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MODELING THE DISSIPATION OF STORM SURGE BY COASTAL WETLANDS

By

ANDREW JOHN LAPETINA

A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA

2013

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© 2013 Andrew Lapetina

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To my Grandma Mary, who supported scholarship throughout her long, beautiful life

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ACKNOWLEDGMENTS

My most sincere thanks go to my supportive parents, Mauro and Susan, for their

boundless love and support of my education. Leslie Tharp will forever have my

adoration and love for accepting my grumpiness on many occasions. I would love to

thank my sister and brother, grandparents, aunts and uncles, many cousins, Gainesville

friends, the News Team and Alexis Neuhaus for support during this period in my life.

Dr. Peter Sheng, my advisor and committee chair, deserves much credit for this

dissertation. Without a telephone call from him in November of 2007, I would never

have pursued my PhD. Furthermore, without his steady pressure and financial support,

I would not have developed into the scientist, thinker, or man I have become these past

5 years. I would like to thank my other committee members, Drs. Arnoldo Valle-

Levinson, Mark Brown, and Alexandru Sheremet for their help during this process.

I would like to thank Drs. Justin Davis, Drew Condon, Vladimir Paramygin, and

Bilge Tutak, for teaching me everything and anything whenever needed, and for bearing

with my innumerable stupid questions. The Gainesville Hogs, Tianyi Liu, Miao Tian,

and Drs. Chloe Winant, Amy Waterhouse, Luciano Absalonsen, and Cihan Sahin

deserve immense credit for keeping me laughing all these years. Renny Zhou and Cici

Feng observed my emotions with aplomb. And lastly God and the Universe brought all

these forces together, making this possible.

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TABLE OF CONTENTS page

ACKNOWLEDGMENTS .................................................................................................. 4

LIST OF FIGURES .......................................................................................................... 8

LIST OF ABBREVIATIONS ........................................................................................... 10

ABSTRACT ................................................................................................................... 12

CHAPTER

1 INTRODUCTION .................................................................................................... 14

2 THREE-DIMENSIONAL MODELING OF STORM SURGE AND INUNDATION INCLUDING THE EFFECTS OF COASTAL VEGETATION ................................... 18

The Need for a 3D Vegetation Model ..................................................................... 18 Brief Description of the TKE Model ......................................................................... 21 Model Validations ................................................................................................... 26

Neumeier Experiment ....................................................................................... 26 Nepf and Vivoni Experiment ............................................................................. 29

Experiments with the 3D Vegetation Resolving Storm Surge Model ...................... 30 Experiment 1 .................................................................................................... 32 Experiment 2 .................................................................................................... 34 Experiment 3 .................................................................................................... 36

Findings of the Three Experiments ......................................................................... 39

3 QUANTIFYING THE REDUCTION OF STORM SURGE BY VARYING CANOPIES AND STORMS .................................................................................... 54

The Need to Quantify the Influence of Vegetation .................................................. 54 Motivation and Method............................................................................................ 54 Experiments ............................................................................................................ 58 Results and Discussion........................................................................................... 59

4 THE INFLUENCE OF VEGETATION ON STORM SURGE AND COASTAL INUNDATION IN THE NORTHERN GULF OF MEXICO ........................................ 65

Applying the Model to a Complex Domain .............................................................. 65 Hurricane Ike .................................................................................................... 66 Vegetation and Storm Surge ............................................................................ 67 The Forerunner and Sediment Deposition........................................................ 68 Purpose and Methods of this Study .................................................................. 70

A Vegetation-Resolving Storm Surge Modeling System ......................................... 71 Vegetation-Resolving CH3D-SSMS ................................................................. 71 Model Setup ..................................................................................................... 73

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Simulation of Surge and Inundation During Hurricane Ike ................................ 75 Results .................................................................................................................... 76

Water Level Comparisons ................................................................................ 76 Water Levels and Velocities within Canopies ................................................... 77 3D Hydrodynamics of the Forerunner .............................................................. 78

Discussion .............................................................................................................. 80 The Value of 3D Vegetation-Resolving Storm Simulations ..................................... 81

5 CONCLUSION ...................................................................................................... 101

LIST OF REFERENCES ............................................................................................. 106

BIOGRAPHICAL SKETCH .......................................................................................... 112

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LIST OF TABLES Table page 2-1 Three pairs of vegetation conditions used in Experiments 1, 2, and 3. Each

pair compares a different 2D and 3D vegetation representation. ....................... 52

2-2 Inundation volumes for hurricanes on each of the pairs of vegetation conditions described in Table 1. ......................................................................... 53

4-1 Northern Gulf storm characteristics .................................................................... 99

4-2 4 day simulation characteristics and results. .................................................... 100

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LIST OF FIGURES

Figure page 2-1 Typical vertical velocity structures for flow through vegetation canopies with

water depth H and vegetation canopy height K .................................................. 40

2-2 Modeled velocity and turbulence profiles and measured data at discrete points for Neumeier’s experiment BB [Neumeier, 2007] ..................................... 41

2-3 Continuous observations and model results [Neumeier, 2007]........................... 42

2-4 Modeled velocity and turbulence profiles and measured data at discrete points for Neumeier’s experiment BB, ignoring skin friction effects in modeling. ............................................................................................................ 43

2-5 Modeled mean velocity, turbulence, and Reynolds Stress for experiments by Nepf and Vivoni [2000]. ...................................................................................... 44

2-6 Domain used, with vegetation within hashed region. Experiment 1 uses a domain from Y=0 to Y=4 km, Experiments 2 and 3 use the entire domain. ........ 45

2-7 Velocity vectors at X= 1 km (Middle of Canopy) for Experiment 1. ..................... 46

2-8 Water levels at X= 500 m (Center of Canopy) for Experiment 1. ........................ 47

2-9 Velocity profiles in the canopy center, 3D simulations, Experiment 1. T=3000s ............................................................................................................. 48

2-10 Percent deviations of water level and velocity for each pair of simulations in Experiment 2. ..................................................................................................... 49

2-11 Percent Deviations of Total Inundation Volume for Various Storms for Different Vegetation Conditions in Experiment 3. ............................................... 50

2-12 Differences between 2D and 3D vegetation in the modeled impacts of vegetation on storm surge. ................................................................................. 51

3-1 Domain upon which experiments 1 and 2 were conducted. ............................... 61

3-2 Dissipation of storm surge by vegetation canopies for a Category 2 (maximum sustained winds of 49 m/s) moving onshore at 6.71 m/s (15mph) .... 62

3-3 Dissipation of storm surge by a 75cm tall vegetation canopy of 200stems/m2 for storms of varying magnitude and forward speed. .......................................... 63

3-4 Maximum water level on landward side of 1.5 km wide hashed region in Figure 2-1 for Category 2 storm. Solid blue line denotes vegetation free simulation, dashed line denotes vegetation present. .......................................... 64

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4-1 Storm track for Hurricane Ike. Provided by National Hurricane Center .............. 83

4-2 Sediment deposits from Hurricanes Rita, Ike, and Gustav. Data from Williams [2012] and Turner and Tweel [2012]. ................................................... 84

4-3 Boundaries of National Wildlife Refuges in Chambers County. .......................... 85

4-4 Bathymetry of the domain for simulating Hurricane Ike. ..................................... 86

4-5 Winds at various airports during Hurricane Ike. Red vectors are data, black vectors are modeled. .......................................................................................... 87

4-6 Classification of cells for vegetation laden simulations. ...................................... 88

4-7 Photos of coastal vegetation within Anahuac, Moody, and McFaddin NWRs (Provided by the United States Fish and Wildlife Service). ................................. 89

4-8 USGS Water Level Stations for Hurricane Ike. ................................................... 90

4-9 Deposition area studied by Williams [2010], and cross section for velocities in Figure 12. ........................................................................................................... 91

4-10 Modeled water level compared to USGS data. Modeled values in red, data in green. ............................................................................................................. 92

4-11 Comparison of modeled vegetation-resolving and vegetation free water levels with data at CHA-003 and CHA-004 in Chambers County, TX. ................ 93

4-12 Comparison of modeled vegetation resolving and vegetation free water levels and vertically averaged speeds .......................................................................... 94

4-13 Wind vectors and water levels around the transect AB on the left, and water velocities in transect AB on the right. .................................................................. 95

4-14 Bottom stresses and velocities along the transect around hurricane landfall. .... 96

4-15 Water levels at locations A and B during Hurricane Ike with and without Coriolis effects. ................................................................................................... 97

4-16 Water levels during Hurricane Ike on the left, water levels during a Hurrricane Rita-like storm making landfall at the same location on the right. ....................... 98

