has both types

of mangrove location, coastal fringe and riverine mangrove, figure 6 shows that each

tile varies in regard to this location description. As a region, it is also particularly at

risk to coastal flooding as shown by [Neumann et al., 2015], which ranks Vietnam as

one of the top ten most at risk to flooding events. Plus, as it is part of mainland Asia,

the tiles do not require inland shielding, whereby the wave rays are limited from

extending over the island to shorelines that the wave ray would not overwise interact

with, this thus simplifies the model.

2 Background 2.1 Literature review of wave attenuation through

vegetation

In order to find the decrease in coastal flooding due to the effect of mangrove


Alfie Hewetson 6

ecosystems, a suitable parametrisation for the wave attenuation must be found. The

relationship between the dissipation of wave height and the distance travelled through

mangroves can be described in several ways. One being an increase in bottom friction

factors, to account for the friction caused by vegetation as suggested by [Camfield

1977, Mӧller et al. 1999, Anderson et al. 2011]. However, most studies use either an

exponential decay or a parabolic decay model, which apply a drag coefficient from the

vegetation to find the wave-induced drag forces and the degree to which this drag force

attenuates the wave, these types of models will be further investigated here.

Equation (1) shows this relationship between the wave transmission coefficient, kt, and

the damping factor due to wave-trunk interactions, α. With the wave transmission

coefficient being the wave height/amplitude at a certain distance into the mangroves

over the wave height/amplitude at point of entry to the mangroves.

𝑘𝑡 =𝑎𝑥𝑎0

=1

1 + 𝛼𝑥 (1)

Using this parabolic model (1), [Dalrymple et al., 1984] suggested a method to find

the damping coefficient. This was derived using the conservation of energy equation

and linear wave theory and assumes that the vegetation is composed of an array of

vertical rigid cylinders, with a constant drag coefficient with respect to depth, as well

as a flat bottom surface. The damping coefficient shown in (2) was found by

integrating the force on the rigid cylinders and as such takes into account both the

wave conditions and the plants properties. The plant properties are found with D, b

and s being the diameter of the cylinder, spacing between cylinders and the height of

the cylinder relative to the bottom, respectively.

𝛼 =2𝐶𝐷3𝜋

(𝐷

𝑏) (

𝑎0𝑏) (𝑠𝑖𝑛ℎ3(𝑘𝑠)

+ 3sinh(𝑘𝑠)) [4𝑘

3sinh(kh)(sinh(2𝑘ℎ) + 2𝑘ℎ)]

(2)

The exponential decay model suggested by [Kobayashi et al., 1993] is shown in (3). It

was derived using the continuity and linearized momentum equation and assumes

linear wave theory is valid and the vegetation is rigid. Where gamma is the exponential

decay coefficient. This value of gamma is found by comparing a calculated normalised

decay coefficient with a measured value. This decay coefficient is found by the

normalised wave number multiplied by the dissipation, γ=εkr, for subaerial vegetation.

The dissipation is shown in equation (4). With b now equal to the area per unit height

of each vegetation strand normal to the horizontal velocity and N is equal to the


Alfie Hewetson 7

number of vegetation strands per unit horizontal area. Although the solution was first

approached as a solution for submerged vegetation, it is shown to be applicable for

subaerial vegetation such as mangroves.

𝑘𝑡 =𝑎𝑥𝑎0

= exp(−𝛾𝑥) (3)

𝜀 =1

9𝜋𝐶𝐷𝑏𝑁𝐻0

sinh(3𝑘𝑟𝑑) + 9sinh(𝑘𝑟𝑑)

[2𝑘𝑟𝑑 + sinh(2𝑘𝑟𝑑)]sinh[𝑘𝑟(ℎ + 𝑑)] (4)

Within this paper the decay coefficient used will be the one used within [Kobayashi et

al., 1993] for subaerial vegetation shown in equation (5) but altered for bv in a way

used by [He et al., 2019]. Where bv is the vegetation area per unit height of each plant

normal to the wave direction and N being t number of plants per unit horizontal area.

𝛾 =1

9𝜋𝐶𝐷𝑏𝑣𝑁𝐻0𝑘

sinh(3𝑘𝑑) + 9sinh(𝑘𝑑)

[2𝑘𝑑 + sinh(2𝑘𝑑)]sinh(𝑘𝑑) (5)

In [Darylympe et al., 1984] the damping coefficient, α is related to the exponential

decay coefficient γ, by investigating the expansion of both (1+ αx)-1 and exp(-γx).

From this for small values of γx and αx the functions act alike. This comparison of

expansions is done in order to relate the damping factor, α with an unspecified

damping factor w, shown in equation (6); this equation comes from the Berkhoff’s

equation being reduced down to the Helmholtz equation for pure damping and the

linear shallow water theory in small depths. Where the solution to w in relation to the

exponential decay coefficient is given in (7).

𝛻ℎ ∙ (𝑛𝑐2𝛻ℎ��) + (𝑛𝜎2 + 𝑖𝜎𝑤)�� = 0

(6)

𝑤 = 2𝑛𝜎 (𝛾

𝑘) [1 + (

𝛾

𝑘)2

]1/2

(7)

For the purposes of this study the exponential decay model will be chosen, as the

parabolic decay equation relies on the assumption that αx is small and can thusly be

related to γx. However, within this study the distances x can grow to be quite large;

with αx and γx possibly exceeding 0.1 breaking the required argument for this

assumption.

2.2 Parameterization of the drag coefficient

The drag coefficient in equation (2) and (5), is due to the assumption that dissipation

is only caused by the drag force [Dalrymple et al., 1984]. As such the dissipation is


Alfie Hewetson 8

equal to the drag force multiplied by the horizontal velocity. With the drag force

equalling the drag term of the Morison equation integrated across the depth of the

vegetation. A recent study by [Suzuki et al., 2019] suggested that the inertial term of

the equation also had an affect on the forcing experienced by the vegetation.

With the choice of the exponential decay model, several variables within equation (5)

must be found, including the drag coefficient, CD. To do this an empirical

parameterization of the flow characteristics are taken to find the bulk drag coefficient.

This parameterization can be conducted in 3 ways, using the Reynolds number (Re),

the Keulegan-Carpenter (KC) number and the Ursell (Ur) number. Equations (8), (9)

and (10) show the Re, KC and Ur number respectively. All 3 terms have a

characteristic length, L, which varies depending on the dimensionless number.

𝑅𝑒 =𝑢𝐿

𝜈 (8)

𝐾𝐶 =𝑢𝑇

𝐿 (9)

𝑈𝑟 =𝐿2𝐻0

ℎ3 (10)

For Ur this length is the wavelength of the wave and a relation between this and the

drag coefficient has been found [He et al., 2019]. However, this approach doesn’t take

into account the mangrove properties, so from an intuitive stand point, it is difficult to

relate the change in mangrove density on the change in the drag coefficient. Therefore,

this approach is only applicable for areas where the mangrove properties match those

used in that experiment. This is further shown in [Nepf, 1999], where a dependence of

the drag coefficient is the stem population density.

