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Stochastic multi-hazard risk analysis of coastal infrastructure
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Content
Copyright 2020
Adam Steven Keen
STOCHASTIC MULTI-HAZARD RISK ANALYSIS OF COASTAL INFRASTRUCTURE
by
Adam Steven Keen
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(CIVIL ENGINEERING)
December 2020
ii
ACKNOWLEDGMENTS
I am grateful to the countless number of people who have supported me along the way.
I would like to extend a special thanks to: Pat & Erica Lynett. Marcel Stive. Eric Nichol. Dan Cox.
Erik Johnson. Rob & Kathy Holman. Tim Maddux. Katy Serafin. Chris Cloyd. Aykut Ayca. Nikos
Kalligeris. Joaquin Moris-Barra. Meagan Wengrove. Philip & Ashley Blackmar. Lauren
Schambach. Ashley Graham. Tom & Edith Poyer. Michael Hunter. Katherine Hayes Rodriguez.
And I want to express my most sincere gratitude to my family: Mom, Dad, Maggie, and Lily.
- Adam S. Keen
iii
TABLE OF CONTENTS
ACKNOWLEDGMENTS .............................................................................................................. ii
LIST OF TABLES ......................................................................................................................... vi
LIST OF FIGURES ...................................................................................................................... vii
ABSTRACT .................................................................................................................................... x
CHAPTER 1. INTRODUCTION ................................................................................................... 1
1.1. A NOTE ABOUT THE STRUCTURE OF THIS DOCUMENT ........................................ 3
CHAPTER 2. MANUSCRIPT 1 (PUBLISHED) ........................................................................... 6
2.1. INTRODUCTION .................................................................................................... 6
2.2. STATISTICAL METHODOLOGY .............................................................................. 9
2.2.1. Data Requirements ........................................................................................ 10
2.2.2. Demand to Capacity Equations for Cleats .................................................... 11
2.2.3. Demand to Capacity Equations for Pile Guides ........................................... 14
2.3. NUMERICAL MODELING OF TSUNAMI EVENT .................................................... 16
2.3.1. Tōhoku, Japan (2011) Tsunami .................................................................... 20
2.3.2. Alaska-Aleutian Tsunami ............................................................................. 25
2.4. POST-TSUNAMI DAMAGE ASSESSMENT ............................................................. 29
2.5. POST-TSUNAMI HAZARD ASSESSMENT .............................................................. 32
2.5.1. Pile Guides .................................................................................................... 33
2.5.2. Cleats............................................................................................................. 36
2.6. DISCUSSION ....................................................................................................... 38
iv
2.7. CONCLUSIONS .................................................................................................... 40
CHAPTER 3. MANUSCRIPT 2 (IN PRESS) .............................................................................. 42
3.1. INTRODUCTION .................................................................................................. 42
3.2. CLEAT AND PILE GUIDE DEMAND ...................................................................... 45
3.2.1. Cleats............................................................................................................. 46
3.2.2. Pile Guides .................................................................................................... 46
3.3. CLEAT AND PILE GUIDE CAPACITIES ................................................................. 47
3.3.1. Cleats............................................................................................................. 50
3.3.2. Hoop-Type Pile Guides................................................................................. 53
3.3.3. Roller-Type Pile Guides ............................................................................... 56
3.3.4. High-Density Polyethylene (HDPE) Pile Guides ......................................... 58
3.4. DAMAGE PREDICTION FOR SMALL CRAFT HARBORS ......................................... 60
3.4.1. Numerical Modeling ..................................................................................... 60
3.4.2. Marina Condition Assessment ...................................................................... 62
3.4.3. Results ........................................................................................................... 63
3.5. CASE STUDY: NOYO HARBOR ............................................................................ 64
3.5.1. Marina Condition Assessment and Risk-Model Calibration ........................ 65
3.5.2. Results and Discussion ................................................................................. 69
3.6. CONCLUSIONS .................................................................................................... 72
CHAPTER 4. MANUSCRIPT 3 (IN PREP) ................................................................................ 73
4.1. INTRODUCTION .................................................................................................. 73
4.2. MULTI-HAZARD RISK FRAMEWORK .................................................................. 76
4.2.1. Stochastic Discrete Hazard Estimate ............................................................ 78
4.2.2. Stochastic Event Realizations ....................................................................... 81
4.2.3. Vulnerability ................................................................................................. 84
4.2.4. Multi-Hazard Infrastructure Failure .............................................................. 85
4.3. MULTI-HAZARD RISK PSEUDO CODE ................................................................. 86
4.3.1. Primary “Run” Script .................................................................................... 88
4.3.2. Hazard Curve Estimate ............................................................................... 100
4.3.3. Post-Processing Script ................................................................................ 106
4.3.4. Non-Standard MATLAB Functions ........................................................... 109
4.4. CASE STUDY: VENTURA HARBOR, CALIFORNIA, USA..................................... 113
4.4.1. Historical Data ............................................................................................ 115
4.4.2. Numerical Modeling Data ........................................................................... 117
4.4.3. Results and Discussion ............................................................................... 119
4.5. CONCLUSION .................................................................................................... 126
v
CHAPTER 5. CONCLUSIONS ................................................................................................. 128
5.1. RECOMMENDATIONS FOR FUTURE WORK ........................................................ 130
REFERENCES ........................................................................................................................... 133
vi
LIST OF TABLES
Table 2.1: Tsunami Event Source Parameters for Southern California Harbors. ......................... 20
Table 2.2: Inputs to the Monte Carlo fragility analysis for the 2011 Tōhoku tsunami event
(by dock) ............................................................................................................................... 24
Table 2.3: Inputs to the Monte Carlo Fragility analysis for the Alaska-Aleutian Islands
Subduction Zone tsunami event (by dock) ........................................................................... 28
Table 3.1: Damage ratings and capacity reduction factors for cleats. .......................................... 52
Table 3.2: Damage ratings and capacity reduction factors for hoop pile guides. ......................... 55
Table 3.3: Damage ratings and capacity reduction factors for roller type pile guides. ................ 58
Table 4.1: Individual and multi-hazard failure probabilities (by zone) for design years
2025 and 2060. .................................................................................................................... 121
vii
LIST OF FIGURES
Figure 2.1: General outline of the process used to define fragility curves based upon a
Monte Carlo based demand-capacity analysis. ..................................................................... 10
Figure 2.2: Typical cleat configuration for Santa Cruz Harbor. ................................................... 14
Figure 2.3: Typical pile guide configuration for Santa Cruz Harbor. ........................................... 15
Figure 2.4: Location of Santa Cruz Harbor along the California Central Coast. .......................... 16
Figure 2.5: Maximum modeled current speeds within Santa Cruz South (left) and North
(right) Harbor for the Magnitude 9.2 Eastern Aleutian-Alaska Scenario, the Magnitude
9.2 Eastern Aleutian-Alaska Scenario, the 2010 Magnitude 8.8 Chile Event
(Historical), the Magnitude 9.4 Chile North Scenario and the 2011 Magnitude 9.0
Japan Event (Historical), respectively (top to bottom). ........................................................ 19
Figure 2.6: Maximum modeled current speed within Santa Cruz North (top) and South
(bottom) Harbor for the 2011 Tōhoku tsunami event. .......................................................... 22
Figure 2.7: Maximum modeled current speed within Santa Cruz North (top) and South
(bottom) Harbor for the theoretical Alaska-Aleutian Islands Subduction Zone tsunami
event ...................................................................................................................................... 26
Figure 2.8: Damage survey of the Santa Cruz Harbor north (top) and south (bottom) basins
showing areas of high (red), medium (yellow) and low (green) slip damage. ..................... 31
Figure 2.9: Fragility curves for pile guides in Santa Cruz Harbor for the 2011 Tōhoku event
and Alaska-Aleutian event (top); fragility curve 95% confidence limits for the 2011
Tōhoku and Alaska-Aleutian event (bottom). Green, yellow and red fragility curves
and markers correspond to low, medium, and high levels of observed damage for the
2011 Tōhoku event. Pink curves and markers are for the Alaska event. .............................. 34
Figure 2.10: Fragility curves for cleats in Santa Cruz Harbor for the 2011 Tōhoku event and
Alaska-Aleutian event (top); fragility curve 95% confidence limits for the 2011
Tōhoku and Alaska-Aleutian event (bottom). Green, yellow and red fragility curves
and markers correspond to low, medium and high levels of observed damage for the
2011 Tōhoku event. Pink curves and markers are for the Alaska event. .............................. 37
Figure 2.11: Current speed and direction results for cleats and pile guides for the 95%
confidence limit. Green, yellow and red fragility markers correspond to low, medium,
and high levels of observed damage for the 2011 Tōhoku event. Pink markers are for
viii
the Alaska event. Squares represent results from the south basin, while circles
represent results from the north basin. .................................................................................. 39
Figure 3.1: California small craft harbors surveyed. .................................................................... 48
Figure 3.2: Capacity reduction factor distributions determined based upon observable
degradation. The five damage class distributions are: no damage (ND), minor damage
(MN), moderate damage (MD), major damage (MJ) and severe damage (SD)
[consistent with the damage states outlined by Waterfront Inspection Task Committee
(2015)]. .................................................................................................................................. 50
Figure 3.3: Typical cleat configuration for California small craft harbors. .................................. 51
Figure 3.4: Typical hoop type pile guide configuration for California small craft harbors. ......... 53
Figure 3.5: Typical roller type pile guide configuration for California small craft harbors. ........ 57
Figure 3.6: Typical high-density polyethylene (HDPE) pile guide configuration for
California small craft harbors. .............................................................................................. 59
Figure 3.7: Location of floating docks in Noyo Basin.................................................................. 65
Figure: 3.8 Representative cleats from Noyo Basin. .................................................................... 66
Figure 3.9: Representative pile guides from Noyo Basin. ............................................................ 66
Figure 3.10: Numerical modeling results of maximum current speed (by tsunami
scenario/event) within Noyo Basin. ...................................................................................... 69
Figure 3.11: Cleat probability of failure results for Noyo River Basin. Low (green) risk
representing probability of failure < 10%, medium (yellow) risk representing
probability of failure between 10% - 99% and high (red) risk representing probability
of failure > 99%. ................................................................................................................... 70
Figure 3.12: Pile guide probability of failure results for Noyo River Basin. Low (green) risk
representing probability of failure < 10%, medium (yellow) risk representing
probability of failure between 10% - 99% and high (red) risk representing probability
of failure > 99%. ................................................................................................................... 71
Figure 4.1: Infrastructure risk is the balance between natural hazard intensity and
infrastructure vulnerability. ................................................................................................... 74
Figure 4.2: The multi-hazard risk framework is outlined in the flow chart. Each discrete
event within the set of events (Rj) is characterized by utilizing the hazard curve
methodology outlined by Geist and Lynett (2014). Each event set is compared against
a pile height datum to establish a single failure estimate. A sum of the individual
failure probabilities characterizes the multi-hazard solution. ............................................... 77
Figure 4.3: Schematic shows how various meteorological, tsunami, and seiche water levels
superimpose to increase the water level relative to the pile height. ...................................... 79
Figure 4.4: Realizations of meteorological water level are shown in black in the above
figure. The hazard curve that relates the intensity and probability of each discrete event
is determined by the envelope of the realizations (red). ....................................................... 80
ix
Figure 4.5: Representative (a) design life vs. return period and (b) design life vs. water level
realization. Sample sets of (c) meteorological, (d) tsunami and (e) seiche water level
realizations ............................................................................................................................ 84
Figure 4.6: Example multi-hazard failure probabilities reveal the balance of meteorological,
tsunami, and seiche hazards as relative contributions to the multi-hazard water level
risk. ........................................................................................................................................ 86
Figure 4.7: (a) The area map shows the location (green) of Ventura Harbor within the
California Bight. The location of the water level, tsunami, and wave gauges are shown
above. [Aerial orthometric imagery downloaded from U.S. Geological Survey (2018).]
(b) Aerial images show the location of East and West Basin within Ventura Harbor
[Base map produced with Pawlowicz (2020) and National Geophysical Data Center
(2006)]. ................................................................................................................................ 114
Figure 4.8: Water level constituents used to construct the future water level hazard for
Ventura Harbor: (a) astronomical water level, (b) seasonal water level, (c) future sea
level rise trends (Kopp et al., 2014; Sweet et al., 2017), (d) tsunami amplitudes (Thio et
al., 2017), (e) metrological and seiche generated mean water level and (f) seiche
generated crest elevation (for Zones 1 and Zone 7 from Figure 4.9). (c-f) Solid lines
indicate the best-fit trend; dashed lines represent 10% and 90% confidence intervals. ..... 116
Figure 4.9: Numerical modeling extraction zones for Ventura Harbor seiche analysis. Zone
1 and Zone 7 (magenta) represent the upper and lower bounds of the multi-hazard
analysis. ............................................................................................................................... 118
Figure 4.10: Single and multi-hazard-based failure probabilities for Ventura Harbor in Zone
1: (a) sea level rise, (b) meteorological water level, and sea level rise, (c) tsunami and
sea level rise, (d) seiche and sea level rise and (e) 5% single and multi-hazard failure. .... 122
Figure 4.11: Single and multi-hazard-based failure probabilities for Ventura Harbor in Zone
7: (a) sea level rise, (b) meteorological water level, and sea level rise, (c) tsunami and
sea level rise, (d) seiche and sea level rise and (e) 5% single and multi-hazard failure.
(Zone 1 multi-hazard result added for reference.) .............................................................. 125
x
ABSTRACT
We live in a changing climate. As global average temperatures increase, ice caps melt, and
sea levels rise. Increasing sea levels remain the most direct and likely future hazard to
infrastructure from the changing climate. The primary objective of this dissertation is to assist in
the infrastructure planning process by providing methodologies that quantify the natural hazard
risk of small craft harbors. Hopefully, this dissertation provides decision makers with a
methodology/platform upon which they can make informed and often difficult decisions about
how best to respond to climate risk. Here, physics-based approaches are used to assess the risk of
small craft harbors quantitatively. When a process is beyond a physical understanding, semi-
empirical approaches are used that rely on correlations between observed damage and quantitative
properties. The dissertation should serve as a step forward in the research community's
understanding of multi-hazard risk assessment at the community level.
1
CHAPTER 1. INTRODUCTION
We live in a changing climate. As global average temperatures increase, ice caps melt, and
sea levels rise. Increasing sea levels remain the most direct and likely future hazard to
infrastructure from the changing climate. Numbers published by the National Oceanic and
Atmospheric Administration (NOAA) based upon 2010 census data state that thirty-nine percent
of the United States’ population lived in counties directly along the shoreline (National Oceanic
and Atmospheric Administration 2018). From 1970 to 2010, the population of these counties
increased by almost 40 percent. NOAA expects this growth trend to continue, estimating an
additional 8 growth percent by 2020. With a potential doubling of the coastal flood frequency in
the coming decades (Vitousek et al. 2017), mitigation measures and community resilience
strategies enacted in response to a changing climate will dictate how coastal storms impact our
communities.
Policy makers, informed by engineers and scientists, will play a critical role in deciding
how best to respond to sea level rise. With limited resources available across federal, state, and
local agencies, policy makers must be strategic with the response. Capturing future hazards,
vulnerability, and risk with sound and unbiased science provides the foundation for fact-based
decision making. Risk frameworks, when applied correctly, should help stakeholders to decide
when and how to apply mitigation funds to optimize the return on investment.
2
Here, the focus is on one class of coastal infrastructure: small craft harbors (also known as
small craft marinas). Small craft harbors are basins within larger bodies of water that protect
commercial and recreational watercraft from natural elements (waves, wind, tides, ice, currents,
etc.) (Task Committee on Marinas 2020 of the Coasts, Oceans, Ports, and Rivers Institute of
ASCE, 2012). Beyond a place to shelter vessels, small craft harbors form socioeconomic hubs
within communities. Commercial fishermen, the tourism industry, and emergency first responders
(to name a few) all heavily depend on harbors to facilitate the movement of goods and people
between land and sea.
Damage caused by natural hazards and the pursuant service disruption can result in
significant economic loss in local communities. In an article published in The New York Times,
McKinley (2011) outlines the standstill and loss to the $12 million fishing industry in Crescent
City, CA experienced after the 2011 Tohoku tsunami. The event forced local fishermen to disperse
to other harbors along the California and Oregon coast, leaving an economic vacuum in Crescent
City that lasted for nearly a decade.
For researches, small craft harbors are a microcosm of the greater community, providing a
“playground” that furthers communities' understanding of coastal infrastructure risk. Traditionally,
tsunamis and coastal storm events have posed the most significant risk to small craft harbors. The
2006 Kuril Islands, 2010 Chile, and 2011 Japan tsunamis collectively caused over $100 million in
damage to California harbors (Wilson et al., 2013). As sea levels start to rise and storm patterns
change, harbormasters will notice changes to their natural surrounding (if they have not already).
Climate change will force harbors to identify a suite of scenarios and assess their risk portfolio
within a non-stationary (e.g. climate change) context.
3
The primary objective of this dissertation is to assist in the planning process by providing
methodologies that quantify the natural hazard risk of small craft harbors. Hopefully, this
dissertation provides decision makers with a methodology/platform upon which they can make
informed and often difficult decisions about how best to respond to climate risk. Here, physics-
based approaches are used to assess the risk of small craft harbors quantitatively. When a process
is beyond a physical understanding, semi-empirical approaches are used that rely on correlations
between observed damage and quantitative properties. The dissertation, as a whole, should serve
as a step forward in the research community's understanding of multi-hazard risk assessment at the
community level.
1.1. A Note About the Structure of This Document
This dissertation is organized in a “manuscript format” with three manuscripts constituting
the main body of the dissertation, followed by a general conclusion. Individual papers stand alone
as independent contributions but are conceptually related to the goal of quantifying future risk to
small craft harbors. The technical content from each paper is mature; however, each manuscript is
in various stages of publication (ranging from “published” to “in preparation”).
The three papers are as follows:
• Manuscript 1 (Chapter 2)
Keen, A. S., Lynett, P. J., Eskijian, M. L., Ayca, A., & Wilson, R. (2017). Monte Carlo–
based approach to estimating fragility curves of floating docks for small craft
marinas. Journal of Waterway, Port, Coastal, and Ocean Engineering, 143(4),
04017004. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000599
4
• Manuscript 2 (Chapter 3)
Keen, A. S., Lynett, P. J., Eskijan, M. L., Ayca, A., & Wilson, R. I. (in press). An approach
to estimate tsunami damage for small craft marinas. Journal of Waterway, Port,
Coastal, and Ocean Engineering. https://doi.org/10.1061/(ASCE)WW.1943-
5460.0000599
• Manuscript 3 (Chapter 4)
Keen, A. S. & Lynett, P. J. (2020). Multi-hazard risk analysis for coastal infrastructure in
a changing climate. Manuscript in preparation.
A general conclusion that summarizes the finding of the three manuscripts is also included.
Manuscript 1 (Chapter 2) entitled “Monte Carlo–based approach to estimating fragility
curves of floating docks for small craft marinas,” is the first paper included in the dissertation. The
chapter outlines an assessment tool that engineers and planners can use to assess the tsunami
hazard to small craft harbors. The methodology is based on the demand and capacity of a floating
dock system. Detailed numerical modeling and damage calibration data from recent tsunamis
benchmarked the approach. Results are provided as fragility curves and give a quantitative
assessment of survivability. This tool yields an indication as to survivability and failure of a
floating dock system of vessels and floating components/piles, subject to tsunami events.
Manuscript 2 (Chapter 3) entitled “An approach to estimate tsunami damage for small craft
marinas,” is the second paper included in the dissertation. Chapter 3 is an extension of Chapter 2
and outlines a predictive tool that quantifies the tsunami risk to small craft harbors. The coupling
of high-resolution numerical modeling with a statistical framework outlined in Chapter 2 is
extended to include observed damage states for structural elements now. When applied to one
small craft marina (in Noyo River Harbor), the methodology was able to replicate likely failure
5
that occurred well below previously identified damage thresholds. Results suggest infrastructure
age and condition (in addition to the hazardous tsunami phenomenon) can contribute to cleat and
pile guide failure.
The final paper included in this dissertation is Manuscript 3 (Chapter 4) entitled “Multi-
hazard risk analysis for coastal infrastructure in a changing climate.” Chapter 4 outlines a
framework to assess the multi-hazard risk to small craft harbors. The work identifies hazards
related to tsunamis, storm surge, harbor seiche, and sea level rise. The statistical model utilizes
published probabilistic hazard analysis methods and annual maxima extreme value theory to
quantify multiple hazards. The proposed methodology was applied, as an example application, to
Ventura Harbor for meteorological, tsunami, and seiche anticipated total water level from 2020 to
2060. With a focus on Ventura’s floating dock vulnerability, results suggest seiche hazards pose
the most significant future failure risk to the harbor.
