A model for emergency logistical resource requirements: supporting socially vulnerable populations affected by the (M) 7.8 San Andreas earthquake scenario in Los Angeles County, California

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A Model for Emergency Logistical Resource Requirements:
Supporting Socially Vulnerable Populations Affected by the (M) 7.8 San Andreas Earthquake Scenario in
Los Angeles County, California

by

Joseph Charles Toland

A Thesis Presented to the
Faculty of the USC Graduate School
University of Southern California
In Partial Fulfillment of the
Requirements for the Degree
Master of Science
(Geographic Information Science and Technology)

December 2018

Copyright © 2018 by Joseph Charles Toland

To my brother, John. Ditto…

iv

Table of Contents
List of Figures ............................................................................................................................... vii
List of Tables .................................................................................................................................. ix
Acknowledgments ........................................................................................................................... x
List of Abbreviations ...................................................................................................................... xi
Abstract ........................................................................................................................................ xiv
Chapter 1 Introduction ..................................................................................................................... 1
1.1. Motivation .......................................................................................................................... 2
1.2. Thesis Organization and Research Objectives ................................................................... 4
Development of a Probabilistic Risk Model for Emergency Resource 1.2.1.
Requirements ............................................................................................................... 6
Applications of the Probabilistic Risk Model ........................................................... 9 1.2.2.
Chapter 2 Emergency Management, Response Operations and Emergency Relief Logistics ...... 12
2.1. Emergency Management Overview ................................................................................. 12
Emergency Relief Logistics and the Commodity Mission ...................................... 15 2.1.1.
2.2. The (M) 7.8 San Andreas Earthquake Scenario and OPLAN .......................................... 19
The Great California ShakeOut Scenario ................................................................ 19 2.2.1.
The Southern California Catastrophic Response Operational Plan (OPLAN) ........ 23 2.2.2.
Food Insecurity and the ShakeOut Scenario ........................................................... 24 2.2.3.
Chapter 3 Model Background ....................................................................................................... 28
3.1. The Risk Equation ............................................................................................................ 28
The Risk Equation in the Current Study .................................................................. 29 3.1.1.
3.2. Estimation of Population Impacts .................................................................................... 31
LandScan Population Data and Dasymetric Mapping Techniques ......................... 32 3.2.1.
3.3. Social Vulnerability .......................................................................................................... 38
v

The Social Vulnerability Index ............................................................................... 39 3.3.1.
Social Vulnerability and Emergency Management ................................................. 43 3.3.2.
3.4. Infrastructure Indicators and Modeling the Hazard Component of the Risk Equation .... 46
HAZUS-MH Loss Estimation Methodology ........................................................... 48 3.4.1.
Limitations of the HAZUS-MH Loss Estimation Methodology and Extension ..... 50 3.4.2.
Electric Power System Damage and Restoration in the ShakeOut Scenario and 3.4.3.
HAZUS ...................................................................................................................... 52
Natural Gas and Water Pipeline Damage and Restoration in the ShakeOut 3.4.4.
Scenario and HAZUS-MH ......................................................................................... 56
Bridge System Damage and Restoration in the ShakeOut Scenario and HAZUS- 3.4.5.
MH ............................................................................................................................. 60
Road and Rail System Damage and Restoration in the ShakeOut Scenario and 3.4.6.
HAZUS ...................................................................................................................... 64
Empirical Restoration Curves for Emergency Logistical Resources ...................... 66 3.4.7.
Chapter 4 Model Implementation .................................................................................................. 70
4.1. Global Assumptions ......................................................................................................... 72
4.2. Implementation of the Probabilistic Risk Model .............................................................. 79
Data requirements and preparation .......................................................................... 79 4.2.1.
Validation of Results with Regression Analysis ..................................................... 85 4.2.2.
4.3. Methodology for Calculation of the Relative Risk Ratio ................................................. 87
Computational Implementation of the Relative Risk Ratio .................................... 87 4.3.1.
4.4. Methodology for Modeling Resource Requirements Over Time ..................................... 88
Impact Categories and Restoration Timelines ......................................................... 89 4.4.1.
Dynamic Resource Requirements Curves ............................................................... 90 4.4.2.
Computational Implementation of the Dynamic Resource Requirements 4.4.3.
Curves ........................................................................................................................ 94
Chapter 5 Model Results ............................................................................................................... 98
vi

5.1. Overview of the Probabilistic Risk Model Results .......................................................... 98
Results from the Hazard Components of the Probabilistic Risk Model .................. 98 5.1.1.
Validation with Regression Analysis .................................................................... 104 5.1.2.
5.2. Applications of the Probabilistic Risk Model ................................................................ 111
Calculation of Resource Requirements Over Time in Los Angeles County ......... 112 5.2.1.
Summary Resource Requirements by Point of Distribution (POD) Sites ............. 122 5.2.2.
Chapter 6 Discussion ................................................................................................................... 125
6.1. Summary of Results ....................................................................................................... 125
Error Analysis ........................................................................................................ 126 6.1.1.
6.2. Issues and Further Research ........................................................................................... 128
Further Development of the Model ....................................................................... 130 6.2.1.
6.3. Conclusion ...................................................................................................................... 132
References ................................................................................................................................... 134
Data Citations ........................................................................................................................ 140
Appendix A The Original Gravity Weighted Huff Model .......................................................... 141
Appendix B HAZUS-MH Power Outage Methodology Extension ............................................ 144
Appendix C Complete Bridge Damage Validation ..................................................................... 149
Appendix D Logistical Resource Summary Report .................................................................... 151

vii

List of Figures
Figure 1. Eight-county Southern California study region from the ShakeOut scenario ................. 1
Figure 2. Organization of the current study within an emergency management context ................ 6
Figure 3. The disaster life-cycle model ......................................................................................... 13
Figure 4. Point of Distribution (POD) sites from the OPLAN and AORs .................................... 17
Figure 5. The “hub-and-spoke” model in emergency relief logistics ............................................ 18
Figure 6. USGS ShakeMap for The (M) 7.8 San Andreas Earthquake Scenario .......................... 20
Figure 7. Modeled ground-motion data for the ShakeOut scenario .............................................. 21
Figure 8. Landscan USA and U.S. Census population in Los Angeles County ............................ 34
Figure 9. LandScan USA 2012 “conus_night” population in Los Angeles County ..................... 35
Figure 10. LandScan 2015 “global” population in Los Angeles County ...................................... 36
Figure 11. Modeled social vulnerability from SoVI

in Los Angeles County ................................ 42
Figure 12. Probability of damage for medium voltage substations with seismic components ..... 53
Figure 13. Repair rate per kilometer for pipeline damage ............................................................. 58
Figure 14. Complete bridge damage in the ShakeOut scenario .................................................... 62
Figure 15. Probability of bridge damage based on weighted average method .............................. 63
Figure 16. Road and rail damage probability from MMI .............................................................. 65
Figure 17. General resource requirements over time from the USACE model ............................. 67
Figure 18. Puerto Rico commodity mission shortfalls in Hurricane Maria .................................. 68
Figure 19. Development and applications of the probabilistic risk model .................................... 72
Figure 20. Database Entity-Relationship diagram ......................................................................... 81
Figure 21. Step 1: Advanced data preparation .............................................................................. 82
Figure 22. Step 2: Computations in MATLAB for the probabilistic risk model .......................... 83
Figure 23. Step 3: Results from the CDF calculations .................................................................. 84
Figure 24. Step 4: Probabilistic damage functions and maximum probability are computed ....... 84
Figure 25. Step 5: Calculation of “at-risk” populations and their resource requirements ............. 85
Figure 26. Step 6: Validation of the model ................................................................................... 86
Figure 27. The final relative risk ratio calculated for the study area ............................................. 87
Figure 28. Simulation A (Minimum)—Dynamic resource requirements curve ............................ 91
Figure 29. Simulation B (Maximum)—Dynamic resource requirements curve ........................... 93
Figure 30. Simulation C (Average)—Dynamic resource requirements curve .............................. 94
viii

Figure 31. Step 1: Direct calculation of resource requirements over time .................................... 95
Figure 32. Step 2: Results of the calculations converted to raster surfaces ................................... 96
Figure 33. Step 3: AORS for summary resource requirements tabulation .................................... 96
Figure 34. Step 4: Calculated resource requirements over time are summarized by AOR ........... 97
Figure 35. Probability of damage calculated for the infrastructure indicators .............................. 99
Figure 36. Results of calculation of the hazard component of the probabilistic risk model ....... 100
Figure 37. Results for the SoVI amplification factor calculation ................................................ 102
Figure 38. Final calculation of “at-risk” population .................................................................... 103
Figure 39. Empirical distribution of model results and beta distribution .................................... 105
Figure 40. Variable distributions and relationships for model components ................................ 106
Figure 41. Variable distributions and relationships for ground-motion parameters ................... 107
Figure 42. Initial binomial GLM regression results .................................................................... 108
Figure 43. Analysis of residuals from the GLM regression results ............................................. 109
Figure 44. Mapping of residuals from the GLM regression results ............................................ 110
Figure 45. Results from calculation of the relative risk ratio to the general population ............. 112
Figure 46. “At-risk” population and resource requirements at day-three .................................... 113
Figure 47. “At-risk” population and resource requirements at day-three—Areas of Detail I ..... 114
Figure 48. “At-risk” population and resource requirements at day-three—Areas of Detail II ... 115
Figure 49. Establish classes for resource requirements over time ............................................... 116
Figure 50. Equation 18 with social vulnerability weighting ....................................................... 117
Figure 51. Summary resource requirements over time for three simulations ............................. 118
Figure 52. Resource requirements over time for Simulation A (Minimum) ............................... 119
Figure 53. Resource requirements over time for Simulation B (Maximum) .............................. 120
Figure 54. Resource requirements over time for Simulation C (Average) .................................. 121
Figure 55. Summary of resource requirements by Point of Distribution (POD) sites ................ 123
Figure 56. Characteristic POD sites and their modeled resource requirements .......................... 124
Figure 57. The Original Gravity Weighted Huff Model python script ....................................... 143
Figure 58. Study area for validation of power outage methodology extension ........................... 145
Figure 59. Substation service areas and the MAUP effect .......................................................... 146
Figure 60. Direct calculation of populations subject to power outages ...................................... 147
Figure 61. Validation of probability of complete bridge damage calculation ............................. 149
ix

List of Tables
Table 1. 2006 2010 Social Vulnerability Component Summary ................................................. 41
Table 2. MMI based damage probabilities for highways and rails ............................................... 65
Table 3. Eight datasets used for development of the probabilistic risk model .............................. 80
Table 4. Average restoration timelines for resource requirements curve ...................................... 90
Table 5. Summary of infrastructure component contribution to hazard results .......................... 101
Table 6. Summary of “at-risk” populations in eight-county study area ...................................... 104
Table 7. Calculated results for the restoration timeline parameter .............................................. 117
Table 8. Summary results for resource requirements over time for three simulations ................ 118
Table 9. Error budget matrix from the model results .................................................................. 127
Table 10. The Original Gravity Weighted Huff Model parameters ............................................ 142

x

Acknowledgments
I’d like to thank Dr. Karen Kemp for bringing this thesis to life, and for providing skillful editing
and guidance in putting all of the material together. Also, thank you to the other members of my
committee, Dr. Jennifer Swift and Dr. Katushiko Oda—and to COL Steven Fleming for his
advice on disaster logistics. A special thanks to my friends and family for their support and
assistance. Thank you Dad and Laura for your expert editing and writing advice. A special
thanks to my brother, Dr. John R.E. Toland, for letting me discuss modeling issues at all hours of
the night—even after you had been teaching and doing research all day. And thank you Mom for
your support and curiosity—and the many meals made with love. Also, thank you to colleagues
that have provided sponsorship for access to data and other information: Jami Childress-Byers,
Dr. Chris Emrich, Dr. Ken Hudnut, Jesse Rozelle, Charlie Simpson and thank you to the USC
Spatial Sciences Institute and staff for your support. But most importantly, this thesis must
acknowledge the disaster survivors from Hurricane Katrina, the Haiti Earthquake, Hurricane
Maria and many others—and for those in future events. Hopefully, we can learn from these
events and build a more prepared and resilient future.