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LIST OF ABBREVIATIONS

1D One-Dimensional

1DV One-Dimensional Vertical

2D Two-Dimensional

3D Three-Dimensional

ADCIRC Advanced CIRCulation Model

CAIV Compared Average Influence of Vegetation

CH3D Curvilinear Hydrodynamics in Three Dimensions

DNS Direct Numerical Simulation

EOHS Envelope of High Speeds

EOHW Envelope of High Water

FEMA Federal Emergency Management Agency

IPET Interagency Panel Evaluation Taskforce

LES Large Eddy Simulation

NAVD 88 North American Vertical Datum 1988

NHC National Hurricane Center

NGDC National Geodetic Data Center

NOAA National Oceanographic and Atmospheric Administration

NOS National Ocean Service

NYS New York State

NWR National Wildlife Refuges

RANS Reynolds Averaged Navier Stokes

RMS Root Mean Square

RSM Reynolds Stress Model

SSMS Storm Surge Modeling System

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SSHS Saffir Simpson Hurricane Scale

SWAN Simulating Waves Nearshore

TIV Total Inundation Volume

TKE Turbulent Kinetic Energy

TKEM Turbulent Kinetic Energy Model

USGS United States Geological Survey

UTC Coordinated Universal Time

VDP Vegetation Dissipation Potential

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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

MODELING THE DISSIPATION OF STORM SURGE BY COASTAL WETLANDS

By

Andrew John Lapetina

December 2013

Chair: Y. Peter Sheng Major: Coastal and Oceanographic Engineering

Coastal wetlands have long been described as natural buffers to storm surge,

however, this assertion has not been quantified or examined in great scientific detail.

This study first examines flow through a vegetation canopy using a 1DV TKE model.

This model is both compact and robust enough to simulate flows within a 3D storm

surge-wave model (CH3D-SWAN). Using this vegetation-resolving 3D model, several

issues are addressed in each chapter of this dissertation.

First, the 1DV model is introduced, validated, and demonstrated. The contrasts

between 2D and 3D simulations of storm surge events are shown, and the improvement

of the 3D vegetation-resolving storm surge model over the 2D model is demonstrated.

Then, questions regarding the ability of coastal vegetation to dissipate storm surge are

addressed. It is shown that tall, dense, and wide canopies are more capable of

dissipating storm surge than their shorter, sparser, and narrower counterparts, and that

fast moving storms have more dissipation than slower storms. In one experiment, it

shown that the dissipation varies from 5-40% depending upon canopy characteristics.

In another, it is shown that storm-dependent dissipation varies from 10-25%.

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Finally, the impacts of vegetation on Hurricane Ike, a storm which struck the Texas

coastline in 2008 are evaluated. The vegetation model reduced errors within

vegetation-laden Chambers County from 17.9% to 9.6%. Other findings from this

simulation of Hurricane Ike are included.

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CHAPTER 1 INTRODUCTION

Coastal scientists have long identified intertidal wetlands as important ecosystems

for primary productivity, nutrient removal, and shoreline stabilization. However, the

complex hydrodynamics of flow through vegetation canopies has limited quantitative

evaluation of their ability to reduce storm surge. The status quo for modeling the

influence of vegetation on storm surge is increasing the Manning coefficient in 2D storm

surge models. This method for representing the influence of vegetation in the water

column is based on 19th century means of predicting 1D flow in a pressure driven

stream. This dissertation presents significant steps forward in quantifying the value of

coastal wetlands for reducing storm surge and coastal hazards.

In the first chapter, a 1D TKE model for flow through vegetation is introduced,

validated, and incorporated into a 3D storm-surge wave modeling system, CH3D-

SSMS. Then three experiments are conducted to explore the utility of the model and its

strengths relative to the enhancement of the Manning coefficient. In the first, a constant

wind field is applied to an idealized continental shelf, and different representations of

vegetation in 2D and 3D are compared. In the second, a hurricane wind field is applied

over an idealized continental shelf, and the same representations are compared. In

both of these, water level and water velocity are used for evaluating the impact of

vegetation. In the third experiment, storms of varying intensity and forward speed are

applied to the domain for the 2D and 3D representations of vegetation. Here, if the 2D

model is indeed a robust representation of vegetation, its results should match those of

the 3D representations, which depends upon a processed-based physical model of flow,

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not an empirical tuning coefficient. This chapter is very similar to a paper by Lapetina

and Sheng which is under review in Estuaries and Coasts.

After demonstrating the utility of the model and its benefits over 2D

representations of vegetation, the 3D model is used to examine two important aspects

of storm surge dissipation by vegetation canopies in Chapter 3. First, the reduction in

storm surge caused by canopies of varying density, width, and height are evaluated.

This is a significant step forward from simply changing a Manning coefficient to produce

empirically based results. Then, using a set of storms of varying intensity and forward

speed, the variability in the reduction of storm surge a given canopy can cause is

evaluated. It should be noted here that canopy is used here in the hydrological sense,

not the ecological sense. Any vegetation or vegetation-like arrays obstructing flow are

considered canopies here, and throughout this dissertation. Much of this chapter has

been published by Sheng et al. [2012].

Lastly, the ability of the model to simulate storm surge in a real storm is evaluated

in Chapter 4. Here, Hurricane Ike is simulated using the vegetation model to improve

results. Within Chambers County, Texas, on the northeast side of Galveston Harbor,

simulating the surge without vegetation produces a significant over estimation of water

levels, which is remedied by the use of the vegetation model. This confirmation of the

validity of the 3D modeling system permits an explicit exploration of the dynamics of

flooding in the coastal region. In addition, the dynamics of Hurricane Ike’s forerunner is

examined. The forerunner was the largest Ekman wave ever recorded, and its 3D

velocities are studied here. Finally, Hurricane Ike induced a sediment deposit pattern

significantly different from comparable storms such as Hurricanes Rita and Gustav. The

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reasons for this difference are diagnosed here. Much of this chapter has been

submitted as a paper to the Journal of Geophysical Research, Oceans.

The necessity and relevance of this dissertation is apparent from recent public

policy propositions and extensive scientific literature. Hurricanes Katrina, Ike, and

Sandy initiated national conversations on the need for coastal wetlands [NYS 2100

Commission, 2012; Louisiana Coastal Wetlands Conservation and Restoration Task

Force, 2010]. Federal investment in coastal wetlands in Louisiana alone via the Coastal

Wetlands Planning, Protection, and Restoration Act ranges between $30 and $80

million annually. Proposals for introducing vegetation as infrastructure in New York City

have been conceived, but lack proper hydrodynamic assessment [Seavitt, 2013]. The

research within this dissertation can ensure investments in coastal wetlands for the

purpose of shoreline stabilization are reasonable and justifiable.

Innumerable journal articles on 1-D flow through vegetation exist [Shimizu and

Tsujimoto, 1996; Nepf and Vivoni, 2000; Neumeier, 2007], but few extend these studies

to study the influence of vegetation in 3D [Temmerman et al., 2005; Ma et al., 2013].

Furthermore, the status quo in modeling the effects of vegetation utilizes a simple 2D

bottom friction representation of vegetation [Zhang et al., 2012; Liu et al., 2013] using

the Manning coefficient. However, this representation of bottom friction dates back to

the 19th century, and while it was introduced for computational expedience with

success in pelagic waters in early circulation models [Blumberg, 1977], the Manning

coefficient demands updating. Overly simplistic models can be dangerous tools when

misused.

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An example of an overly simplistic model highlighting the need for advancement in

coastal modeling is the Natural Capital Project’s Coastal Hazard Web Portal [Arkema et

al., 2013]. It attempts to quantify the risk of related to sea level rise and extreme

weather for the entire United States using a combination of residential real estate

values, wave climate from 2005-2010, and geologic conditions, to offer a picture of how

the presence and absence of local ecosystems affect that risk [Arkema et al., 2013].

While this is a noble goal, it identifies downtown Miami as a relatively low risk area,

likely due to the lack of landfalling hurricanes during this time period, the inability of the

model to move the shoreline due to sea level rise, the housing market in Florida during

this time period, and the model’s semi-empirical means of calculating hurricane

hazards. Any coastal scientist familiar with Miami would hesitate to label it as a

relatively low-risk location.

The model developed in this paper is intended to give a realistic, process-based

picture of the role coastal vegetation plays in hydrodynamics at the scale of a city and

region. It begins with fundamental fluid mechanics, and avoids empirical simplifications

as much as is feasible. Hopefully the results within prove valuable to improving coastal

infrastructure in the face of great change.