For KC this length scale is usually the diameter of the mangrove’s roots or stem. As

such, [Mendez and Losada, 2004] found an empirical relationship between the KC

number and CD using experimental results shown in (11) and (12). Where (12) is a

modified KC number and alpha is a relative stem length. [He et al.,2019] when

parametrising CD found a closer correlation with the KC number than with the Re

number.

𝐶𝐷 =exp(−0.0138𝑄)

𝑄0.3 (11)

𝑄 =𝐾𝐶

𝛼0.76

(12)

The most common parametrisation is using the Reynold’s number [Kobayashi et al.,


Alfie Hewetson 9

1993, Mendez et al., 1999, Maza et al., 2013, Massel et al., 1999, Mazda et al., 1997].

Usually, the characteristic length L, is the diameter of the mangrove root/stem,

however [Mazda et al., 1997] suggested a length scale based upon the total volume of

section minus the volume of vegetation divided by the projected area of the obstacles,

L=(V-VM)/A. This idea can be continued upon as shown by [Maza et al., 2017] to find

a frontal area per unit height, which [He et al., 2019] uses as the length to parametrise

the Re and KC. Due to the variability in root/stem diameter of mangroves, not just

between species but within specific plants, this length scale was chosen.

Several empirical parametrizations have been suggested for the drag coefficient with

respect to the Reynolds number and are found by fitting the values around

experimental results. With [Kobayashi et al., 1993] this was conducted using the value

from ta kelp experiment. This was followed up by [Mendez et al. 1999] who

incorporated the effect of motion, from swaying, shown in (13) (14) for without and

with swaying respectively. This led to a 20% improvement for the correlation

coefficient. This was further calibrated with the inclusion of further experimental

results in the paper by [Maza et al 2013], this is shown in (15) and also includes

movement.

𝐶𝐷 = 0.08 + (2200

𝑅𝑒)2.2

(13)

𝐶𝐷 = 0.40 + (4600

𝑅𝑒)2.9

(14)

𝐶𝐷 = 1.61 + (4600

𝑅𝑒)1.9

(15)

Within this paper (15) will be used to find the drag coefficient. This is due to the work

done by [Augustin et al., 2009, Bradley and Houser, 2009] when comparing the

correlation between the drag coefficient and the parametrization by Re and KC.

[Bradley and Houser, 2009] found there to be no difference between the correlation

coefficient between Re and KC in regard to CD. [Augustin et al., 2009] came to the

conclusion that for emergent vegetation the Re number has a better correlation than

the KC number. As this investigation is conducted on mangroves, which are an

emergent vegetation equation parametrization with the Reynolds number seems the

most appropriate.


Alfie Hewetson 10

2.3 Exploration of terms within the wave attenuation equation

To satisfy the exponential decay equation (3), several more terms are still needed to

be found, these can be split into two categories, those associated with the wave

properties, which will be found in section 3.5, and those associated with the mangrove

properties. In (5) the mangrove properties are denoted by bv, the frontal area of

mangroves per unit height, and N, which is the number of plants per unit area.

Therefore, bv and N must be found for an average mangrove situation. This leads to

several problems due to variability not just of mangrove species but in individual

mangrove shape. [Giesen et al., 2007] Recorded 268 different forms of mangrove

vegetation and narrowed this down to 42 true mangrove species, just for South-East

Asia. [Saenger et al., 1983] had previously recorded a worldwide study which included

60 plant species. It is noted in [Ohira et al., 2013] that 90% of the world’s mangroves

distribution are of the species Rhizophora, this further reduces [Giesen et al., 2007]

from 42 true mangrove species down to the 12 species within the Rhizophoraceae.

Plants of this species are characterised by stilt root [Gil and Tomlison, 1977] as shown

in figure 1.

Figure 1-Mangrove root type, [Tomlinson 1986]

[Ohira et al., 2013] provides a relationship between the diameter at breast height

(DBH) of the stem and the resultant root profile. This was achieved by assuming the

roots have a quadratic relationship with the stem and the ground. With other properties

such as the highest root height and number of the roots being taken as a function of

the DBH. These relationships between the DBH and other properties were found by

fitting observational data from mangrove forests, to form equations to equate the

properties. This approach assumes only primary roots are considered, meaning only

roots that directly connect to the stem. However, [Ohira et al., 2013] further states the

root order as predominantly primary, so this approach is applicable.

This approach allows the problem of finding the mangrove physical properties to just

requiring a value for DBH. This same method was followed by [Maza et al., 2017]

which used a DBH=0.2m, a value that comes from [Alongi, 2008] concerning mature


Alfie Hewetson 11

mangrove trees. Following the method [Ohira et al., 2013], [Maza et al., 2017] found

the values are within the range reported by [Mendez-Alonzo et al., 2015].

Using DBH=0.2m, the mangrove properties results are; highest root height=2.012m,

number of roots=24, with the diameters being from between 0.033 to 0.042. This now

needs to be converted to a frontal area per unit height per tree. Each root is attached to

the stem at evenly spaced distances along the length of the tree from the highest root

height to 0.25m above the ground, each root also has its own diameter which is

consistent along the length of the root. However, this would currently only equate to a

2-dimensional mangrove, in terms of the frontal area, with each root overarching the

preceding root along the same plane. As such each root requires to be given a random

angle at which it emerges from the main stem, assuming this angle isn’t either 0 or 180

degrees, the frontal area associated with this root changes. 4 examples of this are seen

in figure 2, with the total height of the tree being 12m in height, so as to make sure the

tree is always above sea level no matter where the plant sits in the tidal range.

Figure 2- shows 4 randomly generated mangrove trees with varying roots

The frontal area however, is only the area of the mangrove that is submerged in the

water. So, the frontal area becomes dependant on the depth. [Ohira et al., 2013] uses

an integration method to find the value of the frontal area and [Maza et al., 2017] uses

an image processing toolbox to find the frontal area. Using the 1st mangrove in figure

1, the image was dissected using MATLAB, so as to only include any area below a

certain height, which would be defined by the depth. This was repeated for depths from

0 to 12 meters in height. 3 examples are shown in figure 3. As previously stated,

variability between mangrove plants is an issue to be overcome. This is achieved by

repeating the process again with 100 individually random generated mangroves before

the area at the specific depth is averaged, shown in figure 4.


Alfie Hewetson 12

Figure 3- shows the frontal area with depths of 1m, 3m and 5m respectively of the first mangrove in figure 2

Due to the location and the population density of the roots, even though the frontal

area increases with height as shown in figure 4, bv is frontal area per unit height so this

area would be divided by the depth. As such bv is a length and can be used in the

Reynolds number calculation as well.