xi

List of Abbreviations
AFO Area Field Office
AOI Area of Impact
AOR Area of Responsibility
ATC Applied Technology Council
CalOES California Governor’s Office of Emergency Services
CDF Cumulative Distribution Function
CPG Comprehensive Planning Guide
CUSEC Central United States Earthquake Consortium
DHS United States Department of Homeland Security
DLA Defense Logistics Agency
E-R Entity-Relationship
Esri Environmental Systems Research Institute, Inc.
FEMA Federal Emergency Management Agency
FGDB Esri File Geodatabase
GIS Geographic Information Systems
GIST Geographic Information System Science and Technology
GLM Generalized Linear Model
HAZUS-MH
®
FEMA Hazards United States Multi-Hazard Software
HSPD-5 Homeland Security Presidential Directive 5
HVRI Hazards and Vulnerability Research Institute, University of South Carolina
IAEM International Association of Emergency Managers
ICS Incident Command System
xii

LOGRESC
®
The Logistical Resource Model
M Moment Magnitude
MAUP Modifiable Areal Unit Problem
MAE Mid-America Earthquake Center
MMI Modified Mercalli Intensity
NRC National Resource Council of the National Academies
NBI National Bridge Inventory
NHPN National Highway Planning Network
NIMS National Incident Management System
NLCD National Landcover Data
NYC New York City
ODE Ordinary Differential Equation
OEM Office of Emergency Management
OPLAN Southern California Catastrophic Earthquake Response Operational Plan
ORNL Oakridge National Laboratories
PAGER Prompt Assessment of Global Earthquakes for Response
PCA Principal Component Analysis
PGA Peak Ground Acceleration
PGD Peak Ground Deformation
PGV Peak Ground Velocity
PKEMRA Post Katrina Emergency Management Reform Act of 2006
POD Point of Distribution
SA10 (1.0 second) Peak Spectral Acceleration
xiii

SoVI
®
University of South Carolina’s Social Vulnerability Index
SPDE Stochastic Partial Differential Equation
UAC Unified Area Command
UASI Urban Areas Security Initiative
UCERF3 Uniform California Earthquake Rupture Forecast
UCG Unified Coordination Group
UNDRO Office of the United Nations Disaster Relief
USACE United States Army Corps of Engineers
USC University of Southern California
USDA United States Department of Agriculture
USGS United States Geological Survey
UTM Universal Transverse Mercator
VRP Vehicle Routing Problems
WGS World Geodetic System
WHO World Health Organization

xiv

Abstract
Federal, state and local officials are planning for a (M) 7.8 San Andreas Earthquake
Scenario in the Southern California Catastrophic Earthquake Response Plan that would require
initial emergency food and water resources to support from 2.5 million to 3.5 million people over
an eight-county region in Southern California. However, a model that identifies locations of
affected populations—with consideration for social vulnerability, estimates of their emergency
logistical resource requirements, and their resource requirements over time—has yet to be
developed for the emergency response plan.
The aim of this study was to develop a modeling methodology for emergency logistical
resource requirements of affected populations in the (M) 7.8 San Andreas Earthquake Scenario
in Southern California. These initial resource requirements, defined at three-days post-event and
predicted through a probabilistic risk model, were then used to develop a relative risk ratio and to
estimate resources requirements over time. The model results predict an “at-risk” population of
3,352,995 in the eight-county study region. In Los Angeles County, the model predicts an “at-
risk” population of 1,421,415 with initial requirements for 2,842,830 meals and 4,264,245 liters
of water. The model also indicates that communities such as Baldwin Park, Lancaster-Palmdale
and South Los Angeles will have long-term resource requirements.
Through the development of this modeling methodology and its applications, the
planning capability of the Southern California Catastrophic Earthquake Response Plan is
enhanced and provides a more effective baseline for emergency managers to target emergency
logistical resources to communities with the greatest need. The model can be calibrated,
validated, generalized, and applied in other earthquake or multi-hazard scenarios through
subsequent research.
1

Chapter 1 Introduction
This study developed a modeling methodology for emergency logistical resource requirements of
affected populations in the (M) 7.8 San Andreas Earthquake Scenario in Southern California.
This earthquake scenario is expected to catastrophically impact populations, infrastructure and
the economy throughout an eight-county region (Figure 1) in Southern California (Jones et al.
2008).

Figure 1. Eight-county Southern California study region from the ShakeOut scenario. Map from
CalOES and FEMA (2011).

The (M) 7.8 San Andreas Earthquake Scenario, developed by the United States
Geological Survey (USGS) for “The Great California ShakeOut” earthquake annual
preparedness exercises, is the basis for the joint federal, state and local Southern California
Catastrophic Earthquake Response Operational Plan (OPLAN) that will guide disaster response
2

efforts in the event of a catastrophic earthquake in the region (CalOES and FEMA 2011). The
ShakeOut earthquake scenario and the OPLAN identify that a life-sustaining priority is to
provide meals and water to support disaster-affected populations of between 2.5 million and 3.5
million (2 meals per person/day and 3 liters of water per person/day) in the eight-county study
region, from three-days post-event. However, a model that identifies locations of affected
populations—with consideration for social vulnerability, estimates of their emergency logistical
resource requirements and their resource requirements over time—has yet to be developed for
the emergency logistical response plan.
From Hurricane Katrina to recent events in Puerto Rico, identifying emergency resource
requirements remains a perennial gap in emergency management capabilities and the lack of a
standard modeling methodology directly affects the health, security and long-term sustainability
of the most vulnerable communities. Planning for these resource requirements before an event
occurs can mitigate against resource scarcity and food insecurity in the affected communities
when disaster strikes. This study proposes to begin to fill this gap in the literature and in
emergency management capabilities with a novel methodology for modeling emergency
logistical resource requirements in the (M) 7.8 San Andreas Earthquake Scenario.
1.1. Motivation
The United States Geological Survey (USGS) predicts in the Uniform California
Earthquake Rupture Forecast (UCERF3) that there is a 31 percent chance of a (M) +7.5
earthquake occurring in Los Angeles County, California, in the next 30 years (Field et al. 2013).
The (M) 7.8 San Andreas Earthquake ShakeOut Scenario and the OPLAN identify that an
emergency logistical commodity mission will be required to provide life-sustaining support to
nearly 10 percent of the regional population (CalOES and FEMA 2011). However, the ShakeOut
3

scenario and the OPLAN do not include tools such as high-resolution models of affected
populations and their requirements over time, nor plan for the amplifying effects of social
vulnerability. As the literature suggests (e.g. Juntunen 2006; Philips et al. 2010; Gillespie and
Zakour 2013; Lindell 2013) socially vulnerable populations have proportionally higher
emergency resource requirements than the general population and will take longer to recover.
Several recent incidents have highlighted the need for the identification of vulnerable
populations and the locations of high-risk areas that may be used as priority food and water
distribution points in coordination with community groups. In review of the Hurricane Sandy
response, the Hurricane Sandy After Action Report recommended development of a Food and
Water Distribution Task Force. This task force could then be activated before a coastal storm
occurs to target resources to vulnerable communities (NYC 2013).
Most recently in Puerto Rico, resource shortages severely impacted the local populations
and mass migration out of the region was widespread. The 2017 FEMA Hurricane Maria After
Action Report acknowledged that federal agencies faced difficulties knowing what was needed
and where in the aftermath of the storm (FEMA 2018a). An investigative report by The
Guardian noted that:
Federal officials privately admit there [was] a massive shortage of meals in Puerto
Rico three weeks after Hurricane Maria devastated the island. Officials at the
Federal Emergency Management Agency (FEMA) say that the government and
its partners are only providing 200,000 meals a day to meet the needs of more
than 2 million people. That is a daily shortfall of between 1.8 million and 5.8
million meals (Wolffe 2017, 1).

Without estimation of initial affected populations, their location and a model of their
long-term resource requirements, the failure of the emergency logistical resource mission is
much more likely and can result in humanitarian catastrophe (Paci-Green and Berardi 2015).
While the current study and study area are scenario specific and do not relate to hurricane events
4

per se, such as with Hurricane Maria in Puerto Rico, nor the unique socioeconomic,
demographic and physical environment found there, these events support the objectives of the
current study and the conclusion that further research is warranted in order to generalize and
calibrate the modeling methodology for additional types of catastrophic disaster response events.
This study also provides an innovative interdisciplinary application in the development of
Geographic Information System Science and Technology (GIST) through an integration of the
emergency management/logistical planning, spatial analysis/Geographic Information Systems
(GIS) and mathematical modeling problem spaces. In this integrated problem space, a perennial
issue in emergency management planning capabilities is addressed in a scenario that requires
contributions from all three disciplines to be successfully managed. In so doing, this study
provides a public service and social benefit to disaster response planning by providing tools to
mitigate impacts to those populations most vulnerable to disruptions in life-sustaining food and
water supplies in the event of a catastrophic incident.
1.2. Thesis Organization and Research Objectives
As this is an interdisciplinary approach to a complex problem, this thesis research is
directed at several audiences with the ultimate goal of developing a probabilistic risk model (or
probabilistic risk assessment) for emergency logistical resource requirements of affected
populations (at three-days post-event) in the (M) 7.8 San Andreas Earthquake Scenario. A
probabilistic risk model is a systematic and comprehensive methodology to evaluate risks
associated with natural hazards and can provide a standard modeling methodology for estimation
of “at-risk” populations for emergency logistical resource requirements—and so can begin to
address these gaps in emergency management capabilities (Dwyer et al. 2004).
5

In Chapter 2, an overview of emergency management, the ShakeOut earthquake scenario
and the OPLAN are provided. This chapter provides the context for the commodity mission in
the eight-county study region along with an overview of food insecurity and its impacts in the
ShakeOut scenario. Chapter 2 is intended for emergency managers, community planners,
humanitarian relief and disaster logistics specialists and other non-technical audiences. These
audiences can then directly apply the results provided in Chapter 5 and the Appendix D,
“Logistical Resource Summary Report", into their mission without further background.
Chapter 3 is intended for the science and engineering community that require a deeper
background in the model design and methodology. In this chapter, the design of a probabilistic
risk model for populations “at-risk” for emergency logistical resource requirements is
investigated in detail for application in the commodity mission. This chapter introduces each
component of the model, provides a technical background with support from the literature and
the theoretical framework used to produce the model results. After reading Chapter 3, technical
audiences can proceed to Chapter 4, to computationally replicate the results, or go directly to
Chapter 5 and the appendices.
In Chapter 4, the methodology for computational implementation of the probabilistic risk
model is presented, along with applications of the model to calculate relative risk in the eight-
county study area and to calculate resource requirements over time. This chapter is intended for a
technical GIS audience, with all of the information required for successful replication of the
results of the model in ArcGIS 10.6 and other software. The results and discussion are then
presented in Chapter 5 and Chapter 6 respectively, for all audiences.
In Appendix D, resource requirements over time in Los Angeles County as predicted by
the model are summarized by the community Points of Distribution (PODs) for the commodity
6

mission in the OPLAN. This report is designed for non-technical audiences in supporting
operational planning by emergency managers and community planners in the commodity
mission.
Organization of the current study is shown in Figure 2, along with the key components in
the model design to develop a probabilistic risk model for emergency logistical resource
requirements, which are introduced in the next section.