6
CHAPTER 2. MANUSCRIPT 1 (PUBLISHED)
Keen, A. S., Lynett, P. J., Eskijian, M. L., Aykut, A., & Wilson, R. (2017). Monte Carlo–based
approach to estimating fragility curves of floating docks for small craft marinas. Journal
of Waterway, Port, Coastal, and Ocean Engineering, 143(4), 04017004.
doi.org/10.1061/(ASCE)WW.1943-5460.0000385
2.1. Introduction
Tsunamis pose a significant risk to infrastructure located along the United States west coast.
While the frequency of significant tsunami events is small compared with other natural hazards,
the impact of tsunami events (especially to small craft harbors) is high. It is this interplay between
the frequency of events and resultant impact, which drives the tsunami risk. For example, the 2011
tsunami from Japan caused over $100 million in damage to 27 harbors in California (Wilson et al.,
2013). Following the damage resulting from the 2010 Chile and 2011 Japanese teletsunamis,
authors have made significant efforts to understand the mechanisms and potential scope of tsunami
impacts in harbors (Borrero & Goring, 2015; Lynett et al., 2012). The State of California seeks to
7
mitigate subsequent damage from the next major tsunami that might strike the Pacific Coast
(Wilson et al., 2013).
Existing methodologies to predict damage to small craft harbors during tsunami events are
limited. Approaches vary, but the methodologies that do exist have been mainly data-driven
relying on correlations between input parameters and damage. Authors such as Suppasri et al.
(2013), Muhari et al. (2015) and Lynett et al. (2012) have chosen to analyze damage in terms of
loss functions. Loss functions are empirical relationships that relate the amount of expected
damage to a set of input parameters (e.g. tsunami surface elevation, tsunami current magnitude).
Using damage reports from the 2011 Tōhoku tsunami in Japan, Suppasri et al. (2013) derived
independent loss functions for maximum tsunami surface elevation and maximum flow velocities
using linear regression analysis assuming a logarithmic loss function. The loss functions showed
good agreement with data, but their independence limited their applicability. Therefore, Muhari et
al. (2015) extended the work of Suppasri et al. (2013) to developed new multivariate loss functions
to estimate the potential damage of marine vessels based upon a set of input parameters.
Using a semi-qualitative approach, Lynett et al. (2014) compared damage assessments in five
California harbors to high-resolution models results of maximum current speed to derive
approximate damage limits to small craft harbors. Data-driven loss functions are ideal for
applications where the engineer needs to directly estimate the functionality between independent
and dependent variables to assess hazards quickly. However, mathematical correlations do not
necessarily ensure physical significance, making it sometimes difficult to interpret the physics
involved in the hazard assessment.
For instance, authors typically assume quantities such as surface elevation and current speed
are the dominant terms that correlate with damage, while other inputs such as current direction or
8
ship dimensions are not. Well established drag formulations, however, would tend to suggest that
these additional terms would have some impact on the resultant damage. Unless these terms are
added to the analysis (either directly or indirectly), the interaction would not be captured by the
loss functions. Physics-based approaches complicate the methodology but are a necessary
component to extend the community’s understanding of the hazard.
In addition to the overall approaches, it is also essential that the output from vulnerability
models is practical and straightforward. Unlike flow models that output quantities like surface
elevation or current speed (which are directly comparable from model to model), output quantities
between vulnerability models often differ. This ambiguity is because the methodology and
calibration are often dictated by the availability of damage data for discrete events. While one
model might output percent loss, another outputs dollar value loss, and another outputs loss
intensity; inter-model comparisons are rarely performed. The output metrics between models are
not directly comparable and are limited in their application. A generalized physics-based approach
with generalized outputs is advantageous as it can be applied to a variety of scenarios.
This chapter will outline a physics-based tool focused on assessing the tsunami hazard to small
craft harbors. The methodology is based on the demand and also the structural capacity of the
floating dock system, composed of floating docks/fingers and moored vessels. Due to the
uncertainties in the current direction, the exact current speed, and the remaining capacities of the
floating structure, a Monte Carlo approach is used. The equations to determine the forces on the
vessels and floating structure are taken from conventional sources, and the system of vessels,
floating components, and piles are all included in the assessment. The condition of the floating
dock structure is also included; a demand/capacity ratio quantifies the index of failure. Results are
provided as fragility curves that give a quantitative assessment of infrastructure survivability. The
9
derived fragility curves are validated by comparing them with the damage reports from the 2011
Tōhoku event in Santa Cruz Harbor, California. The fragility curves will be used by engineers to
help analyze harbors in California and other regions to identify vulnerable sections of the harbors
so that pre-disaster mitigation function can be sought to make harbor improvements.
2.2. Statistical Methodology
Here, fragility curves for structural components in small craft harbors are estimated using
a Monte Carlo methodology. For background, a Monte Carlo based approach in structural analysis
is a probabilistic tool where the governing equations of motion or structural behavior might be
well known. However, the independent variables of the input (i.e. current speed, current direction)
as well as the structural capacities of the components (e.g. cleats, pile guides) might not be. The
Monte Carlo approach requires a distribution of each input variable (usually with a rectangular,
triangular or Gaussian-shaped relationship), and then randomly samples each distribution within
the described equations to generate a single computational result. The process repeats hundreds or
thousands of times, depending on the accuracy and convergence of the system. A general outline
of the procedure is shown in Figure 2.1. Fragility curves for each component within the system are
estimated using the minimum capacity of the dock system to define the maximum failure
probability from each component on the dock. The approach is akin to essentially looking for the
“weakest link” for each dock during a tsunami event. Neither cumulative damage nor damage that
occurs from debris impacting the boats or docks during the event are considered.
10
Figure 2.1: General outline of the process used to define fragility curves based upon a Monte Carlo based demand-
capacity analysis.
2.2.1. Data Requirements
Inputs to the Monte Carlo model are defined as either deterministic or probabilistic.
Deterministic quantities are those quantities that are known or are expected not to vary within a
scenario. For floating docks, deterministic quantities include finger length, finger width, number
of slips, number of piles, and number of cleats. For this analysis within California, these were
11
quantified using historical high-resolution orthoimagery data available from the United States
Geological Survey (USGS) to estimate these quantities. This approach implies the analysis is being
performed as a damage assessment on the harbor as it exists presently; potential future change to
the harbor layout could also be included in a probabilistic manner but is not included in this model
iteration.
In contrast to deterministic inputs, probabilistic inputs are those quantities which might not
be precisely known but are defined by a probability density function. Probabilistic quantities
include current speed, current direction, water depth, seawater density, vessel length, vessel beam,
vessel draft. Each probabilistic input variable is randomized with a rectangular probability density
function (e.g. equal probability of any value within a range) bounded by defined minima and
maxima. Current speed and current direction were estimated from a high-resolution numerical
model (to be discussed in more detail in later sections). Results are finely sampled using the
parameter surface to define the approximate minimum and maximum within the confines of each
slip.
2.2.2. Demand to Capacity Equations for Cleats
The governing equations for the transverse and longitudinal forces on vessels were used to
calculate the “demand” from the tsunami current (U.S. Army Corps of Engineers et al., 2005). The
approach is intended to be first-order.
For the transverse current forces on a vessel (U.S. Army Corps of Engineers et al., 2005):
𝐹𝐹 𝑦𝑦𝑦𝑦
=
1
2
𝜌𝜌 𝑤𝑤 𝑉𝑉 𝑦𝑦 2
𝐿𝐿 𝑤𝑤𝑤𝑤
𝑇𝑇 𝐶𝐶 𝑦𝑦𝑦𝑦
sin 𝜃𝜃
(2.1)
12
where: 𝜌𝜌 𝑤𝑤 = water density; 𝑉𝑉 𝑦𝑦 = current velocity; 𝐿𝐿 𝑤𝑤𝑤𝑤
= length of the vessel at the waterline; 𝑇𝑇 =
vessel draft; 𝐶𝐶 𝑦𝑦𝑦𝑦
= transverse drag coefficient; and 𝜃𝜃 = angle of velocity relative to the
longitudinal vessel axis.
The transverse drag coefficient was estimated from (U.S. Army Corps of Engineers et al.,
2005):
𝐶𝐶 𝑦𝑦𝑦𝑦
= 𝐶𝐶 0
+ (𝐶𝐶 1
− 𝐶𝐶 0
) �
𝑇𝑇 𝑑𝑑 �
2
(2.2)
where: 𝐶𝐶 0
= deepwater current drag coefficient for 𝑇𝑇 𝑑𝑑 ⁄ ≈ 0; 𝐶𝐶 1
= shallow water drag coefficient
(= 3.2); and 𝑑𝑑 = water depth. The deepwater drag coefficient can be estimated from:
𝐶𝐶 0
= 0.22�𝜒𝜒 (2.3)
With 𝜒𝜒 defined as:
𝜒𝜒 =
𝐿𝐿 𝑤𝑤𝑤𝑤
2
𝐴𝐴 𝑚𝑚 𝐵𝐵 𝑉𝑉
(2.4)
where: 𝐴𝐴 𝑚𝑚 = immersed cross-sectional area of the vessel at midsection; 𝐵𝐵 = maximum vessel
beam at the waterline; and 𝑉𝑉 = submerged volume of the vessel.
Similarly, for the longitudinal current forces on the vessel, not considering propeller loads
which could be highly variable (U.S. Army Corps of Engineers et al., 2005):
𝐹𝐹 𝑥𝑥 𝑦𝑦 = 𝐹𝐹 𝑥𝑥 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹
+ 𝐹𝐹 𝑥𝑥 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 (2.5)
And:
𝐹𝐹 𝑥𝑥 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹
=
1
2
𝜌𝜌 𝑤𝑤 𝑉𝑉 𝑦𝑦 2
𝐵𝐵 𝑇𝑇 𝐶𝐶 𝑥𝑥 𝑦𝑦 𝑥𝑥 cos 𝜃𝜃
(2.6)
where: 𝐶𝐶 𝑥𝑥 𝑦𝑦 𝑥𝑥 = longitudinal current form drag coefficient (= 0.1). And,
𝐹𝐹 𝑥𝑥 𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹𝐹 =
1
2
𝜌𝜌 𝑤𝑤 𝑉𝑉 𝑦𝑦 2
𝐵𝐵 𝑆𝑆 𝐶𝐶 𝑥𝑥 𝑦𝑦 𝑥𝑥 cos 𝜃𝜃
(2.7)
13
where: 𝑆𝑆 = wetted surface area; 𝐶𝐶 𝑥𝑥 𝑦𝑦 𝑥𝑥 = longitudinal current skin friction coefficient. Here, the
wetted surface area is estimated by:
𝑆𝑆 = 1.7 𝑇𝑇 𝐿𝐿 𝑤𝑤𝑤𝑤
2
+ �
𝐷𝐷 𝑇𝑇 𝛾𝛾 𝑤𝑤 � (2.8)
where: 𝛾𝛾 𝑤𝑤 = weight density of water. And the longitudinal current skin friction is a function of
Reynold’s number defined as:
𝐶𝐶 𝑥𝑥 𝑦𝑦 𝑥𝑥 =
0.075
(log
10
𝑅𝑅 𝐹𝐹 − 2)
2
(2.9)
where: 𝑅𝑅 𝐹𝐹 = Reynolds number. For vessels, the Reynolds number is defined as:
𝑅𝑅 𝐹𝐹 = �
𝑉𝑉 𝑦𝑦 𝐿𝐿 𝑤𝑤𝑤𝑤
cos 𝜃𝜃 𝜈𝜈 � (2.10)
where: 𝜈𝜈 = kinematic viscosity of water.
Vessels resist the tsunami “demand” via their cleat connection. An example of a cleat for
Santa Cruz Harbor is shown in Figure 2.2. The analysis presented here assumes that these cleats
act as a system distributing the load evenly across the cleats. Small craft harbors within California
typically secure each vessel within the slip using either a 2 or 4 cleat configuration. Manufacturers
typically mount cleats on the dock with two bolts via a timber connection. By knowing the size
and number of bolts, direct estimates of the cleat capacities are approximated. However, even if
the exact configurations of the cleats are known for each slip, the governing in-situ cleat
“capacities” are nearly impossible to quantify accurately. Most harbors within California have
aged and are not at their original, full capacity. Results are presented with respect to the “required
capacity,” which can be interpreted as the capacity needed to resist the tsunami demand.
14
Figure 2.2: Typical cleat configuration for Santa Cruz Harbor.
2.2.3. Demand to Capacity Equations for Pile Guides
The governing equations for the transverse and longitudinal forces on vessels were used to
calculate the “demand” from the tsunami current on the floating dock system (U.S. Army Corps
of Engineers et al., 2005). The equations to describe the loads on the floating dock and fingers are
the same as used for the vessels. One difference is that the angle for the dock is 90 degrees out of
phase from the vessels (perpendicular to the fingers/vessels); the fingers are in the same line
(approach angle) as the vessels. Additionally, pulling forces from the cleats are assumed not to
affect the pile guides.
Floating docks and fingers resist the tsunami “demand” via the pile guide. An example of a
pile guide for Santa Cruz Harbor is shown in Figure 2.3. For this analysis, forces on the pile guides
are determined based upon the demand equation. The demand averaged based upon the number of
15
pile guides to determine the load per pile guide. Multiple pile guides within a dock system resist
horizontal loads while allowing the dock to adjust to a rising and falling tide. For the pile guide
capacity, a typical pile collar within California consists of between 4 and 8 bolts, which connect
to the dock via a timber connection. By knowing the size and number of bolts, capacities for each
pile guide can be directly estimated. However, even if the exact configuration of pile guides by
dock is known (like the cleat capacities), it is nearly impossible to quantify the in-situ pile guide
capacities accurately. Therefore, like the cleat capacities, the results are presented with respect to
the “required capacity” and can be interpreted as the capacity needed to resist the tsunami demand.
Figure 2.3: Typical pile guide configuration for Santa Cruz Harbor.
16
2.3. Numerical Modeling of Tsunami Event
Santa Cruz Harbor is a small municipal harbor located along the Central California coast. The
location of Santa Cruz Harbor is shown in Figure 2.4. The harbor consists of two long and narrow
basins that extend inland from the shoreline. The north and south basins were built nearly a decade
apart, which resulted in differences in material construction between the two basins. The south
basin was completed in 1963 and was initially built using timber deck materials and piles typical
of the period. By the time the north basin was completed in 1972, floating dock construction had
changed favoring a more robust composite type construction (Mesiti-Miller Engineering Inc.,
2011).
Figure 2.4: Location of Santa Cruz Harbor along the California Central Coast.
17
According to the Santa Cruz Port District website, Santa Cruz Harbor has space for
approximately 1,000 wet-berthed and 275 dry-stored vessels. Roughly 15% of these vessels are
commercial fishing boats, 35% pleasure powerboats, and 50% pleasure sailboats (Santa Cruz Port
District, 2016). Of the approximately 800 wet slips, 35% of the vessels are within the 6.1 m or less
range, 40% are within the 9.1 m range, 20% are within the 12.2 m range, and 5% are within the
15.2 m or greater range.
Since the harbor’s completion, harbor administration had replaced very few of the docks
leaving the harbor vulnerable to tsunami events. During the 2011 Tohoku tsunami, a series of
waves caused significant damage to Santa Cruz Harbor. Numerical models of two tsunami events
were analyzed for Santa Cruz Harbor to assess the harbor’s vulnerability using the Monte Carlo
methodology. One scenario was the 2011 Tōhoku tsunami that damaged all floating docks within
Santa Cruz Harbor. Another scenario was a hypothetical tsunami generated by a large earthquake
(magnitude 9.2) along the Alaska-Aleutian Islands Subduction Zone.
The hydrodynamic modeling for this study uses the numerical model “Method of Splitting
Tsunamis” (MOST) (Titov & Synolakis, 1998; Titov, 1997; Titov & Gonzalez, 1997). The model
can simulate the full development of the tsunami from wave generation to wave run-up. Tsunami
propagation is modeled based upon the elastic deformation theory (Okada, 1985), while inundation
is modeled based upon a derivation of the VTCS model (Titov & Synolakis, 1998). The model has
been extensively validated for several global scenarios. Variants of the MOST model have been in
constant use for tsunami hazard assessments in California since the mid-1990s (Lynett et al., 2014).
The reader is referred to Titov and Gonzalez (1997) for further information on the model as well
as general validation.
18
In this study, MOST is used to propagate tsunami waves from source to the nearshore region,
using a system of nested grids. The outermost grid at 4 arc min resolution covers the entire Pacific
basin. Three additional grids of increasingly finer resolution were derived from data provided by
National Oceanic and Atmospheric Administration’s (NOAA) National Geophysical Data Center
specifically for tsunami forecasting and modeling efforts (Grothe et al., 2012). The innermost
nearshore grid has a 10 m resolution and takes boundary input from the previous MOST nested
layer.
While model predictions of surface elevation are commonly compared with tide gauge data,
comparisons with current speed are less common, principally due to the lack of data. Therefore,
the MOST modeling work for Santa Cruz Harbor is validated against the high-order Boussinesq-
type model Cornell University Long and Intermediate Wave Modeling Package (COULWAVE)
(Lynett et al., 2014). Model results suggest that while not as accurate as the higher-order
COULWAVE model, the MOST tsunami model satisfactorily reproduces measured tsunami-
induced current speeds (Lynett et al., 2014).
A total of five events were modeled for Santa Cruz Harbor including two historical events
and three realistic scenarios. The 5 events include the 2010 magnitude 8.8 Chile event (historical),
a magnitude 9.0 Cascadia scenario, the 2011 magnitude 9.0 Japan event (historical), a magnitude
9.4 Chile North scenario, and a magnitude 9.2 Eastern Aleutian-Alaska scenario. A summary of
these five events is shown in Figure 2.5 and Table 2.1. Two events, the 2011 magnitude 9.0 Japan
event and the 9.2 Eastern Aleutian-Alaska scenario, are analyzed here. The 2011 magnitude 9.0
Japan event was selected as the primary event because of the amount of damage caused by that
event and documentation available to validate the methodologies. The 9.2 Eastern Aleutian-Alaska
scenario was selected as a second event because of the potential impact of that event on Santa Cruz
19
Harbor. This event would produce the most substantial current velocities in the harbor of any of
the modeled events.
Figure 2.5: Maximum modeled current speeds within Santa Cruz South (left) and North (right) Harbor for the
Magnitude 9.2 Eastern Aleutian-Alaska Scenario, the Magnitude 9.2 Eastern Aleutian-Alaska Scenario, the 2010
Magnitude 8.8 Chile Event (Historical), the Magnitude 9.4 Chile North Scenario and the 2011 Magnitude 9.0 Japan
Event (Historical), respectively (top to bottom).
20
Table 2.1: Tsunami Event Source Parameters for Southern California Harbors.
Length
(km)
Width
(km)
Average Slip
(m)
Magnitude
(Mw)
Magnitude 9.2 Eastern Aleutian-Alaska
Scenario
1
700 100 25.0 9.2
Magnitude 9.0 Cascadia Scenario
1
1040 100 11.0 9.1
2010 Magnitude 8.8 Chile Event
(Historical)
2
700 150 14.4 8.8
Magnitude 9.4 Chile North Scenario
1
1400 100 25.0 9.4
2011 Magnitude 9.0 Japan Event
(Historical)
3
500 200 12.5 9.1
1. Uslu (2008)
2. Tang et al. (2010)
3. Shao et al. (2011)
2.3.1. Tōhoku, Japan (2011) Tsunami
The 2011 Tōhoku earthquake was a magnitude 9.0, which occurred on March 11, 2011. The
epicenter of the earthquake was approximately 70 km east of the Oshika Peninsula of Tōhoku. The
seismic event generated a powerful tsunami, the impacts of which were felt throughout the Pacific
Basin. In the far-field, many ports, harbors, and maritime facilities along the U.S. West Coast were
adversely affected by surges and currents induced by the 2011 Tōhoku tsunami (Wilson et al.,
2012, 2013).
The tsunami reached Santa Cruz approximately ten hours after the seismic event, creating
strong currents within the harbor. Santa Cruz Harbor experienced strong currents starting the
morning of March 11, 2011 and continuing through to the afternoon of March 12, 2011. There
were no measured currents available within the harbor; however, eyewitness reports and post-
event video analysis indicated current speeds of up to 4 m/s as the tsunami entered the harbor
(Ewing, 2011), and maximum current speeds within the harbor of 5-7 m/s just north of the two
central bridges which separate the north and south harbor (Wilson et al., 2013).