Figure 4- Shows the average frontal area of mangroves against depth of water. Up to the highest root height 2.012m the area follows a combination of the quadratic relationship for the root [Ohira et al.,2013] and a linear relationship from the stem. After the highest root height, it follows the linear relationship of the stem.

With the frontal area found, only N, the number of trees per unit area is needed for

equation (5). Again [Maza et al., 2017] encountered this problem for its experimental

study and took a value of 722 trees per hectare. This was based on [Ward et al., 2006]

that reported a density of a typical Rhizophora forest being around 600 trees per

hectare. Converting this to meters gives N=0.06 trees/m2.


Alfie Hewetson 13

3 Datasets 3.1 Mangrove location

To find the affect that mangroves can have on coastal flooding, the location of

mangroves are needed. As such the Global Mangrove Watch dataset was used which

gives the mangrove coverage between 1996-2016[Bunting et al., 2018]. This uses

radar satellite sensing to locate regions of mangroves, first by classifying areas using

ALOS PALSAR data before then refining using Landsat data. This map has a precision

of approximately 1 ha, with a mangrove accuracy of around 94%.

Figure 5- Global mangrove distribution in 2010 mangrove baseline map.

In the baseline year of 2010 137,600km2 of mangrove was found, with this being fairly

localised in specific areas. Such as 32.2% of this being found in Southeast Asia.

Latitude is another defining attribute, with 96% of the mangroves being found with

23.4 degrees North and 23.4 degrees south.

Within this study the mangrove extent in 1996 and 2016 will be studied and the change

in flooding due to the reduction in mangrove will be analysed as well as the difference

when there is no mangroves. To reduce the size of the data being used during each

stage of the programming, each mangrove section that has been categorised in that

year will be assigned to it nearest point within a 5-degree grid, as shown in figure 6.


Alfie Hewetson 14

Figure 6-Shows the mangrove extent all 3 tiles. The top tile shows a distribution of dense coastal fringe mangroves. The middle tile is sparsely populated coastal fringe. The bottom tile is for a riverine mangrove location. The bottom tile mangrove at the seaward extent of what would be the Mekong delta, south of Ho Chi Minh city.


Alfie Hewetson 15

3.2 Extreme sea level-tide and storm

Extreme sea levels are a function of 3 factors; meteorological effects, such as storm

surges and waves, astronomical, such as the tides and sea-level rise [Vousdoukas et

al., 2018]. This study does not currently look at future scenarios under climate change,

therefore extreme sea-level is governed by just the meteorological and astronomical

forcing.

While there is evidence that mangroves attenuate storm surges [Zhang et al., 2012,

Montgomery et al., 2019], there is less understanding in this area when compared to

mangroves ability to attenuate waves. So, in investigating coastal flooding only the

effects that mangroves can have on wave reduction will be included. This means the

extreme sea-level can be split into 2 components, 1st being waves, where mangrove

interaction is studied, and 2nd being tide and storm surges, which do not interact with

mangroves. The wave data is presented in section 3.5.

Figure 7- [Muis 2016] combined height of 1 in 100-year tide and storm surge

The 2nd component uses the data from [Muis et al., 2016] which gives a combined

storm surge and high tide for a 1 in 100-year event. These values were found by a

time-series, between 1979-2014 being created through hydrodynamic models before


Alfie Hewetson 16

using the annual maxima method fitted to a Gumbel distribution, to find the 1 in 100-

year event. This data can be seen as an underestimate of extremes due to the resolution

of the data [Muis et al., 2016]. The results for this are imposed along the world’s

coastlines, the results of this is shown in figure 7.

3.3 MERIT topography

The degree to which land is flooded is dependent on the underlying topography and

what the height of this is relative to the extreme sea-level. As such a suitable

topographic map must be found. 2 areas are of particular importance; coastal low-lying

areas, the areas that are of particular risk of flooding, and locations that have

mangroves. The land that is of particular risk of flooding is inherently required to

produce a flood risk map. The land height in which mangroves is situated is needed

for another aspect of the calculations, as equation (5) requires the depth of the body of

mangroves. Considering that mangroves live in the intertidal region; accurate

topographic measurements are required for when this area is inundated during the

extreme flooding event, so as to apply this inundation depth to (5). As figure 6 shows

mangroves are also particularly prone to growing in rivers and the deltas of rivers,

therefore the topographic map will have particular focus on these areas.

The map chosen was the MERIT DEM hydrologically adjusted elevation, which uses

the MERIT DEM as the baseline before adjusting river networks to satisfy the

condition that ‘downstream is not higher than its upstream [Yamazaki et al 2019]. This

map will improve the accuracy in estuaries and deltas when calculating the depth

acting on the mangroves. The elevation data is given in 5-degree x 5-degree grids made

up of 6000x6000 cells, with an elevation resolution of 10cm. This means it is accurate

to 3 arc seconds, roughly 90m at the equator.

As previously stated, the extreme sea level is split into 2 components, storm surge/tide

elevation and wave elevation. This first component found by [Muis et al., 2016] is

located along the coastline of the world. This was transposed on to the elevation grids

by associating the sea level rise at each cell within 6000x6000 elevation grid with its

nearest value of ESL, those shown in figure 7. The elevation within the cell would be

reduced by this closest value of ESL.


Alfie Hewetson 17

Figure 8-Shows the topography for Northern Vietnam region, where the height is between 10m and -10m. This topography has already been dropped down relative to the SLR at the location.

This method to superimpose the ESL from tide and storm surge onto land can lead to

jumps in the value of reduction, as the nearest data point for the ESL moves from one

spot to another despite only 1 step between cells. Meaning 2 cells which are next to

each other with equal elevation could be reduced by different ESL values and thus

appear not level. However as seen in figure 7, ESL from tide and storms doesn’t have

large changes in values between data points, as the data points are scattered regularly

along the coastlines. Also, elevations in the centre of landmasses could be reduced

incorrectly in regards to flooding. This would be caused by a cell being reduced in

height by its closest point of ESL; but due to surrounding topography shielding this

area from flooding, the flood may be driven at this location by a different point of ESL.

However, this would happen in the centre of landmasses, which characteristically have

a greater elevation at least to escape the effects of coastal flooding, as such this

shouldn’t affect the results.

3.4 Wave data The second component of the extreme sea-level is the increase in surface elevation


Alfie Hewetson 18

caused by the waves. The objective of analysing the wave data is to find a 1 in 100-

year wave event that will be a driver for coastal flooding. This component is the

variable in which mangroves can affect and cause reduction to total flooding. To find

the 1 in 100-year event a time-series of wave heights is analysed and a probability

density function is created, whereby the 1 in a 100-year wave can be taken.

The wave data is based on the analysis by [Hemer and Trenham, 2016], whereby 8

separate CMIP5 global wind-wave climate models were evaluated for accuracy based

on the ensemble average of the dataset. The 8 different models are shown in table 1.

As noted in [Hemer and Trenham, 2016], the underperformance of CNRM-CM5,

means this model will not be included within the analysis.