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CHAPTER 2 THREE-DIMENSIONAL MODELING OF STORM SURGE AND INUNDATION

INCLUDING THE EFFECTS OF COASTAL VEGETATION

The Need for a 3D Vegetation Model

Understanding the complex fluid mechanics of flow through vegetation is critical to

quantifying the role vegetation plays in large scale coastal dynamics, in particular during

storm surge events. Novel means of addressing growing threats of storm surge to

fragile urban centers such as New York City demand improvements in coastal modeling

of storm surge in soft, vegetation-based infrastructure [Seavitt, 2013]. Already,

expensive wetland restoration projects are being implemented along the Gulf Coast, but

a fully physics-based assessment of the feasibility for this environmental engineering

strategy does not exist [Louisiana Coastal Wetlands Conservation and Restoration Task

Force, 2010]. Small scale projects for the expansion of coastal wetlands in urban areas

have been proposed [NYS 2100 Commission, 2012]. However, because of the large

spatial scale of hurricanes, small scale pilot projects will not yield as much information

on the ability of coastal wetlands to reduce storm surge as a comprehensive modeling

study can.

When an aquatic or atmospheric boundary layer encounters a vegetation canopy,

several processes occur to modify the flow. Mean currents are reduced within the

vegetation canopy due to profile drag and skin friction, proportionally to the frontal area

Af and the wetted area Aw, respectively. Turbulence is produced within the canopy

proportionally to the frontal area, and dissipated proportionally to the wetted area

[Lewellen and Sheng, 1980]. In a typical vegetation-free boundary layer, dissipation of

turbulence is dependent upon the length scale of the turbulence, largely a function of

distance from the boundary [Pope, 2010]. When vegetation is present, this length scale

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is reduced, increasing dissipation rates. Finally, over submerged vegetation, faster

velocities will exist in the vegetation-free region and slower velocities within the

vegetation canopy, leading to the development of a shear layer [Nepf and Vivoni, 2000].

This shear layer causes turbulence production and transport, and the effects of

vegetation extend throughout the water column [Nepf and Vivoni, 2000].

The status quo for calculating the influence of vegetation on storm surge is by

increasing the Manning coefficient within a 2D surge model over an area where

vegetation is present. Using a bottom friction term dependent upon velocity, depth, and

the Manning coefficient [Wamsley et al., 2010; Loder et al., 2009; Zhang et al., 2012],

this approach ignores the non-linearities regarding the mechanics of flow through

canopies, particularly when the ratio of water depth H to canopy height K varies

significantly over the time period under consideration. During a storm surge event in a

coastal wetland, initial water levels are typically at the base of coastal vegetation,

generally Spartina or mangroves. As wind increases, water levels increase, and the

ratio of H to K approaches 1. While H/K is less than 1, the canopy is emergent, and

horizontal velocity varies little vertically [Nepf and Vivoni, 2000]. As the event

continues, the canopy becomes completely submerged and H/K surpasses 1. At this

point, the flow has two layers, a vegetation free upper layer and a vegetation-laden

lower layer. Laboratory studies of pressure-driven flow show shear effects are

important here [Nepf and Vivoni, 2000]. When the water level greatly exceeds the

vegetation canopy height, the flow essentially has a rough bottom, and has a relatively

uniform vertical structure, as compared to a shear layer (Figure 2-1).

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A 2D surge model assumes horizontal velocities are nearly vertically

homogeneous with negligible vertical shear effects, but this assumption is highly

questionable in shallow, wind driven flows such as storm surge events, as well as flows

through submerged vegetation canopies. In most 2D surge models, all friction from

bottom friction and vegetation is bundled in a single term, generally dependent upon

water depth, a friction coefficient, and vertically averaged velocity. Because flow

structure is highly dependent upon the depth to vegetation height ratio, as well as the

mechanism of forcing (surface wind or barotropic pressure), both of which change

significantly over a storm surge event, 3D modeling of flow in canopies is necessary.

Sheng et al. [2012] modeled storm surge through vegetation canopies in 3D, finding that

taller, denser, and wider canopies reduced flooding, and that storm surge dissipation

was greatest for fast and strong storms. Here, this modeling system is compared to the

traditional, 2D approach.

In a review of storm surge modeling, Bode and Hardy [1997] found that the

importance of 3D models lies in their ability to determine the vertical profile of storm-

induced currents. They state that 3D models permit a more physically based

determination of bottom friction than a 2D parameterization can, and that while 2D

models are used widely for computing water levels, this approach may have a

questionable validity for determining dynamics [Bode and Hardy, 1997]. Most

importantly, they point out that determining the 3D velocity profile is essential to

quantifying the influence surge has on offshore structures such as oil platforms [Bode

and Hardy, 1997], and this principle extends to quantifying the influence vegetation has

on surge.

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This paper first introduces the model and presents validations of a compact and

efficient one-dimensional vertical (1DV) model for flow through vegetation canopies for

several steady and unsteady flow situations. These examples highlight the model’s

ability to simulate all aforementioned processes which occur when flow encounters a

vegetation canopy. Then, this 1DV model is incorporated into a 3D storm surge

modeling system (CH3D-SSMS) to simulate the effects of coastal vegetation on a

basin-wide scale. Lastly, the value of the 3D model over a simple 2D model is

demonstrated through three experiments.

Brief Description of the TKE Model

The 1DV TKE model is a simplified version of a Reynolds Stress Model (RSM)

developed by Lewellen and Sheng [1980] which begin with the RANS equations:

continuity, mean momentum, and Reynolds Stress. The mean momentum equations

include the profile drag Dp and the skin friction drag Ds which are modeled as:

(2-1)

(2-2)

Hence the total drag is equal to:

(2-3)

with:

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(2-4)

where ui and uj are flow velocity components, Cp is the profile drag coefficient, Cf is the

skin friction coefficient, Aw is the wetted area per unit volume, Af is the frontal area per

unit volume, q is the square root of twice the TKE, Λ is turbulent length scale, c1 is a

constant, and ν is molecular viscosity. The drag term shown in Equation 2-1 is different

from those typically used by civil engineers or ocean engineers, but is believed to be

more accurate and suitable for turbulent flow in vegetation canopies, since the root

mean square turbulent velocity is included in the quadratic stress relationship.

In the limit of no vegetation, the RSM from which this TKE model is derived is

equivalent to the RSM for vegetation-free flow described in Sheng and Villaret [1989].

For simplicity, the RANS equations for the RSM are written in tensor form:

Mean Continuity Equation

(2-5)

Mean Momentum Equation

(2-6)

Reynolds Stress Equation

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(2-7)

where (i, j, k) = (1, 2, 3), xi are coordinate axes, t is time, (ui, uj, uk) are the mean

velocity components, (ui’ , uj

’, uk’ ) are the fluctuating velocity components, the overbar

represents the Reynolds averaging, g is gravitational acceleration, εijk is alternating

tensor, Ω is the Earth’s rotation, δij is the Kronecker delta, q is the total rms fluctuating

velocity, κ is molecular diffusivity, and λ is the turbulence macroscale which is a

measure of the average turbulent eddy size. The right hand side of Equation 2-7, which

represents the dynamic equation for the Reynolds stresses, contains two vegetation

terms, two shear production terms, two rotation terms, one diffusion term, one tendency

towards isotropy term, and one dissipation term [Sheng and Villaret, 1989]. While the

general RSM and TKEM include the buoyancy effects associated with temperature and

salinity variation in the flow, those terms are neglected here for simplicity. In the 1DV

model for vegetation, only vertical gradients in the momentum equation are considered.

In the Reynolds stress equations, both a source and a sink term have been added:

(2-8)

where the first term represents the creation of wake turbulence due to the profile drag,

and the second term recognizes the dissipation of Reynolds stress by the skin friction.

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Equation A3 can be simplified as:

(2-9)

and the dynamics of turbulence are represented by the following equation for q2:

(2-10)

In the RSM equations (Eqns A2 and A3), the skin friction drag and profile drag are

treated separately for two reasons. First, the species transport to the leaf surface is

analogous to only the skin friction portion of the drag. Second, in solving for the

turbulent fluctuations within the canopy the energy lost to the mean flow due to profile

drag will show up directly as TKE [Lewellen and Sheng, 1980]. In the Reynolds stress

equations, the first term on the right hand side represents the creation of wake

turbulence due to the profile drag, and the second term recognizes the dissipation of

Reynolds stress by the skin friction. The profile drag can also break up eddies to

increase the dissipation which is accounted for by reducing the dissipation length scale

Λ, giving [Wilson and Shaw, 1977]:

(2-11)

(2-12)

where α is a model constant dependent upon canopy geometry.

The mean flow equations for the TKEM are the same as those for the RSM. It

can be shown that when the time scale of mean flow evolution is much greater than the

time scale of turbulence (Λ/q), the evolution term and diffusion terms in the Reynolds

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stress equation become negligible with respect to other terms [Sheng and Villaret,

1989]. In the derivation and validations, the Coriolis terms are excluded because they

are relatively small within the boundary layer.