Figure 2. Organization of the current study within an emergency management context

Development of a Probabilistic Risk Model for Emergency Resource Requirements 1.2.1.
The main research objective in this study is to develop a probabilistic risk model for
emergency logistical resource requirements of affected populations in the (M) 7.8 San Andreas
Earthquake Scenario. The proposed methodology to implement this goal includes several key
7

components, which are introduced below with reference to their corresponding section in the
thesis document.
The probabilistic risk model is based on computational implementation of the risk
equation as identified by Dwyer et al. (2004), and originally defined by the Office of the United
Nations Disaster Relief (UNDRO), to determine the expected population “at-risk” with respect to
the general population. In this equation, risk is defined as the product of vulnerability, population
and hazard—and is used to directly calculate the “at-risk” population for emergency logistical
resource requirements. This risk equation guides the entire framework of the current study and is
further investigated in Section 3.1, along with the vulnerability, population and hazard
components.
Modeled ground-motion data from the ShakeOut scenario is used to represent the
geophysical properties of the earthquake in the current study, and is presented in Section 2.2.2
from Jones et al. (2008). Ground-motion data represent the characteristic geophysical properties
of an earthquake in measurements such as magnitude, intensity, velocity and acceleration over a
geographic region.
The OPLAN is used to establish the assumptions for population impact, food insecurity
and resource requirements and support, which is discussed in Section 2.2.3. LandScan 2015
“global” and LandScan USA 2012 “conus_night” population databases are used to represent the
affected population and are described in Section 3.2. The University of South Carolina’s Social
Vulnerability Index (SoVI
®
) model from Cutter et al. (2003) is investigated in Section 3.3 and is
used to characterize vulnerability in impacted populations.
From the literature, impacts to six infrastructure indicators are shown to be key factors
affecting food insecurity in disasters. These are investigated in Section 3.4 and are identified as
8

electric power system damage (Section 3.4.3), natural gas and water pipeline damage (Section
3.4.4), bridge damage (Section 3.4.5), road and rail damage (Section 3.4.6). Indicators are a
means of converting data into usable information, where the data are chosen to be relevant to the
problem of concern, consistent over both time and space and measurable (Dwyer et al. 2004).
Damage functions (or fragility curves) and restoration functions of these six
infrastructure indicators from the Hazards United States Multi-Hazard (HAZUS-MH
®
4.0)
Technical Manual and Applied Technology Council report (ATC-13) are then used to
characterize the hazard component of the model, in Chapter 4. Damage functions are
mathematical models used in structural engineering to calculate the probability of direct physical
damages to infrastructure induced by geophysical ground-motion (FEMA 2003). These damage
functions are incorporated into restoration functions (also called restoration curves or restoration
timelines), which determine the general timeframe (in days) for repair or replacement back to
full capacity.
Social vulnerability (investigated in Section 3.3) is also a key factor in food insecurity, as
it is a measure of the socioeconomic and demographic factors that affect a community’s ability
to respond to and recover from environmental hazards (Cutter et al. 2003). In the methodology of
Section 4.2, the new hazard curve is then amplified by the social vulnerability from the SoVI
model. In the current study, amplification (or attenuation) is defined through local social
vulnerability conditions that proportionally increase (or decrease) the population’s vulnerability
to the hazard. In general, amplification increases a hazard and traditionally represents the
magnifying local site conditions of surficial soils, topography or other environmental factors
(FEMA 2003).
9

Finally, in the methodology for development of the probabilistic risk model, the resulting
probabilities of emergency logistical resource requirements are applied to the LandScan 2015
“global” population data (from Section 3.2) developed by Bhaduri et al. (2007). The expected
population impacted in the model then determines the final “at-risk” populations for emergency
logistical resource requirements in the eight-county study area. These final model results are
aligned with the OPLAN assumption of supporting resource requirements for between 2.5
million and 3.5 million people (2 meals per person/day and 3 liters of water per person/day) in
the eight-county study region, at three-days post-event (CalOES and FEMA 2011).
The model is validated (Section 4.2.2) to quantify the distributions and relationships of
the underlying indicator variables in the model results. Logistic regression and associated
statistical tests are performed for analysis of variable contributions in the results and to determine
a confidence interval for these estimates. The final result is a probabilistic risk model for
emergency logistical resource requirements of affected populations in the eight-county study
region, at three-days post-event.
Applications of the Probabilistic Risk Model 1.2.2.
In Section 4.3, the results from the probabilistic risk model are applied to develop a
relative risk ratio for emergency resource requirements in the eight-county study region. In
general, a relative risk ratio is the ratio of the probability of an event occurring in an exposed
population to its occurrence in the general population. In the current study, this is defined as the
calculation of the ratio of populations “at-risk” for emergency resource requirements versus the
general population (Bithell 1990). Community trends in relative risk can then be identified for
community vulnerability planning in the preparedness and mitigation phases of the disaster
lifecycle (Dwyer et al. 2004).
10

In Section 4.4, the results from the probabilistic risk model are applied in Los Angeles
County through LandScan USA 2012 “conus_night” population data to determine logistical
resource requirements over time for the commodity mission in the OPLAN (CalOES and FEMA
2011). The “at-risk” populations and their resource requirements at three-days post-event are
used as the initial conditions for a set of restoration curves for resource requirements (from
Section 3.4.7) for Los Angeles County. From these curves, at-risk populations and their
emergency logistical resource requirements at future time intervals within the disaster lifecycle
(e.g. at t = 7, 14, 30, 45, 60 and 90-days) are simulated. From these results, estimates of total
resources are calculated for response operations and logistical commodity mission planning
support. Emergency managers can then identify and prioritize communities with ongoing
resource requirement issues.
The final results of the modeled resource requirements in Los Angeles County are
provided in Appendix D as a summary report designed for emergency managers and community
planners. Results are aggregated for all of the 143 Point of Distribution (POD) sites in Los
Angeles County identified in the OPLAN (CalOES and FEMA 2011), which are discussed in
Section 2.1.1. Areas of Responsibility (AORs) for each POD are modeled in Appendix A to
allow aggregation of the results to PODs. In this report, “at-risk” populations and their resource
requirements (as truckloads and pallets of food and water) for seven operational periods in the
recovery timeline are calculated, based on standard shipping formulas and logistical metrics
(Johnson and Coryell 2016).
Through the development of this modeling methodology, and its results, the planning
capability of the Southern California Catastrophic Earthquake Response Operational Plan
(OPLAN) is enhanced. This provides a more effective baseline for emergency responders to
11

target resources to communities with the greatest need. The model can be calibrated, validated,
generalized and applied in other earthquake and multi-hazard scenarios through subsequent
research.

12

Chapter 2 Emergency Management, Response Operations and Emergency
Relief Logistics
This chapter situates the development of a modeling methodology for emergency logistical
resource requirements of affected populations in the (M) 7.8 San Andreas Earthquake Scenario
within the discipline of emergency management and establishes the general framework for
disaster response and emergency logistical relief missions. The later sections explore the (M) 7.8
San Andreas Earthquake Scenario and its implementation in the Southern California
Catastrophic Earthquake Response Operational Plan (OPLAN), which serves as the specific
context for this study. Food insecurity and its impacts in the (M) 7.8 San Andreas Earthquake
Scenario are then addressed in the final section, which serves as the primary motivation for this
study.
2.1. Emergency Management Overview
A disaster can be defined as a sudden event, such as an accident or a natural catastrophe
that causes great damage or loss of life (Cutter et al. 2006). A disaster (alternatively an incident
or event in some jurisdictions) is the result of risk, hazard and vulnerability where a singular
large-scale, high-impact event can affect populations, infrastructure, property, the environment
and the economic stability of a region. Emergency management is the discipline that manages
disasters through international, federal, state, local, tribal, voluntary and private sector
organizations and their respective authorities (FEMA 2006).
Emergency management is defined by the Federal Emergency Management Agency
(FEMA) and the International Association of Emergency Managers (IAEM) as “the managerial
function charged to create the framework within which communities reduce vulnerability to
hazards and cope with disasters” (FEMA 2006, 2). Emergency management and disaster
13

response operations (at all levels) prioritize the following: (1) Reduce the loss of life; (2)
Minimize property loss and damage to the environment; and (3) Plan and prepare for all threats
and hazards (FEMA 2006). This is accomplished through the disaster life-cycle model shown in
Figure 3, which was developed by FEMA for comprehensive emergency management. The
disaster lifecycle model is composed of four phases of emergency management: Preparedness,
Mitigation, Response and Recovery (FEMA 2006).

Figure 3. The disaster life-cycle model (FEMA 2006)

Response operations coordinate life-saving and life-sustaining missions by emergency
management authorities to save lives, protect property and the environment and to meet basic
humanitarian needs after an event has occurred. Recovery operations include missions such as
housing and infrastructure restoration and repair that can support the rebuilding of an impacted
community. Mitigation lessens the impacts of disasters through building increased disaster
14

resilience in communities. Preparedness provides the capabilities to identify and plan for risks
before an incident occurs (FEMA 2006).
When a disaster such as the (M) 7.8 San Andreas Earthquake Scenario occurs, the
response phase of the disaster lifecycle begins. One of the highest priorities in response
operations is the mission for the distribution of life-sustaining emergency logistical resources
(i.e. commodities), such as food and water, to affected populations (CalOES and FEMA 2011;
Lu et al. 2016). Within the incident, joint federal, state and local priorities are managed by senior
leadership in the Unified Coordination Group (UCG), through the Incident Command System
(ICS) and the Incident Action Planning process (FEMA 2006). The Incident Action Planning
process is the standardized, on-scene, all-hazards approach to incident management established
by the National Incident Management System (NIMS) under Homeland Security Presidential
Directive 5 (HSPD-5).
In the Incident Action Planning process, the Area of Impact (AOI) is identified and
operational periods are established. The AOI represents the area directly affected by the disaster
and may be further divided into geographic Areas of Responsibility (AORs) and Operational
Branches and Divisions, under a Unified Area Command (UAC) managed at an Area Field
Office (AFO). Operational periods generally range from 12 to 24 hours in the response phase,
and are important in the current study as they are key points in time at which to model future
resource requirements. One of the benefits of the UAC is that it can manage large-scale
integrated resource ordering and distribution during each operational period, supporting complex
emergency relief logistics missions in response operations (FEMA 2006).
While the emergency logistical resource mission begins in the response phase, its end can
generally be considered the point at which the incident is stabilized and priorities can be shifted
15

to recovery. The literature notes that the long-term success of the logistical resource mission can
stabilize impacted communities and decrease the likelihood of displacement of populations
through mass migration out of the region, as well as prevent the public health issues that will
arise in communities unable to meet basic humanitarian needs (Paci-Green and Berardi 2015).
These emergency relief missions are supported by impact models and through population
and demographic data analysis in the impacted area (NRC 2007). The results of these analyses
are used for decision support and situation awareness in the emergency logistical resource
mission. Population data can support the determination of priorities for how much and what
types of aid (e.g. food, water and medical supplies) are needed and provide a community-level
determination of where the aid should be delivered (UASI 2014). Geographic Information
Systems (GIS) has provided an important intersection for emergency relief logistics and response
operations and has made it possible for emergency managers to target resources to areas with the
greatest risk, or after an event, to those with the greatest impact (Cova 1999).
Emergency Relief Logistics and the Commodity Mission 2.1.1.
Emergency relief logistics (also known as emergency logistics, disaster logistics, or
humanitarian logistics) refers to the process of planning, executing and efficiently controlling the
request, procurement, movement, staging, storage and dissemination of life-sustaining
commodities throughout the entire supply chain management process until reception at the
demand locations (CalOES and UASI 2015). Logistics is a key capability for disaster response
and is a key component for emergency response planning at the local, regional, state, tribal and
national level. Logistics planning for a disaster involves understanding of the environmental,
sociopolitical, demographic and physical characteristics of the region. In general, logistical
planning addresses the following issues:
16