ID Full model name Model

1 Australian Community Climate and Earth System

Simulator 1.0

ACCESS1.0

2 Beijing Climate Centre, Climate System Model 1-

1

BCC-CSM1.1

3 Centre National de Recherches Meteorologiques

Coupled Global Climate Model, version 5

CNRM-CM5

4 Geophysical Fluid Dynamics Laboratory Earth

System Model 2M

GFDL-ESM2M

5 Hadley Centre Global Environment Model 2, earth

System

HadGEM2-ES

6 Institute of Numerical Mathematics Coupled

Model, version 4.0

INMCM4

7 Model for Interdisciplinary Research on Climate,

version 5

MIROC5

8 Meteorological Research Institute Coupled

Atmosphere-Ocean General circulation model,

version 3

MRI-CGCM3

Table 1- showing the 8 models that were applied to WaveWatch III by [Hemer and Trenham, 2016] to find the wave time-series at each point. Including CNRM-CM5, which was removed

due to underperformance when compared to the ensembled average.

The original dataset for hindcast data runs from the beginning of 1979 to the end of

2005. To reduce the computational requirement only 10 years are taken from 1995 to

2005. Although the CMIP5 models have various spatial resolutions, these have already


Alfie Hewetson 19

been interpolated onto a 1-degree x 1-degree map. The dataset is made up of a time-

series of 6-hour intervals, within each interval the values for significant wave height,

peak frequency and the wave direction were taken to be further used. This time-series

was made up of 14720 individual timesteps for each point.

Figure 9- Value of significant wave height for the first timestep in December 2005, ACCESS1.0. This has no respect to direction and waves could be propagating in any direction

The wave direction is given as a degree relative to North as a whole number. Meaning

the direction can be anywhere from 0degrees to 359degrees. The time-series was taken

at each location on the grid and discretised into 12 bins relative to the wave direction.

The bins each account for 30 degrees of possible wave direction, centred on points 0

to 330. For example, the bin centred on 0 takes values from 346 degrees to 15 degrees.

Each bin accounts for the significant wave height and peak frequency at that point on

the map.

This discretising process splits the total time-series into 12 parts at each location. For

each of these 12 sections a 1 in 100-year wave needed to be found. This required the

distribution of significant wave heights to be fitted to a statistical model, relating the

height of the waves to the probability of occurrence of the wave.


Alfie Hewetson 20

𝑦 = 𝑓(𝑥|𝑎, 𝑏) = (1

𝑏𝑎𝛤(𝑎)) 𝑥𝑎−1𝑒−𝑥/𝑏

(15)

Several parametric models for significant wave height have been studied. Such as the

Log-normal distribution and the Weibull distribution [Battjes, 1972]. However, these

models can be inaccurate with the return values produced [Guedes Soares and

Henriques, 1996]. [Ochi, 1992] suggested that the long-term distribution of significant

wave heights on a probability density function follows a gamma distribution. This was

further studied and confirmed by [Ferreira and Guedes Soares 1999]. Therefore, a

gamma distribution is used, as shown in equation (16), a being the shape parameter

and b being the scale parameter. This distribution was fitted to the data using

MATLAB. However, this was only carried out if the data within the bin for each point

contained 30 or more data points, this was to ensure the reliability of the correlation of

the distribution, without having to conduct a correlation test for each run. 30 data

points account for 0.2% of the data at any given point.

Figure 10-Shows the associated probability at point(361/57600) for ACCESS1.0 for waves in 0degree direction, 1168 Hs values fall within this bin out of the total time-series .(Left) is the fitted probability density curve.(Right) is a histogram based on the input data.

With the probability profile found, a significant wave height with a 1 in 100-year

probability was taken from the distribution. This meant that a new wave map was

found, like that in figure 9, where a 1 in 100-year wave for a particular direction bin

and for a particular model was given. The next step required an ensemble average to

be taken between the 7 different models, this is to remove any bias given in a particular

model. However, due to the sensitivity of the climate models over multiple timesteps,

the directional component can be highly variable between models. This means that

some models have values for waves in directional bins which others do not. To avoid


Alfie Hewetson 21

averaging against empty values, which in turn would reduce the results. Each location,

would only be averaged by models in which a significant 1 in 100-year wave was

found. For example, if at a point only ACCESS1.0 and MIROC5 had a value for

significant wave height for that particular direction, then the resultant wave height

would be the sum of these 2 models divided by 2. Likewise, if all 7 models have a

value at a particular point in a particular direction, then the resultant wave height would

be the sum of this divided by 7. The results of this are shown in figure 11 for 0degree

directional component. (Further wave height maps for the other directions are found

in the appendix).

Figure 11- Significant wave height for waves with directional component of 0degrees (345-15). Averaged for all 7 models as described. Blank patches of the map are areas where under 30 values for the entire time-series are found for all 7 models. The map shows that these areas tend to be areas that are fetch limited by land, as 0degrees means the wind direction is coming from the North. Further maps for different directions of wind can be found in the Appendix A, as well as directional maps for peak frequency Appendix B.

Also required from the wave data is the peak frequency. This in turn was split into

directional bins in the same way as described as the wave heights. However, rather

than fit to a probability density function, only the mean of the values of peak frequency

within the bin was taken. This was then averaged between the 7 models in the same

wave the wave heights were.


Alfie Hewetson 22

Figure 12- Wave rose for significant wave height in meters for location 361/57600, with the direction being the angle in which the wave is coming from, for ensembled data of the 7 models.

4 Methodology

To see the effects of coastal flooding and how mangroves can suppress this, two

outputs must be found. One, coastal flooding without consideration for mangroves,

and two, with mangroves. As previously stated, to find the associated coastal

flooding several datasets must be coupled, to interact with one another. In this study

each situation is conducted relative to the topography grid which is 5degrees x

5degrees in size. As such tiles are not considered to be interacting with one another

and are calculated one at a time.

1. Firstly, the associated waves for the tile being calculated are found. This is

achieved by finding the coordinates at the center of the tile, and comparing

the coordinates of the wave data. The wave data is located on a map of 1-

degree resolution, with each point placed on half degrees. Any wave

coordinates more than 5 degrees away from the center of the tile were

discounted, with this distance coming from Pythagoras of the longitudinal

and latitudinal difference. 5 degrees was chosen as the distance as even


Alfie Hewetson 23

waves located outside of the tile can still propagate into the tile and cause

flooding. The number of wave coordinates associated with this tile is the

number of iterations that must be run for this tile. This process is shown in

figure 13.

Figure 13- Displays the possible wave location associated with the tile N20E105. The tile is shown in red, with each possible wave location for this tile shown in blue. Only wave locations in the sea will have values for wave, so of the total number of blue dots, 69, only a dozen will run.