Av and Kv are turbulent eddy viscosity and diffusivity, which can be derived as:

(2-13)

where

(2-14)

where σt is the Schmidt number, and e2 = u2 + v2 + w2. Using the vegetation-free RSM,

Sheng and Villaret [1989] obtained accurate results for a wave bottom boundary layer, a

thermal boundary layer, and a sediment-laden bottom boundary layer. At the top and

bottom boundaries, . Using the vegetation-free RSM, Sheng and Villaret [1989]

obtained accurate results for a wave bottom boundary layer, a thermal boundary layer,

and a sediment-laden bottom boundary layer. The momentum equation (2-6) and the

TKE equation (2-10) are discretized and coupled, each is able to be solved efficiently

with a simple tridiagonal matrix scheme. Due to more robust representation of the

physical processes involved, the coefficients of the TKE model, including those related

to the vegetation induced drag, generally remain invariant for applications to a variety of

problems. This is a major advantage over Manning coefficient approach to represent

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vegetation which requires ad hoc tuning of the coefficient since the appropriate

processes are not included in the model.

Model Validations

The validations presented here will demonstrate (1) the skill of the model in

simulating flow and turbulence in a variety of vegetation canopies and water depth to

canopy height ratios, and (2) the importance of separating the effects of frontal area and

wetted area in the modeling of flow through vegetation.

Neumeier Experiment

To ensure this vegetation model produces accurate results for three dimensional

storm surge simulation, it is validated against an unsteady flume experiment. Neumeier

[2007] studied flow and turbulence at the edge of Spartina anglica salt marshes,

conducting numerous experiments assessing the changes in mean velocity and

turbulent kinetic energy profiles in a 5 m long, 0.3 m wide, and 0.46 cm deep flume by

measuring flow characteristics at different points along the centerline. His results are

used to evaluate the ability of the TKEM to simulate velocities and turbulence in

unsteady flow over vegetation canopies. In his study, live Spartina anglica plants were

transferred from the field into a laboratory flume, installed 2 m from the flume entrance

all the way to the flume exit, and vertical profiles of velocity, TKE, and Reynolds Stress

were taken at the frontal edge of the vegetation canopy, as well as at 6 discrete points

(0.2 m, 0.5 m, 1.0 m, 1.5 m, 2.0 m and 2.5 m) downstream from the vegetation edge

along the centerline. While Neumeier experimented with a variety of different vegetation

to water depth ratios, vegetation densities, and maximum velocities, the focus here is on

his Case BB, which has extensive published data.

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To simulate the unsteady flow using a 1DV model, a substitution of the time

derivative is necessary:

(2-15)

in Eqns (7) and (A2) where Ū is the vertically averaged velocity, constant

throughout the flume. Neumeier measured it at 6.6 cm/s. Shoot density for this

experiment was 1200 stems per m2, with an average stem diameter of 3-4.5 mm and

the vertically varying Af and Aw are determined from the provided statistics [Neumeier,

2007], and a complex method detailed by Neumeier [2005] for determining Af and Aw in

real, complex canopies. Vegetation height K is 19.0 cm, and water depth H is 32.0 cm.

Novak et al. [2000] studied the effects of canopy density on flow in wind tunnel

experiments and in the field, and found an inverse correlation between stem density and

drag coefficient due to sheltering effects. Novak et al. [2000] calculated a drag

coefficient of 0.3 for an experiment with a density of 333 stems/m2. This study treats

the profile drag and skin friction drag separately, and used Cp=0.13 and c1=0.15, along

with α=0.0021, which gave the best results. Cp values between 0.1 to 0.5 were

considered, and because c1 had less influence on determining mean velocity than Cp, its

value was determined to optimize TKE. α is selected based upon Cp to produce

reasonable values of turbulence macro length scale Λ. The simulation was run with 64

vertical layers with a horizontal spatial discretization of 0.065cm. Increasing the number

of layers or decreasing mesh size did not alter results. Profiles of modeled velocity and

turbulence at discrete points are compared to data in Figure 2-2. Additionally, simulated

spatially varying velocity and turbulence are compared to observed data in Figure 2-3.

Deviations can be attributed to the complexity of the vegetation canopy, which was real

28

vegetation rather than idealized cylinders or flexible plastic. Average error for velocities

is 0.59 cm/s, with a correlation coefficient r2 value of 0.98, and error for TKE is 0.015

cm/s, with a correlation coefficient r2 value of 0.95. These results show that the TKEM

is capable of simulating the unsteady velocity and turbulence profiles commonly

expected in storm surge conditions.

To demonstrate the importance of treating the vegetation drag as two separate

terms in Eqns. 7 and A2, a simulation was run with the same flow and mesh conditions

with the frontal area Af increased to include the wetted area Aw, and Aw set to 0. This

made the skin friction drag term zero, but enhanced the profile drag to produce

reasonable mean flow results, as shown in Figure 2-4. To reflect the combined influence

of the profile and skin friction drag in reducing flow, Cp was increased by c1 to be 0.28.

In Eqn. 5, Λ is limited by Af, Cp, and α. With both Cp and Af increased substantially, α

was increased to 0.02 to keep Λ at the same order of magnitude. The results at

discrete points are plotted in Figure 2-4. The velocity profiles are not as accurate as

when skin friction and profile drag are considered separately, and the turbulence

profiles reflect the need for leaf dissipation. The value of using separate terms for the

production and dissipation of turbulence due to frontal area Af and wetted area Aw is

apparent from these figures.

Physically, the process by which wetted area dissipates turbulence is understood

as a severe reduction in the maximum eddy size permissible within a leafy canopy.

Because of physical blockage, large eddies cannot propagate through leaves, limiting

the maximum eddy size and expediting dissipation.

29

As shown in Figure 2-3, turbulence is generated under the canopy surface from

wake generation at x=0 cm, and then is produced downstream at the canopy surface

because of shear production. Past x=100 cm, turbulence in the canopy is dissipated,

and mean flow is modeled within an accuracy of 1.5 cm/s. While this TKEM is not of the

sophistication of a direct numerical simulation (DNS) model, the results demonstrate the

fact that the model does properly account for the production and dissipation of

turbulence via multiple mechanisms within a vegetation canopy. Modeled turbulence at

the frontal edge of the canopy was less than observed because a spatially constant

drag coefficient was used. In reality, in the front of the canopy where sheltering effects

are negligible, the drag coefficient should be slightly higher. One attractive feature of the

TKEM is that it is much more efficient than the DNS model, due to the generally much

smaller grid size and time step associated with the DNS model, and can be readily

incorporated into a 3D regional circulation model, as is done in this study.

Nepf and Vivoni Experiment

In addition to simulating the effects of vegetation on flow in a spatially varying

flume, the experiments of Nepf and Vivoni [2000] are used to examine the ability of the

model to simulate flow in fully submerged and emergent conditions. Rather than using

real vegetation canopies, Nepf and Vivoni [2000] used a flexible plastic resembling

eelgrass in a 24 m long, 38 cm wide flume, with a canopy length of 7.4. The two

extreme experimental cases are shown here: a fully emergent case and a case with an

H to K ratio of 2.75. In both cases, the vegetation canopy was 16 cm high, the stem

density was 330 stems/m2, and the flow was controlled by a surface gradient of 0.0002.

Flow was measured at steady state [Nepf and Vivoni, 2000]. The simulations used 64

vertical layers, began with a vertically uniform velocity and were run until reaching

30

steady state; varying these conditions did not affect results. Nepf and Vivoni [2000]

provide extensive details on their quantification of Af and Aw. Cp was 0.15, α was 0.05,

and c1 was 2.7. Figure 2-5 demonstrates the ability of the model to simulate Reynolds

stress, turbulence, and mean velocity.

The results from simulating the experiments of Nepf and Vivoni [2000] show that

the model can simulate flow over various kinds of vegetation, including highly flexible

seagrass-like canopies. Additionally, the model can simulate flows in both emergent

and submerged conditions, a major advantage for storm surge events, where water

level H to canopy height K ratios change greatly over the course of a storm.

These validations show that including a robust vegetation model in a 3D storm

surge model is a viable alternative to using Manning coefficient formulations in a 2D

storm surge model. The ability to model spatially unsteady conditions in the Neumeier

[2007] experiments is evidence that the model can properly simulate unsteady

conditions present during hurricanes. Properly and accurately modeling turbulence

generation mechanisms in vegetation canopies is a critical requirement for quantifying

the impact of wetlands in dissipating storm surge.