21
Source terms for the 2011 Tōhoku tsunami were taken from Shao et al. (2011). Modeled
maximum currents speeds for Santa Cruz North Harbor and South Harbor are shown in Figure 2.6.
The model results show significant heterogeneity in the current field with the strongest currents
occurring at the harbor entrance and in the channel transition from the south to the north harbor.
The model results also agree reasonably well with the maximum observed current speed being on
the order of 3.5 m/s.
22
Figure 2.6: Maximum modeled current speed within Santa Cruz North (top) and South (bottom) Harbor for the 2011
Tōhoku tsunami event.
A summary of the vessel, tsunami, and oceanographic characteristics used as input to the
Monte Carlo analysis is provided in Table 2.2 but does not include dock dimensions since these
23
parameters are deterministic and scale with the mean vessel parameters. Additionally, vessels on
the ends of the docks were limited to the size which fits within the slips. Ultimately this method
attempts to identify high yet average pulling forces on the dock, which are important to identifying
vulnerability.
24
Table 2.2: Inputs to the Monte Carlo fragility analysis for the 2011 Tōhoku tsunami event (by dock)
Vessel Tsunami Oceanographic
Dock
Length
Overall
(m)
Maximum
Beam
(m)
Current
Speed
(m/s)
Current
Direction
(deg)
Water
Depth
(m MLS)
Specific Gravity of
Seawater
(-)
Min Max Min Max Min Max Min Max Min Max Min Max
N 7.6 9.1 3.0 3.7 1.0 2.0 0 5 0.7 4.7 1.025 1.040
O 9.1 9.1 3.7 3.7 1.4 1.8 0 7 1.0 4.3 1.025 1.040
W-1 7.6 7.6 3.0 3.0 1.4 2.6 0 10 1.1 3.0 1.025 1.040
W-2 7.6 7.6 3.0 3.0 1.4 2.5 2 13 1.2 2.9 1.025 1.040
W-3 7.6 7.6 3.0 3.0 1.7 2.5 8 17 1.7 3.0 1.025 1.040
J-1 9.1 9.1 3.7 3.7 1.0 1.4 13 89 0.8 3.6 1.025 1.040
U-1 9.1 9.1 3.7 3.7 2.4 3.8 1 40 1.8 4.4 1.025 1.040
U-2 9.1 9.1 3.7 3.7 1.6 3.3 0 54 0.8 3.3 1.025 1.040
V-1 9.1 9.1 3.7 3.7 1.4 3.1 5 15 1.1 3.1 1.025 1.040
V-2 9.1 9.1 3.7 3.7 1.3 2.8 0 13 1.0 3.2 1.025 1.040
25
2.3.2. Alaska-Aleutian Tsunami
Over the past century, five large earthquakes have occurred along the Alaska-Aleutian
Subduction Zone (AASZ). The 1964 Alaskan earthquake (magnitude 9.2) was one of these and
generated a tsunami that caused significant damage along the California coast (Borrero, 2002;
Lander et al., 1993; Uslu, 2008). Hence, AASZ is a crucial source region for California that should
be taken into account in a tsunami hazard assessment. The hypothetical tsunami scenario is a
variation of the 1964 earthquake but is located to the west of the 1964 rupture. The estimated
rupture area is 700 km long and 100 km wide, and has an average slip of 25 m, which corresponds
to a magnitude 9.2 earthquake. Barberopoulou et al. (2011) developed the event source terms.
The maximum current speed for the AASZ event in Santa Cruz North and South Harbor are
shown in Figure 2.7. Model results of the Alaska-Aleutian event show significantly higher current
speeds as compared with the Tōhoku event. This increase can largely be correlated with the
difference in the size of the tsunami’s amplitude. Compared with the Tōhoku event, model results
show that inundation from the Alaska-Aleutian tsunami extends well beyond the banks of Santa
Cruz Harbor, permitting more water volume to enter the harbor, and creating stronger currents
within the harbor. These strong currents suggest that damage from this event would not be isolated
to the harbor basins but could extend landward to expand the damage footprint.
26
Figure 2.7: Maximum modeled current speed within Santa Cruz North (top) and South (bottom) Harbor for the
theoretical Alaska-Aleutian Islands Subduction Zone tsunami event
27
A summary of the vessel, tsunami, and oceanographic characteristics used as input to the
Monte Carlo analysis are provided in Table 2.3. Like the 2011 Japan event, the dock dimensions
are not included. Additionally, slips on the ends of the docks were limited to the length, which fits
within the adjacent slips to identify high yet average pulling forces on the dock.
28
Table 2.3: Inputs to the Monte Carlo Fragility analysis for the Alaska-Aleutian Islands Subduction Zone tsunami event (by dock)
Vessel Tsunami Oceanographic
Dock
Length
Overall
(m)
Maximum
Beam
(m)
Current
Speed
(m/s)
Current
Direction
(deg)
Water
Depth
(m MLS)
Specific Gravity of
Seawater
(-)
Min Max Min Max Min Max Min Max Min Max Min Max
N 7.6 9.1 3.0 3.7 2.9 4.8 0 31 2.7 6.0 1.025 1.040
O 9.1 9.1 3.7 3.7 2.8 4.4 1 17 2.8 5.8 1.025 1.040
W-1 7.6 7.6 3.0 3.0 2.5 4.5 2 63 2.2 4.1 1.025 1.040
W-2 7.6 7.6 3.0 3.0 2.5 4.7 1 63 2.3 4.0 1.025 1.040
W-3 7.6 7.6 3.0 3.0 3.1 4.5 1 34 2.8 4.1 1.025 1.040
J-1 9.1 9.1 3.7 3.7 2.4 6.7 40 88 2.3 4.9 1.025 1.040
U-1 9.1 9.1 3.7 3.7 3.7 5.0 1 27 2.6 5.6 1.025 1.040
U-2 9.1 9.1 3.7 3.7 2.5 4.9 0 62 1.3 4.4 1.025 1.040
V-1 9.1 9.1 3.7 3.7 2.7 5.3 0 40 2.1 4.2 1.025 1.040
V-2 9.1 9.1 3.7 3.7 2.5 5.0 3 73 2.1 4.3 1.025 1.040
29
2.4. Post-Tsunami Damage Assessment
After the 2011 Tōhoku tsunami event, the Santa Cruz Port District hired Mesiti-Miller
Engineering Inc. to conduct a damage evaluation of facilities for the small craft harbor. The
assessment consisted of a visual inspection of all floating facilities supported by guide piles; fixed
structures within Santa Cruz were not included. Typical damage to the dock facilities included
loose/missing flotation, cleat pullout, cracked whalers, and broken pile guides.
There are two components in a floating dock system primarily believed to cause damage within
the harbor: cleat and pile guide failure. Cleat (and line) failure are primarily responsible for boats
becoming loose during tsunami events. Post-tsunami photographs taken by Mesiti-Miller
Engineering Inc. indicate sections of the dock where the cleats were ripped from their mountings
with only small sections of the bolts remaining. Less common are indications of lines breaking
most likely because sections of lines that remain after the tsunami can be removed by the occupants
and replaced.
Incidents of pile guide failure have been documented by Dengler et al. (2009) in Crescent City
Harbor during a post-tsunami damage assessment of the 2006 Kuril event. Dengler et al. (2009)
attribute pile guide failure to the strong currents pinning the pile guides against the pilings and the
guides being unable to adjust to the rising water level, which leads to failure. The event is
somewhat challenging to analyze deterministically because of the degree of uncertainty involved
in defining the input variables. This failure mechanism will be addressed probabilistically in later
iterations of the model.
30
Post-tsunami photographs by Mesiti-Miller Engineering Inc. support a second tension failure
mechanism where tension from the pile guides pulling against the piles leads to the guides being
torn from their mounting in the dock. What the photos show are areas along the floating dock
where the pile guides are disconnected from the dock without any evidence of whalers (or other
dock components) being crushed.
Mesiti-Miller Engineering Inc. gave each dock within Santa Cruz a rating from A to F with A
representing little/no damage and F representing complete failure. From this assessment, Mesiti-
Miller Engineers Inc. concluded that every floating dock suffered some degree of damage (Mesiti-
Miller Engineering Inc., 2011). The ratings developed by Mesiti-Miller Engineering Inc. were
transformed into low, medium, and high damage ratings for each dock within Santa Cruz Harbor.
The low category corresponds to a rating from A-B, the medium category corresponds to a rating
from C-D, and a high category corresponds to a rating of F. A polygon representing the boundaries
of each dock was estimated from USGS aerial images then color-coded with the corresponding
damage level. The result is a spatial map of damage within north and south Santa Cruz Harbor (see
Figure 2.8).
31
Figure 2.8: Damage survey of the Santa Cruz Harbor north (top) and south (bottom) basins showing areas of high
(red), medium (yellow) and low (green) slip damage.
32
The north harbor sustained the most severe damage during the tsunami event. The damage
within the basin, however, was spatially heterogeneous. Some areas in the north harbor
experienced little impacts while tsunami currents destroyed other docks. Docks W-1, W-2, and W-
3 sustained very minor damage during the tsunami event and are shown in green. Docks U-1, U-
2, V-1, and V-2 sustained a high degree of damage and are shown in red. Eyewitness accounts
have indicated that damage at these docks occurred early in the tsunami event. Docks H, I-1, and
I-2 also sustained a high degree of damage. However, these docks were damaged by debris which
had accumulated within the harbor as a result of the initial waves. Debris impact damage is
considered beyond the scope of this study.
Most of the South Harbor sustained moderate damage during the tsunami event. The exception
to this would be dock AA, the fuel dock, and the launch ramp, which were not damaged during
the event. This is likely because these are fixed structures, not floating docks like the rest of the
harbor. Mesiti-Miller Engineering attributes the difference in damage between the two harbors to
the differences in infrastructure ages between the north and south basin.
2.5. Post-Tsunami Hazard Assessment
A hindcast assessment of the 2011 tsunami event and predictive assessment of the hypothetical
Alaska-Aleutian event was conducted using the methodology outlined in previous sections.
Current speeds and directions from each event were taken from the model results. One key
weakness of this analysis is that the capacities of each component before the 2011 event were not
known. Therefore, fragility curves are defined in terms of the required capacity for damage to
occur. The output capacities can be correlated with the event damage from the previous section.
33
The curves can be used to infer component capacities, and then be used by engineers to assess
under what scenarios damage to a harbor could occur. Only a limited number of docks were
analyzed to validate the methodology with docks selected based upon the characteristics of the
flow field, dock location within the harbor and layout.
2.5.1. Pile Guides
Fragility curves for pile guides from the Monte Carlo analysis are presented in Figure 2.9. The
results are presented with respect to the required capacity. The scatter plot in the bottom panel
corresponds to the 95% confidence level of each fragility curve by dock, or the capacity (with 95%
confidence) would lead to a component failure for the particular tsunami scenario.
34
Figure 2.9: Fragility curves for pile guides in Santa Cruz Harbor for the 2011 Tōhoku event and Alaska-Aleutian
event (top); fragility curve 95% confidence limits for the 2011 Tōhoku and Alaska-Aleutian event (bottom). Green,
yellow and red fragility curves and markers correspond to low, medium, and high levels of observed damage for the
2011 Tōhoku event. Pink curves and markers are for the Alaska event.
In this figure, green, yellow, and red fragility curves correspond to low, medium, and high
levels of damage, as taken from the damage report for the 2011 Tōhoku event. Assuming that all
pile guides have the same structural capacity, the Monte Carol results should show an increasing
trend for the required capacity from green, to yellow to red. The reason for this expectation is that,
35
if all components have the same structural capacity, those components that were not damaged
(green curves) should have needed a relatively small required capacity to prevent failure, or
equivalently experienced a relatively small demand. Conversely, those components that were
damaged (red curves) should have needed a relatively large capacity, in fact, a capacity beyond
the structural capacity to prevent failure. However, the results show a noticeable difference
between the north (solid lines) and south (dashed lines) basins. The difference in the capacities
required to resist failure of the south basin is significantly less than those of the north; a
consequence of the difference in age of the two basins. The south basin was finished in 1962 and
was constructed of mostly wood docks and piles. The north was finished in 1973 and was
constructed of mostly updated composite material, which is known (from a material standpoint) to
be stronger than the older wood construction. The results indicate that the capacity of the wood
docks in the south basin was likely less than the composite docks in the north basin. This result
highlights the need to understand (or at the very least have a means to differentiate) the underlying
structural capacity of the system independent of the system demand.
In the north basin, the results also show three distinct regimes in line with low, medium, and
high levels of damage from the post-tsunami survey. These regimes indicate when and where the
transition from no damage to damage could be. For instance, the results for dock J-1 and W-2 had
nearly the same required capacity but were classified as low and moderate levels of damage. This
result would, therefore, tend to suggest that the transition between low to moderate damage is
somewhere between the two results. Similarly, this implies that the structural capacity of pile
guides in the north basin was also likely near the Monte Carol predicted required capacity of the
J-1 and W-2 docks.
36
Results for the theoretical Alaska-Aleutian event are presented as capacity-based fragility
curves with 95% confidence limits in Figure 2.9. For this scenario, all of the fragility curves have
higher required capacities than the Tōhoku event. This result suggests that if the Alaska-Aleutian
event were to occur, all of Santa Cruz Harbor would be severely damaged by the event. If a smaller
event were to be modeled, engineers could use the result to assess which docks are vulnerable to
the deterministic event. Identifying vulnerabilities will help to distinguish where rehabilitation
efforts are best focused.
The results of the pile guide analysis highlight the skill of the Monte Carlo methodology to
predict tsunami damage within a small craft harbor. When coupled with a damage report, the
method was able to predict the grouping of areas of high, medium, and low damage as well as
differentiate between underlying structural capacities of the north and south basin. Once calibrated,
fragility curves for other events (such as the Alaska-Aleutian event) can be developed and used by
engineers to determine the capacity required to withstand the design event.
2.5.2. Cleats
Fragility curves for cleats from the Monte Carlo analysis are presented in Figure 2.10 (with
respect to the required capacity). The results indicate, like the pile guide analysis, a distinct
difference between the north (solid) and south (dashed) basins. However, focusing on the north
basin only, the cleat results show some difference in ordering between the medium and high
damage levels compared with the pile guide analysis. The Monte Carlo analysis would suggest
that Dock J-1 should have experienced relatively severe cleat damage (instead of the observed
moderate damage) or that docks V-1 and V-2 experienced moderate cleat damage (instead of the
observed severe damage).
37
Figure 2.10: Fragility curves for cleats in Santa Cruz Harbor for the 2011 Tōhoku event and Alaska-Aleutian event
(top); fragility curve 95% confidence limits for the 2011 Tōhoku and Alaska-Aleutian event (bottom). Green, yellow
and red fragility curves and markers correspond to low, medium and high levels of observed damage for the 2011
Tōhoku event. Pink curves and markers are for the Alaska event.
One issue with the damage reports provided by Mesiti-Miller Engineers Inc. is that the reports
do not provide enough detail as to the severity of the cleat damage. They do provide the number
of damaged cleats for some docks (such as J-1), but the tsunami completely destroyed other docks
(such as U-1). Therefore, only a coarse interpretation of the reports can be used to draw speculative
38
conclusions about the nature of the cleat damage. If the tsunami did destroy a dock (such as U-1)
it is reasonable to also assume that some cleats were also destroyed. Because of this, the
conclusions made with respect to cleat damage cannot be as strong as the pile guide damage. The
results do highlight the applicability of the method to help engineers estimate (in a global sense)
how damage can be dispersed across the basin. Additionally, these results can be used to identify
where within a harbor, vessels are likely to break free from their mooring lines and become adrift,
float onshore with or without the dock or sink.
2.6. Discussion
The results of the Monte Carlo analysis highlight the methodology's ability to predict tsunami
damage within a small craft harbor. Primary inputs to the Monte Carlo analysis current speed,
current direction, vessel/dock dimensions, as well as the underlying structural capacity of the dock.
Using the results of the Monte Carlo analysis, mean estimates of the current speed and current
direction (converted to the orientation of the respective docks) were estimated and plotted as a
function of damage type. This technique is also known as inverse modeling since the inputs are
extracted from the results. The scatter plot is shown in Figure 2.11. The same color-coding is used
as the color-coding presented previously. Squares represent results from the south basin, while
circles represent results from the north basin.
39
Figure 2.11: Current speed and direction results for cleats and pile guides for the 95% confidence limit. Green, yellow
and red fragility markers correspond to low, medium, and high levels of observed damage for the 2011 Tōhoku event.
Pink markers are for the Alaska event. Squares represent results from the south basin, while circles represent results
from the north basin.
The scatter plot shows that the severity of the damage is not dependent on the magnitude of
maximum current speed alone. The incident current direction also plays a role in structural damage.
The results indicate that the high current speeds with low incident angles, as well as the low current
40
speed with high incident angles, produce the demand required to produce moderate to severe levels
of damage.
The selection of input parameters is an important consideration and varies from author to
author. Suppasri et al. (2013) found significant correlations between surface elevation, current
speed, and damage. Muhari et al. (2015), on the other hand, found significant correlations between
current speed, vessel size, and hull type. Results presented here suggest that current speed, current
direction, vessel properties that control its drag load, and underlying structural capacity are
important to the fragility analysis of small craft harbors.
Overall, the results highlight the need to develop physics-based models rather than simply
relying on data-driven correlations. Even simple physical formulations, such as the drag equation,
give some guidance as to which terms might be valuable in the hazard analysis. The method
presented here represents one possible approach and is the first step towards a fragility-based
analysis in harbors.
2.7. Conclusions
This chapter outlines an assessment tool that can be used to quantify the tsunami hazard to
small craft harbors. The methodology is based on the demand-to-capacity ratio of a floating dock
system. The results of this analysis highlight the skill of the Monte Carlo methodology to predict
tsunami damage within a small craft harbor. When coupled with a damage report, the method was
able to predict the grouping of areas of high, medium, and low damage as well as differentiate
between underlying structural capacities in different areas of the same harbor. Once calibrated,
fragility curves for other events (such as the Alaska-Aleutian event) can be developed and used by
41
engineers to determine the capacity required to withstand the design event. Eventually, a suite of
scenarios could be analyzed to determine in a probabilistic sense what the required dock capacities
should be to withstand extreme events.
42
CHAPTER 3. MANUSCRIPT 2 (IN PRESS)
Keen, A. S., Lynett, P. J., Eskijan, M. L., Ayca, A., & Wilson, R. I. (in press). An approach to
estimate tsunami damage for small craft marinas. Journal of Waterway, Port, Coastal,
and Ocean Engineering.
3.1. Introduction
The California coastline, and especially infrastructure in its ports and harbors, is
susceptible to damaging tsunamis from both local and distant tsunami sources. During the tsunamis
of 2006 from the Kuril Islands, 2010 from Chile, and 2011 from Japan, California harbors
sustained over $100M in total damage (Wilson et al., 2013). Harbors, including Crescent City
Harbor, Noyo River Harbor, and Santa Cruz harbor, were among the harbors that saw the greatest
impact from the 2011 Japan tsunami (Wilson et al., 2013). The damage survey conducted after the
events showed that the mooring systems responsible for keeping the vessels and floating docks in
place commonly fail (Dengler et al., 2009; Wilson et al., 2013).
43
Structural failures of this type and magnitude suggest harbor improvements and mitigation
measures can greatly reduce tsunami damage from future events. A study headed by the U.S.
Geological Survey (USGS) indicated that although a large, distant-source tsunami (i.e. from
Alaska) could cause tens of billions of dollars of damage to coastal ports and harbors, 80-90% of
that damage could be reduced by implementing tsunami mitigation and related resilience strategies
(Ross et al., 2013). These resilience strategies could not only reduce the direct damage to the
harbors but also significantly improve recovery times.
With limited resources available across all levels of government, optimizing the return on
investment is the primary consideration for decision makers. Project value for any mitigation or
resilience strategy is related to increased levels of safety for small craft harbors. To better assist
harbors with pre-tsunami mitigation, local, state, and federal entities generally require a predictive
tool to understand the future risk to small craft harbors.
Risk, in a fundamental sense, can be defined as the product of hazard and vulnerability.
The term hazard relates to the probability of occurrence of a potentially damaging phenomenon
(Dewan, 2013). The vulnerability relates to the degree of loss that results from the occurrence of
the phenomenon (Dewan, 2013). Developing and applying a consistent risk framework by
equitably characterizing the tsunami hazard and harbor vulnerability across multiple harbors is the
key to helping decision makers understand the value of mitigation and resilience strategies.