2. As some of the wave data is located outside of the topographic data, the

topography must be extended. This is due to the output of the waves

appearing as a matrix representing the wave-front, with a width of 1200 cells

and a length of 2400 cells. For wave coordinates outside of the original

topography, this wave-front matrix would be dropped onto coordinates within

the topography, if the wave-front propagates into the domain. However, in

order to reduce computational power, the only coordinates used are those

representing where the start of the wave-front is and those representing the

center of the tile. As such making an empty matrix made up of 18000x18000

cells, which represents a grid centered at the same point as the tile, but

equivalent to 3 times the size in coordinates, now allows the wave-front


Alfie Hewetson 24

matrix to be dropped onto the topography, with the central 6000x6000 cells

being the original topography matrix, without having to use a coordinate grid.

Figure 14- The red square is the original topography grid, the blue square is the extended topography grid, the green square is the path of the wave-front matrix coming from [19.5,106.5]. This shows a wave that is propagating from outside the grid to the inside of the grid. The blue square, of the extended topography has to be large enough so that even when the wave-front is pointed in the opposite direction (South), the green grid does not exceed the blue grid, which would cause a fault in the code.

3. For each wave point, 12 further iterations must be conducted to account for

each of the 12 possible directions. As mentioned before, the wave is

represented as a matrix of the wave-front, with a width of 1200 cells,

equivalent to 1degree (roughly 112km at the equator). Plus, a length, in the

direction of travel of the wave, of 2400 cells, equivalent to 2 degrees(224km).

1degree was chosen as the width as this is the resolution of the wave data, 2

degrees was chosen as the length of the wave data to ensure that the wave

propagates to its uppermost extent into the land. Depending on whether

mangroves are present within this wave-front, results in a change in contents

of the matrix.

From this point on the approach changes depending on the inclusion of


Alfie Hewetson 25

mangroves into the study. The following is for when mangroves are present and

included.

4. For when mangroves are present the associated wave attenuation is a function

of the properties of the wave. Therefore, the Deepwater wave number, k, and

the wave frequency, ω, are found at this point based on the peak frequency at

this location, for the direction.

5. The wave matrix is split into 1200 straight lines with a length of 2 degrees.

The lines are placed evenly alongside the coordinate point half a degree either

side and propagate out 2 degrees from the original point. Each line is then

calculated individually, so as to work out the value of the wave height along

the corresponding column of the wave matrix.

Figure 15- Shows the wave-front at point [20.5,107.5], for visualization only 10 of the lines have been shown, propagating from the original point 2 degrees forward.

6. Taking an individual line, representing a column of the wave matrix, is first

rotated around the wave coordinate to represent the direction of the wave

propagation. This line is then passed through the mangrove data, to see

if/where the line intersects the mangrove forest. Each point of intersection is

recorded.


Alfie Hewetson 26

Figure 16-Shows the first of the 1200 lines, shown in green, for coordinate [20.5,107.5] that has been rotated 300degrees around that coordinate, shown in blue. This wave ray propagates into land and intersects the mangrove, shown in black, at the intersection points shown in red. In total the mangrove is intersected 10 times, meaning there are 5 mangrove patches that the wave ray passes through.

7. Each point of intersection now has a known location in latitude and

longitude. Using interpolation, the depth at these locations can be found by

overlaying this to the topography grid. Working on the assumption that the

line must always enter and leave the mangrove patch, implies an even

number of intersection points, in cases where the value is odd, it is assumed

that the line ends in the forest, so the end of the line is taken as an intersection

point. Using this information, an average depth between the intersection

points can be found. This follows the assumption that the bottom is flat, with

the slope being evened out by taking the average value between the points.

8. With this value for depth the dispersion equation can be applied to find a new

wave number relative to the depth.

9. The mangrove data is given to 0.001 degrees. Therefore, the line of 2 degrees

length is converted to 20000 cells, to maintain accuracy through the wave

attenuation process.

10. At this point equations (3), (5) and (15) must be answered, to find the

resultant wave attenuation along the line. Firstly, the vegetation frontal area is

found as a function of the depth, by removing the resultant value on figure 4,

before then dividing by the depth again. Next, the Reynolds number must be

found to satisfy equation (15). This requires knowledge of the maximum

wave velocity which is given in equation (16). This wave velocity is the


Alfie Hewetson 27

characteristic wave velocity given in [Kobayashi et al., 1993]. This

characteristic velocity is the maximum velocity of the flow field, when the

interaction of the vegetation with the flow field is included, due to the

vegetation being subaerial the cosh terms cancel. With these known, the γ

value can be found, equation (5) for the patch of mangrove between the

points of intersection. Alongside this, the distance between the intersection

points are required, as well as how far along the new 20000 cell line that

these intersection points sit. With this distance known equation (3) can be

applied to find a resultant wave height on leaving the patch of mangrove. If

this mangrove patch is the first patch along the line, the value for H0 is taken

as the Hs dictated by the wave data. However, if this is a subsequent

mangrove patch H0 is given as the wave height on leaving the previous

mangrove patch.

𝑢𝑚𝑎𝑥 =𝑘𝑔𝐻𝑠

2𝜔

cosh(𝑘𝑑)

cosh(𝑘(ℎ + 𝑑))=𝑘𝑔𝐻𝑠

2𝜔

(16)

11. Next, the rest of the points along this line must be filled in following an

exponential relationship between intersection points of mangroves, and

continuous values of Hs the preceding Hs elsewhere. This 20000-cell line now

must be interpolated onto a 2400 cell line, before being introduced as a single

column of the wave matrix.

12. This column of the wave matrix is then converted to a flooding matrix by

using equation (17) from [U.S. Army Corps of engineers, 2002] to find the

change in sea level due to wave set-up.

𝜂 = 0.2 ∗ 𝐻𝑠

(17)

13. This process from 6 to 11 must then be repeated for all 1200 lines.


Alfie Hewetson 28

Figure 17- shows a completed flooding matrix for a case with mangroves. With a cell width of 1200 and cell length of 2400, the flooding potential is in meters. The initial wave of 1m leads to a flooding potential of 0.2m from wave runup. This wave-front has moved through mangroves at certain locations causing the blue patches where the height has been dissipated.

Within the process outlined between 6 and 11, there are several possible jumps.

For lines which do not intersect mangroves a constant Hs is used, so wave

attenuation is not calculated. If the mangrove is elevated above the sea level, and

as such has a negative value for depth, the wave height is taken as constant and

no wave attenuation would be seen to occur.

This method with mangroves differs from that without. Without mangroves, the

wave-front matrix is assumed to be constant with every single value being the Hs

given from the wave data at the coordinate.

14. The flooding matrix, even on occasions where the lines were rotated during

generation, face north (direction of wave propagation). As such a rotation

matrix is used to rotate the flooding matrix relative to the wave direction.


Alfie Hewetson 29

Figure 18-Shows a rotation of a wave propagating from [20.5,107.5] in a case with no mangrove. The wave is coming from a 90-degree angle relative to North, so has had to be rotated 270 degrees around its initial point.