Experiments with the 3D Vegetation Resolving Storm Surge Model

The validated 1D TKE model is incorporated into a 3D storm surge model to

explore the role of vegetation in a storm surge event. The status quo for modeling the

effects of vegetation is through enhancing the Manning coefficient within a 2D

circulation/hydrodynamic model. To explore the differences between the status quo 2D

approach vs. the new 3D vegetation resolving approach, three simple experiments are

presented here.

31

The experiments compare two models: a 2D, depth averaged circulation-wave

storm surge model (CH3D-SWAN, run in 2D) which represents vegetation by increasing

the Manning coefficient and a vegetation-resolving, fully 3D, circulation-wave model

(CH3D-SWAN, see Sheng and Liu 2011) which resolves vertical turbulence and velocity

with the 1DV model described here. Details on the model equations, boundaries, and

numerical methods of the basic 3D model are described elsewhere [Sheng et al.,

2010a]. All simulations use a domain with an idealized bottom slope of 1:1000 over 50

km of the continental shelf which represents the typical bottom slope in the northern

Gulf of Mexico (Figure 2-6). Along the shoreline, at an elevation of zero, and extending

along the entire domain, is a strip of land where vegetation is introduced. Experiment 1

uses a domain width of 4 km, while Experiments 2 and 3 use a 80 km wide domain. In

both 2D and 3D cases, wave boundaries are parametrically forced and were found to

have little influence on onshore flooding. Water levels at the boundaries are open, and

the boundaries are far enough away from the area of study that they do not influence

results.

The grid cells are 100 m x 100 m, and adjusting grid size does not affect results.

The vertical resolution is 4 layers, increasing to 8 layers does not appreciably affect

results but increases simulation time. Af is derived in a fashion similar to that of Nepf

and Vivoni [2000], and Temmermann et al. [2005]:

(2-16)

where N is the stem density, D is the stem diameter of 0.005 m and Aw is assumed to

be 8 times that of Af, as modeled by Lewellen and Sheng [1980]. α = 0.1, as in

Lewellen and Sheng [1980]. Cp = 0.2, and c1 = 0.125.

32

Numerous 2D modeling studies evaluate the accuracy of their simulations by

matching simulated water levels to observed ones during storm surge events [Wamsley

et al., 2010; Rego and Li, 2010; Zhang et al., 2012]. Furthermore, water level is often

considered as a proxy measurement for the impact of a storm surge event [IPET 2008].

Ample studies [Zhang et al., 2012; Wamsley et al., 2010] show that 2D storm surge

modelers can adjust the Manning coefficient (sometimes from the canonical 0.02 up to

0.14 or down to 0.01) to produce a water surface which better matches observations. In

its original form, the Manning coefficient was an empirical value to describe the bottom

roughness associated with the nearly 1D flow of a stream [Chow, 1959]. The use of a

single value for a bottom friction coefficient was then introduced into circulation models

as a simple way of representing bottom friction in 2D estuarine flows under normal tidal

forcing [Blumberg, 1977]. The Manning coefficient was not intended for simulation of

highly sheared flows such as those in vegetation canopies, nor was it originally

developed within circulation models to simulate wind-driven surges onto land. In the

following, comparisons between the effects of 2D and 3D representations of vegetation

on surge will be shown in Experiment 1, the utility of the Manning coefficient for

modeling storm surge will be compared to the 3D vegetation resolving model in

Experiment 2, and the potential effects of using a 3D vegetation resolving model or the

2D Manning coefficient is examined in Experiment 3.

Experiment 1

The first experiment explores the mechanisms by which 2D and 3D

representations of vegetation influence a wind-driven surge of water. On a 4km wide

strip of the domain shown in Figure 2-6, 44.7 m/s (100 mph, equivalent to a Category 2

storm on the Saffir Simpson Hurricane Scale) wind is blown from left to right across the

33

domain. Six different model configurations are used, three in 2D, and three in 3D,

summarized in Table 2-1. Each 2D representation is paired with a 3D representation.

Pair 1 considers vegetation-free conditions, Pair 2 compares sparsely vegetated

conditions, and Pair 3 represents densely vegetated conditions. During the simulations,

which lasted 10000 seconds at 1 second timestep, water progressed onshore, and

velocity and water levels were recorded at the shoreward (X=0), center (X=500m),

landward (X=1km), and upland (X=12km) locations.

Vertically averaged velocities for the duration of the simulations at the rear of the

canopy are shown in Figure 2-7, and water levels in the center of the canopy are shown

in Figure 2-8. To explore 3D velocities within the canopy during inundation, velocity

profiles 3000 seconds into the simulation are shown in Figure 2-9. By this point in time,

flow is fully developed, but is still primarily wind driven. It is important to note that this

experiment was run with 8 and 12 vertical layers, and this increased vertical resolution

did not produce significant deviations from the 4 layer simulation results presented here.

Experiment 1 shows that wind driven flows through 2D and 3D vegetation

canopies produce similar maximum water levels at one instance in time, as well as

slightly deviant velocities for the vast majority of the simulation. As the initial surge of

water washes onshore, simulated 2D velocities exceed 3D velocities. Two explanations

exist: the drag effects of this 3D representation of are smaller than those of 2D

simulations, or shear effects from fully submerged flow in 3D simulations are

uncaptured by 2D simulations.

Furthermore, it shows that in vegetation-free wind driven flow in water depths of

nearly 2 m, velocities can vary up to 70 cm/s from the bottom of the water column to the

34

top. In vegetation laden flow, turbulence produced within the canopy is transported up

in the water column, resulting in nearly vertically uniform mean flow. The vertical

velocity gradient in vegetation laden flow is surprisingly small, but is likely low because

shear effects are damped out by high velocities and high turbulent mixing. Because this

profile deviates significantly from the pressure driven flow profiles of Nepf and Vivoni

[2000], Neumeier [2007], and many other flume tests, it indicates a major need for full

scale laboratory testing of hurricane force wind driven flow through submerged

vegetation canopies. Unfortunately, no laboratory studies of this nature exist.

Experiment 2

In the second experiment, to objectively compare the impact of 2D and 3D

representations of vegetation on more realistic storm surge events, 3 pairs of hurricane

simulations are run. Every simulation in this experiment uses the same wind forcing, a

Category 2 storm on the Saffir Simpson Hurricane Scale moving at 6.71 m/s (15 mph)

across the domain from left to right. Winds are parameterized from the Holland wind

model [Holland, 1980], and waves are included through two-way coupling between

CH3D and SWAN, which includes a vegetation model for wave energy [Suzuki et al.,

2012].

During each model simulation, maximum water levels and velocities at every grid

cell are recorded, producing an Envelope of High Water (EOHW) and an Envelope of

High Speeds (EOHS) at the end of each simulation. The total inundation volume (TIV)

of water flooding the area beyond the coastal vegetation can be calculated for each

simulation as:

35

(2-17)

TIV, along with spatial plots of EOHW and EOHS are compared for each pair of

2D and 3D simulations in the results and discussion section. While momentum

transport and flooding are of equal importance to manifest the impacts of a storm on

coastal infrastructure, most studies do not compare simulated velocities vs. observed

ones. Therefore, differences in calculated velocities will be considered here to quantify

the impact of representations of coastal vegetation.

As shown in Table 2-2, for each pair of simulations, differences in TIV simulated

by 2D and 3D models are all less than 1%. If this were a comparison of a set of

observed high water marks from a real storm on a real domain, the 2D and 3D

simulations would both be of very high precision.

Absolute percent deviations were calculated according to:

(2-18)

The percent deviations between the 2D and 3D water levels show very little

difference on the landward side of the vegetation canopy (Figure 2-10). However

significant differences between horizontal velocities, on the order of 25%, exist both

within and behind the vegetation canopy (Figure 2-10). These can be attributed to

differences in how 2D and 3D simulations simulate momentum.

Building on Experiment 1, Experiment 2 compares the differences in momentum

fluxes associated with 2D and 3D storm surge models. In it, three pairs of simulations

which produced very similar water levels produced very different spatial plots of

maximum vertically averaged momentum flux, particularly within the vegetation canopy.

36

This shows that while a 2D Manning’s n representation of vegetation may help produce

reasonable water levels as compared to observations, it will not necessarily produce a

reasonable picture of momentum exchanges within a vegetation canopy. The 2D

Manning’s n approach has never been validated as a means for calculating vegetation

effects in complex, wind-driven, sheared flows like those in submerged vegetation

during storm surge events.

Experiment 3

Experiment 3 expands on the simulations of Experiment 2. Using the same

domain and hurricane track as experiment 1, the 3 pairs of vegetation conditions are

subjected to storms of categories 1, 3, 4, and 5. Results for these 24 storms are

recorded in the same fashion as Experiment 2. In theory, if the Manning coefficient

were a robust representation of bottom roughness in flow with or without vegetation, the

deviation between 2D and 3D results for TIV should be quite small for a variety of

different storms.