• What resources are required, how many, where and for how long?
• How can they be obtained or procured?
• How can they be transported to the demand locations?
• How can they be received, staged, stored, distributed and tracked?
• Which entities and actors have roles in management of the logistics supply chain?
A priority for emergency relief logistics is to establish primary staging areas at pre-
designated locations for logistical resource receiving, storage and distribution. Secondary staging
areas may also be established at transportation hubs, military bases, shelters or other facilities
that can support the response. A major function of the staging areas is to support the distribution
of commodities to the Point of Distribution (POD) sites in the impacted community (UASI
2014).
A POD site is a central location in the community where affected populations receive
life-sustaining commodities, such as pre-packaged, shelf-stable meals and bottled water
following a disaster (UASI 2014; CalOES and UASI 2015). Resource ordering and fulfillment
for each POD site is managed through the Operational Divisions and Branches by the UAC with
the Unified Coordination Group (UCG). Each community POD site should be publicly
accessible and situated within an Area of Responsibility (AOR) that represents the affected
community in the immediate vicinity. POD sites can also be co-located with emergency shelter
sites or other facilities involved in the disaster response effort.
In the current study, AORs are calculated using the Huff Model, a probability of travel
model, to estimate the populations closest to the POD site that will be served. This supplemental
analysis is documented in Appendix A. The POD sites from the OPLAN with the AORs from
Appendix A are shown below in Figure 4 (CalOES and FEMA 2011).
17

Figure 4. Point of Distribution (POD) sites from the OPLAN and AORs in Los Angeles County

POD operations are encouraged to integrate with the general humanitarian mass feeding
and food supply-chain restoration strategy in coordination with the voluntary agencies and
private sector to best serve the emergency resource requirements of the impacted community.
These resource requirements may be met through pre-packaged, shelf-stable meals and bottled
water, but also by voluntary agency hot-meal kitchen services or private sector relief (CalOES
and UASI 2015).
Shipments of food commodities are delivered to the staging areas and are distributed to
each POD in a “hub-and-spoke” model during the operational period (Figure 5). Resource
18

ordering is based reactively on the “burn rate” of the previous operational period and projected
population served (CalOES and UASI 2015). This model naturally divides the logistical planning
process into a “supply-side”, composed of the distribution components such as the POD sites and
staging areas and a “demand-side”, which includes the population resource requirements.

Figure 5. The “hub-and-spoke” model in emergency relief logistics (UASI 2015)

Many studies focus on “supply-side” resource supply allocation models and investigate
construction and optimization of a linear resource distribution network “hub-and-spoke”
structure (e.g. from the staging areas to the PODs, in the OPLAN). These “supply-side” research
questions have been addressed in various linear programming and mathematical models for
multi-modal emergency distribution transportation problems proposed for emergency logistics
planning. These are often related to vehicle routing problems (VRP), emergency logistics
distribution models, cost-optimization and location-allocation models for emergency logistical
resource distribution in disasters (e.g. Fiedrich et al. 2000; Sheu 2007; Lu et al. 2016).
19

There are surprisingly few studies that focus on the “demand-side” through modeling
resource requirements of the affected populations in the AORs up to the spoke nodes. A few
examples can be found in Yi et al. (2007) and Huang (2016). In the (M) 7.8 San Andreas
Earthquake Scenario, the POD site locations are fixed and determining optimal distribution
locations and routing of resources to these facilities is outside of the scope of the current study.
Therefore, a probabilistic “demand-side” resource requirements model is an appropriate research
objective in consideration of the OPLAN and ShakeOut scenario.
2.2. The (M) 7.8 San Andreas Earthquake Scenario and OPLAN
The catastrophic (M) 7.8 San Andreas Earthquake Scenario, developed by the United
States Geological Survey (USGS) for “The Great California ShakeOut” earthquake annual
preparedness exercises, is the basis for the joint federal, state and local Southern California
Catastrophic Earthquake Response Operational Plan (OPLAN) that guides disaster response
efforts in the event of a catastrophic earthquake in the region (CalOES and FEMA 2011). The
emergency relief logistics mission and identification of the emergency logistical resource
requirements for affected populations can be implemented in the framework of the (M) 7.8 San
Andreas Earthquake Scenario, and operationalized through the Southern California Catastrophic
Response Operational Plan.
The Great California ShakeOut Scenario 2.2.1.
The USGS predicts in the Uniform California Earthquake Rupture Forecast (UCERF3)
that there is a 31 percent chance of a (M) +7.5 earthquake occurring in Los Angeles in the next
30 years (Field et al. 2013). The catastrophic (M) 7.8 San Andreas Earthquake Scenario,
developed by the USGS for “The Great California ShakeOut” earthquake annual preparedness
exercises and updated for the “Ardent Sentry” exercises is a (M) 7.8 earthquake on the
20

southernmost 300 km (200 mi) of the San Andreas Fault between the Salton Sea and Lake
Hughes (Jones et al. 2008) as shown in Figure 6.

Figure 6. USGS ShakeMap for The (M) 7.8 San Andreas Earthquake Scenario. Figure from
Jones et al. (2008).

The southern San Andreas Fault has produced earthquakes of magnitude 7.8 roughly
every 150 years and was identified in UCERF3 as the most likely source of a large earthquake in
California (Field et al. 2013). The segment of the fault modeled in the ShakeOut earthquake
scenario most recently ruptured over 300 years ago—so a large earthquake is overdue (Jones et
al. 2008). For the ShakeOut earthquake scenario, the USGS developed modeled ground-motion
ShakeMap data on this portion of the San Andreas fault (Figure 7). ShakeMap is developed by
the USGS Earthquake Hazards Program and is the tool that produces maps and modeled ground-
motion data in standard GIS compatible formats (Earle et al. 2009).
21

Figure 7. Modeled ground-motion data for the ShakeOut scenario. Above left, PGA; right, PGV;
below left, SA10; right, MMI. Coverage in the eight-county study region is similar. Data from
Jones et al. (2008).
22

In the ShakeOut scenario, the FEMA Hazards United States (HAZUS-MH) multi-hazard
loss estimation software, along with recommendations from expert panels, was used to estimate
damage to building stock and lifeline infrastructure. Physics-based modeled ground-motion
ShakeMaps, as shown in Figure 7 for Peak Ground Acceleration (PGA), Peak Ground Velocity
(PGV), 1.0 Second Spectral Acceleration (SA10) and Modified Mercalli Intensity (MMI),
replaced the default HAZUS-MH data for the (M) 7.8 San Andreas Earthquake Scenario (Jones
et al. 2008). The FEMA HAZUS-MH loss estimation results were then supplemented with the
outcomes of 18 focus-studies and panel discussions by experts in sectors with catastrophic
impacts in the ShakeOut scenario.
Several observations from the ShakeOut scenario are relevant to the current study. Many
of the HAZUS-MH loss estimation approaches were found insufficient and so were abandoned
in favor of expert opinion or supplemental studies (Jones et al. 2008). These included 10 lifeline
studies for highways, oil and gas pipelines, rail, water supply and electric power. As the
ShakeOut scenario was not successfully able to produce a network system analysis to model
electric power system damage and outages, estimates are based only on the expert opinion from
the ShakeOut panel discussions (Jones et al. 2008).
One successful result in the ShakeOut scenario was the development of a transportation
network analysis and damage assessment. This was completed through a supplemental study and
indicated that bridge damage was one of the most significant factors in the initial transportation
impacts and restoration timeline (Werner et al. 2008). These observations are important in
investigation of infrastructure indicator damage and the infrastructure restoration timelines used
in the modeling methodology of Chapter 3.
23

The intention behind the development of the ShakeOut scenario was for it to be
integrated with emergency response and recovery exercises, seminars and plans (Jones et al.
2008). These response operations missions are addressed in the Southern California Catastrophic
Response Plan described in the next section.
The Southern California Catastrophic Response Operational Plan (OPLAN) 2.2.2.
The Southern California Catastrophic Response Operational Plan (OPLAN) is developed
based on the six-step planning process established in the FEMA Comprehensive Planning Guide
101 (CPG) for catastrophic planning, under authority of the Post Katrina Emergency
Management Reform Act of 2006 (PKEMRA). The OPLAN is currently in the second-step of
the six-step planning process, “Understanding the Situation”, which is focused on assessing risk
(FEMA 2010). While the OPLAN is a living document and several small revisions of the (M) 7.8
San Andreas Earthquake ShakeOut Scenario have been made, both remain essentially unchanged
since 2011. The OPLAN is jointly developed by the California Governor’s Office of Emergency
Services (CalOES) and the Federal Emergency Management Agency (FEMA). Access to the
OPLAN was granted for the purpose of this study.
The OPLAN incorporates the ShakeOut scenario from the (M) 7.8 San Andreas
Earthquake event and then investigates impacts with a focus on emergency management and
response operations in the eight-county Southern California region as shown in Figure 1 above.
These counties and their 2015 population estimates are: Los Angeles (10.17 million), Kern
(882,176), Ventura (850,536), Orange (3.17 million), San Bernardino (2.13 million), Riverside
(2.36 million), San Diego (3.3 million) and Imperial (180,191). Population estimates provided by
the United States Census Bureau.
24