15. This rotated flooding matrix is then overlaid on top of the extend topography

grid. However, only the topography in the central section, from 6000 to

12000 in x and y, is the actual topography from the tile. So only the flooding

matrix within the central zone will be compared with regards to flooding.

Any cell in which the flooding matrix cell is greater in value than the

corresponding topography cell will be assumed to be flooded and will be

assigned as 1. Any cell where the topography is greater will be assigned 0.

16. This is then repeated for each of the 12 directions as well as for each wave

coordinate that is within the 5-degree range.

17. This will result in the final output of a flooding map.

5 Results and discussion 5.1 Validation

In order to validate the results garnered by this report, the values for wave attenuation

must be compared to pre-existing field results. Table 2 shows field studies by which

the results can be tested against.

Location-mangrove

setting

Incident wave height H

and period T

Wave reduction

Tong King Delta,

Vietnam- [Mazda et al.,

1997], for 3 different

H=-

T=5-8s

r=0.01-0.1 per 100m

r=0.001-0.01 per m

H=- r=0.08-0.15 per 100m


Alfie Hewetson 30

densities and plant types T=5-8s r=0.008-0.015 per 100m

H=-

T=5-8s

r=0.15-0.22 per 100m

r=0.015-0.022 per m

Vinh Quang, Vietnam –

[Mazda et al., 2006]

H=0.11-0.16

T=8-10s

r=0.002-0.006 per m

Do Son, Vietnam-

[Quartel et al., 2007]

H=0.15-0.25m

T=4-6s

r=0.004-0.012 per m

Red river Delta, Vietnam

[Bao ,2011]

H=0.15-0.27m

T=-

r=0.0055-0.01 per m

Can Gio, Vietnam- [Bao,

2011]

H=0.55m

T=-

r=0.017 per m

Table 2- Part of the table from [Horstman et al., 2014] showing the wave reduction, r, for various field experiments across Vietnam. With r=ΔH/(H*Δx).

These locations are mainly centred around Northern Vietnam, but finding the exact

locations from the reports is difficult. Therefore, the validation will be conducted by

running a single loop from the method already outlined, where only a single wave

coordinate with a single angle will be used. The point used will be [20.5,107.5] as seen

in figure 15 but working with an angle of 120degrees, so will propagate towards the

coast at a 300degree angle. This point is used as it is the closest point to the Tong King

delta, where most of the studies of the table were conducted. The angle of 300degree

is used as it means the wave is coming as close to perpendicular to the shoreline as the

wave data would allow with the 30degree discretisation. If the wave is perpendicular

to the shoreline, a greater length of the shoreline can be analysed. To validate the

results the significant wave height and frequency will be changed to closely match the

values in the table, so a wave height of 0.13m and a frequency of 1/9s-1 was used.


Alfie Hewetson 31

Figure 19-Both graphs show the same results, with the first graph showing the results of all the data points. With the second graph only showing the data points of the smallest values of the exponential decay coefficient

First, however the exponential decay coefficient can be investigated and compared to

the value of the exponential decay coefficient found from [Beudin et al., 2017]

equalling 3.9x10-3m-1. However, this study was for eelgrass, though it should give an

indication to a realistic answer. Figure 19 shows two graphs displaying the same

information but with the right graph only showing the smallest values of the

exponential decay coefficient rather than the entire data set. Each data point is

representative of a mangrove patch. So, within each wave ray several mangrove

patches may be crossed. This is mentioned to explain the graph on the left of figure

19. As a number of the values for the exponential decay coefficient are far larger than

what would be expected considering what [Beudin et al., 2017] found. Which is true,

however, these large values of γ are caused by mangrove patches which follow on

from preceding patches. As equation 5 is proportional to the drag coefficient, CD,

which in turn is a function of the Reynolds number, Re, which is proportional to the

velocity, u, which is proportional to the wave height, Hs. As the drag coefficient is

defined by equation (15), decreasing the Reynolds number causes an increase in the

drag coefficient. The decrease in the Reynold’s number is caused by the decrease in

the wave height by the preceding mangrove patch. If this wave height has been

attenuated to a large extent by the previous mangrove, the resultant drag coefficient

can be huge, which then dominates the exponential decay equation. This would be

partly because the Reynolds number has become smaller than the validity of equation

(15) allows as stated by [Maza et al., 2013]. However, for Reynolds numbers that

small, means the wave has already been largely attenuated, meaning the larger the


Alfie Hewetson 32

value of the incorrect exponential decay coefficient, the closer it is to zero. This

knowledge can then be coupled with the general shape of the right graph of figure 19.

The general trend of the data shows an exponential decrease when seen from a log axis

with the horizontal spread being successive mangrove patches changing the wave

height at input. These values are larger than the value suggested by [Beudin et al.,

2017] which would make sense due to the physical parameters dictated by the eelgrass

and mangrove plants. More importantly these values are larger than the value for the

exponential decay coefficient for bed friction, suggested by [MacVean and Lacy,

2014] of 3.2x10-4m-1. This means the assumption that wave-trunk interaction

dominates over the dissipation by bed friction.

Figure 20- Shows the distribution for wave reduction against depth for every patch of mangrove that is passed through and causes attenuation.

The wave height reduction, r, was found through taking the mean of the values shown

in figure 20. This value for r was found to be 0.0126 per m which sits in the range or

slightly above those shown in table 2. This slight overprediction is to be expected

between the values due to the variability of the mangrove species. All the results in

table 2 come are either Kandelia candel or Sonneratia, with the exception of [Bao,

2011] which is described as mixed vegetation. These species of mangrove tend to be

less dense than the Rhizophora, for example in the field study by [Horstman et al.,


Alfie Hewetson 33

2014], Sonneratia have a volumetric density of roughly 4.5% while Rhizophora has a

density of 5.8% to 20% and reaching 32% in water less than 1m. This increased density

would lead to an increase in the wave reduction factor. This slight over prediction is

likely to be larger than the r value which has been currently found. As figure 19 shows,

increasing the depth decreases the exponential decay coefficient, in turn reducing the

wave reduction coefficient. Currently the model is using the depth in mangroves from

the extreme sea-level from high tide and storm surge. The field data is unlikely to have

been recorded in these conditions and as such was likely recorded in shallower waters,

with a higher decay coefficient caused by the decrease in depth.

Id Incident wave height H

and period T

Wave reduction

1 Hs=0.13m

Fp=1/9s-1

r=0.0126 per m

2 Hs=0.55m

Fp=1/8s-1

r=0.0144 per m

3 Hs=0.14m

Fp=1/9s-1

r=0.0127 per m

4 Hs=0.2m

Fp=1/5s-1

r=0.0115 per m

Table 3- Shows 4 runs that are used in an attempt to validate this model. Id 1 is the generic run, used to compare against all results as previously seen. Id 2 is to validate against Can

Gio, Vietnam. Id 3 is to validate against Vinh Quang, Vietnam. Id 4 is used to validate against Do Son, Vietnam.