Experiment 3 shows that the deviations between 2D and 3D simulated TIV for a

Category 2 storm are less than 1%, but grow to 12.5% for Category 5 storms (Figure 2-

11). With certainty, these deviations for an individual storm can be reduced by adjusting

the Manning coefficient according to the storm intensity, but that makes the model less

robust because the Manning coefficient simply becomes a tuning coefficient.

Because a hurricane occurs over a long period of time and space, the deviations

shown in Figure 2-11 do not highlight the isolated impacts of vegetation. To isolate the

impacts of vegetation, cross sections of the EOHW were taken from Y=0 to Y=40 km on

the seaward side of the canopy (X=0), and on the landward side of the canopy (X=1

km). The average water levels of these cross sections were taken from both the 2D and

37

3D EOHWs, and differenced. In turn, these differences between the front and back of

the vegetation canopy for the 2D and 3D storm for each category were differenced.

This quantity, the Comparative Average Influence of Vegetation (CAIV), seeks to isolate

the influence of the vegetation modeling:

(2-19)

CAIV is plotted in Figure 2-12. Note that CAIV for a vegetation free simulation

should be small but non-zero, because water levels calculated at different locations

within any storm surge simulation will vary over the space of 1 km, regardless of the

presence or absence of a vegetation canopy.

Experiment 3 finds that the conclusions of Experiment 2 regarding water level are

true only for Category 2 storms. Figure 2-11 makes apparent that TIV between 2D and

3D simulations vary considerably for different storms when vegetation is modeled.

While 2D and 3D representations of vegetation can produce nearly identical water

levels for a given storm, the similarities in these results do not carry over to storms of

varying magnitude. This is an addition to the corpus of literature showing significant

differences between 2D and 3D storm surge simulations [Weisberg and Zhang, 2008;

Sheng et al., 2010a], and it agrees with other literature showing that 2D and 3D

simulations for a single storm can produce similar results [Weaver and Luettich, 2009].

38

The CAIV offers a more local and nuanced perspective on differences in modeling

the influence of vegetation in 2D or 3D, and allows for comparison between the

Manning coefficient and the TKEM. By comparing the average influence of vegetation

between a 2D representation and a 3D representation, Figure 2-12 shows that

vegetation free 2D and 3D simulations produce similar results near the shoreline for all

storms, because CAIV is less than 10 cm. Additionally, for a category 2 storm, the

vegetation representations produce very similar results, and the CAIV is less than 10

cm for sparse and dense vegetation. However, when these vegetation conditions are

subjected to larger storms, sizable deviations (up to 40 cm) in average water level

emerge. Field studies of water levels at individual locations in front of and behind

canopies found differences on the order of 50 cm, indicating these modeling differences

could produce deviations of 100% from observed water levels [Krauss et al., 2009].

These results indicate that while the 2D bottom friction coefficient of a model can

be altered to produce results very similar to a 3D vegetation-resolving model, the

bottom friction coefficient cannot be readily prescribed for predicting flooding associated

with a different event. Instead, the Manning coefficient needs to be adjusted for

different flow situations over similar bottom roughness conditions. It appears that the

original Manning coefficient was conceived as a means of describing a physical

condition in a 1D stream, and this representation of bottom friction is not as valuable for

modeling wind-driven shallow flows such as storm surge events. This applies to both

vegetation-free and vegetation-laden flows. In a 3D vegetation-free flow model, the

bottom roughness is parameterized in terms of zo, roughness length, within a turbulent

bottom boundary layer. In a 2D vegetation-free flow model, the turbulent bottom

39

boundary layer is not resolved, and the Manning coefficient becomes an empirical

tuning coefficient because it depends on the bottom roughness as well as flow

conditions. Using the Manning coefficient for simulating complex unsteady flow such as

storm surge is analogous to using a simple parametric vertical eddy viscosity to

simulate stratified flow.

Findings of the Three Experiments

This paper presents a vegetation-resolving 3D storm surge-wave model which

includes a 1D Vertical (1DV) TKE model incorporating the effects of vegetation on flow

and turbulence. This 1DV model is compact, robust, versatile, and is validated with

data from several flume experiments, showing it can produce accurate results of

Reynolds Stress, turbulence intensity, and velocity. A unique feature of this 1DV model

is the inclusion of turbulence dissipation from leaf structures. This has little impact on

simulating velocities, but is critical to accurate modeling of turbulence. The role of

wetted area on turbulence structures merits further inquiry.

Data from three experiments are used for comparing the impact of 2D and 3D

representations of vegetation effects on storm surge modeling. In the first experiment,

vegetation laden wind driven flows are shown to have low vertical velocity variations as

compared to vegetation free flows. Furthermore, shear effects within vegetation

canopies appear to be less important to reducing water velocities than drag and

turbulent transport. In the second experiment, results show that 2D representations

may produce very similar EOHWs to 3D representations, but spatial plots of maximum

velocity from these experiments show that velocity from 2D and 3D representations of

vegetation differ significantly. This is not inconsequential, as momentum effects of

storm surge play a major role in how surge affects coastal infrastructure and

40

ecosystems [Howes et al., 2010]. Additional research is needed to obtain more velocity

measurements within coastal vegetation during storm surge events, to further elucidate

how momentum is modified by canopies.

In the third experiment, the ability of the Manning coefficient to accurately

represent coastal vegetation and determine water level is questioned, due to significant

differences in water levels for seemingly similar 2D and 3D representations of

vegetation. 2D representations of vegetation can match 3D representations very well

for a single storm, but sizable inconsistencies are shown for a wide variety of storms.

When larger storms are modeled and vegetation effects are included, deviations up to

40 cm in 2D and 3D water levels exist immediately around the coastal vegetation. This

suggests that while changing the Manning coefficient to match water levels for a single

storm may produce good results; this is not a reliable way to predict the impacts of

future storms of varying intensities.

Figure 2-1. Typical vertical velocity structures for flow through vegetation canopies with water depth H and vegetation canopy height K

41

Figure 2-2. Modeled velocity and turbulence profiles and measured data at discrete points for Neumeier’s experiment BB [Neumeier, 2007]

42

Figure 2-3. Continuous observations and model results [Neumeier, 2007]

43

Figure 2-4. Modeled velocity and turbulence profiles and measured data at discrete points for Neumeier’s experiment BB, ignoring skin friction effects in modeling.

44

Figure 2-5. Modeled mean velocity, turbulence, and Reynolds Stress for experiments

by Nepf and Vivoni [2000].

45

Figure 2-6. Domain used, with vegetation within hashed region. Experiment 1 uses a

domain from Y=0 to Y=4 km, Experiments 2 and 3 use the entire domain.

46

Figure 2-7. Velocity vectors at X= 1 km (Middle of Canopy) for Experiment 1.

47

Figure 2-8. Water levels at X= 500 m (Center of Canopy) for Experiment 1.

48

Figure 2-9. Velocity profiles in the canopy center, 3D simulations, Experiment 1. T=3000s

49

Figure 2-10. Percent deviations of water level and velocity for each pair of simulations in Experiment 2.

50

Figure 2-11. Percent Deviations of Total Inundation Volume for Various Storms for Different Vegetation Conditions in Experiment 3.

51

Figure 2-12. Differences between 2D and 3D vegetation in the modeled impacts of vegetation on storm surge.

52

Table 2-1. Three pairs of vegetation conditions used in Experiments 1, 2, and 3. Each pair compares a different 2D and 3D vegetation representation.

Pair Vegetation Description at Shoreline

Storm Surge Model

Manning’s n Vegetation Condition

1 Vegetation Free

2D 0.02 NA

3D NA None 2 Sparse

Vegetation 2D 0.037 NA

3D NA 200 stems/m2, 75 cm tall

3 Dense Vegetation

2D 0.056 NA

3D NA 300 stems/m2, 125 cm tall

53

Table 2-2. Inundation volumes for hurricanes on each of the pairs of vegetation conditions described in Table 1.