Planning assumptions in the OPLAN are based on the expert opinion of over 1,500
emergency management professionals in the federal, state, local, voluntary organization and
private sector (CalOES and FEMA 2011). Estimates provide information such as the number of
displaced and affected population as well as casualties, with a focus on response operations
mission priorities. The OPLAN projects that there will be:
• 1,800 deaths
• 53,000 injuries
• 300,000 buildings with “extensive” or “complete” damage
• Immediate displacement of 255,000 households with 542,000 individuals requiring
immediate mass care and shelter
• 2.5 million individuals needing basic logistical resources (e.g. food and water) after
three days
• $213 billion in damages
The OPLAN identifies the immediate displaced population (from t = 0 to t < 3 days)
based on the ShakeOut scenario with expected emergency logistical resource requirements
planned for 542,000 displaced persons over three-days (at 2 meals per person/day and 3 liters
water per person/day). The planning assumptions for (t = 3 days) and beyond from the OPLAN
that 2.5 million individuals that shelter in place will require basic resource support. This is
extended up to 3.5 million people in the “Commodity Estimate” planning section and is the basis
for the current study (CalOES and FEMA 2011).
Food Insecurity and the ShakeOut Scenario 2.2.3.
The Greater Los Angeles Basin Region is not self-sufficient in food, as much of the
perishable food for the region is regularly transported by rail or truck from San Joaquin Valley
and Imperial County sources (Jones et al. 2008). The OPLAN concludes that there will be a food
25

distribution crisis in the first two weeks after the earthquake and that an emergency logistical
commodity mission will be required to sustain a feeding program for an estimated 45 to 90 days
(CalOES and FEMA 2011). Resources to support these disaster-affected populations will be
required in the eight-county Southern California Region, after three-day local and emergency
supplies of food are depleted and until utility service, food distribution and food industry
services are restored. Therefore, the ShakeOut scenario expects food insecurity issues to impact
affected populations throughout the eight-county region, in varying degrees.
The United States Department of Agriculture (USDA) defines food security as “access by
all people at all times to enough food for an active, healthy life” (Coleman-Jensen et al. 2017, 2).
Food insecurity can similarly be defined as when these conditions are not met. Food security in a
community is threatened when a disaster occurs to a population vulnerable to a hazard,
regardless of whether it is a broad segment of the general population or its socially vulnerable
members (Paci-Green and Berardi 2015).
For modern households, food security is now defined by the availability of nearby
prepared food products for purchase through “fast-food” chains, take-out ordering, or prepared
hot-food products available at nearby markets—rather than by home pantry storage as it was in
the 20
th
century (Guthrie et al. 2013; Paci-Green and Berardi 2015). Therefore, households have
far fewer staples, canned goods and supplies readily available for emergencies. These changes in
household food consumption patterns make emergency management planning assumptions that
households in a community might remain self-sufficient (in terms of food and water) for a week
or more after a disaster, increasingly unrealistic (Paci-Green and Berardi 2015).
Food security during a disaster serves several long-term goals. Most importantly, food
security prevents individuals and communities from declining into emergency health crises and
26

civil unrest. Food security also reduces the likelihood of population “out-migration” from the
impacted area, which is inevitable if basic life-sustaining resources are not available (Paci-Green
and Berardi 2015). Emergency managers therefore plan for the general population to be self-
sufficient in food for only three days, as the OPLAN indicates (CalOES and FEMA 2011).
However, as the literature notes (e.g. Juntunen 2006; Philips et al. 2010; Gillespie and Zakour
2013; Lindell 2013), socially vulnerable populations will require more initial resources and for
longer times—and so even these assumptions are tenuous. While healthy adults may be more
resilient if confronted by a week or more of food insecurity, socially vulnerable groups (e.g.
young children, pregnant and nursing women, disabled, sick and elderly) may be especially
vulnerable (WHO 2000).
The (M) 7.8 San Andreas Earthquake ShakeOut Scenario will be a “no-notice” event, so
damage to food supply and distribution will be unexpected and severe (CalOES and FEMA
2011). An event like the ShakeOut scenario will directly impact food access for households at all
income levels to some degree. However, food insecurity will not impact households equally, as
the literature suggests (Paci-Green and Berardi 2015). These issues of social vulnerability and
their relation to food insecurity and logistical resource requirements are further investigated in
Section 3.3.
While it is noted that resource demand in the affected area may be stochastic and
unpredictable (Camacho-Vallejo et al. 2014), the OPLAN and other studies suggests that impact
to food security in the ShakeOut scenario can indeed be predicted through the interconnection to
infrastructure functionality (CalOES and FEMA 2011). In a large no-notice earthquake, power
outages will cause perishable foods to spoil, leaving only non-perishable food stores (CalOES
and UASI 2015). Businesses (including supermarkets and restaurants) are highly dependent on
27

power, water and transportation to function (CalOES and UASI 2015) and will be closed and
have limited resources until power and water are restored (CalOES and FEMA 2011). As
CalOES and FEMA (2015) indicates, significant damage to the food supply chain (because of
damage to buildings, stores, warehouses and food distribution centers) in combination with
interruptions to lifeline transportation infrastructure (Jones et al. 2008; Paci-Green and Berardi
2015), will reduce the amount of food available in the impacted area. These infrastructure
damages can therefore be considered as indicators for food insecurity and logistical resource
requirements and are further investigated in Section 3.4.
In conclusion, the complex supply chain and distribution network of food brought into
the region, along with a decline in household food storage, means food security is interconnected
with power, water, transportation and business interruption and the complex supply chains
affecting delivery of food products. With individual preparedness for emergency food storage
estimated at only three days of supplies, social vulnerability then amplifies these food insecurity
issues. Planning for these resource requirements before the (M) 7.8 San Andreas Earthquake
Scenario occurs can mitigate against resource scarcity and food insecurity in the affected
communities when disaster strikes.
As the main motivation for the current study, a modeling methodology has yet to be
developed that identifies locations of affected populations and summary estimates of their
emergency logistical resource requirements and resource requirements over time. In
consideration of this, the OPLAN is therefore limited in its capacity to address these issues. The
current study proposes to begin to fill this gap in the literature and in emergency management
planning capabilities with a novel methodology for modeling emergency logistical resource
requirements in the (M) 7.8 San Andreas Earthquake Scenario.
28

Chapter 3 Model Background
This chapter introduces the components of the risk equation, which guides the entire framework
of the current study to develop a probabilistic risk model for emergency logistical resource
requirements of affected populations in the (M) 7.8 San Andreas Earthquake Scenario. This
includes methodologies for estimation of population impacts for disaster response and an
investigation of at-risk populations, social vulnerability and their relation to food insecurity in
disasters. The final section investigates the hazard component of the risk equation as determined
by specific indicators of infrastructure impact and restoration and how these indicators can be
used to model emergency logistical resource requirements, develop a relative risk ratio and to
estimate resource requirements over time.
3.1. The Risk Equation
This study identifies populations “at-risk” for emergency logistical resource requirements
in the (M) 7.8 San Andreas Earthquake Scenario. Risk, or the expected population “at-risk”, is
defined as:
Risk = Hazard ×Vulnerability × Population (1)

This equation is based on the definition from Dwyer et al. (2004) to define risk in the
management of a disaster. In general, risk is defined as the probability or expectation of loss.
Hazard is a condition of probability posing the threat of harm to populations, infrastructure,
property, the environment or the economy. Vulnerability is the degree of susceptibility to which
populations or infrastructure are likely to be affected. Population is the affected population in the
current study but more generally is a component of the elements exposed, which can also include
infrastructure, building stock and/or socioeconomic factors in more general applications of the
29

risk equation. The resulting at-risk population in the risk equation is then multiplied by a
resources-per-person multiplier to determine the total resource requirements (Cova 1999; Dwyer
et al. 2004).
This risk equation guides the entire framework for the current study and is
computationally implemented to develop a probabilistic risk model of the affected at-risk
population and their emergency food and water requirements. These requirements are based on
the Southern California Catastrophic Earthquake Response Operational Plan (OPLAN)
assumptions that 2.5 million to 3.5 million people require initial emergency logistical resources
in the eight-county region at three-days post-event (t = 3 days). These components of the risk
equation are introduced below with the rest of Chapter 3 dedicated to investigating them in detail
for application in the current study.
The Risk Equation in the Current Study 3.1.1.
The hazard component of the probabilistic risk model is based on modeled ground-
motion data for the (M) 7.8 San Andreas Earthquake Scenario, developed by the United States
Geological Survey (USGS) for the “ShakeOut” exercises and the OPLAN (see Figure 7). The
USGS provides modeled ground-motion spatial data as Modified Mercalli Intensity (MMI), Peak
Ground Acceleration (PGA), Peak Ground Velocity (PGV) and 1.0 Second Spectral Acceleration
(SA10) over the eight-county study area (Jones et al. 2008). This is then evaluated in
combination with six damage functions from the FEMA Hazards United States (HAZUS-MH)
Technical Manual and ATC-13 (1985) to estimate probability of damage for six infrastructure
indicators (FEMA 2003). It is shown from the literature (e.g. Jones et al. 2008; CalOES and
FEMA 2011; CalOES and UASI 2015; Paci-Green and Berardi 2015) that these six damage
functions, which model probability of electric power system damage and outages, water and
30

natural gas pipeline infrastructure damage and transportation infrastructure damage, provide the
most comprehensive set of indicators representing food insecurity in the hazard component of
the risk equation.
For vulnerability, this study concentrates on social vulnerability through the social
vulnerability (SoVI) index originally developed by the University of South Carolina, Hazards
and Vulnerability Research Institute in Cutter et al. (2003). “Socially Vulnerable” populations
are defined by the social, economic, demographic and housing characteristics that influence a
community’s ability to respond to and recover from environmental hazards (HVRI 2018). In the
SoVI index, social vulnerability in the 2010 U.S. Decennial Census is identified through
inductive indices of seven socioeconomic and demographic variables by Principal Component
Analysis (PCA). The resulting composite factor scores for social vulnerability from the SoVI

study are normalized and rescaled for computational implementation as an amplification factor in
the probabilistic risk model, matching community recovery rates from a key study in social
vulnerability research (Hobor 2015). This result preserves the relative relationships from the
original data in computational determination of initial resource requirements and the length of
time of resource need (HVRI 2018).
To estimate at-risk populations in the eight-county study region, the probabilistic risk
model includes LandScan 2015 “global” (~1 km, 30 arcsecond) population raster grid cells over
the eight-county study region. LandScan 2015 is a product of Oakridge National Laboratories
(ORNL), with licensing to the University of Southern California (USC), that uses a dasymetric
mapping technique to model populations based on underlying aggregated data from 2010 U.S.
Decennial Census blocks, National Landcover Data (NLCD), transportation, water and other
demographic and commercial datasets (Bhaduri et al. 2007).
31

Oakridge National Laboratories, in coordination with the United States Department of
Homeland Security (U.S. DHS) has also developed LandScan USA 2012 “conus_night”, a high-
resolution (~90 m, 3 arcsecond) version of the population data for emergency management
application (Bhaduri et al. 2007), which has been approved for use in this study. High-resolution
(~90 m, 3 arcsecond) data from LandScan USA 2012 is used in application of the probabilistic
risk model to the Los Angeles County study region to investigate initial community level
emergency resource requirements and resources requirements over time.
Resources are then defined as population multiplied by two meals per person/day and
three liters of water per person/day. These multipliers are standard emergency management
planning assumptions and are used in the OPLAN (CalOES and FEMA 2011). The final results
are the total resource requirements for the at-risk populations over the study region, which are
calculated discretely through each respective grid cell in computational implementation of the
risk equation.
3.2. Estimation of Population Impacts
Estimation of the total population impacted by an event and identification of their
demographic characteristics and location are the first steps in mounting an effective humanitarian
response (NRC 2007). Assessments of at-risk populations involve the connection between
population within the Area of Impact (AOI), magnitude of the hazard impact and the resilience
of the community and built environment. Therefore, the quality and resolution of population
datasets used to estimate population impacts have a direct relationship to response operations and
correspondingly to the effectiveness of life-saving and life-sustaining missions.
For international humanitarian relief impact assessment, the main system that
incorporates earthquake event information with “exposed” population (defined as all populations
32

in the AOI) is the Prompt Assessment of Global Earthquakes for Response (PAGER) system
(Earle et al. 2009). PAGER is developed by the USGS as an automated system that produces
reports and messaging concerning the impact of earthquakes. PAGER summarizes the population
per cell, based on LandScan 2015 “global” population data at given MMI intensity values
estimated by ShakeMap to produce a population exposure table. This is currently the best
indication of the potential initial population impact of an earthquake event.
The PAGER system is the most general approach to estimate exposed populations and
economic impacts following significant earthquakes worldwide using LandScan “global”
population data with MMI as a key indicator for severity (Earle et al. 2009). In the current study,
the LandScan 2015 “global” population data is also used to investigate affected populations.
While PAGER uses an algorithm that is different than the current study, LandScan “global”
population data is becoming a standard baseline for population impact assessment in the disaster
response community—so it is also appropriate for use in the current study.
LandScan Population Data and Dasymetric Mapping Techniques 3.2.1.
Los Angeles County, with 88 incorporated cities, is the most populous county in the
nation with over 10.17 million people (exceeded only by eight states), based on 2015 United
States Census Bureau estimates. The eight-county Southern California Region, the basis for the
OPLAN, has a population estimated at 23.6 million (2015). In order to map these populations at
a community level, and to identify spatial patterns in emergency logistical resource requirements,
dasymetric-mapping techniques through the Landscan 2015 “global” population database and the
LandScan USA 2012 “conus_night” population database are employed in the current study.
In dasymetric mapping, data is transformed from an arbitrary spatial extent in the original
source data (e.g. 2010 U.S. Decennial Census block geography) to standardized zones (e.g.
33