For tsunamis in small craft harbors, “potentially damaging phenomenon” includes
significant changes in water surface elevation as well as associated strong currents. Handling the
tsunami hazard in small craft harbors in a probabilistic framework remains an area of active
research, and studies are limited. Instead, authors typically opt for a deterministic approach
44
assessing several historical events or likely scenarios to quantify the hazard. Globally, several
authors (Borrero, Goring, et al., 2015; Borrero, Lynett, et al., 2015; Borrero & Goring, 2015;
Lynett et al., 2012) have assessed the tsunami hazard. Barberopoulou et al. (2011), Lynett et al.
(2014), and Chapter 2 of this document specifically addressed tsunami hazards within California
ports, harbors, and marinas.
Existing methodologies to characterize harbor vulnerability and predict damage to small
craft harbors during tsunami events are limited. Approaches vary, but the methodologies that do
exist have been mainly data-driven, relying on correlations between input parameters and
documented damage. For instance, using damage reports from the 2011 Tōhoku tsunami in Japan,
Suppasri et al. (2013) derived independent loss functions for maximum tsunami surface elevation
and maximum flow velocities using linear regression analysis assuming a logarithmic loss
function. Muhari et al. (2015) extended the work of Suppasri et al. (2013) to develop new
multivariate loss functions to estimate the potential damage of marine vessels. Lynett et al. (2014)
compared damage reports for five California small craft marinas with numerically modeled current
speeds within each harbor. The semi-quantitative approach was able to correlate the current speed
thresholds with basic thresholds of damage. In Chapter 2, a Monte Carlo physics-based approach
to estimate damage levels to cleats and pile guides was developed. The method, however, did not
consider infrastructure deterioration with time, which should result in a decrease in strength or
capacity and an increased probability of failure.
This chapter presents a risk framework that can be used by decision makers to assess
existing and future tsunami risks to small craft harbors in California. Coupling of high-resolution
numerical modeling with the statistical framework outlined in Chapter 2 is extended to include
45
observed damage states for structural elements in small craft harbors to quantitatively estimate
risk. Section 3.2 will briefly outline the statistical fragility curve methodology presented in Chapter
2. Section 3.3 will summarize results from the small craft harbor inspection program. The program,
which included twelve California small craft harbors, focused on empirically estimating installed
capacities as well as damage states of structural elements in harbors. The risk methodology will
be outlined in Section 3.4 and applied to the Noyo River Basin in Northern California in Section
3.5. Conclusions are summarized in Section 3.6.
3.2. Cleat and Pile Guide Demand
Cleat and pile guide tsunami demand in small craft harbors is estimated using fragility
curves. For a full description of the methodology, the reader is referred to Chapter 2. Fragility
curves for structural components in small craft harbors are estimated using a Monte Carlo
methodology. A Monte Carlo-based approach in structural analysis is a probabilistic tool where
the governing equations of motion or structural behavior might be well known, but the independent
variables of the input (i.e. current speed, current direction) as well as the structural capacities of
the components (e.g. cleats, pile guides) might not be. The Monte Carlo approach requires a
distribution of each input variable (usually with a rectangular, triangular or Gaussian-shaped
relationship), and then randomly samples each distribution within the described equations to
generate a single computational result. The process repeats hundreds or thousands of times,
depending on the accuracy and convergence of the system.
46
3.2.1. Cleats
The transverse and longitudinal forces on vessels were used to calculate the “demand” from
the tsunami current using equations from U.S. Army Corps of Engineers et al. (2005). The
governing equations are outlined in Section 2.2.2.
Total tsunami demand can be defined as the magnitude of the directional components:
𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷 𝑑𝑑 = �𝐹𝐹 𝑥𝑥 𝑦𝑦 2
+ 𝐹𝐹 𝑦𝑦𝑦𝑦
2
(3.1)
Vessels resist the tsunami demand via their cleat connection. The analysis presented here assumes
that these cleats act as a system distributing the load evenly across the cleats. Small craft harbors
within California generally secure each vessel within the slip using either a 2 or 4 cleat
configuration. Cleats are usually mounted on the dock with two bolts via a timber connection. By
knowing the size and number of bolts, capacities for each cleat can be directly estimated (to be
discussed in detail in Section 3.2.1).
3.2.2. Pile Guides
The same equations used to estimate the longitudinal and transverse forces vessels to the
floating dock infrastructure are used in the pile guide demand estimate (see Section 2.2.3). The
equations used to describe the hydrodynamic loads from the tsunami on the floating dock system
are the same equations applied to estimate the vessel demand except (for floating docks) the
structural demand is 90 degrees out of phase with the vessel orientation (perpendicular to the
fingers/vessels); the fingers are in the same line as the vessels (see Chapter 2).
Floating docks and fingers resist the hydrodynamic tsunami demand via the pile guide.
Forces on the pile guides are determined based upon the demand equations. Chapter 2 show that
47
floating dock demand can be averaged based upon the number of pile guides to determine the
average load per pile guide. Multiple pile guides within a dock system resist horizontal loads while
allowing the dock to adjust to a rising and falling tide. For the pile guide capacity in California
marinas, a typical pile guide collar will consist of between 4 and 8 bolts, which connect to the dock
via a timber connection.
3.3. Cleat and Pile Guide Capacities
Within a demand/capacity framework, the capacity of the system plays a crucial role in
determining the probability of failure. As a tsunami enters a harbor, the tsunami currents generate
a force demand on the system. No matter how weak these currents are, there must be enough
capacity to resist the demand from the tsunami currents. Engineers typically think of structural
loads in terms of design capacity. However, over time, aging infrastructure decreases the structural
capacity (or increased vulnerability). A harbor that may have once resisted a tsunami current with
new cleats and pile guides has the potential to experience a significant decrease in the structural
capacity and the inherent increase in risk, without sufficient upkeep.
To better understand how aging structural components, increase a harbor’s vulnerability to
tsunami currents, an extensive field survey of small craft harbors within California was conducted.
Twelve harbors within California were surveyed and are shown in Figure 3.1. Harbor locations
ranged from the northernmost harbor in California, Crescent City, to Oceanside Harbor in San
Diego County along the U.S. Southern Border. Harbors were selected based upon known
vulnerability to tsunami events [Wilson et al. (2013) provide an exhaustive listing of known
tsunami damage from the 2010 Chile tsunami and 2011 Tohoku tsunami] and the degree of
48
cooperation from the local owners. Considerations also included selection to cover the full range
of harbor configurations, climatic conditions, and infrastructure age.
Figure 3.1: California small craft harbors surveyed.
The framework for the surveys was developed based upon the methodologies outlined in
“Waterfront Facilities Inspection and Assessment” (Waterfront Inspection Task Committee,
2015). The surveys focused on two critical components: the cleats and pile guides. At each harbor,
the survey team would evaluate each dock segment and photograph a representative sample of
cleats and pile guides. Care was taken to ensure the sample was sufficiently large to cover the full
parameter space as well as randomized to minizine observational bias. Surveys could last up to
five hours depending on the size of the harbor, condition of the docks, and harbor allowed access.
The field campaign identified one type of cleat and three types of pile guides. The three
types of pile guides were: the hoop type pile guide, the roller type pile guide, and the high-density
49
polyethylene (HDPE) pile guide. The framework outlined by Waterfront Inspection Task
Committee (2015) depends on first estimating the capacity of a newly and properly installed
element (listed as “No Defects”). Damage states (ranging from “Minor” to “Severe”) are then
assigned to observable defects in each element. The damage states are incorporated into the
probabilistic damage model using reduction factors (ranging from 1.0 for the “No Defects” state
to 0.25 for the “Severe” state) applied to the capacity element based upon the damage state.
The survey of California harbors and the photo analysis indicated that cleat and pile guide
conditions within a harbor primarily center around an expected mean with some natural variably.
Expert judgment was used to construct a trapezoidal distribution (Figure 3.2) for each damage
state that allows natural variability in each damage state to be included in the probabilistic model.
The five damage class distributions (from Figure 3.2) are: no damage (ND), minor damage (MN),
moderate damage (MD), major damage (MJ) and severe damage (SD) [consistent with the damage
states outlined by Waterfront Inspection Task Committee (2015) and those published in this
dissertation].
50
Figure 3.2: Capacity reduction factor distributions determined based upon observable degradation. The five damage
class distributions are: no damage (ND), minor damage (MN), moderate damage (MD), major damage (MJ) and
severe damage (SD) [consistent with the damage states outlined by Waterfront Inspection Task Committee (2015)].
3.3.1. Cleats
Site visits to the twelve harbors identified only one type of cleat used to connect vessels to
floating docks. A sample of this style of cleat is shown in Figure 3.3. Cleat sizes ranged from 8-in
for smaller vessels to 24-inches for the largest vessels. The cleat is connected to the dock through
the whaler with two bolts. A survey of marine cleat manufacturers indicated that increasing cleat
size corresponds to an increased bolt size. The survey also suggests the maritime industry
standardized the cleat/bolt pairs. The equation to determine the cleat capacity is:
Capacity
Cleat
= α γ n
bolt
σ
bolt
(3.2)
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where: 𝛼𝛼 = capacity reduction factor, 𝛾𝛾 = capacity calibration factor (O[2]), 𝐷𝐷 𝑥𝑥𝑏𝑏 𝑤𝑤 𝑏𝑏 = number of
bolts (generally 2) and 𝜎𝜎 𝑥𝑥𝑏𝑏 𝑤𝑤 𝑏𝑏 = bolt tension capacity. The form of this equation is consistent with
the expected cleat failure mode (pullout or tension failure) with the added term, α, representative
of the cleat’s aging, weathering, and decreased capacity.
Figure 3.3: Typical cleat configuration for California small craft harbors.
Observed damage states and empirical capacity reduction factors for cleats are presented
in Table 3.1. The damage states closely relate the amount of corrosion and pitting to the remaining
capacity of the cleat. One important note is that the amount of pitting/corrosion on the cleat does
not directly relate to damage to the cleat itself. Typically, it is the bolts that fail and pull the cleat
out of the dock. Observations from the field indicate the amount of cleat pitting/corrosion is a
reasonable indicator of the remaining cleat capacity (Waterfront Inspection Task Committee
52
2015). In cases where cleats fail, dock managers frequently opt to replace both the cleat and bolts
instead of replacing only the bolts and leaving the corroded cleat.
Table 3.1: Damage ratings and capacity reduction factors for cleats.
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3.3.2. Hoop-Type Pile Guides
Hoop-type pile guides are one of the three types of pile guides identified during the field
survey commonly used in harbors that support their floating docks with round piles. A sample of
this style of hoop-type pile guide is shown in Figure 3.4. These types of pile guides consist of a
section of metal pipe curved into a C-shape that wraps around the pile. The hoop is fastened to the
dock with a metal bracket bolted through the whalers. Dock manufacturers typically use 2 or 4
bolts. The two metal segments are either welded together or bolted together. Like the cleats, failure
modes for this system indicate that heavy corrosion and/or bolt pullout failure are the most
common failure modes.
Figure 3.4: Typical hoop type pile guide configuration for California small craft harbors.
The equation to determine the hoop type pile guide capacity is:
54
𝐶𝐶𝐷𝐷𝐶𝐶 𝐷𝐷𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑝𝑝𝑝𝑝 −ℎ𝑏𝑏𝑏𝑏𝑝𝑝 = 𝛼𝛼 𝛾𝛾 𝐷𝐷 𝑥𝑥𝑏𝑏𝑤𝑤𝑏𝑏 𝜎𝜎 𝑥𝑥𝑏𝑏 𝑤𝑤 𝑏𝑏 (3.3)
Observed damage states for hoop-type pile guides are shown Table 3.2. The form of this equation
is consistent with the expected hoop-type failure mode (shear failure) with the added term, α,
representative of the pile guide’s aging and decreased capacity with increased design life.
55
Table 3.2: Damage ratings and capacity reduction factors for hoop pile guides.
The damage states closely relate the amount of corrosion and pitting to the remaining
capacity of the pile guide. In cases where extreme corrosion resulting in section loss has occurred,
56
the above equation does not capture the failure mode. However, with failure capacities at 20% of
the remaining design capacity, this approximation should be representative of the reduced capacity
mode.
3.3.3. Roller-Type Pile Guides
Roller-type pile guides are the second of the three types of pile guides identified during the
field survey used in harbors that support their floating docks with square piles. A sample of this
type of pile guide is shown in Figure 3.5. Roller type pile guides consist of a mounting bracket
bolted to the floating dock. The pile roller is frequently bolted to this bracket using two bolts.
Unlike cleats and hoop-type pile guides, which are mostly maintenance-free, the roller that defines
the roller type pile guide requires frequent maintenance. The roller must be able to slide along the
pile and adjust to changes in the water level. If the roller can’t move freely, the dock can become
pinned up against the pile and likely fail. This added step requires facilities managers to regularly
assess all rollers at their facility and replace the assembly should it not have proper movement.
Unlike the cleat and hoop-type pile guide which experience “pullout failure”, roller type pile
guides can experience shear failure during a tsunami event. The equation to determine the roller
type pile guide capacity is defined as:
𝐶𝐶𝐷𝐷𝐶𝐶 𝐷𝐷𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑝𝑝𝑝𝑝 −𝑟𝑟 𝑏𝑏𝑤𝑤𝑤𝑤 𝑟𝑟𝑟𝑟 = 𝛼𝛼 𝛾𝛾 𝐷𝐷 𝑥𝑥𝑏𝑏 𝑤𝑤 𝑏𝑏 𝜏𝜏 𝑥𝑥𝑏𝑏 𝑤𝑤 𝑏𝑏 (3.4)
where: 𝜏𝜏 𝑥𝑥𝑏𝑏 𝑤𝑤 𝑏𝑏 = bolt shear capacity. The form of this equation is consistent with the expected failure
mode (shear failure) with the added term, α, representative of the pile guide’s aging, and decreased
capacity with increased design life.
57
Figure 3.5: Typical roller type pile guide configuration for California small craft harbors.
Observed damage states for roller-type pile guides are shown Table 3.3. Much like cleat
and hoop type pile guide failure, the damage states for roller type pile guides closely relate the
amount of corrosion and pitting to the remaining capacity of the pile guide. However, for roller-
type pile guides, there are only three typical damage states (instead of five). Photos from the field
visits suggest that refining the damage states into more groups was difficult, given the first-order
magnitude and purpose of this methodology. Adjusting the probability density functions which
define the uncertainty in the capacity reduction factors should capture the uncertainty in the
damage states.
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Table 3.3: Damage ratings and capacity reduction factors for roller type pile guides.
3.3.4. High-Density Polyethylene (HDPE) Pile Guides
The final type of pile guide typical of small craft harbors in California is the high-density
polyethylene (HDPE) pile guide. An example of an HDPE pile guide is shown in Figure 3.6. This
type of pile guide represents a technology advancement and is ordinarily found in newly built
harbors or harbors that experienced damage from the 2010 Chile tsunami or the 2011 Tohoku
tsunami. For instance, Crescent City Harbor, which was nearly destroyed in the 2011 Tohoku
tsunami, replaced all the pile guides in the harbor with HDPE pile guides.
59
Figure 3.6: Typical high-density polyethylene (HDPE) pile guide configuration for California small craft harbors.
One advantage of HDPE pile guides is that they are nearly maintenance-free. The pile
guides are not vulnerable to corrosion like hoop type pile guides, nor do they require regular
service like a roller type pile guide. However, since HDPE pile guides represent newly built
construction, developing an understanding of the failure modes and the aging process is not
currently possible. Therefore, the model of the roller type pile guide is used, assuming that the
reduction in the coefficient of static friction between concrete/steel and concrete/HDPE reasonably
captures the capacity of a newly built HDPE pile guide.
The equation to determine the capacity of a roller type pile guide is defined as:
𝐶𝐶𝐷𝐷𝐶𝐶 𝐷𝐷𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 𝑝𝑝𝑝𝑝 −𝑟𝑟 𝑏𝑏𝑤𝑤𝑤𝑤 𝑟𝑟𝑟𝑟 = 2.5 (2 𝛾𝛾 𝜏𝜏 𝑥𝑥𝑏𝑏 𝑤𝑤 𝑏𝑏 ) (3.5)
where 2.5 represents that ratio between the static friction between steel and HDPE (Zhang, 2016)
and steel and concrete (Rabbat & Russell, 1985) and two is representative of the number of bolts
60
of an equivalent roller type pile guide. It is repeated here that since an HDPE pile guide is reliably
new construction, an age reduction factor is not included in Eq. 3.5.
3.4. Damage Prediction for Small Craft Harbors
This demand/capacity framework intends to provide harbor maintenance and decision
makers with a tool to understand the future risk to small craft harbors. In this section, the
probabilistic damage (risk) methodology is outlined for California marinas. The methodology will
be applied to a small craft harbor in Northern California, Noyo River Harbor, in the next section.
3.4.1. Numerical Modeling
The first decision that planners need to make when applying the demand/capacity
methodology is whether to estimate the tsunami hazard in a probabilistic or deterministic sense.
For the first iteration of the model, the methodology is deterministic due to the lack of offshore
tsunami hazard curves and because of the high computational cost required to estimate current
speed hazard curves at parcel scales within the harbor.
The hydrodynamic model “Method of Splitting Tsunamis” (MOST) (Titov and Gonzalez
1997; Titov and Synolakis 1998) is applied to twelve small craft marinas in California. MOST
simulates the principle phases of tsunami propagation from initial generation, through propagation
and wave run-up (including wave breaking). Initial wave generation in MOST is modeled with
elastic deformation theory from Okada (1985). Wave propagation and inundation are modeled
based upon a derivation of the model published by Titov and Synolakis (1998). MOST variants
have been in constant use for tsunami hazard assessments in California since the mid-1990s (e.g.
61
Lynett et al. (2014)). MOST has also been validated as part of the National Tsunami Hazard
Mitigation Program model benchmarking workshop (Lynett et al., 2017; National Tsunami Hazard
Mitigation Program (NTHMP), 2012). Please refer to Titov (1997) and Titov & Gonzalez (1997)
for further information about MOST as well as model validation.
MOST uses a series of nested grids to propagate the tsunami from the tsunami source to
the small craft marinas. The coarsest grid, at 4-arc min resolution, covers the whole Pacific Ocean
basin. Three additional grids of increasingly finer resolution help refine the numerical results as
the wave propagates from the source to the marina. The innermost grid (known as the nearshore
inundation grid) has a 10 m resolution, taking boundary input from the previous MOST nested
layers. Each grid uses bathymetric and topographic data published by the National Oceanic and
Atmospheric Administration’s (NOAA) National Geophysical Data Center specifically developed
for tsunami forecasting and modeling efforts by Grothe et al. (2012).
Hydrodynamic model predictions of tsunami surface elevation are commonly compared
with tide gauge data. Current speed comparisons are less common, principally due to the limited
data availability. Kalligeris et al. (2016) published current speed drifter data for Ventura Harbor,
and provided a reasonable MOST-data comparison, although the Lagrangian drifter data is difficult
to compare directly with a tsunami model. Therefore, authors validated the MOST small craft
marina modeling for California against the high-order Boussinesq-type model Cornell University
Long and Intermediate Wave Modeling Package (COULWAVE) (Lynett et al., 2014). A
comparison of MOST and COULWAVE results suggest that, while not as accurate as the higher-
order COULWAVE model, the MOST tsunami model satisfactorily reproduces measured
tsunami-induced current speeds and is conservative in its values (Lynett et al., 2014). MOST’s
62
conservative results and fractional run time (compared with COULWAVE) means MOST is an
ideal tool for understanding tsunami-generated hydrodynamic hazards and risk within ports and
harbors.
3.4.2. Marina Condition Assessment
Once the suite of tsunami events was modeled, the demand/capacity framework was applied
to a harbor. Deterministic and probabilistic inputs are needed for the Monte Carlo modeling.
Deterministic quantities are those quantities that are known or those not expected to vary within a
scenario. Deterministic quantities for floating docks include finger length, finger width, number
of slips, number of piles, and number of cleats. These quantities are estimated from historical high-
resolution orthoimagery data from the USGS.
In contrast to deterministic inputs, probabilistic inputs are those quantities which might not
be exactly known but can be defined by a probability density function to account for the associated
uncertainty. These quantities would include current speed, current direction, water depth, seawater
density, vessel length, vessel beam, and vessel draft. Each input variable was randomized,
assuming a rectangular probability density function (e.g. equal probability of any value within a
range) bounded by defined minima and maxima and can be isolated from the modeling results.
For each slip, cleat and pile guide capacity are estimated from the site visit and tables
outlined in Section 3. It is common within a harbor to see a range of capacities as facilities
managers update components and replace older sections of the harbor when damaged by tsunami
or storm events. In most of the surveys, aging hoop or roller type pile guides are updated with
HDPE pile guides if the infrastructure could support the redesign. While photographing every
component within a harbor is not necessary, variability does point to the need to document general
63
conditions within a harbor (roller pile guide vs. HDPE pile guide) to estimate risk at the parcel
scale accurately.