Pair Vegetation Description at Shoreline

Dimensionality TIV (m3) % Deviation

1 Vegetation Free

2D 4.22 x 108 NA

3D 4.189 x 108 None 2 Sparse

Vegetation 2D 3.768 x 108 NA

3D 3.747 x 108 200 stems/m2, 75 cm tall

3 Dense Vegetation

2D 3.210 x 108 NA

3D 3.190 x 108 300 stems/m2, 125 cm tall

54

CHAPTER 3 QUANTIFYING THE REDUCTION OF STORM SURGE BY VARYING CANOPIES AND

STORMS

The Need to Quantify the Influence of Vegetation

Significant buffering of storm surges by vegetation canopies has been suggested

by limited observations and simple numerical studies, particularly following recent

Hurricanes Katrina, Rita, and Wilma. Here storm surge and inundation are modeled

over idealized topographies using a three-dimensional vegetation-resolving storm surge

model coupled to a shallow water wave model and show that a sufficiently wide and tall

vegetation canopy reduces inundation on land by 5 to 40 percent, depending upon

various storm and canopy parameters. Effectiveness of the vegetation in dissipating

storm surge and inundation depends on the intensity and forward speed of the

hurricane, as well as the density, height, and width of the vegetation canopy. Reducing

the threat to coastal vegetation from development, sea level rise, and other

anthropogenic factors would help to protect many coastal regions against storm surges.

Motivation and Method

The effectiveness of coastal vegetation as natural barriers against storm surges

and waves is analyzed. Sparse observations have found a decrease in storm surge of

nearly 1 m over a 20 km transect [Krauss et al., 2009]. But the few existing observations

are not sufficient to quantitatively determine the importance of different vegetation

parameters, such as density, width, and height, in blocking storm surge and reducing

inundation, because of their inability to isolate the effects of vegetation-induced drag

and Reynolds Stresses from changes in bathymetry, bottom friction, and individual

storm characteristics.

55

Recent numerical simulations of storm surge over vegetation canopies [Wamsley

et al., 2010, Loder et al., 2009] used a two-dimensional storm surge model and

parameterized the vegetation-induced friction with a Manning coefficient (0.1-0.3) an

order of magnitude larger than that for sand (0.02). This 2D approximation, however,

fails to adequately account for the complex flow over and within vegetation in storm and

non-storm conditions. This study uses a 3D model and explicitly accounts for the drag

forces (skin friction drag and profile drag) introduced by the vegetation canopy

throughout the water column, as well the creation of turbulent kinetic energy (TKE) by

the wakes behind vegetation [Nepf and Vivoni, 2000] and Reynolds stresses associated

with shear.

Here a three-dimensional vegetation-resolving storm surge model with idealized

topography is used to estimate the effect of vegetation canopies on storm surge and

inundation. The inundation is defined as the total inundation volume generated by a

storm. The effect of vegetation on total inundation volume is measured by a quantity

defined as the Vegetation Dissipation Potential (VDP), which is the percent reduction of

total inundation volume (TIV) due to the presence of vegetation canopy. VDP,

determined for a given simulation is:

(3-1)

where H (x,y) is the maximum water level over the course of an entire simulation, and

where the subscript v indicates the presence of a vegetation canopy and the subscript 0

indicates the absence of a canopy. The VDP represents the maximum possible

vegetation-induced reduction of inundation by taking into account all effects of the

56

canopy in all directions and using a change in maximum occurring water level over a

large area, allowing comparison between different hurricanes. This approach enables

accurate calculation of the total dissipative effects of the vegetation canopy for an entire

storm over an entire domain. For example, if 10 km3 is the total inundation volume from

a given hurricane with no vegetation present, but a vegetation canopy reduced this

volume to 6 km3, the vegetation dissipates 40% of the storm surge, and the VDP is

40%. The benefit of this spatially integrated metric over the single-point metric (Hv/Ho at

a given x,y location) is demonstrated by the significant spatial variability of Hv/Ho [Loder

et al., 2009] which underscores the need for a spatially integrated vegetation dissipation

potential (VDP) to quantify the impacts of vegetation on a regional scale.

The coupled CH3D-SWAN model, an integrated storm surge-wave model, was

selected in part for its demonstrated skill in reproducing the observed storm surges and

waves during hurricanes [Sheng et al., 2010a, 2010b; Davis et al., 2010]. The model

includes a TKE model to represent the vegetation-induced skin friction drag and profile

drag as well as the turbulence generation by the wakes behind the vegetation, by

simplifying a vegetation-resolving Reynolds Stress turbulence model [Lewellen and

Sheng, 1980]. In the mean flow equations, the skin friction drag and the profile drag are

proportional to the wetted vegetation area and frontal vegetation area, respectively, both

using a quadratic stress law. In the TKE equation, the generation of TKE by the

turbulent wakes behind the vegetation is included. The drag coefficients are set to 0.125

and 0.2 for skin friction drag and profile drag, respectively, both consistent with the

available literature [Novak et al., 2000]. Detailed CH3D model equations and boundary

conditions can be found in Sheng et al. [2010a and b] and Sheng and Liu [2011], while

57

detailed SWAN equations are found in Booij et al. [1999] and Suzuki et al. [2012].

Detailed vegetation-resolving TKE model equations are shown in Chapter 2. The TKE

model is found to accurately simulate unsteady flow and turbulence over vegetation

canopy in laboratory flume experiments [Neumeier, 2007] as well as steady flows [Nepf

and Vivoni, 2010].

The major improvement to understanding the physics of storm surge provided

here is the inclusion of drag, shear and Reynolds stress from the vegetation to allow

accurate quantitative calculation of vegetation dissipation. Prior efforts to study the

influence of vegetation on storm surge were limited to simulating it entirely as bottom

friction, but this study uses more realistic and complete physical modeling of flow

through emergent and submerged canopies. During a storm surge event, coastal

vegetation starts as fully emergent, and as water moves onshore, transitions to having a

water depth equal to canopy height. Eventually, the vegetation is fully submerged.

Flow and turbulence structures are highly dependent upon water depth to vegetation

height ratios in a non-linear fashion [Nepf and Vivoni, 2000], and the inclusion of

Reynolds Stresses, shear and drag in these simulations is necessary.

Important parameters of storms to consider include storm intensity and forward

speed. Storm intensity is dictated by wind speed via the Saffir Simpson scale with

higher maximum wind speeds correlating to higher category storms. Forward speed,

the translational speed of the eye of the storm, determines the duration over which the

storm is driving water onshore. Intuition and limited observations suggest that faster

moving storms will have higher dissipation, because there is less time for the storm

wind to overcome friction from the vegetation canopy. Important parameters of the

58

vegetation canopy to consider are vegetation height, vegetation density, and width of

the vegetation zone. Laboratory experiments have demonstrated that increases in

vegetation height and density cause flow reduction and turbulence production, which

would increase VDP [Neumeier, 2007; Nepf and Vivoni, 2000]. It is expected that wider

canopies would result in greater dissipation, but the rate of increase is unknown.

Experiments

For these simulations, an idealized bottom slope of 1:1000 over 50 km of the

continental shelf is used which represents the typical bottom slope in the northern Gulf

of Mexico (Figure 3-1). Along the shoreline, at an elevation of zero, and extending

along the entire domain, is a strip of land where vegetation is introduced. Winds are

parameterized from the Holland wind model [Holland, 1980], and waves are included

through two-way coupling between CH3D and SWAN, which includes a vegetation

model for wave energy [Suzuki et al., 2012]. However, while waves are included in the

model simulation, their contribution to inundation is negligible on gently sloping shelves

where coastal vegetation canopies exist [Resio and Westerink, 2008], and observations

show that waves are depth limited and dissipated within a few wavelengths from the

canopy edge [Smith et al., 2010]. These findings are consistent with our model results.

Results from two experiments are presented here. In experiment 1, a Category 2

storm (maximum sustained winds of 49 m/s) moves at 6.71 m/s (15 mph) onshore over

vegetation canopies varying in height (50- 125 cm), density (100-300 stems/m2), and

width (0.5-1.5 km), and the variability in dissipation is found. In experiment two, a

typical canopy (75cm tall, 200 stems/m2, 1 km wide) is forced with storms of varying

intensity (Category 1-5) (maximum sustained winds between 33.8 m/s and 70.2 m/s)

and forward speed (4.47- 8.94 m/s) (10-20 mph). Vegetation was a spartina-like

59

canopy, with a stem diameter of 1.3 cm and a leaf area 8 times that of the frontal area,

like other studies using leafy vegetation [Lewellen and Sheng, 1980]. We consider

landfalling hurricanes perpendicular to the coastline which produce the highest possible

storm surge compared to hurricane approaching from other directions. Results for each

experiment are shown in Figures 3-2 and 3-3, respectively. The model results follow

similar trajectory and pattern as Loder et al. [2009]. However, Loder et al. [2009]

measured the vegetation dissipation by considering individual stations which, in

combination with the use of a simplistic 2D model and Manning’s n approach to

parameterize vegetation dissipation, produced excessively high dissipation (~90%) by

vegetation.