LandScan “global” (~1 km) based raster grid cells) that incorporate the use of additional data
sets representing the variation in the underlying statistical surface (Aubrecht et al. 2013). The
LandScan 2015 “global” (~1 km) and the LandScan 2012 “conus_night” (~90 m) population
datasets both employ dasymetric mapping techniques by utilizing ancillary data to disaggregate
coarse 2010 U.S. Decennial Census geography to areas which expose the distribution of the
underlying population density (Bhaduri et al. 2007). An important benefit of using these
techniques is that LandScan data in comparison with the 2010 U.S. Decennial Census block (or
higher) level results in virtually equivalent total population counts. The total population for the
census block can then be recovered by summation of the populations of the individual cells
divided by the sum of the weights for all of the cells within it.
The LandScan dasymetric-mapping algorithm (Equation 2) is based on a ten-factor
weighting process (as W
Cell i,j
) for each of the respective ~1 km or ~90 m cells (as
Population
Cell i,j
), based on the proportional 2010 U.S. Decennial Census block population (as
PC
Block
) from Bhaduri et al. (2007):
Population
Cell i,j
= PC
Block
× W
Cell i,j
(2)

W
Cell i,j
=

LC
i,j
× PR
i,j
× PRR
i,j
× S
i,j
× LC
i,j
× LM
i,j
× PRKS
i,j
× SCH
i,j
× PRSN
i,j
× ARPT
i,j
× WTR
i,j

LC = Weight of National Landcover Database (NLCD)
PR = Weight for Proximity to Roads
PRR = Weight for Proximity to Railroads
S = Weight for Slope factor
LM = Weight for Landmark polygon feature
PRKS = Weight for Parks and Open Space
SCH = Weight for Schools (K-12)
PRSN = Weight for Prisons
ARPT = Weight for Airports
WTR = Weight for Water Bodies
i,j = The Vertical and Horizontal Index for Each Raster Cell

One of the key weighting factors used by LandScan is the National Landcover dataset
(NLCD), which can exclude unpopulated places in the dasymetric mapping results (Bhaduri et
al. 2007). Using a 90-meter spatial sensitivity filter, a cross validation sensitivity analysis (Cai et
34

al. 2006) resulted in 72.5 percent accuracy in predicting the populated cells over residential
locations and a 99 percent accuracy in predicting unpopulated areas in comparison with U.S.
Census estimates and high resolution ortho-photography. The result is that Landscan dasymetric
algorithm can identify where populations actually are, and where they are not, located in a study
area which is essential for identifying affected populations and supporting emergency resource
distribution.
A significant level of correlation between LandScan USA and the U.S. Decennial Census
block populations in Los Angeles County also results with an R-squared statistic of .93 as shown
in Figure 8 from the study by Bhaduri et al. (2007). In the current study, this is an important
consideration, as social vulnerability modeled by SoVI uses 2010 U.S. Decennial Census tracts
to aggregate the cumulative factor scores, and so this correlation minimizes uncertainty in the
SoVI weighting calculation of the probabilistic risk model.

Figure 8. Landscan USA and U.S. Census population in Los Angeles County. Graph from
Bhaduri et al. (2007).
35

LandScan USA 2012 “conus_night” (Figure 9) is the highest resolution population data
available, and also the first to model diurnal population dynamics at a high-resolution (Bhaduri
et al. 2007). These dynamics are important in the current study, as nighttime populations are the
most accurate representation of when populations are most stable and where long-term
emergency logistical resource requirements are most likely needed for affected populations.

Figure 9. LandScan USA 2012 “conus_night” population in Los Angeles County
36

Figure 10. LandScan 2015 “global” population in Los Angeles County. Coverage in the eight-
county study region is similar.

For the LandScan USA 2012 “conus_night” population data used in the current study,
nighttime population is defined by Bhaduri et al. (2007) as:

Nighttime Population = Nighttime Residential Population + Nighttime Workers
+ Tourists + Business travelers + Static Population (3)
37

For Los Angeles County, this results in a study area with 1,440,225 raster grid cells and a
population of 9.66 million from the LandScan USA 2012 (~90 m) population dataset. For the
eight-county study region 180,380 raster cells result for LandScan 2015 “global” (~1 km)
population data (Figure 10, previous page) with a population of 22.36 million. These results can
then be tractably converted to point centroids for analysis, which is investigated further in
Chapter 4.
Some limitations to the LandScan population datasets do exist, however. As a dasymetric
model, model validation is impractical and can only be achieved in comparison to the original
aggregated data, rather than with ground truth studies (Bhaduri et al. 2007). Another limitation of
the LandScan datasets are that they do not incorporate any other socioeconomic or demographic
population characteristics found in the aggregated U.S. Decennial Census data other than the
total population count. These characteristics, as the next section investigates, are critical in
identifying the vulnerability associated with the lack of emergency food and resources in a
disaster (NRC 2007; Paci-Green and Berardi 2015).
Another approach using LandScan 2015 “global” population data is the method
recommended by Hansen and Bausch (2007) for extension of the HAZUS-MH loss estimation
methodology in international applications. This method provides the added benefits of
dasymetric mapping techniques for identifying population locations at a high-resolution, which
extends the HAZUS-MH loss estimation methodology beyond its default 2010 U.S. Decennial
Census geography-based approach. This method is similar to that proposed in the current study
for modeling affected populations and connects the HAZUS-MH loss estimation methodology
with the LandScan 2015 “global” population database.
38

For the current model design, LandScan data are used to represent the baseline population
in the study areas without any modification and are identified by raster cell

as:
[LandScan
Population
] (4)

This notation is used for computational implementation of the risk equation as the population
component. The bracket notation implies an Esri featureclass or raster dataset, with associated
attribute (in one-to-one relationships) used in the computation of a single new raster grid cell
(Cell
i,j
) attribute or centroid point data attribute. This is introduced as the standard notation used
in the current study to represent GIS data, outside of a VBScript or Python-based computational
context.
From this section, it has been shown that mapping and analysis of the locations of
exposed populations forms an essential first step in assessment of population impacts and social
vulnerability in an impacted area. However, as the literature notes (e.g. NRC 2007; Paci-Green
and Berardi 2015), once an event occurs, demographic structure and socioeconomic
characteristics play an increasingly important role in estimation of vulnerability and risk and (as
in the current study) specifically in regard to the risk for emergency logistical resource
requirements. In the next section, these social vulnerability characteristics are investigated along
with their relationship to food insecurity in disasters.
3.3. Social Vulnerability
Within the last 30 years, and especially after Hurricane Katrina, disaster research has
focused on the pre-disaster political and socioeconomic conditions creating uneven vulnerability
to natural hazards in the general population (Fussell 2015). The “vulnerability model” theorizes
that socioeconomic, demographic and political processes (along with hazard exposure) affecting
39

the distribution of resources among groups of people produce vulnerability to natural hazards
and can lead to a “disaster” (Tierney 2007).
Vulnerability can be defined as the potential for loss of life, injury or property from
hazards, in addition to the definition in the previous section. The “hazards-of-place” model from
Cutter (1996) combines the “biophysical vulnerability” (from the hazard and the environment)
and “social vulnerability” to define a “place vulnerability”. The current study is concerned
chiefly with social vulnerability, as elements of physical vulnerability are included in the
modeling components proposed and their impacts to affected populations.
The Social Vulnerability Index 3.3.1.
Social vulnerability is defined as: “the social, economic, demographic and housing
characteristics that influence a community’s ability to respond to, cope with, recover from, and
adapt to environmental hazards” (HVRI 2018, 1). For the current study, a working definition can
be used from Cutter and Finch (2008) that social vulnerability “identifies sensitive populations
that may be less likely to respond to, cope with, and recover from a natural disaster” (Cutter and
Finch (2008, 2301). With this definition applied in the current study, the focus is then on the
identification of sensitive “at-risk” populations that may be more likely to have emergency
resource requirements.
Several studies indicate that disasters disproportionately impact demographically and
socioeconomically disadvantaged groups, both in their initial impacts and in their ability to
recover from them in the long term (e.g. Fothergill et al. 1999; Cutter et al. 2003; Fothergill and
Peek 2004; Juntunen 2006; Philips et al. 2010; Gillespie and Zakour 2013; Lindell 2013).
Vulnerability to disasters is amplified by demographic characteristics and represented by
indicators (Cutter et al. 2003). For example, people with physical or mental disabilities, the
40

elderly or young, families in poverty or those who speak English as a second language, can have
a much more difficult experience than the general population in disasters (Juntunen 2006; Philips
et al. 2010). Among the most vulnerable populations are low-income individuals and families
that lack the economic or physical resources to purchase or store basic emergency provisions
such as food and water; repair their home; replace their property; or support themselves for the
long term during recovery (Gillespie and Zakour 2013; Paci-Green and Berardi 2015).
As a result, the poor are more likely to lack the basic resiliency (e.g. income and/or
assets) needed to prepare for a possible disaster or to recover from one (Cutter et al. 2003). These
studies suggest that specific socioeconomic and demographic indicators can be used to isolate
this social vulnerability and investigate its risks independently from other components, such as
physical vulnerability and hazard-of-place models.
In the current study, The Social Vulnerability Index (SoVI), developed by the University
of South Carolina, Hazards and Vulnerability Research Institute (HVRI) is applied as a
sophisticated social vulnerability model that incorporates these findings. The Social
Vulnerability Index can then be incorporated into the current study to provide an amplification
factor for social vulnerability in the probabilistic risk model for emergency resource
requirements.
The Social Vulnerability Index (SoVI) is a place-based social vulnerability index that
includes demographic factor indices for population growth, socioeconomic status, gender,
race/ethnicity, age, family structure, occupation, social dependence and special-needs (Cutter et
al. 2003). For the built environment, it includes factor indices from land use such as: value,
occupation of housing units, density of medical facilities, extent of infrastructure and rental
versus ownership status. These factor indices were developed from the 2010 U.S. Decennial
41

Census and the Five-Year American Community Survey, 06-10. Using a factor analytic approach
and principal component analysis (PCA), 30 socioeconomic and demographic variables were
reduced to seven independent factors that accounted for about 72.5 percent of the variance in the
results (HRVI 2018) as shown in Table 1.
Table 1. 2006 2010 Social Vulnerability Component Summary. Data from HVRI (2018).

42

The final results of the SoVI

model are a nationwide dataset, updated for the 2010 U.S.
Decennial Census tract geography, that establishes relative factor scores for each component’s
contribution to social vulnerability, which are applied to each 2010 U.S. Decennial Census tract
in the SoVI index, as shown in Figure 11.