The demand/capacity framework is applied on a slip-by-slip basis. First, failure probability
is estimated for each slip, and averaged over the entire dock finger. While the method can be
applied without calibration and has shown to give reasonable results, a calibration factor allows us
to calibrate the failure probabilities against known failure events. Without available calibration
data, the recommended nominal calibration factor is 2.0, a value representative of the factor of
safety applied during engineering design.
Damage reports from the harbors that sustained damage in the 2010 Chile tsunami and
2011 Tohoku tsunami summarized in Wilson et al. (2013) were typically used for calibration by
varying the calibration factor from 1.0 to 3.0. Incremental increases in the calibration factor
produce calibration results that correspond with a known tsunami scenario. These results show
where the calibration shifts the results from one threshold to the next (as a function of calibration
factor). The calibration factor that reproduces the damage during the tsunami event is applied to
the model for the remaining scenarios. Calibration factor for cleats and pile guides in California
ranged from 1.8 to 2.2, depending on the harbor.
3.4.3. Results
Results for each harbor are presented as risk tables with low (green) risk representing the
probability of failure < 10%, medium (yellow) risk representing the probability of failure between
10% - 99% and high (red) risk representing the probability of failure > 99%. While these limits
may seem somewhat arbitrary, they are empirically derived based upon observed damage ratings.
64
The ratings are outlined by Mesiti-Miller Engineering Inc. (2011) for recorded damage in Santa
Cruz Harbor during the 2011 Tohoku tsunami (see Chapter 2).
This basic approach has been applied to twelve small craft marinas in California, spanning
from Oceanside Harbor in Southern California to Crescent City Harbor in Northern California.
While the focus here is on one small craft marina in Northern California, Noyo River Harbor, the
methodology should be valid for harbors along the United States West Coast where smaller
amplitude, long period tele-tsunamis have the potential to impact vessel and harbor operations. For
nearfield tsunamis, Suppasri et al. (2013) and Muhari et al. (2015) have published a methodology
to quantify vessel loss function based upon vessel data from the 2011 Tohoku tsunami that would
be more appropriate. The approach presented here for tele-tsunamis, and the one presented by
Suppasri et al. (2013) and Muhari et al. (2015) are informed by correlations between numerically
modeled tsunami characteristics and vessel damage. The inclusion of a calibration factor in the
methodology helps generalize the approach to harbors outside of California.
3.5. Case Study: Noyo Harbor
Noyo Harbor District is a small port located along the Northern California Coast (see
Figure 3.1). The harbor was built near the mouth of the Noyo River in the town of Noyo, just south
of Fort Bragg, California. Noyo Harbor consists of two basins. Noyo Basin is the largest of the
two basins and harbors predominantly commercial vessels. A map of Noyo Basin is shown in
Figure 3.7. Dolphin Basin, upriver from Noyo Basin, is the smaller of the two and harbors mostly
recreational vessels; Dolphin Basin was not included in the survey. During the 2011 Japan tsunami,
a series of waves caused significant damage to floating docks within Noyo Basin (Wilson et al.,
65
2013). The ends of Docks B and C were torn from the pile guides. Since that event, harbor
administrators have replaced the destroyed section of Dock B but not Dock C.
Figure 3.7: Location of floating docks in Noyo Basin.
3.5.1. Marina Condition Assessment and Risk-Model Calibration
A survey of Noyo Basin was conducted on March 10
th
, 2016. With 256 slips, surveyors
were able to photograph every slip and pile guide in the harbor. Representative cleats and pile
guides from the survey are shown in Figure: 3.8 and Figure 3.9, respectively. Frequent
precipitation in Noyo River has caused the cleats and pile guides to corrode at a rate faster than
66
average. With limited funds available to the facilities manager, the harbor is unable to keep up
with the corrosion, which leaves the harbor in a vulnerable state to tsunami events.
Figure: 3.8 Representative cleats from Noyo Basin.
Figure 3.9: Representative pile guides from Noyo Basin.
67
The corrosion of the cleats and pile guides results in a severe reduction from the original
capacities. Cleats were measured to be 250 mm (10-inches) during the field survey. M16 (1/2-
inch) bolts are commonly associated with a 250-mm cleat (Sea-Dog Corporation 2018). The
tension capacity of an M16 bolt (Grade 8.8) is 70.15 kN (British Standards 2005), which places
the total new capacity of the cleat at 140.3 kN. An assessment of the cleat conditions based upon
Table 3. and Figure: 3.8 places the cleat in the Severe Damage Class (Class 5) range with corrosion
exceeding 75% of the cleat. The cleat capacity range should be between 0 kN and 35.1 kN (see
Figure 3.2).
The hoop-type pile guides were observed to be in a similar state of major corrosion with
fractional or missing section loss common across most of the hoop-type pile guides. The pile
guides’ proximity and exposure to the water further accelerate the aging process. Four M16 (1/2-
inch) bolts are commonly associated with pile guides in Noyo River. The tension capacity of an
M16 bolt (Grade 8.8) places the total capacity of the pile guide at 280.6 kN. An assessment of the
pile guide conditions based upon Table 3.2 and Figure 3.9 places the pile guide in the Severe
Damage Class (Class 5) range with section loss present in many of the pile guide hoops. The pile
guide capacity range should, therefore, be between 0 kN and 70.2 kN (see Figure 3.2).
Cleat and pile guide damage for Noyo River can be used to calibrate the structural
capacities within the risk model to reflect conditions within the harbor more accurately. During
the harbor visit on March 10
th
, the surveyors were able to ask the Noyo River harbormaster about
the maintenance and damage history of the floating dock infrastructure. The harbormaster verified
that the ends of Docks B and C failed during the 2011 tsunami event. Using this information, the
risk model can be calibrated via the cleat and pile guild capacity calibration factor, 𝛾𝛾 , by varying
68
the calibration factor and running the various iterations representative of the 2011 tsunami event
in Noyo River. The calibration is considered convergent when the 𝛾𝛾 reproduces the reported
damage (in this case, high damage potential for docks B and C). The calibration factor was then
applied to the remaining tsunami events and scenarios. Calibrating against damage in Noyo River
during the 2011 Japan event shows good agreement with observed capacities with the capacity
scale factor equal to 2.1 for cleats and pile guides.
Since the damage that occurred to Noyo River in 2011, no significant upgrades to
infrastructure have been undertaken, and only a small segment of the damage floating docks have
been replaced. Now, these damage classes and capacity scale factors are applied to the suite of
historic and probable tsunami event scenarios. If updates to the harbor had been performed since
the 2011 tsunami, the damage classes within the risk model would need to change (from Damage
Class 5) to reflect the upgraded conditions and increased capacity (to Damage Class 1 or 2).
MOST was used to evaluate several historic and probable scenarios for Noyo River Harbor.
The following events and scenarios were analyzed as part of this analysis: 2010 Magnitude 8.8
Chile Event (Historical), Magnitude 9.0 Cascadia Scenario, 2011 Magnitude 9.0 Japan Event
(Historical), Magnitude 9.4 Chile North Scenario and Magnitude 9.2 Eastern Aleutian-Alaska
Scenario. The maximum current speed modeling results for the five scenarios are shown in Figure
3.10. The tsunami source parameters for Noyo River are summarized in Table 2.1. Two historical
events for Noyo River were selected because of the amount of damage the tsunamis caused within
the harbor, and documentation was available to validate the damage. The probable scenarios were
selected because of their potential impacts on the harbor. The 9.2 Eastern Aleutian-Alaska scenario
would produce the most substantial current velocities in Noyo River of any of the modeled events.
69
Figure 3.10: Numerical modeling results of maximum current speed (by tsunami scenario/event) within Noyo Basin.
3.5.2. Results and Discussion
Results of the cleat analysis (see Figure 3.11) indicate that Noyo Basin is most vulnerable
to the Magnitude 9.2 Eastern Aleutian-Alaska Scenario. The modeling indicates that Docks B, C,
and D have a high level of vulnerability, while Docks A, E, F, G, and H have a moderate level of
vulnerability. The MOST results suggest that the current speeds increase near the harbor entrance
(near Docks B, C, and D), generating the different damage potential. After the Aleutian-Alaska
Scenario, the results indicate that the next event Noyo Basin would be most vulnerable to is the
Magnitude 9.0 Cascadia Scenario. In terms of all scenarios, Dock B would be most vulnerable to
the modeled tsunami events with two of the six events indicating high vulnerability and four of the
six events indicating moderate vulnerability. The next most vulnerable locations would be Docks
C and D.
70
Figure 3.11: Cleat probability of failure results for Noyo River Basin. Low (green) risk representing probability of
failure < 10%, medium (yellow) risk representing probability of failure between 10% - 99% and high (red) risk
representing probability of failure > 99%.
Like the cleat analysis, results of the pile guide analysis (Figure 3.12) indicate that Noyo
Basin is most vulnerable to the Magnitude 9.2 Eastern Aleutian-Alaska Scenario. The modeling
indicates that Docks B, C, D, and E have a high level of vulnerability, while Docks A, F, G, and
H have a moderate level of vulnerability. After the Aleutian-Alaska Scenario, the results indicate
that the next event Noyo Basin would be vulnerable to the Magnitude 9.0 Cascadia Scenario. In
terms of all scenarios, Dock B would be most vulnerable to the modeled tsunami events with two
of the six events indicating high vulnerability and four of the six events indicating moderate
vulnerability. The next most vulnerably would be Docks C, D, and E.
71
Figure 3.12: Pile guide probability of failure results for Noyo River Basin. Low (green) risk representing probability
of failure < 10%, medium (yellow) risk representing probability of failure between 10% - 99% and high (red) risk
representing probability of failure > 99%.
The strength of the probabilistic risk approach is the method’s ability to characterize not
only the tsunami hazard but also the infrastructure vulnerability. Previous approaches by Lynett et
al. (2014) and Chapter 2, focus primarily on capturing the tsunami hazard as a bulk property of
tsunami damage. Lynett et al. (2014), for instance, provides a rudimentary damage threshold based
upon the maximum current speeds. For current speeds less than 1.5 m/s, the authors expect no
damage; for current speeds greater than 4.5 m/s, extreme damage (structural failure) is possible.
The results suggest significant damage in Noyo River occurred with a current speed of less than
4.5 m/s during the 2011 tsunami (see Figure 3.10). This result, along with the cleat and pile guide
results from the risk model, suggests that the underlying condition (infrastructure vulnerability) of
the cleats and floating docks is ultimately responsible for future damage potential summarized in
Figure 3.11 and Figure 3.12.
72
3.6. Conclusions
This chapter presents a risk framework that can be used by harbor maintenance and
decision makers to assess future tsunami risks to small craft harbors in California. The
methodology is based on the demand-to-capacity ratio of a floating dock system with physics-
based probabilistic inputs used to characterize uncertainty in demand. Empirically derived
probabilistic inputs are used to characterize uncertainty in the capacity. An extensive field
campaign that included a survey of damage states within twelve California harbors was carried for
two years. The campaign included failure modes and damage states (representative of the
infrastructure aging process) that correspond with empirically derived capacity estimates.
When applied to a small craft marina, here Noyo River, the method was able to characterize
the historically observed damage in the harbor from the 2011 tsunami event with little calibration.
Although the tsunami generated currents in Noyo River were small relative to many other marinas
in California, the method presented here correctly characterized the vulnerability of the harbor and
the resultant risk. The results illustrate the balance between event hazard and infrastructure
vulnerability that ultimately contributed to Noyo River’s risk.
Coupling the approach with future tsunami scenarios provides risk managers with a reliable
method to characterize vulnerabilities within the harbor. With limited resources available across
all levels of government, optimizing the return on investment is the primary consideration for
decision makers. The method presented in this chapter provides a direct quantitative estimate that
decision makers can use to quantify their return on investment (benefit-cost) and relative risk
reduction for any mitigation project.
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CHAPTER 4. MANUSCRIPT 3 (IN PREP)
Keen, A. S. & Lynett, P. J. (2020). Multi-hazard risk analysis for coastal infrastructure in a
changing climate. Manuscript in preparation.
4.1. Introduction
Numbers published by the National Oceanic and Atmospheric Administration (NOAA)
based upon 2010 census data state that nearly 121 million people live in counties directly on the
shoreline (National Oceanic and Atmospheric Administration, 2018). From 1970 to 2010, the
population of these counties increased by almost 40 percent. In this densely populated coastal zone,
our society meets the sea. As sea levels rise and storm patterns change, we can expect this
relationship to continue to evolve. Mitigation and resilience strategies enacted in response to
increasing coastal flooding from sea level rise will dictate how flooding events continue to impact
these densely populated communities.
Policy makers, informed by engineers and scientists, play a crucial role, deciding how best
to respond to sea level rise at the community scale. Policy makers are primarily responsible for
74
distributing money to coastal communities for mitigation and resilience projects. With limited
funds available across federal, state, and local agencies, maximizing increased levels of safety
while minimizing cost is a primary goal of any project. Capturing future hazards, vulnerability,
and infrastructure risk with sound and unbiased science provides the foundation for the decision-
making process.
At the parcel scale, previous authors have defined infrastructure risk (see Figure 4.1) as the
probability of damage occurring (Dewan, 2013). Two independent terms, natural hazard intensity
and infrastructure vulnerability, balance to evaluate risk. Natural hazard intensity relates the
probability of occurrence of a potentially damaging phenomenon to the phenomenon intensity
(Dewan 2013). Infrastructure vulnerability relates to the degree of loss that results from the
occurrence of the phenomenon (Dewan 2013). Applied at the community or regional scale, the
balance of these terms can help policy makers identify where potentially hazardous events are
likely to impact a region.
Figure 4.1: Infrastructure risk is the balance between natural hazard intensity and infrastructure vulnerability.
75
In Chapter 3, a risk-based framework was applied to a small craft marina in California to
quantify the tsunami risk within the harbor. The intensity of a discrete number of tsunami events
was modeled with MOST (Titov, 1997; Titov & Gonzalez, 1997). When coupled with the
underlying age and condition of the harbor, the risk framework was able to identify vessels and
floating docks within the harbor that may be vulnerable to damage. Hazard scenarios that are likely
to cause damage in the harbor are identified (see Chapter 3).
For a given design horizon, infrastructure is typically vulnerable to a suite of natural
hazards, with one of the various hazards typically defining the service level. As sea levels increase,
however, infrastructure near the coast may experience a shifting hazard portfolio as the relative
sea level alters the natural balance. Aging infrastructure may increase the infrastructure risk with
time. Understanding how hazards and vulnerabilities shift over various time horizons can help
communities understand how their risk portfolio may change and how communities may be able
to adapt to a changing climate.
In this chapter, Ventura Harbor, a small craft marina along the West Coast of the United
States is evaluated. This chapter presents a new framework for multi-hazard risk analysis known
as Coastal Risk MH. The framework is based upon infrastructure (e.g. small craft marinas) design
life. Throughout a harbors design life, a harbor is vulnerable to a suite of natural hazards, including
meteorological, tsunami, and seiche events over relatively short time scales, and sea level rise over
long time scales. For much of history, harbormasters have relied on pile freeboard to protect the
floating docks from failure during king tides or storm events. Accelerated sea level rise decreases
the freeboard height. Helping harbormasters understand how their risk profile may change is an
important step in their planning process.
76
4.2. Multi-Hazard Risk Framework
The design life-based approach to multi-hazard risk analysis is built upon the concept that
natural hazards of various types and intensity may all impact a structure during its design life.
While the structure in question could be any type of engineered structure (e.g. homes, buildings,
utilities), in this chapter, the focus is on small craft marinas and the floating docks within. With
most marinas built more than 30 years ago, many floating docks within California are providing
services well outside of their design service life. The service extension leaves marinas vulnerable
to damage from events below the established design parameters, with sea level rise expected to
exacerbate the damage potential.
Small craft marinas are already seeing some consequences of sea level rise. Many harbors
believe historical freeboard protects them from water level events. During king tide events in
California, harbormasters have observed floating docks nearly “topping out” against the pile (J.
Higgins, personal communication, January 24, 2018). The reduction in freeboard leaves harbors
vulnerable, with the engineering solutions of mitigation and retrofits (usually taking the form of
pile extensions) expensive and time-consuming.
Although many harbormasters understand the potential risk sea level rise poses, they often
view the problem as a future risk, not a current risk. In a technical advisory role, scientists can help
marina administrations understand how coastal infrastructure (i.e. floating docks) risk portfolio
changes with increasing sea levels. This approach will help harbormasters to quantify planning
horizons and prioritize where and when retrofits may be appropriate.
This chapter will outline a methodology to help engineers and planners quantify the future
failure risk to small craft marinas and apply the statistical multi-hazard risk framework (known as
77
Coastal Risk MH) to a harbor. Within Coastal Risk MH, event hazards are handled stochastically
via probabilistic hazard analysis (Geist & Lynett, 2014). The approach defines a set of discrete
event hazards representing the range of possible water levels a harbor could see in the future
decades. Structure vulnerability is related to the actual height of the piles within the harbor with
the failure risk a binary representation of the water level and pile height (the water level is either
above the top of the pile or not). Future extreme event distributions are treated stochastically with
various realizations of events used to quantify the time-dependent failure risk. The overview of the
method is shown in Figure 4.2.
Figure 4.2: The multi-hazard risk framework is outlined in the flow chart. Each discrete event within the set of events
(Rj) is characterized by utilizing the hazard curve methodology outlined by Geist and Lynett (2014). Each event set is
compared against a pile height datum to establish a single failure estimate. A sum of the individual failure
probabilities characterizes the multi-hazard solution.
78
4.2.1. Stochastic Discrete Hazard Estimate
Along the West Coast of the United States, meteorological, tsunami, seiche, and sea level
rise constitutes the suite of likely oceanographic hazards to small craft marinas. Shock hazards like
meteorological, tsunami, and seiche events are short-period events that impact infrastructure for
hours to days. These events can be considered discrete, independent events, governed by the
geophysical processes’ hazard curve.
Astronomical and seasonal water level changes associated with the El Niño–Southern
Oscillation (ENSO) continuously modulate the discrete events, shifting the total water level
elevation relative to the mean water level and vertical datum. Figure 4.3 illustrates how various
water level realizations superimpose to increase or decrease the water level hazard with time, even
though each respective hazard cure is different.
As global oceans rise, sea level rise acts as longer-term infrastructure stress increasing the
impact of the shock events relative to their respective hazard curves. Many authors (Lin &
Shullman, 2017; Melet et al., 2018; Vitousek et al., 2017; Vousdoukas et al., 2018) have shown
sea level rise’s non-stationarity effect on existing design levels. The added stress from sea level
rise increases the frequency of occurrence of design events and reduces the equivalent level of
safety for infrastructure.
79
Figure 4.3: Schematic shows how various meteorological, tsunami, and seiche water levels superimpose to increase
the water level relative to the pile height.
Quantifying future changes to the water level both in terms of probability and intensity is
essential to engineers and planners. Sea level rise uncertainty, in short, medium- and long-term
planning horizons, poses the most significant challenge to stakeholders. Probabilistic hazard
analysis provides an ideal platform to incorporate the intensity of each shock event, the modulation
generated by long-term water level trends (both present and future), and the uncertainty that is
common among geophysical problems. Geist and Parsons (2006) and Geist and Lynett (2014)
extended probabilistic hazard analysis to oceanographic problems by adapting a long-standing
probabilistic method for determining ground motion exceedance caused by earthquake known as
probabilistic seismic hazard analysis (Cornell, 1968).
Probabilistic hazard analysis was founded on the idea of separating the return periods of
input variables from hazard recurrence (Geist & Lynett, 2014). Using a Monte Carlo methodology,
80
variables constrained by prescribed probability density functions are input to a given set of
governing equations to generate realizations which define the hazard parameter space. Monte
Carlo frameworks are ideal where the governing equations may be well known, but the
independent variables of the input may not be known entirely (see Chapter 2). The process repeats
hundreds or thousands of times to generate a statistical understanding of design parameters (e.g.
still water level). Once the statistical parameters space is defined, the maximum envelope of these
realizations defines what is known as the hazard curve (Geist & Lynett, 2014). An example of a
total water level hazard curve is shown in Figure 4.4.
Figure 4.4: Realizations of meteorological water level are shown in black in the above figure. The hazard curve that
relates the intensity and probability of each discrete event is determined by the envelope of the realizations (red).
Meteorological, tsunami, and seiche based water levels are all considered discrete,
independent events. For example, the occurrence of a tsunami should not influence the occurrence
81
of a meteorological event. The governing equation for each water level hazard is conceptually a
sum of individual components.