Results and Discussion

The first experiment clearly shows that dissipation is greater in canopies of

increased density, height and width. As shown in Figure 3-2, VDP varies between 5-

40%, it increases approximately 3-fold when canopy density increases from 100 to 300

stems/m2, when canopy height increases from 50 to 125 cm, or when canopy width

increases from 0.5 to 1.5 km. It is clear that the three factors are equally important in

increasing vegetation dissipation although canopy width seems slightly more important.

Increases associated with density are results of greater drag within the canopy and

greater turbulence production. Increases associated with height are results of the shift

of shear layers upwards, which reduces depth integrated flows within the canopy.

Increases from increased canopy width are a result of the canopy’s influence on a

greater spatial dimension of the surge.

As shown in Figure 3-1, each simulation begins with water levels at an elevation of

0, and water levels increase as inundation occurs, with flood water eventually receding.

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The result within the vegetation canopies is that at various times some cells have

emergent flow while others have fully submerged flow, and some canopies have highly

submerged flow. Figure 3-4 illustrates this by showing a transect parallel to the y-axis

on the landward side of the hashed region of Figure 3-1. Compared in each panel are

maximum water levels from a vegetation free simulation and the maximum water levels

with 1.5 km wide canopies. Note that for some locations in 1-1.25 m canopies, flow is

always emergent, whereas shorter canopies have highly submerged flows. Figure 3-4

also illustrates the inability of the variation in water level at a single location to properly

account for the total influence of the canopy on the storm surge event, and thus the

value of the VDP.

The second experiment shows that fast and strong storms exhibit greater VDP as

compared to slow and weak storms. Fast storms have higher dissipation because

onshore winds are present for a shorter duration, indicating an increased relative

resistance of vegetation as compared to slow storms with onshore winds lasting longer.

VDP doubles as the forward speed doubles from 4.47 to 8.94 m/s. Strong storms blow

faster winds, and because profile drag and skin friction follow quadratic relationships,

greater resistance to inundation is observed, particularly at higher forward speed. Also,

strong storms blow stronger winds over a larger length of canopy, utilizing the

dissipative potential of a greater area of canopy than weak storms. This agrees with

limited observations from slow moving and fast moving storms [Resio and Westerink,

2008]. It is interesting to note that, at a slow forward speed, vegetation dissipation is

not very significant (VDP < 15%) even in a Category 5 hurricane.

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Figure 3-1. Domain upon which experiments 1 and 2 were conducted.

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Figure 3-2. Dissipation of storm surge by vegetation canopies for a Category 2

(maximum sustained winds of 49 m/s) moving onshore at 6.71 m/s (15mph)

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Figure 3-3 Dissipation of storm surge by a 75cm tall vegetation canopy of 200stems/m2

for storms of varying magnitude and forward speed.

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Figure 3-4. Maximum water level on landward side of 1.5 km wide hashed region in

Figure 2-1 for Category 2 storm. Solid blue line denotes vegetation free simulation, dashed line denotes vegetation present.

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CHAPTER 4 THE INFLUENCE OF VEGETATION ON STORM SURGE AND COASTAL

INUNDATION IN THE NORTHERN GULF OF MEXICO

Applying the Model to a Complex Domain

Hurricane Ike made landfall near Galveston, TX on September 13th, 2008 (Figure

4-1). While the storm was noted for its unusually high storm surge well ahead of landfall

[Kennedy et al., 2011], it was also a remarkably well documented case of the influence

of vegetation on storm surge. In this paper, a 3D, vegetation-resolving storm surge-

wave model is used to accurately simulate the surge and coastal inundation during

Hurricane Ike, and the influence of vegetation on inundation patterns in Chambers

County, TX, is examined through both observations and model results. By combining

modeling with observations during Ike to study the impact of vegetation on storm surge

and coastal inundation during a major hurricane, this chapter is a major step forward in

quantifying the potential effectiveness of expensive wetland restoration projects on the

Gulf of Mexico coast.

Major Atlantic hurricanes such as Hurricanes Sandy, Katrina, and Ike have

initiated national discussions on the importance of coastal wetlands to protecting

infrastructure and urban environments in the 21st century. These storms have been

catalysts for immense investments into wetland enhancement and restoration, but the

value of them for reducing storm surge remains scientifically unclear [Louisiana Coastal

Wetlands Conservation and Restoration Task Force, 2010; NYS 2100 Commission,

2012]. Surge measurements from storm events show that observed water levels behind

wetlands are lower than those in front of them [Krauss et al., 2009], but none of these

observations allow comparison with data over similar bathymetry without vegetation.

Furthermore, many 2D modeling studies have found that increasing the Manning

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coefficient within areas of heavy vegetation reduces water levels [IPET, 2008; Loder et

al., 2009; Zhang et al., 2012]. This, however, is an extremely obvious conclusion, with

limited scientific merit.

This chapter explores the field observations of the dissipation of storm surge by

vegetation for an actual storm, while deepening the scientific understanding of this

critical earth science process. Moreover, as investments in coastal wetlands increase,

the need for sound scientific understanding of the role tropical storms play in the growth

and decay of these ecosystems is necessary. Many studies have found that storms can

erode coastal wetlands [Howes et al., 2010; Barras, 2007], but other recent studies

have found marine sediment deposited on large coastal wetlands, and posited that

sediment deposition from hurricanes may play a major role in the healthy growth of this

ecosystem, depositing far more sediment than riparian sources [Turner et al., 2006].

While some of the geological and ecological science regarding the deposition of marine

sediment on the coast is disputed [Turner et al., 2006; Törnqvist et al., 2007; Turner et

al., 2007], most infer that improvements in modeling the hydrodynamics of storm surge,

such as including the effects of vegetation in 3D, can improve our understanding of this

sediment deposition [Törnqvist et al., 2007; Turner et al., 2007; Williams, 2010].

Hurricane Ike

Previous efforts to model Hurricane Ike’s storm surge have focused on either

capturing the hurricane’s forerunner in a 2D simulation [Kennedy et al., 2011], or on

considering different coastal landforms on the Bolivar Peninsula [Rego and Li, 2010].

The forerunner was the result of an Ekman setup of water near the Louisiana-Texas

border, which initiated a counter-clockwise moving trapped coastal wave around the

Gulf of Mexico [Kennedy et al., 2011]. This wave was roughly 1.5 m in amplitude, and

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significantly affected evacuation efforts and the storm’s overall surge and damage.

Rego and Li [2010] also simulated the forerunner, and used their study to consider how

changes to the landform of the Bolivar Peninsula could influence surge level. Other

studies found immense amounts of sediment were transported during Hurricane Ike,

particularly between the Bolivar Peninsula and Sabine Pass [Williams, 2010]. This

study examines the role of the forerunner in the observed deposition. More information

on the details of Hurricane Ike is covered in the next main section.

Vegetation and Storm Surge

Observed estimates about the role of vegetation in storm surge events argue that

1 km of marsh could reduce storm surge by 4.2-9.4 cm [Krauss et al., 2009], but recent

science has found a more complicated relationship, and the interaction is dependent

upon the storm and vegetation characteristics [Resio and Westerink, 2008; Krauss et

al., 2009; Sheng et al., 2012; Liu et al., 2013]. Studies utilizing 2D representations of

vegetation found unsurprisingly that increases in the Manning coefficient in an effort to

simulate taller or denser canopies resulted in steep decreases in water levels behind

the vegetation [Loder et al., 2009]. Chapter 3 determined that taller, denser, and wider

canopies reduce storm surge, and that storm surge from fast and strong storms is

dissipated more than surge from a slow and weak storm. The model described in

Chapters 2 and 3 is applied here to the real domain of the Louisiana-Texas shelf in

Hurricane Ike.

Historically, the inclusion of vegetation into a storm surge model has been handled

via an increase in the bottom friction coefficient for a 2D model [Loder et al., 2009], but

many believe that this scheme, while computationally expedient, fails to capture

processes important to inundation [Georgiou et al., 2012]. Similarly, while the

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enhancement of bottom friction can be done to tune a model for effective hindcasting

[Wamsley et al., 2010], it has not been shown to aid in forecasting inundation, water

level, or flow velocities for a wide variety of storms [Lapetina and Sheng, 2013]. Given

heavy investment into wetlands as a flood-mitigating infrastructure [Louisiana Coastal

Wetlands Conservation and Restoration Task Force, 2010], advanced storm surge

models which accurately include the effects of vegetation are necessary. Earlier studies

of the dynamics in tidally driven estuaries have included simple k-ε models in small (~O

300 m) domains [Temmermann et al., 2005], but vegetation-resolving models have

never been introduced at the scale of a storm surge model.

The major hindrances to properly evaluating the role of wetlands in dissipating

storm surge are the impossibilities of isolating the effects of vegetation on the

mom