Figure 11. Modeled social vulnerability from SoVI

in Los Angeles County. Data coverage in the
eight-county study region is similar and is shown in Figure 37.
43

The authors summarize these factor scores as a new composite ranked distribution for
each tract, which in the eight-county study region range from between -15.93 to 14.78 with an
associated ordinal classification based on standard deviations, as shown in Figure 11 (HVRI
2018). The ordinal scheme ranges from: Low (-15.93 to -3.68), Medium Low (-3.67 to -1.23),
Medium (-1.22 to 1.22), Medium High (1.23 to 3.67), and High (3.68 to 14.78) social
vulnerability, based on the composite factor score. While the SoVI scores cannot be compared
absolutely, the composite factor scores can be used to show the relative social vulnerability
relationship of a census tract to others from its place on the continuum of values within the
range.
Social Vulnerability and Emergency Management 3.3.2.
The identification of socially vulnerable populations and the characteristics contributing
to social vulnerability are critical elements of successful emergency preparedness, response,
recovery and mitigation planning in disaster response (Cutter et at. 2006). As the literature notes
(e.g. Juntunen 2006; Philips et al. 2010; Gillespie and Zakour 2013; Lindell 2013), socially
vulnerable populations will require increased assistance (i.e. resources) throughout a disaster and
have the most difficulty recovering.
It is this access to emergency life-saving and life-sustaining resources that exposes the
main mechanisms through which hazards produce socioeconomic and demographic disparities—
where socially vulnerable populations simply require more resources initially and for longer
periods than the general population. These conclusions indicate that integration of social
vulnerability models into the emergency management lifecycle should be a key priority.
However, this has been difficult, as there have been few social vulnerability validation studies in
the literature. Hobor (2015) is one of the few studies to have provided some validation of social
44

factors (i.e. indicators that are characterized through SoVI as “social vulnerability” in the current
study) in relation to trajectories of recovery in New Orleans, Louisiana, and their correlation with
long-term population fluctuations from 2000-2013 affected primarily by Hurricane Katrina
recovery.
Hobor’s results show that neighborhoods in New Orleans that have come back to around
75 percent of their pre-Hurricane Katrina population are the mean with those at 80 percent and
above considered very successful and those below 60 percent are distressed. The study indicates
that community recovery rates in New Orleans for Hurricane Katrina ranged from a standard
deviation of approximately (±) 22 percent, with a mean rate of 75 percent, in consideration of
social factors in the main trajectories of recovery (Hobor 2015).
As the best available validation of social vulnerability’s influence in community
recovery, these observations of (±) 22 percent range as amplification of initial resource
requirements and recovery are taken as a key assumption in the current model design. This
captures the findings from the literature that indicate socially vulnerable populations require a
greater initial percentage of resources than the general population and take longer to recover, as
identified above.
In order to computationally implement the Social Vulnerability Index (SoVI) with an
amplification factor, the range of ranked factor scores from the original SoVI

model are rescaled
to a weighting that reflects the observations from Hobor (2015) of a (±) 22 percent range in
standard deviation—which is calculated from 0.78 to 1.22, with 1 being the mean.
Standard statistical normalization procedures are used through feature scaling (Dodge
2003) to accomplish this in the model design as:

45

(5)

The result is a vulnerability component of the computationally implemented risk equation that is
combined with the hazard component as a product to represent social vulnerability amplification
in the affected population. This also preserves the ranked social vulnerability relationships in the
original data.
One final study by Noriega (2011) connects social vulnerability in cities within Los
Angeles County to the (M) 7.8 San Andreas Earthquake Scenario in terms of economic losses
and resources. The social vulnerability of cities in Los Angeles County “at-risk” from the (M)
7.8 San Andreas Earthquake Scenario was investigated with the intention of informing the
distribution of resources before an event occurs. In relation to the current study, these findings
suggest that in the event of the (M) 7.8 San Andreas Earthquake Scenario, communities with
lower incomes, large minority populations and other social vulnerability characteristics may have
a disproportionate impact, and therefore disproportionate resource requirement, from the general
population.
Noriega’s research in Los Angeles County concluded that the identification and location
of socially vulnerable populations before a disaster can help target locations for initial resources
after a disaster. Therefore, the objective to integrate social vulnerability amplification into the
probabilistic risk model of emergency logistical resource requirements for affected populations
in the (M) 7.8 San Andreas Earthquake Scenario is aligned with the recent research
recommendations from Noriega (2011) in the Los Angeles County study region and so continues
that work.
46

In conclusion, it is this access to emergency life-saving and life-sustaining resources—
whether tangible resources in disaster response, recovery or mitigation, socioeconomic
resources, or political—that leads to the most successful outcomes to all affected populations,
and especially the socially vulnerable. In the current study, “resources” in the original risk
equation are restricted to life-sustaining logistical commodities (e.g. food and water) and the
resource requirements of disaster-affected populations—and so access to these resources is
therefore the key determinant for food security in the disaster-affected populations.
As introduced in Section 2.2.3, food insecurity and its impacts in the ShakeOut scenario
are directly related to social vulnerability and the complex interdependencies involved in food
transportation, storage and commercial business networks that are interconnected with power,
water and transportation infrastructure damage. Dwyer et al. (2004) also notes that vulnerability
to food insecurity could not be determined by a single variable but, rather, through a combination
of indicators, which is the approach to be used in the current model design.
Therefore, an appropriate research goal is to develop a modeling methodology for
emergency logistical resource requirements and to estimate at-risk populations, by proxy,
through using indicators from the infrastructure damage and restoration timelines along with
social vulnerability factors in the (M) 7.8 San Andreas Earthquake ShakeOut Scenario.
3.4. Infrastructure Indicators and Modeling the Hazard Component of the
Risk Equation
The United States Department of Homeland Security (U.S. DHS) and 42 U.S. Code § 519
define a critical lifeline infrastructure (or lifeline infrastructures) as the systems and assets,
whether physical or virtual, so vital that their disruption would have a debilitating effect on
public health and safety. Components of lifeline infrastructure observed in the findings of the
47

previous sections include transportation, power and water systems. Different types of lifeline
infrastructure systems and their components can be interconnected dependently on each other,
which can be defined as infrastructure interdependency. Infrastructure interdependency is
important in the current model design, as the components of the lifeline infrastructure, and their
restoration timelines become increasingly connected as resource requirements are estimated over
time (Bach et al. 2013).
An important factor for lifeline infrastructure in the United States is that privatization of
utilities and their various proprietary service areas have resulted in a decentralized and often
fragmented market with an increased number of actors operating in a single area (Bach et al.
2013). As the HAZUS-MH Technical Manual notes, detailed analyses and understanding of the
interactions between components in a private sector lifeline utility requires their cooperation,
data and an advanced system (network) analysis—which is difficult to coordinate and outside of
the scope of the current study (FEMA 2003). This was also the conclusion in the ShakeOut
scenario, as network analyses for most lifeline utility infrastructure sectors were not performed.
In the current model design, these issues limit the methodology for modeling lifeline
infrastructure systems to established damage functions and supporting assumptions that relate
infrastructure component distribution to population density. These assumptions are investigated
further in Chapter 4. A simplified methodology is proposed for the current study using the
established HAZUS-MH damage functions, with some extension, to align with the HAZUS-MH
based ShakeOut scenario methodology.
In this approach, key components of the infrastructure systems are chosen that are
sufficiently connected with population impacts and food insecurity. These are identified from the
48

literature (e.g. from Jones et al. 2008; CalOES and FEMA 2011; CalOES and UASI 2015; Paci-
Green and Berardi 2015) as:
• Electric Power System Damage
• Natural Gas Pipeline Damage
• Water Pipeline Damage
• Bridge Damage
• Road Damage
• Rail Damage
The rest of this chapter investigates these infrastructure indicators as simplified
independent components of the hazard in the risk equation through both the HAZUS-MH
damage functions and through the ShakeOut scenario.
HAZUS-MH Loss Estimation Methodology 3.4.1.
The Hazards United States Multi-Hazard (HAZUS-MH) loss estimation software is the
FEMA standardized multi-hazard methodology that contains models for estimating potential
losses from earthquakes and other disasters (Buika 2000; FEMA 2003; Kircher et al. 2006). It is
considered the preeminent and authoritative loss-estimation methodology in the United States.
The HAZUS-MH Technical Manual is a compilation of methodologies and data covering earth
science, structural engineering, social science and economics and is the basis for the HAZUS-
MH loss estimation methodology and software application, which itself is based on ATC-13
(1985). ATC-13 (1985) is the original study by FEMA and the Applied Technology Council
used to estimate the economic impacts of a major California earthquake on the state, region and
nation (FEMA 2003).
The HAZUS-MH Technical Manual has established general damage and restoration
functions for lifeline infrastructure components, which can be implemented independently from
49

the HAZUS-MH software. The HAZUS-MH loss estimation methodology is one of the
foundational components of the ShakeOut scenario and the OPLAN (Jones et al. 2008; CalOES
and FEMA 2011). Therefore, it is an appropriate research goal to develop an approach to
modeling emergency logistical resource requirements of affected at-risk populations that aligns
with the HAZUS-MH loss estimation methodology. This methodology is employed, with some
extension, using the HAZUS-MH Technical Manual and ATC-13 (1985) damage functions of
the six indicators and infrastructure restoration timelines.
HAZUS-MH damage functions describe the probability (by lognormal cumulative
distribution functions) of reaching or exceeding a specific damage state given ground-motion
ShakeMap data (FEMA 2003). Restoration functions evaluate the loss of function and restoration
sources (by normal cumulative distribution function) up to and including a specific time (in days)
based on these same data sources. The damage states are identified as “minor”, “moderate”,
“extensive” and “complete” and are used in both the probabilistic risk model and the estimation
of resource requirements over time.
The damage functions used for computation of damage probabilities of the six
infrastructure indicators are based on ground-motion parameters from the ShakeOut scenario
(Jones et al. 2008). Most of these damage functions are formulated as cumulative distribution
functions (CDFs) and are defined as:

(6)