The governing equation for a discrete meteorological water level event elevation, z
meti
, is
given as:
z
meti
= z
astro
+ z
season
+ z
SLR
+ z
met
(4.1)
where: z
astro
= astronomical water level, z
season
= seasonal water level, z
SLR
= non-stationary sea
level rise and z
met
= meteorological water level.
The governing equation for a discrete tsunami water level event elevation, z
tsu
, is
represented as:
z
tsu
= z
astro
+ z
season
+ z
SLR
+ z
tsu
(4.2)
where: z
tsu
= tsunami water level.
The governing equation for a discrete seiche water level event elevation, z
seiche
, is given
as:
z
seiche
= z
astro
+ z
season
+ z
SLR
+ z
mean
+ z
crest
(4.3)
where: z
mean
= wave setup and z
crest
= spatially dependent seiche crest elevation. Note that the
crest elevation for seiche events within harbors consists of two additional terms. The first term,
z
mean
, is related to the setup produced in the harbor from offshore wave breaking. The second term,
z
crest
, is related to the dynamic seiche motions.
4.2.2. Stochastic Event Realizations
Extreme value theory is a unique branch of statistics in that it develops techniques to
describe the unusual, instead of the usual (Coles, 2001). By definition, extreme values are scarce,
82
often requiring models to extrapolate beyond what is observed in the data record. Engineers and
planners use extreme value theory to help quantify an expected value of a defined extreme event
for a structure’s service life (Goda, 2000).
Extreme value theory is incorporated into the risk-framework to estimate the frequency and
intensity of extreme events. There are many methods to estimate an expected value of an extreme
event, such as the annual maximum method or the point-over-threshold method. Each method has
advantages and disadvantages, but the ultimate choice is somewhat subjective (Goda, 2000). The
annual maxima approach is one of the most common methods used in the analysis of extreme river
discharges and other natural hazard events (Goda, 2000). This extreme value approach is
incorporated into Coastal Risk MH.
The extreme value model is included in the risk framework via the concept of the return
period. Goda (2000) defines the return period as the average duration of time during which extreme
events exceeding a certain threshold would occur once. Note that a return period defines a
threshold, not an exact value. Using the annual maximum method, the number of extreme events
that are expected to occur during an infrastructure parcel’s design life is equal to the integer number
of design life years. The annual maximum method implies a series or set of extreme events exists
for a given time horizon.
This return period set, 𝑅𝑅 𝑗𝑗 , is defined as:
R
j
∈ [ r
i
]
j
= [ r
1
, r
2
, …, r
T
]
j
(4.4)
where: r
i
= i-th return period realization and T = integer number of design life years. The subscript
𝐶𝐶 indicates that the number of realizations equals the integer number of design life years. The
subscript j implies that, like probabilistic hazard analysis, the failure probability is also stochastic.
83
Multiple realizations of the integer return period set are used to sample the probabilistic space. A
representative set of return periods and expected water level elevations is shown in Figure 4.5.
Each integer return period is characterized as the inverse exceedance percentage:
r
i
=
1
1 - F(z
i
)
(4.5)
where: F(z
i
) = i-th prescribed cumulative distribution function bounded by F=[0,1]. Probability
theory typically guides the cumulative distribution function selection. Here, a white-noise
cumulative density function is used via a random number generator (for F) to estimate the return
period value for each realization (r
i
). Note that, at this point, we do not know which values of z
i
correspond to the randomly sampled values of F.
With a set of return periods defining the time and probability level for a randomly generated
set of events, there is a corresponding set of water levels, Z
𝑗𝑗 . The water level set is given as:
Z
j
∈ [z
i
]
j
∈ [ z
1
(r
1
,t
1
), z
2
(r
2
,t
2
), …, z
N
(r
N
,t
N
) ]
j
(4.6)
where: z
i
= i-th total water level realization. Probabilistic hazard analysis connects the return period
(r
i
) with various geophysical amplitudes (i.e. tsunami, seiche, etc.) to quantify the probabilistic
total water level (z
i
). An illustrative return period and water level set are shown in Figure 4.5 (a)
and (b).
84
Figure 4.5: Representative (a) design life vs. return period and (b) design life vs. water level realization. Sample sets
of (c) meteorological, (d) tsunami and (e) seiche water level realizations
4.2.3. Vulnerability
Vulnerability describes how susceptible a structure is at a prescribed water level by relating
the amount of expected damage to floating docks from that water level. In small craft marinas, pile
lengths vary relative to the harbor bathymetry with maximum pile elevations similar.
Vulnerability is assumed stationary in time and binary in nature, which is reasonable here
as the pile elevations are not expected to change in time. The water level either exceeds the
prescribed pile elevation (failure), or it does not (no failure).
p� Z
j
� = �
0 Z
j
≤ z
ref
1 Z
j
> z
ref
(4.7)
where: 𝑧𝑧 𝑟𝑟𝑟𝑟𝑟𝑟 = reference pile height elevation and p is the binary chance of pile failure.
85
4.2.4. Multi-Hazard Infrastructure Failure
The structure failure probability describes the damage or economic loss relative to pile
elevation. The structure failure probability for each hazard (e.g. metrological water level, tsunami
water level, seiche water level) is characterized by the fraction of realizations with a pile failure:
P =
∑ p
j
N
j=1
N
(4.8)
where: N = integer number stochastic-event realizations.
Up to this point, the risk is conducted in parallel for the three hazard types: meteorological,
tsunami, and seiche water level. Each failure risk defined by the hazard type characterizes the
failure probability for each event type. The total structural failure probability is a sum of the
individual components’ probabilities (defined by Eq. 4.8):
P = P
met
+ P
tsu
+ P
seiche
(4.9)
where: P
met
= structure failure risk probability from meteorological water level, 𝑃𝑃 𝑏𝑏 𝑡𝑡𝑡𝑡
= structure
failure risk probability from tsunami water level and 𝑃𝑃 𝑡𝑡𝑟𝑟 𝑠𝑠 𝑦𝑦 ℎ𝑟𝑟 = structure failure risk probability
from seiche water level.
Figure 4.6 shows a representative multi-hazard result with the design year along the x-axis
and the pile-top elevation along the y-axis. Five-percent chance of failure contour illustrating the
annual failure probability for meteorological, tsunami, and seiche components are shown as red,
blue, and green lines, respectively (Eq. 4.8). The black line specifies the multi-hazard failure risk
for the three hazards (Eq. 4.9). The result illustrates the time-dependent failure risk in terms of the
individual and multi-hazard estimate. The relative offsets from the multi-hazard estimate (black)
give some indication of the intensity and projected development of the multi-hazard risk. Tsunami-
86
based risk (blue) provides the least likelihood of failure in the marina, whereas seiche based risk
(green) provides the highest likelihood of failure.
Figure 4.6: Example multi-hazard failure probabilities reveal the balance of meteorological, tsunami, and seiche
hazards as relative contributions to the multi-hazard water level risk.
4.3. Multi-Hazard Risk Pseudo Code
This section will focus on Coastal Risk MH’s code structure using a pseudocode outline
within a MATLAB syntax. MATLAB is a multi-paradigm numerical computing environment and
proprietary programming language developed by MathWorks (MathWorks, 2020a). MATLAB’s
software and scripting code combination allow users to create and edit scripts within a graphical
user interface. MathWorks releases multiple updated versions of their software annually. The
updates can include changes to built-in functions and syntax that result in incompatibility issues.
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Coastal Risk MH was built with MATLAB Version R2018a (MathWorks, 2020b) and tested on
both Windows and Linux systems.
Coastal Risk MH is a stochastic risk model. The word stochastic implies that a process is
random but that the process can be analyzed statistically. Here, sampling is used to constrain the
random variability with the natural system. A key feature of any stochastic model is that the
number of realizations required to describe a solution are typically unknown beforehand. Applying
a model to a new location requires the user to sample a set series of realization (e.g. 100, 1000,
10000, etc) and compare the number of realizations to the solution mean and standard deviation.
As the number of realizations increases, the solution standard deviation should decrease. A
solution is considered convergent when a user determines the solution standard deviation (a
representation of uncertainty) is “sufficiently small” to describe a solution.
Stochastic models need to be flexible and able to accommodate a wide number of possible
realizations. MATLAB was originally developed with vector and matrix operations in mind.
Implementing a vectorized MATLAB code remains the most efficient computational method when
the number of realizations is small. As the number of realizations increases within a stochastic
model and/or the processes become increasingly complex, computer hardware quickly becomes a
limitation. Coastal Risk MH is primarily a loop-based and scalar-oriented MATLAB script
wrapped around a vectorized computational kernel meant to limit the computational and storage
demand.
Coastal Risk MH is comprised of three primary MATLAB scripts (two “run” scripts and a
kernel function). The three scripts can be categorized as:
• Primary “Run” Script
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• Probabilistic Hazard Function
• Post-Processing Script
In addition to the three MATLAB scripts and the standard MATLAB functions from the R2018a
release, Coastal Risk MH uses three non-standard MATLAB functions. The components of each
script are included in Section 4.3.4.
Since the code below is a form of pseudocode, some functions (e.g. clear ind) and
precision arguments intended to limit the hardware demand were removed to increase the
pseudocode’s readability. References to the theoretical foundation are also included in the
commentary to each code segment. For more information related to the foundational theory, please
refer to Section 4.2 or specific reference in the adjacent commentary.
4.3.1. Primary “Run” Script
The MATLAB script, coastal_risk_mh_main.m, is the primary code a user would edit and
run within MATLAB. Here, an example case is presented for meteorological water levels. To
apply the model at a given location, a user would need to change the input variables and probability
distribution parameters to reflect local engineering needs (e.g. design life) and ocean dynamics
(e.g. astronomical tide distribution, seasonal water level distribution, etc.). The user would then
conduct the convergence analysis discussed in the introduction to this section before finalizing the
final model formulation.
Primary “Run” Script
Initialize script by clearing the workspace of variables and closing all open figure windows.
clear; close all
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Input Variables: Deterministic and Stochastic Parameterization –
The deterministic parameter design_life (units of integer years) defines the total number of
computational years Coastal Risk MH will analyze. This parameter should be consistent with the
number of years a project is expected to remain in service, starting from initial construction. This
parameter can typically be found within a design basis document for a coastal infrastructure
project.
design_life = 40
The deterministic parameter design_step (units of integer years) defines the temporal
resolution within Coastal Risk MH. Coastal Risk MH’s run time is strongly dependent on this
parameter. It is recommended that a new user start with a coarse design_step (e.g. 10 yr) and
then reduce the design_step to produce a convergent result as required for the project needs.
This parameter is used for indexing and must be an integer and must be evenly divisible into
design_life.
design_step = 10
The deterministic parameter yrStart (units of years) defines the calendar start date within
Coastal Risk MH.
yrStart = 2020
The deterministic parameter pile_ht (units of meters NAVD88) defines the reference pile
height elevation within Coastal Risk MH. The parameter is defined as a vector using MATLAB
syntax where the first and last number are the minimum (1.50) and maximum (5.50) pile
heights, respectively. The vertical resolution within Coastal Risk MH and size of the vector is
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controlled by the center number (0.5), separated by colons. (Note: This vector syntax is
commonplace withing MATLAB and will be used in other sections of the code.)
pile_ht = 1.50:0.5:5.50
The stochastic parameter n_mc1 (units of integer number) defines the number of realizations
used to define each hazard curve event.
n_mc1 = 2000
The stochastic parameter n_mc2 (units of integer number) defines the number of event time series
realizations.
n_mc2 = 2000
Input Probability Distributions: Oceanographic Parameterization –
The deterministic parameter tide_datum (units of meters NAVD88) is a reference datum
applied to each total water level estimate. The variable must convert the total water level datum to
be consistent with the pile height elevation datum.
tide_datum = 0.7925
The vector tide_x (units of meters mean sea level) defines the independent axis of the
astronomical tide cumulative density function. The cumulative density function is usually
estimated before running Coastal Risk MH by analyzing the astronomical components within a
water level record. (An approach to estimate the astronomical components within a water level
record will be presented in Section 4.4.1.)
tide_x = [-2.000 -1.500 -1.000 0.000 1.000 1.500 2.000]
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The vector tide_y (units of decimal percent) defines the dependent axis of the astronomical tide
cumulative density function. The vector should continuously increase from 0 to 1. The size of the
vector should correspond with tide_y.
tide_y = [0.000 0.001 0.027 0.503 0.987 0.995 1.000]
The vector SLanom_x (units of meters mean sea level) defines the independent axis of the
seasonal water level cumulative density function. The cumulative density function is usually
estimated before running Coastal Risk MH by analyzing the slowly varying component within a
water level record. (An approach to estimate the seasonal components within a water level record
will be discussed in Section 4.4.1.)
SLanom_x = ...
[-0.3000 -0.2000 -0.1000 0.0000 0.1000 0.2000 0.3000]
The vector SLanom_y (units of decimal percent) defines the dependent axis of the seasonal water
level cumulative density function. The vector should continuously increase from 0 to 1. The size
of the vector should correspond with SLanom_x.
SLanom_y = ...
[0.0000 0.0000 0.0207 0.6075 0.9700 0.9998 1.0000]
The vector return_periods (units of years) defines the independent axis of a hazard
recurrence.
return_periods = [75 100 150 250 500 750 1000]
The vector met_05_rp (units of meters) defines the 5% confidence interval (lower bound) of a
hazard recurrence. The size of the vector should correspond with return_periods. (A
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hazard’s mean and confidence bound are typically defined prior to running Coastal Risk MH using
a point over threshold approach. The method will be discussed in Section 4.4.1.)
met_05_rp = [0.07 0.08 0.08 0.09 0.10 0.12 0.12]
The vector met_mu_rp (units of meters) defines the hazard recurrence best-fit line. The size of
the vector should correspond with return_periods.
met_mu_rp = [0.15 0.16 0.17 0.19 0.21 0.23 0.24]
The vector met_95_rp (units of meters) defines the 95% confidence interval (upper bound) of a
hazard recurrence. The size of the vector should correspond with return_periods.
met_95_rp = [0.27 0.29 0.31 0.34 0.39 0.42 0.44]
The vector SLR_time (units of years) defines the independent time axis of the local mean sea
level projections. Here, the methodology of Kopp et al. (2014) and Sweet et al. (2017) is used to
define each sea level rise exceedance curve.
SLR_time = ...
[2000 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100]
The vector SLR_y (units of decimal percentage) defines the exceedance probability for each local
mean sea level rise projection.
SLR_y = [1,0.96,0.17,0.013,0.003,0.001]
The vector SLR_x(1,:) (units of meters) defines the water level exceedance curve for the 100%
exceedance sea level rise projection. The number of columns should correspond with the length of
SLR_time.
SLR_x(1,:) = ...
[0.00,0.02,0.05,0.08,0.12,0.16,0.19,0.22,0.25,0.28,0.30]
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The vector SLR_x(2,:) (units of meters) defines the water level exceedance curve for the 96%
exceedance sea level rise projection. The number of columns should correspond with the length of
SLR_time.
SLR_x(2,:) = ...
[0.00,0.02,0.07,0.10,0.15,0.20,0.25,0.30,0.35,0.40,0.44]
The vector SLR_x(3,:) (units of meters) defines the water level exceedance curve for the 17%
exceedance sea level rise projection. The number of columns should correspond with the length of
SLR_time.
SLR_x(3,:) = ...
[0.00,0.04,0.10,0.16,0.24,0.34,0.44,0.56,0.71,0.86,1.01]
The vector SLR_x(4,:) (units of meters) defines the water level exceedance curve for the 1.3%
exceedance sea level rise projection. The number of columns should correspond with the length of
SLR_time.
SLR_x(4,:) = ...
[0.00,0.06,0.12,0.20,0.33,0.50,0.67,0.88,1.12,1.38,1.71]
The vector SLR_x(5,:) (units of meters) defines the water level exceedance curve for the 0.3%
exceedance sea level rise projection. The number of columns should correspond with the length of
SLR_time.
SLR_x(5,:) = ...
[0.00,0.08,0.15,0.26,0.44,0.68,0.94,1.24,1.60,2.00,2.46]
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The vector SLR_x(6,:) (units of meters) defines the water level exceedance curve for the 0.1%
exceedance sea level rise projection. The number of columns should correspond with the length of
SLR_time.
SLR_x(6,:) = ...
[0.00,0.08,0.17,0.32,0.53,0.80,1.15,1.54,1.99,2.48,3.06]
Pre-Fit Sea Level Rise Trends –
Tabulated sea level rise data provided by Sweet et al. (2017) is coarse and can affect the sampling
scheme used within Coastal Risk MH. Therefore, a 1
st
order polynomial fit is estimated for each
sea level rise projection and used to define the correspond cumulative density function. This
approach helps to avoid the associated precision errors for near-term sea level rise projections.
for ni1 = 1:length(SLR_x)
Define time vector, t, for regression analysis.
t = transpose(SLR_time)
Define exceedance and water level vector, y, for regression analysis.
y = transpose(SLR_x(ni1,:))
Define sea level rise projection start date, SLR_to.
SLR_to = min(t)
Redefine time vector, t, for regression analysis using a new time datum.
t = t - SLR_to
Fit the function (of the form 𝐶𝐶 = 𝐷𝐷 𝐶𝐶 𝑥𝑥 ) to the sea level rise projections using built-in MATLAB
function fit.m.
cfit = fit(t,y,'power1')
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Export variables from 1
st
order power fit function to MATLAB workspace using built-in
MATLAB function coeffvalues.m.
coef = coeffvalues(cfit)
Save leading coefficient from 1
st
order power fit to new variable, SLR_a. The length of SLR_a
should correspond with the number of exceedance values in the sea level rise projection (defined
by SLR_y).
SLR_a(1,ni1) = coef(1)
Save power coefficient to new variable, SLR_b. The length of SLR_b should correspond with the
number of exceedance values in the sea level rise projection (defined by SLR_y).
SLR_b(1,ni1) = coef(2)
End of 1
st
order regression analysis.
end
Define Computation Start and End Date –
Define end date of the computation, yrEnd. This value should not exceed the maximum value of
SLR_time.
yrEnd = yrStart + design_life
Main Computation –
The main computation within Coastal Risk MH is a loop-based and scalar-oriented script wrapped
around a vectorized computational kernel. The stochastic event and hazard kernels are embedded
within three nested for loops. The outermost for loop provides the deterministic pile height
elevation parameter used to compare water levels elevations against pile height elevations during
the vulnerability analysis (see Eq. 4.7).
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for ni3 = 1:length(pile_ht)
The middle for loop characterizes the number of stochastic event time series realizations analyzed
within Coastal Risk MH. (The indexing used in this for loop corresponds to the index j in Eq. 4.4
that denotes the number of stochastic event time series realizations.)
for n_mc2i = 1:n_mc2
The inner most for loop characterizes the temporal length of each stochastic event time series.
(The indexing used in this for loop corresponds to the index i used in Eq. 4.4 to denote the number
of stochastic event time series realizations.)
for ni1 = design_step:design_step:design_life
Stochastic Event Realizations (See Section 4.2.2) –
Generates a vector of random return period realizations assuming a white-noise distribution. This
function corresponds to Eq. 4.4 and 4.5 and uses built-in MATLAB function rand.m.
rp1 = 1./(1 - rand(ni1,1))
Generate a vector of random date/time realizations assuming a white-noise distribution. This code
segment uses built-in MATLAB function rand.m.
date1 = rand(ni1,1)*ni1
Indexing to sort return period realization by their corresponding date/time. This code segment uses
built-in MATLAB function sort.m.
[~,ind] = sort(date1)
Sort date/times in ascending order using indexing from sort.m.
date1 = date1(ind)
Sort return period realizations according to corresponding date/time order.
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rp1 = rp1(ind)
Stochastic Hazard Estimate (Using Parallel MATLAB) –
This parfor loop isolates various parameters for the probabilistic hazard analysis. A parfor
loop is a parallelized MATLAB syntax of a standard for loop. If Coastal Risk MH is run on a
computer with only one CPU, MATLAB will default to using a standard for loop.
parfor ni2 = 1:length(date1)
Stochastic Hazard Estimate: Sea Level Rise Realization –
Center date/time datum according to the sea level rise calendar start date.
datei = yrStart + date1(ni2)
Estimate sea level rise cumulative density function for date/time realization using previous 1
st
order regression analysis results.
SLR_xi = SLR_a.*(datei-SLR_to).^SLR_b
Stochastic Hazard Estimate: Probabilistic Hazard Analysis Kernel –
This kernel function estimates the non-stationary probabilistic hazard curve for the set of scalar
and vector parameters. The probabilistic hazard analysis theory is described in Section 4.2.1 while
the corresponding MATLAB function will be presented in 4.3.2.