5.2 Limitations

A number of factors that would affect the results are not currently included within this

study. This is a result of either simplifications or lack of knowledge currently existing

in the field.

Firstly, the mangrove properties. This has already been mentioned in both the

background section and the validation section, and that is the assumption of the single

mangrove species is representative of all species of mangrove. The limitations of this

have already been noted, with the Rhizophora species being an upper range value due

to its increased density. Within the mangrove properties is the current lack of canopy,

the leaves, branches and foliage of the plant. This affects the results in two ways. One,

the reduced vegetation area from not having this included, leading to a lower bv in turn


Alfie Hewetson 34

reducing the exponential decay coefficient than if a canopy was included. Two, [He,

et al., 2019] found that models with a canopy produce a larger drag force than models

with just the stem and the roots. Meaning canopies can have a major effect on the

results. This is compounded within this study due to the use of extreme sea-levels

elevating the sea-level, leading to conditions which would place the flow in the region

that contains canopy. These factors could be improved by an inclusion of the species

type within the mangrove data for all locations, plus by finding an empirical

relationship for canopy density, like what [Ohira et al., 2013] did for the roots. These

improvements could also be enhanced by associating the mangrove with above ground

biomass density as used [Mafi-Gholami et al., 2020] but using volume density rather

than mass density. This could then be used in a similar manner to the length scale of

L=(V-VM)/A proposed by [Mazda et al, 1997].

The next limitation comes from the natural geography and the possible changes on the

account of rivers and estuaries. Currently, the code is set to give an exponential decay

coefficient of 0 if the mangroves are above the extreme sea-level. This is wrong in two

ways. One, if there is still flooding of the wave up to this point as found using 0.2*Hs

[U.S. Army Corps of engineers, 2002], the mangrove would still obstruct the wave.

However, equation (5) requires a known depth of water, and would not function for

mangrove dissipation in the swash zone. Two, rivers and estuaries would allow waves

to propagate up their length, while the relative water height above sea level would

increase, due to the increased water level that causes rivers to flow. This issue was

partially resolved by using the MERIT topographic map [Yamazaki et al 2019], which

thus corrects the bottom surface of the river bed. However, it does not go as far as

giving the depth of the river at each section along its length, which in turn can also be

highly variable due to seasonal changes. More work is required on how mangroves

can attenuate flooding in the swash zone before it can be empirically implemented. To

find the depth of river at each section and thus an increased depth of the wave, an

adjusted water body map could be made, but the height of the river would likely be

found from the height of the banks of the river and would likely overcomplicate the

simplified flooding model.

Human geography also causes a limitation due to the built landscape. As built flood

defences are not currently considered, which would block the flood potential on low

lying land. This could be rectified in the model by knowing the locations of the defence

and knowing the height required to overtop the defence. However [Hillen et al., 2010]


Alfie Hewetson 35

found that characteristically, at time of writing, hard coastal defences in Vietnam could

only withstand a 1 in 50-year flooding event.

Another limitation is that of mangrove interaction between patches. As the results of

equation (3) results in a change of wave height, but assumes the wave characteristics

do not change beyond that. [Beudin et al., 2017] reported a 15% change in the mean

wavelength and a 10% change in the mean wave period. This isn’t too much of an

issue as no change in the peak wave frequency was observed, which is used in the

calculations. On leaving the mangrove patch, the waves become scattered due to the

irregularity of damping of the patch causing diffraction [Dalrymple et al., 1984].

Scattered waves can cause early breaking due to constructive interference, but also

change the flow conditions on entering the next patch.

[Beudin et al., 2017] further studied the effects of tide/currents on the dissipation of

waves through vegetation. This found that the difference in wave height dissipation

can double in ebb conditions or reduce by 40% in flood conditions. Currently in this

study however no currents are included either from rivers or tides.

The biggest limitation currently observed is that of wave breaking. According to [Vo-

luong and Massel, 2008], the two principal drivers of wave energy dissipation are

wave-trunk interaction and wave breaking, assuming a mild slope thus reducing the

bed friction. This implies that wave breaking and wave-trunk interaction are of similar

magnitudes. This non-inclusion of the wave breaking causes several problems. Firstly,

in terms of the attenuation from mangroves, as if the wave has already broken, then

the interacting wave may already be reduced in height by the breaking process.

Secondly, mangroves have been shown to suppress wave set-up [Suzuki et al., 2019].

Which according to [Bowen et al., 1968], wave set up results from wave shoaling and

breaking. A solution for wave energy dissipation in vegetation under breaking waves

has been proposed by [Mendez and Losada, 2004], which combines a vegetation

energy dissipation rate with the wave breaking energy dissipation rate.

Beyond wave breaking, several other coastal processes have been ignored within this

study. First, wave refraction; currently the wave rays travel only in straight lines from

the wave-front origin and are not affected by the bathymetry. Secondly, wave shoaling

is only accounted for as a function of the wave setup as outlined by [Bowen et al.,

1968]. When wave shoaling would lead to an increase in wave height as the wave

moves into shallower water. To incorporate these coastal processes into this current

model would be computationally expensive. However, if the model was changed with


Alfie Hewetson 36

respect to the wave data, so the wave data points are placed along the shoreline, with

only the waves travelling perpendicular to the shore being analysed. This would result

in a model which would account for wave refraction, by removing the cause of

refraction.

Of these limitations some solutions have been provided, however this model currently

acts to simplify the conditions in a way that can then be validated to field data and

applied anywhere. A limitation, currently, to using this code anywhere in the world is

how the code is applied to small land masses, such as islands. Currently, the wave rays

are fixed at 2 degrees length, and if the wave is unattenuated, the wave height and

consequent flooding is fixed along this length. This causes a problem in the cases of

small islands with a diameter of less than two degrees. As waves from one side of the

island could cause flooding on the far side of the island despite an increased inland

topography shielding the area from flooding. This could be achieved by limiting the

wave ray length to stop on reaching a height greater than the possible flooding.

However, this would require another coupling between the wave ray and the

topography, which would further strain the computational requirements. In this paper,

the answer was to use Vietnam as a case study due, to it not being an island.

5.3 Flooding extent

The same forcing conditions were applied to 3 scenarios; a case with no mangroves, a

case with the mangrove distribution in 1996 and a case with mangrove distribution in

2016. The results of this are given in table 4. What can be clearly seen across all 3 tiles

is for coastal Vietnam the main flood forcing comes from storm surge and tidal

component. The top tile has 81.1% of its flooding caused by tide and storm surge, for

the middle and bottom tile it is 79.77% and 59.24% respectively. This shows that the

wave component is of increasing importance especially considered that the storm and

tide forcing is relatively consistent along the Vietnam coast as shown in figure 7. This

is likely due to the sheltering Vietnam receives from neighbouring islands, with

Northern Vietnam being sheltered by the island Hainan. This in turn reduces the fetch

and the subsequent wave heights.