[return_periods1,hazard_curve1] = ...
hazard_curve_wl_slr(...
n_mc1, ...
return_periods, ...
tide_datum,...
tide_x, tide_y, ...
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SLanom_x, SLanom_y, ...
met_mu_rp, met_05_rp, met_95_rp,...
SLR_xi, SLR_y)
Stochastic Hazard Estimate: Probabilistic Hazard Estimate –
Linearly interpolate water level hazard curve with the scalar return period realization. Uses built-
in MATLAB function interp1.m. This line of code corresponds to Eq. 4.6.
WL(ni2) = ...
interp1(return_periods1,hazard_curve1,rp1(ni2))
End of stochastic hazard analysis parfor loop.
end
Vulnerability Estimate –
Flag if ANY of the water level realizations in the return period set exceed the deterministic pile
height elevation. Uses built-in MATLAB function find.m.
flag = find(WL > pile_ht(ni3))
If any of the water level realizations exceeded the deterministic pile height elevation. This line of
code corresponds to Eq. 4.7.
if isfinite(flag)
Save the vulnerability result as binary “true” representation. The failure probability as a function
of pile height elevation will be estimated using a post-processing script (See Section 4.3.3).
failure_count(n_mc2i,ni1) = 1
If none of the water level realizations exceeded the deterministic pile height elevation. This line of
code corresponds to Eq. 4.7.
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else
Save the vulnerability result as binary “false” representation. The failure probability as a function
of pile height elevation will be estimated using a post-processing script (See Section 4.3.3).
failure_count(n_mc2i,ni1) = 0
End of vulnerability estimate.
end
End of stochastic event realization indexing for loop.
end
End of stochastic event time series realizations for loop.
end
Save Model Data to MATLAB Binary –
Save model results to output file using a binary MATLAB format. Quantities that are saved
include:
• computation start date (yrStart)
• computation end date (yrEnd)
• failure count (failure_count)
• total number of stochastic event realizations (n_mc2)
save(['water_level_met_',sprintf('%02.0f',ni3),'.mat']),...
'yrStart','yrEnd','failure_count','n_mc2')
End of pile height elevation for loop.
end
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4.3.2. Hazard Curve Estimate
The kernel function, hazard_curve_wl_slr.m, estimates the probabilistic hazard curve for a
corresponding event return period realization (e.g. water level). The function is used by the primary
run script and must maintain the same file name for MATLAB to recognize it. Please refer to
Section 4.2.1 for the foundational probabilistic hazard curve theory.
hazard_curve_wl_slr.m
The probabilistic hazard curve function uses the following inputs from the main run script
(presented in Section 4.3.1):
• number of hazard curve realizations (n_mc2)
• return period vector (return_periods)
• tidal datum (tide_datum_rp)
• astronomical tide cumulative density function (tide_x/tide_y)
• seasonal water level cumulative density function (SLanom_x/SLanom_y)
• meteorological water level hazard curve with confidence bounds (met_mu_rp/
met_05_rp/met_95_rp)
• non-stationary sea level rise cumulative density function (SLR_xi/SLR_y)
And generates the following output quantities that are passed to main script:
• return period vector (return_periods_o)
• non-stationary hazard curve realization (hazard_curve_o)
function [return_periods_o, hazard_curve_o] = ...
hazard_curve_wl_slr(...
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n_mc2,...
return_periods,...
tide_datum_rp,...
tide_x,tide_y,...
SLanom_x,SLanom_y,...
met_mu_rp,met_05_rp,met_95_rp,...
SLR_xi,SLR_y)
Input Variables: Condition Data for Analysis –
Set number of realizations used in the stochastic hazard curve analysis.
N = n_mc2
Use return period inputs to generate finer return period grid for stochastic analysis.
rp_interp = ...
10.^[log10(min(return_periods)):0.02: ...
log10(max(return_periods))
This for loop steps through each interpolated return period preforming the stochastic hazard
curve analysis for each value. Uses built-in MALAB function length.m.
for i = 1:length(rp_interp)
Linearly interpolate best-fit hazard curve onto interpolated return period value. Uses built-in
MATLAB function interp1.m.
met_mu = ...
interp1(return_periods, met_mu_rp,rp_interp(i))
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Linearly interpolate 5% confidence (lower) bound onto interpolated return period value. Uses
built-in MATLAB function interp1.m.
met_05_rp = ...
interp1(return_periods, met_05_rp,rp_interp(i))
Linearly interpolate 95% confidence (upper) bound onto interpolated return period value. Uses
built-in MATLAB function interp1.m.
met_95_rp = ...
interp1(return_periods, met_95_rp,rp_interp(i))
Generate Random Realizations of Each Water Level Component –
Generate astronomical tide random realizations using astronomical tide cumulative density
function data. Uses non-standard MATLAB function random_cdf.m described in Section 4.3.4.
[tide_randvar] = random_cdf(tide_x,tide_y,N)
Generate seasonal water level random realizations using seasonal water level cumulative density
function data. Uses non-standard MATLAB function random_cdf.m described in Section 4.3.4.
[SLanom_randvar] = random_cdf(SLanom_x,SLanom_y,N)
Estimate meteorological water level standard deviation from the extreme value mean, 5% and 95%
confidence interval data. Uses non-standard MATLAB function generate_cdf.m described in
Section 4.3.4.
[~,~,met_dev] = ...
generate_CDF(met_mu_rp, met_05_rp, met_95_rp)
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Generate meteorological water level random realizations using Box–Muller Transform (Box &
Muller, 1958). Uses non-standard MATLAB function calc_randvar_BoxMuller.m described in
Section 4.3.4.
[surge_randvar] = ...
calc_randvar_BoxMuller(N,surge_mu,surge_dev)
Generate sea level rise random realizations using non-stationary sea level rise cumulative density
function data. Uses non-standard MATLAB function random_cdf.m described in Section 4.3.4.
[SLR_randvar] = random_cdf(SLR_xi,SLR_y,N)
Generate Stochastic Water Level Realization –
Calculate meteorological total water level realizations using Eq. 4.1.
water_level = ...
SLR_randvar + surge_randvar + SLanom_randvar + ...
tide_randvar
Estimate corresponding meteorological total water level hazard independent cumulative density
function.
rand_CDF = [0:1/N:1-1/N]
Estimate Water Level Confidence Interval –
Estimate meteorological water level exceedance curve using total water level realizations.
confidence_water_level(:,i) = sort(water_level)
End of stochastic hazard curve analysis using interpolated return period grid.
end
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Combined Individual CDFs into Single Matrix –
This for loop steps through each total water level curve and combines the dependent and
independent components of the cumulative density functions into a single matrix.
for i = 1:length(rp_interp)
Combined all total water level realizations into one matrix.
water_level_combined( (i-1)*N+2:i*N+1) = ...
confidence_water_level(:,i)'
Combined all cumulative density data into one single matrix and translate the result from the
cumulative density function into an exceedance curve.
CDF_combined( (i-1)*N+2:i*N+1) = ...
[rp_interp(i)./(1-rand_CDF)]
End of the for loop that combines dependent and independent components into a single matrix.
end
Combined cumulative density function data and total water level realizations into single matrix.
all_data = [CDF_combined water_level_combined]
Sort combined data in ascending order according to independent portion of the cumulative density
function.
all_data_sort = sortrows(all_data,1)
Estimate Hazard Curve from Return Period Analysis –
Use return period inputs to generate finer log-scale return period grid for hazard curve analysis.
Uses built-in MATLAB function min.m, log10.m and max.m.
recurrence_hazard_curve = ...
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10.^[log10(min(return_periods)/2):0.01: ...
log10(max(return_periods)*N/2)]
Precondition water level matrix for hazard curve analysis. Uses built-in MATLAB function
zeros.m.
water_level_hazard_curve = ...
zeros(length(recurrence_hazard_curve),1)
This for loop will step thorough the stochastic water level analysis and find upper and lower
bounds of the analysis used to estimate the resultant hazard curve. Uses built-in MATLAB function
length.m.
for i = 1:length(recurrence_hazard_curve)
Find lower bound from return period analysis. Uses standard MATLAB function find.m.
ilow = ...
find(all_data_sort(:,1) > ...
recurrence_hazard_curve( ...
max(i-1,1)),1)
Find upper bound from return period analysis. Uses standard MATLAB function find.m.
ihigh = ...
find(all_data_sort(:,1) > ...
recurrence_hazard_curve( ...
min(i+1,length(recurrence_hazard_curve))),1)
Find maximum envelope of the realizations used to define the hazard curve. Uses standard
MATLAB function max.m.
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water_level_hazard_curve(i) = ...
max(all_data_sort(ilow:ihigh,2))
End of hazard curve analysis.
end
Export Variables –
Linearly interpolate total water level hazard curve onto coarser input return period vector.
recurrence_hazard_curve_rp = ...
interp1(recurrence_hazard_curve*.5, ...
water_level_hazard_curve,retu rn_periods)
Define output return period vector. (In this case the same as the input.)
return_periods_o = return_periods
Define output hazard curve vector and transform datum from mean sea level to reference datum.
(In this case the reference datum is NAVD88.)
hazard_curve_o = recurrence_hazard_curve_rp + tide_datum_rp
4.3.3. Post-Processing Script
Once all the water level hazard and vulnerability scripts have finished, the final step is to
estimate the single and multi-hazard infrastructure risk for the given location. This post-processing
script outlines a basic method to load, post-process, and view meteorological water level results.
For other hazards like tsunamis or seiche modes, this script can be expanded to include those
additional terms. Users can copy and paste existing portions of this code and update variable names
to reflect the other relevant hazards.
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Post-Process Model Data
Initialize script by clearing the workspace of variables and closing all open figure windows.
clear; close all
Model Parameters -
The deterministic parameter yrStart (units of years) defines the calendar start date within
Coastal Risk MH. This parameter value should be consistent with the same yrStart value
defined in Section 4.3.1.
yrStart = 2020
The deterministic input parameter design_life (units of integer years) defines the total
number of computational years Coastal Risk MH analyzed. This parameter value should be
consistent with the same design_life value defined in Section 4.3.1.
design_life = 40
The deterministic input parameter design_step (units of integer years) defines the temporal
resolution within Coastal Risk MH. This parameter value should be consistent with the same
variable design_step value defined in Section 4.3.1.
design_step = 10
The deterministic input vector pile_ht (units of meters NAVD88) defines the reference pile
height elevations within Coastal Risk MH. This vector should be consistent with the same variable
pile_ht defined in Section 4.3.1.
pile_ht = 1.50:0.5:5.5
Define calendar years using input data.
design_yr = yrStart + (design_step:design_step:design_life)
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Load Model Results –
Point to folder where model results are located.
path1 = 'model_results'
Find file names of all meteorological water level results found in located folder. Uses built-in
MATLAB functions dir.m and fullfile.m.
filei = dir(fullfile(path1,'*water_level_met_*'))
The for loop steps though each meteorological total water level result and loads the model data
from each .mat file. Uses built-in MATLAB function length.m.
for ni1 = 1:length(filei)
Load data from each .mat file located in path1. Uses built-in MATLAB functions load.m and
fullfile.m.
datai = load(fullfile(path1, filei(ni1).name))
Converts data from tally of failure counts to failure percentage. Uses built-in MATLAB function
sum.m.
failure_prc_ met(ni1,:) = ...
100*sum(datai.failure_count,1)/datai.n_mc2
End the for loop after loading each meteorological total water level result.
end
Remove Indices from Model Data –
Find indices with valid model data.
ind = design_step:design_step:size(failure_prc_swl,2)
Remove unused indices from model data.
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failure_prc_swl = failure_prc_swl(:,ind)
Plot Model Data –
Convert design_yr and pile_ht vectors into matrices used in the plotting syntax. The code
segment uses built-in MATLAB function meshgrid.m.
[design_yr_grd,pile_ht_grd] = meshgrid(design_yr,pile_ht)
Open new figure window. The code segment uses built-in MATLAB function figure.m
fig = figure
Plot raw model results using default parameters. Uses bult-in MATLAB function imagesc.m.
imagesc(design_yr_grd(:),pile_ht_grd(:),failure_prc_swl)
Adjust plot axis according to a Cartesian orientation. Uses built-in MATLAB function axis.m.
axis xy
Plot label along the x axis. Uses built-in MATLAB function xlabel.m.
xlabel('Design Year (yr)')
Plot label along the y axis. Uses built-in MATLAB function ylabel.m.
ylabel('Pile Height (m NAVD88)')
4.3.4. Non-Standard MATLAB Functions
In addition to the three MATLAB scripts outlined above and the standard MATLAB
functions from the R2018a release, Coastal Risk MH includes three non-standard MATLAB
functions. These three functions are named: random_cdf.m, generate_cdf.m and
calc_randvar_BoxMuller.m.
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random_cdf.m
The probabilistic hazard curve function (see Section 4.3.2) uses the following code (named
random_cdf.m) to generate realizations of various input parameters. The function uses the
following input quantities:
• dependent variable of CDF (x)
• independent variable of CDF (y)
• number of realizations (N)
The function generates the following output quantities that are passed to main function:
• random realizations (xi)
function xi = random_cdf(x,y,N)
Input Variables: Condition Data for Interpolation -
Threshold to define the precision error.
thresh = 1e-4
Find cumulative density function above and below threshold value. Preconditions data for
interpolation.
ind = find(y > thresh & y < (1-thresh))
Remove values from independent portion of cumulative density function that fall outside threshold
values. Uses built-in MATLAB function find.m.
x = x(ind)
Remove values from dependent portion of cumulative density function that fall outside threshold
values.
y = y(ind)
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Find values within independent portion of cumulative density function that may be repeated.
Preconditions data for interpolation.
[~,ind,~] = unique(x)
Remove values from independent portion of cumulative density function that are repeated.
x = x(ind)
Remove values from dependent portion of cumulative density function that are repeated.
y = y(ind)
Main Computation: Generate Random Realization Based Upon Input –
Generate N random realizations between 0 and 1. Uses built-in MATLAB function rand.m.
yi = rand(N,1)
Use linearly interpolation to find corresponding independent cumulative density function values.
Uses built-in MATLAB function interp1.m.
xi = interp1(y,x,yi)
generate_cdf.m
The probabilistic hazard curve function (see Section 4.3.2) uses the following code (named
generate_cdf.m) to estimate a distribution’s standard deviation from non-exceedance values. The
function uses the following input quantities:
• the mean value of the variable (mu)
• the variable value at the lower confidence level of 5% (nonexceed_x_05)
• the variable value at the lower confidence level of 95% (nonexceed_x_95)
The function generates the following output quantities that are passed to main function:
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• the standard deviation of the distribution (dev)
function [~,~,dev] = ...
generate_CDF(mu,nonexceed_x_05,nonexceed_x_95)
Estimate standard deviation from 5% non-exceedance.
dev_05 = ((nonexceed_x_05-mu)/sqrt(2))/erfinv((0.05-.5)/.5)
Estimate standard deviation from 95% non-exceedance
dev_95 = ((nonexceed_x_95-mu)/sqrt(2))/erfinv((0.95-.5)/.5)
Estimates mean standard deviation from the 5% and 95% estimates.
dev = (dev_05+dev_95)/2
calc_randvar_BoxMuller.m
function [randvar] = calc_randvar_BoxMuller(N,mu,dev)
The probabilistic hazard curve function (see Section 4.3.2) uses the following code (named
calc_randvar_BoxMuller.m) to estimate N number of random variables using a Box-Mueller
Transform (Box & Muller, 1958). This function uses the following input quantities:
• number of random samples (N)
• mean of distribution (mu)
• standard deviation of distribution (dev)
The function generates the following output quantities that are passed to main function:
• random sample of N numbers (randvar)
Estimate Box-Muller Parameters –
If u(1,:) and u(2,:) are pairs of random variables between 0 and 1.
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u = rand(2,N/2)
Then the polar representation of these random is defined as,
r = sqrt(-2*log(u(1,:)))
And theta.
theta = 2*pi*u(2,:)
The Box-Muller Transformation creates new independent, random variables with a standard
normal distribution described by X,
X = r.*cos(theta)
And Y in Cartesian coordinates.
Y = r.*sin(theta)
Output: Scale to Target Distribution –
The property of unit variance can scale the results to fit the target distribution.
randvar = ([X ,Y])*(dev)+mu
4.4. Case Study: Ventura Harbor, California, USA
Ventura Harbor is a private, recreational, and commercial harbor located within Ventura
County, California, USA (see Figure 4.7). Ventura Harbor contains two basins: East Basin and
West Basin. Three operating companies manage most recreational slips in East Basin. The
National Park Service (NPS) also operates vessels from a dock located at the harbor entrance. The
West Basin is a collection of privately owned docks attached to private homes. The system of
canals that connects the residents’ docks to the Ventura Harbor entrance channel is visible in
Figure 4.7 (a) near the top of the image.
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Ventura Harbor is an ideal location to study how sea level rise projections and uncertainty
may influence the future oceanographic hazard, ultimately shifting coastal infrastructures’ risk
profile. While Ventura Harbor has historically seen little damage from tsunami events (Wilson et
al., 2012, 2013), during significant tidal events, some of the docks in the East Basin can float to
within 0.5 m of the tops of the dock piles. With the possibility of 0.5 m of sea level rise by 2050
(Kopp et al., 2014), local government and harbor administrators have become increasingly
concerned with the harbor’s changing risk profile. Administrators are troubled by the temporal and
monetary constraints required to mitigate against future dock failure and are looking for technical
guidance to help with planning purposes.
Figure 4.7: (a) The area map shows the location (green) of Ventura Harbor within the California Bight. The location
of the water level, tsunami, and wave gauges are shown above. [Aerial orthometric imagery downloaded from U.S.
Geological Survey (2018).] (b) Aerial images show the location of East and West Basin within Ventura Harbor [Base
map produced with Pawlowicz (2020) and National Geophysical Data Center (2006)].
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4.4.1. Historical Data
Water level data provided by the National Oceanic and Atmospheric Administration
(NOAA) was analyzed from Station 9410840 – Santa Monica. The location of Station 9410840 is
shown in Figure 4.7 (b), approximately 75 km to the southeast of Ventura Harbor. The Santa
Monica tidal station was selected for the case study because of the station’s proximity to Ventura
Harbor. The high-quality data record contains nearly 35 years of 1-min water level data and
minimal data loss (<15% missing).
Water level records along the United States West Coast contain water levels generated
from multiple processes that vary in temporal scale and magnitude. Shorter scale processes, like
high-order tidal harmonics, occur on time scales of a few hours. Tidal harmonics comprise
approximately 80% of the water level variance in Santa Monica. Seasonal processes, like the
ENSO cycle, occur over time scales of weeks to months. A tide gauge can include seiche motions
since many tide gauges are located within harbors. However, the analysis suggests that the
construction of the tide gauge acts as a stilling basin for seiche time scales. We, therefore, selected
to characterize the seiche hazard using a numerical model (to be discussed in the next section)
instead of using the historical water level record.
For the analysis, the water level record can be separated into three components:
astronomical tide, seasonal water level variability, and meteorological water level. Astronomical
tide (Figure 4.8 [a]) was estimated by regressing 156 known tidal constituents onto the tidal record
via a least-squares regression. A 14-day low-pass filter of the residual water levels identified the
seasonal water level component within the broader tide gauge time series.
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The metrological water level (see Figure 4.8 [e]) hazard curve was derived using data from
the residual water level record with the astronomical and seasonal water level removed. With 35
years of data, a point-over-threshold analysis fits a Weibull distribution to the residual data using
the methodology outlined by Goda (2000). Historical and future sea level rise (see Figure 4.8 [c])
is quantified via the methodology outlined by Kopp et al. (2014) and Sweet et al. (2017) for the
Santa Monica tide gauge.
Figure 4.8: Water level constituents used to construct the future water level hazard for Ventura Harbor: (a)
astronomical water level, (b) seasonal water level, (c) future sea level rise trends (Kopp et al., 2014; Sweet et al.,
2017), (d) tsunami amplitudes (Thio et al., 2017), (e) metrological and seiche generated mean water level and (f)
seiche generated crest elevation (for Zones 1 and Zone 7 from Figure 4.9). (c-f) Solid lines indicate the best-fit trend;
dashed lines represent 10% and 90% confidence intervals.
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4.4.2. Numerical Modeling Data
Harbor seiches are a specific type of seiche motion that occurs in partially enclosed basins
(i.e. small craft marina), connected through one or more openings to the sea (Rabinovich, 2009).
The resonant amplitudes and periods of seiches are strongly dependent upon basin geometry and
depth, typically showing substantial spatial variability in natural basins. Spatial components of
harbor seiche modes within Ventura Harbor are resolved using the Boussinesq wave model known
as Celeris (Tavakkol, 2019; Tavakkol & Lynett, 2017, 2020). The Boussinesq model solves the
extended Boussinesq equations with a hybrid finite volume–finite difference method that resolves
the moving shoreline boundaries. Celeris performs the simulations and visualizations on the
graphics processing unit (GPU) with Direct3D libraries that enable the model to run faster than
real-time. Celeris provides a first-of-its-kind interactive modeling platform for coastal wave
applications and supports simultaneous visualization with both photorealistic and colormap
rendering capabilities. Please refer the reader to Tavakkol and Lynett (2017) and Tavakkol (2019)
for more info on the Celeris foundation as well as validation.
Celeris runs differently than most Boussinesq wave models. The data and memory
requirements of running a Boussinesq-type model on a GPU limit the model’s ability to efficiently
write output data to disk. To avoid extreme computational costs associated with writing data, seven
representative points within Ventura Harbor were selected to analyze the spatial variability of the
seiche modes. The representative zones for each extraction point are shown in Figure 4.9. Each of
the seven points within the harbor was selected to characterize the expected maximum and
minimum seiche amplitudes within the harbor. Each of the points are located ~10 meters away
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from the harbor boundaries to limit the influence of runup and rundown (swash) effects on the
recorded time series.
Figure 4.9: Numerical modeling extraction zones for Ventura Harbor seiche analysis. Zone 1 and Zone 7 (magenta)
represent the upper and lower bounds of the multi-hazard analysis.
Model bathymetry and topography data for Ventura Harbor were taken from bathymetry
grids available in the public domain, initially developed for tsunami modeling by NOAA’s
National Centers for Environmental Information (NCEI). Directional wave data was available
from the National Buoy Data Center (NDBC) Station 46217 for the period from 2011 to 2020. The
location of the wave buoy is shown in Figure 4.7 (b). Linear shoaling and refraction theory
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transformed the wave climate from the wave buoy to the offshore (~10 m contour) model
boundary. The wave climate time series at the model boundary was then analyzed and used to
construct as the offshore boundary condition for the Celeris harbor modeling. Representative bulk
parameters were wave height (0.5 – 5.5 m), peak wave period (7.5 – 20 sec), and peak wave
direction (-15
o
deg to 15
o
) within the wave record.
Celeris model data was saved at each of the seven time-series output locations once the
model reached a dynamic steady state. Approximately 2.5 hours of data, exported at 1 Hz was
post-processed. Celeris modeling results was decomposed into main components: a mean water
level (i.e. wave setup) and a dynamic water level component (i.e. seiche crest elevation). Model
results show wave setup is spatially homogeneous in Ventura Harbor. An up-crossing analysis
defined each seiche wave, and for the water level analysis, the component above the mean water
level (i.e. crest elevation) was used. Seiche periods within the harbor ranged from 1-15 min. The
mean water level increase and crest elevation (90% exceedance) hazard curves are shown in Figure
4.8. Zone 1 and Zone 7 represent the upper and lower bounds of seiche modes within the harbor.
4.4.3. Results and Discussion
Coastal Risk MH was run in Ventura Harbor for each hazard: meteorological, tsunami and
seiche generated water levels. Sea level rise was also included as a non-stationary datum to
characterize the sea level rise’s long-term stress on each hazard. The model was started in the year
2020 and allowed to run for 40 years. The first 10 years is an approximation for the total amount
of time it would take harbor administration to procure and construct mitigation measures.
Representative mitigation measures increase the service life of a harbor for 30 years (or 40 years
total).
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Once the time horizon is selected, the first step in the modeling procedure is to understand
the variability of the modeling inputs and results as a function of statistical resolution. The
stochastic nature of the multi-hazard model implies results may not be predicted precisely but can
be understood statistically in terms of a “best-estimate” with an associated confidence limit. Before
running a final model in Ventura Harbor, a convergence analysis was conducted to understand this
statistical variability of the model results. (While the total number of realizations is theoretically
infinite, eventually converging to an “exact solution”, practical limits are set by available
computing resources.) Realizations for each hazard curve were tested for 1000, 2000, 2500, and
5000 iterations along with the same number for total water level time series. The pile reference
height vertical resolutions of 0.05 m, 0.01 m, and 0.20 m were also analyzed. Ultimately, the total
number of realizations for each hazard curve (z
i
) and total water level time series (Z
j
) was set to
be 2000 with a vertical pile height resolution of 0.05 m. Convergence analysis indicates that this
configuration results in approximately a 0.5% error in results.
Individual and multi-hazard risk results for Zone 1 in Ventura Harbor are presented in
Table 4.1 and Figure 4.10. Figure 4.10 (a-d) illustrates individual hazard failure probabilities for
sea level rise, meteorological, tsunami, and harbor seiche total water levels, respectively. Each
subplot includes 2%, 5%, 10%, and 50% annual failure probability curves and color shading. The
5% failure probabilities for individual and multi-hazard failure probabilities are shown in Figure
4.10 (e). The multi-hazard estimate is comprised of the meteorological, tsunami, and seiche based
individual water levels (from Eq. 4.5). It is reiterated here that sea level rise is included in each
hazard as a non-stationary datum offset, not as an additional component to the multi-hazard
estimate.
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Table 4.1: Individual and multi-hazard failure probabilities (by zone) for design years 2025 and 2060. Values given
are the necessary pile heights (m) to provide the specified design-life failure probability (2%, 5%, 10%).
Zone 1
Zone 7
Design Horizon 2025 2060 2025 2060
2% Failure Probability
Meteorological 2.47 2.94 2.47 2.94
Tsunami 2.25 2.80 2.25 2.80
Seiche 2.68 3.14 2.49 3.00
Multi-Hazard 2.70 3.17 2.54 3.04
5% Failure Probability
Meteorological 2.39 2.88 2.39 2.88
Tsunami 2.23 2.74 2.23 2.74
Seiche 2.61 3.09 2.44 2.93
Multi-Hazard 2.61 3.09 2.49 2.98
10% Failure Probability
Meteorological 2.30 2.80 2.30 2.80
Tsunami 2.20 2.69 2.20 2.69
Seiche 2.50 3.02 2.39 2.87
Multi-Hazard 2.52 3.02 2.42 2.92
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Figure 4.10: Single and multi-hazard-based failure probabilities for Ventura Harbor in Zone 1: (a) sea level rise, (b)
meteorological water level, and sea level rise, (c) tsunami and sea level rise, (d) seiche and sea level rise and (e) 5%
single and multi-hazard failure chance over the design life.
Individual hazard results in Zone 1 (see Table 4.1 and Figure 4.10) illustrate that the lowest
induvial hazard risk coincides with tsunami-based risk. The results suggest that the minimum pile
height needed to obtain a 5% design-life failure probability from tsunami hazards in 2025 is about
2.23 m NAVD88. This value increases to 2.74 m NAVD88 in 2060 for the equivalent 5% failure
probability. The most substantial individual hazard risk stems from harbor seiche within Ventura
Harbor. The results indicate that the minimum pile height needed to obtain a 5% probability of
failure from harbor seiche hazards in 2025 is about 2.61 m NAVD88 and 3.09 m NAVD88 in
2060.
Two main processes produce the offset between the individual tsunami and seiche total
water levels. Lower return period events dominate failure curves for short time horizons (2020-
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2025). Even though the one-thousand-year return period event is higher for tsunamis than for
seiche hazards, the early flattening (< 100-yr return period) of the tsunami hazard curve versus the
seiche curves drives down the failure probabilities. For the longer time horizon (2020-2060), larger
return period realization naturally bounds the failure probability curves. Along with sea level rise,
these more significant realizations increase the minimum pile height needed to obtain a 5% failure
probability for both tsunami and seiche hazards.
The multi-hazard result indicates that harbor seiche motions comprise most of the hazard
risk in Ventura Harbor for Zone 1. The results reveal that the minimum pile height needed to obtain
a 5% probability of failure from all hazards in 2025 is 2.61 m NAVD88. In 2060 the number
increases to 3.09 m NAVD88. A comparison between seiche and multi-hazard total water levels
in Figure 4.10 (f) illustrates that two trends are nearly identical. (Meteorological and tsunami
contribute little to the multi-hazard estimate in Zone 1.) While at first glance, this may seem
counter-intuitive, it is essential to remember that meteorological, tsunami, and seiche total water
levels are assumed statistically independent. The multi-hazard estimate was modeled by
combining the individual hazards in probability space.
Our results are consistent with the discussions with harbor staff in Ventura Harbor. The
existing hazard that the harbor staff perceives to floating docks within Ventura Harbor is the result
of a large spring tide and a significant wave event that “pushes” the wave setup into the harbor (J.
Higgins, personal communication, January 24, 2018). The harbormaster has indicated that floating
docks near the entrance are typically the first to creep near the tops of the piles. Docks in Zone 1
interact with the most significant amount of energy from the incoming waves. Celeris modeling
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results show docks are likely influenced by a combination of short wave swell that seeps into the
harbor and the seiche modes generated from this forcing.
Individual results for meteorological and tsunami failure probabilities in Zone 7 are the
same as Zone 1. Seiche motions, principally the dynamic crest elevation component, vary spatially
within the harbor. Model results for Zone 7 (see Table 4.1 and Figure 4.11) indicate the 5%
probability of failure from seiche motions is 2.44 m in 2025, increasing to 2.93 m in 2060 along
an equivalent failure probability contour. (As opposed to 2.61 m in 2025 and 3.09 in 2060 for Zone
1.) The increase from Zone 1 to Zone 7 can be attributed to the difference in crest elevations
between the two zones (see Figure 4.8). Unlike the multi-hazard result from Zone 1, there is a
noticeable offset between the seiche and multi-hazard curves. The balances shift throughout
Ventura Harbor with meteorological water levels becoming increasingly important (relative to the
dominant seiche hazard in Zone 1) towards the back of the harbor.
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Figure 4.11: Single and multi-hazard-based failure probabilities for Ventura Harbor in Zone 7: (a) sea level rise, (b)
meteorological water level, and sea level rise, (c) tsunami and sea level rise, (d) seiche and sea level rise and (e) 5%
single and multi-hazard failure. (Zone 1 multi-hazard result added for reference.)
The multi-hazard estimates from Zone 1 and Zone 7 in 2060 are 3.09 m NAVD88 and 2.98
m NAVD88, respectively. Although there is only an 11 cm difference between 5% failure
probability for Zone 1 and 7, this result can be used by policy makers for planning purposes. By
comparing the two hazard curves, it can be can shown that Zone 1 is approximately ten years ahead
of Zone 7 in terms of the minimum pile height required to prevent 5% failure (meaning that piles
of a given height will fail in Zone 1 before they fail in Zone 7). Although numerical results like
ours only inform part of the mitigation planning, the elevation difference between Zone 1 and 7
suggests that policy makers can stage mitigation and resilience measures, focusing first in Zone 1
before moving towards the back of the harbor.
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4.5. Conclusion
Mitigation and resilience strategies enacted in response to increasing coastal flooding
dictate how events impact our communities. Capturing future hazards, vulnerability, and
infrastructure risk with sound and unbiased science provides the foundation for the decision-
making process. This chapter presents a new methodology for multi-hazard risk analysis. The
model utilized established probabilistic hazard analysis methods (Geist & Lynett, 2014; Geist &
Parsons, 2006) and annual maxima extreme value theory (Coles, 2001; Goda, 2000) to quantify
the future hazards. Non-stationarity sea level rise is included in the framework utilizing the
methodology outlined by Kopp et al. (2014) and Sweet et al. (2017).
The stochastic model was applied to Ventura Harbor to quantify meteorological, tsunami
and seiche projected total water level risk from 2020 to 2060. Each hazard was assumed to be
statistically independent, which allows the individual hazard results to be combined in statistical
space resulting in the multi-hazard total water level. Existing and future total water levels in
Ventura were compared against deterministic pile heights (a proxy for coastal infrastructure
flooding) to assess the harbor’s floating dock vulnerability and failure risk. Results for 2%, 5%,
and 10% design-life failure probabilities were estimated but the discussion in this chapter is on the
5% failure probability as the representative contour.
The results suggest that the minimum pile height needed to obtain a 5% probability of
failure from all hazards in 2025 is about 2.61 m NAVD88 and increases to 3.09 m NAVD88 for
Zone 1. Stochastic model results indicate that elevations are slightly less for Zone 7. The minimum
pile height needed to obtain a 5% probability of failure from all hazards for Zone 7 in 2025 is 2.49
m NAVD88 and increases to 2.89 m NAVD88 in 2060. Although numerical results only inform
127
part of the mitigation cycle, these results imply that policy makers can stage mitigation and
resilience measures to help alleviate the financial burden. Zone 1 is approximately ten years ahead
of Zone 7 in terms of the minimum pile height required to prevent 5% failure.
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CHAPTER 5. CONCLUSIONS
For researchers, small craft harbors are a microcosm of the communities that surround
them. Harbors offer a “playground” to understand future coastal infrastructure risk within a
societal system. Traditionally, tsunamis and coastal storm events have posed the greatest risk to
small craft harbors in California. As sea levels start to rise and storm patterns change, small craft
harbors will be forced to look at a suite of scenarios and assess their risk portfolio (with the help
of federal, state, and local entities). This dissertation quantifies the future risk to small craft harbors
and to provides decision makers with a methodology/platform upon which they can make well
informed and often difficult decisions regarding how best to address climate risk.
In Chapter 2, an assessment tool that can be used to quantify the tsunami hazard to small
craft harbors is outlined. The methodology was based on the demand-to-capacity ratio of a floating
dock system. Structural characteristics were incorporated deterministically, while natural
uncertainties (of the inputs) were largely constrained using the Monte-Carlo approach. Detailed
numerical modeling and damage calibration data from recent tsunamis in Santa Cruz Harbor
benchmarked the approach. The results of the analysis highlight the skill of the stochastic
technique to predict tsunami damage within a small craft harbor. When coupled with a damage
129
report, the method was able to predict the grouping of areas of high, medium, and low damage as
well as differentiate between underlying structural capacities in different areas of the same harbor.
Chapter 3 presents a risk framework that could be used by harbor maintenance and decision
makers to assess future tsunami risks to small craft harbors. The methodology is based on the
demand-to-capacity ratio of a floating dock system from Chapter 2. Empirically derived
probabilistic quantities are used to characterize the uncertainty of the capacity. Observations from
an extensive field campaign are used that included a survey of damage states within twelve
California harbors. The campaign investigated failure modes, and damage state (representative of
the infrastructure aging process) that allows engineers to derive these capacity estimates
empirically.
When applied to a small craft marina, Noyo River, the method was able to characterize the
historically observed damage in the harbor from the 2011 tsunami event with little calibration.
Although the tsunami-generated currents in Noyo River were small, relative to many other marinas
in California, the method reasonably characterized the vulnerability of the harbor and the resultant
risk. Additionally, this result suggests that the 1.5 m/s damage initiation threshold and 4.5 m/s
failure threshold (Lynett et al., 2014) may not be appropriate for some harbors. The balance
between event hazard and infrastructure vulnerability ultimately contributed to any harbor’s risk.
The last chapter (Chapter 4) aimed to present a new methodology for multi-hazard risk
analysis to coastal infrastructure. The model utilized published probabilistic hazard analysis
methods (Geist & Lynett, 2014; Geist & Parsons, 2006) and annual maxima extreme value theory
(Coles, 2001; Goda, 2000) to quantify the future hazards. Non-stationarity sea level rise is included
in the framework utilizing the methodology outlined by Kopp et al. (2014) and Sweet et al. (2017).
130
In an illustrative example, the stochastic model was applied to the floating docks in Ventura
Harbor. The model was used to quantify meteorological, tsunami, and seiche projected total water
level risk from 2020 to 2060. Existing and future total water levels in Ventura are compared against
deterministic pile heights (a proxy for coastal infrastructure flooding) to assess the harbor’s
floating dock vulnerability and failure risk and show results for 2%, 5%, and 10% design-life
failure probabilities. The discussion focused on the representative 5% failure probability. The
results suggest that harbor seiche is the primary hazard to Ventura Harbor. Sea level rise will likely
act as a long-term stressor to increase the infrastructure risk to Ventura Harbor and other California
small craft harbors.
The Coastal Risk MH result showed some spatial variability within Ventura. Near the
entrance of the harbor where swell and seiche mix, the minimum pile height needed to obtain a
5% design life probability of failure from all hazards in 2025 is about 2.61 m NAVD88. This
minimum pile height increases to 3.09 m NAVD88 in 2060. Stochastic model results indicate that
elevations decrease slightly towards the back of the harbor. The minimum pile height needed to
obtain a 5% probability of failure from all hazards for Zone 7 in 2025 is 2.49 m NAVD88 and
increases to 2.89 m NAVD88 in 2060. Although numerical results only inform part of the
mitigation cycle, these results imply that policy makers can stage mitigation and resilience
measures to help alleviate the financial burden.
5.1. Recommendations for Future Work
There are several opportunities for this dissertation to be picked up and for the research to
carried forward. I would first recommend the theory in Chapter 2 and 3 be validated for small craft
131
harbors outside California. The State of California is 1240 km long, bounded by Oregon in the
north and Mexico along the southern border. An incredible amount of cultural and socioeconomic
variability exists within the state. I observed during harbor site visits that the infrastructure
supporting small craft harbor service was often a mirror of the local community. Wealthier areas
were able to charge higher slip fees to support a maintenance program. These dockmasters often
opt to replace sections of floating dock instead of servicing major components. Harbors in less
well-to-do areas struggled to keep pace with basic dock maintenance.
While I have been able to apply the methodologies to 12 different harbors in California,
representing a wide range of conditions, I have not moved beyond political boundaries. Tele-
tsunamis are basin phenomenon. The Western States of Oregon, Washington, Alaska, and Hawaii
are all vulnerable to tele-tsunamis like California. The physics-based approach that I incorporated
into the model foundation in Chapter 2 and 3 is flexible. The framework should be generalizable
to harbors in the other Western States, but further application and validation are recommended.
Like the risk model outlined in Chapter 3, I would suggest that the multi-hazard framework
(Chapter 4) is applied and validated to harbors outside of Southern California. The oceanographic
climate is dynamic. I expect the geophysical balances between meteorological, tsunami, harbor
seiche, and sea level rise to differ geographically. Tsunami model results presented by Thio et al.
(2017) for California, for instance, indicate that the offshore tsunami surface elevation hazard
should intensify with increasing latitude. I expect resonance processes will also differ for each
harbor because of differences in the external wave climate and the harbor basin geometry.
With modifications, the multi-hazard model could also be implemented in harbors along
the U.S. East Coast. Tsunami risks in the Eastern States of Louisiana, Mississippi, Alabama,
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Florida, and Georgia are small. However, the meteorological surge and wave climate associated
with hurricanes in the Atlantic can generate meteorological water levels an order of magnitude
larger than those recorded on the West Coast. The multi-hazard model should capture the
corresponding geophysical variance between meteorological, tsunami, harbor seiche, and sea level
rise on each coast. Comparisons at larger geophysical scales are incredibly important. They help
policy makers at the federal level appropriate money and resources to help facilitate our
anthropogenic response to sea level rise. These comparisons are lacking within the science
community but will become increasingly important in the coming decades.
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Abstract (if available)
Abstract
We live in a changing climate. As global average temperatures increase, ice caps melt, and sea levels rise. Increasing sea levels remain the most direct and likely future hazard to infrastructure from the changing climate. The primary objective of this dissertation is to assist in the infrastructure planning process by providing methodologies that quantify the natural hazard risk of small craft harbors. Hopefully, this dissertation provides decision makers with a methodology/platform upon which they can make informed and often difficult decisions about how best to respond to climate risk. Here, physics-based approaches are used to assess the risk of small craft harbors quantitatively. When a process is beyond a physical understanding, semi-empirical approaches are used that rely on correlations between observed damage and quantitative properties. The dissertation should serve as a step forward in the research community's understanding of multi-hazard risk assessment at the community level.
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Creator
Keen, Adam Steven
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Core Title
Stochastic multi-hazard risk analysis of coastal infrastructure
School
Viterbi School of Engineering
Degree
Doctor of Philosophy
Degree Program
Civil Engineering
Publication Date
09/15/2020
Defense Date
12/14/2020
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coastal infrastructure,multi-hazard risk,OAI-PMH Harvest,sea level rise,small craft harbors,storm surge,tsunamis
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Tags
coastal infrastructure
multi-hazard risk
sea level rise
small craft harbors
storm surge
tsunamis