Top tile Middle tile Lower tile


Alfie Hewetson 37

[22.5,107.5] [17.5,107.5] [12.5,107.5]

Flood due to mean sea level 6276238 19048899 8623465

Flood due to storm surge plus tide 6921875 19342865 8793928

Flood due to storm surge plus tide

plus wave (no mangrove)

7072074 19417408 8911216


plus wave (1996 mangrove)

7071965 19417408 8911216


plus wave (2016 mangrove)

7071965 19417408 8911216

Table 4- shows the total number of cells which have been flooded within each tile. The flood due to mean sea level, is just the cells accounting for region of the tile already in the sea and

has no result from flood forcing, but is there to note the difference.

The degree of flooding can also be seen between the samples, table 5 shows the area

of flooding in hectares of each tile. Clearly from this it can be seen that the top tile has

the greatest degree of flooding by more than twice the amount of flooding than the

middle and lower tile. This is largely to due with the increased amount of low-lying

land that can become easily flooded.

Table 5-shows the area in hectares(10000m2) of the associated flooding, 1996 and 2016 mangroves have been compiled to a single variable due to no change being seen in table 4. Each cell is 3 seconds by 3 seconds in size, which equates to roughly 90m by 90m, giving an

area per cell of 8100m2

The objective of this paper was to produce a model whereby the effects of wave

attenuation by vegetation are included on a flood risk map. Only in the top tile did

vegetation make an impact on the resultant flooding. This largely comes down to the

dominance of the forcing of storm surge and tide on the flooding map. As figure 17

shows mangroves do have an ability to reduce the wave height and to reduce the flood

potential coming from the waves. For the middle tile, where the mangrove was a sparse

coastal fringe, mangroves had no affect on the attenuation. The same is true for the

Top tile

[22.5,107.5]

Middle tile

[17.5,107.5]

Lower tile

[12.5,107.5]

Flood due to storm surge plus tide 522966 238112 138075


plus wave (no mangrove)

644627 298492 233078


plus wave (mangrove)

644539 298492 233078


Alfie Hewetson 38

bottom tile where the mangrove was predominately riverine.

Figure 21- Shows the total flooding in the top tile. Where red is the flooding from storm and tide and blue is the increase through wave set up.

On seeing the visualisation of the flooding, a reanalysis of the original input data was

conducted. In doing this the wave forcing was found to be incorrect, by virtue of the

wave angle being 180 degrees off. As the direction that the wave was coming from

was used as the direction the wave was propagating. This results in a major reduction

in wave height, as any wave that is currently implemented in the results, can have no

more than 2 degrees of fetch. It cannot have more than two degrees as that is the length

of the wave ray, So, to have more than 2 degrees of fetch means the wave location is

more than 2 degrees from land and as such wouldn’t have an affect on the study.

This also explains why the bottom tile has a greater percentage of its flooding from

waves than the other tiles. Due to the circular curve of the shoreline, waves propagating

at angles to the shoreline can have an increased fetch by being blown at a tangent to

the coastline. This would develop larger waves which would increase the flooding

from the wave component.


Alfie Hewetson 39

Figure 22-Shows the total flooding in the middle tile. With red the storm surge and tide forcing and blue being the wave forcing.

Figure 23- Shows the flooding in the bottom tile, wave forcing in blue and tide and storm surge in red

.


Alfie Hewetson 40

6 Conclusions

To fully extend this model to find the resultant flooding extent a reassessment of the

wave data is required. This would be accomplished by finding the waves which are

travelling perpendicular to the coastline at nearshore locations.

The validation section showed that when waves were travelling perpendicular to the

shoreline, due to the chosen wave direction, a realistic attenuation was found which

fit field values, if over predicting the dissipation, due to the increased vegetation

density. As such the use of wave rays and mangrove data collected from satellites

can be used to estimate the resultant wave attenuation.

To fully complete the aims of this project the code must be run again but with a

change to the wave conditions. On attempting this before, it was found that the new

wave conditions take on average twice as long as before. This at least implies that a

change is occurring to the results. This is likely because more wave states exist, in

areas that would be otherwise heavily fetch limited. However, due to the time

limitations of this project this has not yet happened.

To take the project further though would be possible, with the validation showing the

possibilities of combining satellite measurements of coastal ecosystems and wave

data, to create flooding maps. Numerous other forms of ecosystem have the ability to

attenuate wave [Narayan et al., 2016], such as salt marshes, coral reefs and sea

grasses. [Kobayashi et al., 1993] was originally implemented for wave dissipation

through submerged kelp beds, as such the method outlined in this paper can be

applied and used in the same manner and would only require, inputs of the physical

characteristics of the kelp beds. Similar implementation could be carried out on other

ecosystems.


Alfie Hewetson 41

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Database References

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Alfie Hewetson 49

Global wind-wave 21st century climate projections. v2. CSIRO. Service Collection.

https://doi.org/10.4225/08/55C991CC3F0E8

A Significant wave height maps with

respect to the direction

Figure 24-30 degrees direction


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Figure 25-60 degree direction

Figure 26- 90 degree direction


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Figure 32-270 degree direction


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B Peak wave frequency with respect to

direction

Figure 35- 0 degrees direction



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C MATLAB code used

Code is available by request to: [email protected]

• Wave_replace.m- converts the monthly time-series nc files into MATLAB

files.

• Wave_struct.m- converts the monthly time-series into a yearly time-series

• Wave_direction.m- uses the yearly timeseries and carries out the procedure

outlined in section 3.4 to find the 1 in 100 year significant wave height.

• Wave_freq.m- Then find the associated mean peak frequency for the 1 in 100

year significant wave heights, as outlined in section 3.4.

• Wave_grid.m- makes a grid for the wave data relative to an nd grid

• rerun.m- opens up the tif file of the topography data and converts it to a mat

file. It then changes the topography based on the closest point of storm/tide

surge to the new topography height.

• Frontal_area.m- applies [Ohira, 2013] to find the mangrove frontal area, as

described in section 2.3

• Mangrove_shorten.m-This reduces the entire shapefile from section 3.1 to

mangrove relative to 5degree by 5degree grids

• Var_change.m-Is used to select the tiles that are going to be used in the analysis

in this case Vietnam tiles it picks out the 3 tiles within that region

• Land_grid.m-Reads the tiles and finds each tiles centre point

• Land_coord.m- This takes the 6000 by 6000 topography grid and applies a

coordinate system to each cell within the topography grid.

• Flood_Mangrove_finalN_shorten.m- This is the overarching flooding code.

That takes the outputs from the previous codes in order to run. Require the

significant wave height grid, peak frequency grid, wave grid, topography grid,

mangrove location, mangrove frontal area and knowing the selected tiles. It

then runs the code onto the associated flood grid. Using the method in section

4.

mailto:[email protected]

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