The normal CDF function represents the cumulative probability that the random variable
X is less than or equal to a number x (Pitman 2006), which in the current study is used to
50

estimate restoration times up to and including a specific time (in days) for each damage state
(FEMA 2003). The lognormal CDF function is the maximum entropy probability distribution for
a random variable X and so in the current study this represents the cumulative probability of
being in, or exceeding, each damage state given a specific level of ground motion. A maximum
entropy probability distribution is defined as having entropy that is at least as great as that of all
other members of a class of probability distributions, where entropy can be considered as a
measure of information loss (Jaynes 2003). A CDF can be generated and evaluated with only two
parameters: a mean, µ or log(µ) for the lognormal CDF, and a standard deviation, σ, through
MATLAB statistics libraries.
Limitations of the HAZUS-MH Loss Estimation Methodology and Extension 3.4.2.
In order to handle more complex approaches for modeling logistical resource
requirements, the HAZUS-MH loss estimation methodology must be extended. For example,
while HAZUS-MH provides some estimates for lifeline utility outages, which could be
considered prima facie as the required indicators in the probabilistic risk model for modeling
emergency resource requirements for affected populations at (t = 3), further investigation shows
that those estimates use a methodology that is incomplete and subject to too much uncertainty
(see Section 3.4.3 and Appendix B). Currently, HAZUS-MH neither has the built-in capability to
model the disaster-affected population’s emergency resource requirements after (t = 0) days, nor
provide these estimates with enough precision and with a complex enough methodology for
emergency managers to support community level emergency logistical resource planning for
affected populations.
One of the more advanced studies to extend the capabilities of HAZUS-MH for modeling
emergency resources is the MAE (2009) study for the New Madrid Seismic Zone developed by
51

the Mid-America Earthquake (MAE) Center and the Central United States Earthquake
Consortium (CUSEC). In that study, the authors define at-risk populations as those displaced
households (due to structural damage) and those without water and/or power for at least 72
hours. They provide estimates for affected populations up to (t = 3) days post-event, with similar
application to the approach proposed in the current study. However, they do so completely
within the HAZUS-MH loss estimation software platform, and so are limited by the inherent
uncertainty within this methodology. Their estimates are made without considerations for social
vulnerability and an advanced social vulnerability model. They also do not incorporate the
indicators representing the interconnections between transportation infrastructure damage with
water and power infrastructure restoration that the literature suggests drive food insecurity
issues.
The MAE (2009) study identifies these issues as major gaps in the HAZUS-MH
modeling capabilities for logistical planning support. In the “New Models and New
Components” development recommendations of their study, they identify several gaps in the
current capabilities for logistical planning support and situation awareness. These include
modeling community level resource requirements, modeling mass care resource requirements in
consideration of social vulnerability, and modeling resource requirements over time in logistical
planning.
In summary, all of the literature points to the interconnections between critical lifeline
power, water and transportation system infrastructure as indicators associated with food
insecurity and business interruption, with amplification by social vulnerability factors. The
current study, therefore, attempts to address some of these identified capability gaps through a
probabilistic risk modeling methodology for emergency logistical resource requirements, with
52

some extension of the HAZUS-MH loss estimation methodology using the damage functions
from the HAZUS-MH Technical Manual and ATC-13 (1985) study.
An overview of the narrative of impacts from the Shakeout scenario and connection with
the HAZUS-MH loss estimation methodology provides the final justification for the choice of
the six indicators and restoration functions.
Electric Power System Damage and Restoration in the ShakeOut Scenario and HAZUS 3.4.3.
Throughout the eight-county region, energy lifeline infrastructure system impacts in the
ShakeOut scenario include electric power system damage and outages as well as natural gas
pipeline impacts. The scenario narrative indicates that:
Electric power is lost throughout the distribution systems in the study area
immediately, and it is restored to 90 percent of those capable of receiving it
within three days. Los Angeles, San Bernardino, and Riverside Counties
immediately lose all electric power. Gas pipeline damage reduces the ability to
produce power within the affected areas of those counties. Within 24 hours,
repairs restore 30-50 percent of service; within three to ten days, 75-90 percent of
those capable of receiving power have service restored; and in one to four months
virtually all power is restored (Jones et al. 2008, 94).

The HAZUS-MH Technical Manual estimates electric power system outages in the
region to be dependent on the functionality of medium voltage substations (FEMA 2003). An
electric substation is a facility that operates as the source of power supply for the community in
the local service area. These components of electric power systems are among some of the most
vulnerable in an earthquake. Damage to medium voltage substations can impact large areas.
However, many of the substations in California have been seismically retrofitted (Jones et al.
2008). These service areas, which are often proprietary business information, were not available
for the ShakeOut scenario or for the HAZUS-MH loss estimation methodology in the current
study.
53

To generate the CDF damage functions for medium voltage substations with seismic
components (Figure 12) the following parameters are used from the HAZUS-MH Technical
Manual: minor, (µ = 0.15, σ = 0.6); moderate, (µ = 0.25, σ = 0.5); extensive, (µ = 0.35, σ = 0.4);
and complete, (µ = 0.7, σ = 0.4).

Figure 12. Probability of damage for medium voltage substations with seismic components

Restoration functions for electric substations and distribution circuits in the HAZUS-MH
loss estimation methodology are based on empirical data from G&E (1994) and are shown in
FEMA (2003) to mostly be vulnerable to Peak Ground Acceleration (PGA). Restoration
functions (also called restoration curves or restoration timelines) determine the estimated
timeframe for repair or replacement back to full capacity (100 percent) of the infrastructure
systems, where the discrete time (in days) for complete restoration at each damage state are
calculated or estimated.
54

Discrete power restoration timelines, based on the HAZUS-MH damage categories show
for 100 percent restoration: minor (3-days), moderate (7-days), extensive (30-days) and complete
(90-days). Power restoration timelines from the ShakeOut scenario are based on expert panel
recommendations and are estimated at: minor (6-days), moderate (9-days), extensive (21-days)
and complete (120-days). It should be noted that the ShakeOut estimates include a range of
uncertainty in the narrative for the restoration timelines, which is not found in the HAZUS-MH
Technical Manual restoration timeline curves.
To associate power damage and power restoration timelines with power outages (and
affected populations) in the impacted areas, the HAZUS-MH Technical Manual recommends a
performance evaluation methodology (shown in Equation 7). This methodology is employed in
the current study to calculate the probability for power outages at day-three (FEMA 2003):

(7)

The default power restoration times from the HAZUS-MH Technical Manual are updated
in the current study to include information from both the ShakeOut scenario and the empirical
sources from the HAZUS-MH loss estimation methodology (FEMA 2003; Jones et al. 2008). In
general, the ShakeOut scenario estimates a rapid infrastructure recovery at day-three, while the
HAZUS-MH restoration times estimate a slower recovery. The “none”, “minor” and “moderate”
damage states are estimated at near 100 percent recovered in both HAZUS-MH and the
ShakeOut scenario at day-three and so these values are chosen to reflect this rapid recovery of
minimally impacted areas. The “extensive” damage state is taken as the average of the HAZUS-
55

MH and the ShakeOut scenario restoration time as 49 percent. In this case, due to the large range
of uncertainty in the ShakeOut estimates for restoration times, the timelines diverge from the
HAZUS-MH loss estimation methodology estimates significantly—therefore an average is
chosen to account for both sources. Finally, the “complete” damage state

is taken from the
HAZUS-MH restoration times, as 4 percent—which also captures the observation from the
ShakeOut scenario that a maximum 120-day restoration timeline will be expected in the most
severely impacted areas. These values are then used to calculate [POWER
Damage
] at day-three.
In general, the HAZUS-MH loss estimation methodology is primarily focused around
estimation of discrete infrastructure damage and restoration and so population impact estimation
is much less advanced. An extension of the methodology is therefore required, as the current
HAZUS-MH loss estimation methodology for populations affected by power utility outage is
subject to a large degree of uncertainty. This is, in part, due to the modifiable areal unit problem
(MAUP) in the variation of real world service area extents. The MAUP is a source of significant
statistical bias and can significantly impact the results of calculations (Fotheringham et al. 1991).
MAUP effects result when spatial phenomena, such as populations, are aggregated into areas.
The resulting summary values are influenced by both the shape and scale of the aggregation unit
(Openshaw 1984).
The HAZUS-MH loss estimation methodology for power utility outage is to average the
probability of damage for all of the discretely located substations. A single “percentage-of-
impact” weighting factor is then applied to the population of the entire study area such that every
2010 U.S. Decennial Census tract gets the same impact weight (FEMA 2003). Populations in the
most severely impacted regions will be systematically underestimated and those in the least
impacted regions will be overestimated based on that method and variably sized service areas as
56

an additional weighting factor (and the MAUP effect) are not even considered—so this
methodology is not appropriate for determination of real-world population locations with
emergency resource requirements.
To extend and improve this methodology for the current study, the assumption is made
that the substations are more-or-less evenly distributed in the study region at the LandScan cell
resolution, proportional to population density. The probability of outage is calculated, as the
HAZUS-MH Technical Manual suggests using Equation 7 (FEMA 2003). Affected populations
are then directly calculated based on the discrete Landscan raster cell population. This addresses
the MAUP problem, within the uncertainty range inherent in the original method.
To validate this extension of the HAZUS-MH loss estimation methodology, it is
sufficient to show that in the current study region this assumption and calculation of power
outage affected population decreases the uncertainty of the original HAZUS-MH method, or that
it is at least as good as the current standard. This conclusion is confirmed by further investigation
provided in Appendix B.
Natural Gas and Water Pipeline Damage and Restoration in the ShakeOut Scenario and 3.4.4.
HAZUS-MH
Infrastructure indicators and food insecurity, as the literature has shown, are
interconnected to business restoration because without electricity, gas, water and a transportation
system, businesses are unable to function. Water utility service loss is a key factor in business
interruption, as water loss can affect eight out of ten businesses in a disaster-impacted region
(Jones et al. 2008).
As the ShakeOut scenario and OPLAN indicate, in some of the most heavily impacted
areas the number of pipe breaks will be so severe the entire system will need to be recreated
(Jones et al. 2008). These areas may not have residential, commercial or industrial water supplies
57

(and so also severe business interruption and food insecurity) for up to six months. Some of the
more moderately impacted areas may expect up to two months without functioning water
utilities. The lack of water conveyance (i.e. functioning pipelines) “becomes the largest factor in
business interruption losses for the ShakeOut scenario, resulting in $50 billion in lost economic
activity” (Jones et al. 2008, 9).
Business interruption has cascading negative effects throughout the community, whether
businesses are specifically related to food security (e.g. grocery stores, restaurants and
supermarkets) or are peripherally interconnected through the supply-chain and the regional
economy (Rose et al. 2012). These factors inevitably affect the most vulnerable populations in a
greater amount and for longer periods, as the literature has shown.
The ShakeOut scenario narrative continues for pipeline damages and their restoration
timelines:
Pipeline damage causes the loss of piped drinking water in much of the most
strongly shaken areas (with MMI VIII+ shaking) for a week or more (Jones et al.
2008, 95)

Communities within about 10 miles of the fault and small communities in isolated
regions have pipeline damage so severe as to impair piped water supply for up to
six months, with repairs proceeding in some prioritized fashion. Perhaps 5 percent
of customers in small regions throughout Los Angeles, Riverside, and San
Bernardino Counties have pipeline damage requiring between one week and two
months to repair, before piped water supply is available (Jones et al. 2008, 150).

The HAZUS-MH methodology calculates water and gas pipeline damage based on Peak
Ground Velocity (PGV) or Peak Ground Deformation (PGD) and assumes an 80 percent brittle
pipeline ratio (FEMA 2003). Therefore, there is some divergence from the ShakeOut
methodology, which estimates restoration timelines through the water utility expert panel by
MMI, liquefaction and landslide potential (Jones et al. 2008). In the current study, the brittle
pipeline damage function is assumed for all pipelines in the model design as a cautious approach
58

to avoid underestimation and is based on Peak Ground Velocity (PGV) only, as ground
deformation data for liquefaction and landslide were not available.
The brittle pipeline damage function is based on the empirical data of O'Rourke and
Ayala (1993). The data correspond to empirical brittle pipeline damage observed in six historic
earthquakes in the United States and Mexico, where the diameter of the pipe is not considered in
modeling the damage function. The following equation is provided for the repair rate (in
repairs/km which can also be considered as the damage rate) of brittle pipelines with PGV in
cm/sec (FEMA 2003):
Repair_Rate ≅ 0.0001 × (PGV)
2.25
(8)
A study by Isoyama and Katayama (1982) defined the original probability function for
pipeline failure, which was assumed to follow a Poisson distribution due to the inherent
uncertainty in vulnerability assessment. The probability was then converted to the average break
rate, as in (Figure 13) from O'Rourke and Ayala (1993).

Figure 13. Repair rate per kilometer for pipeline damage. Graph from FEMA (2003).
59

In the current study, a simplified approach is applied, with results similar to the
continuing work of Isoyama et al. (1998) and Sousa et al. (2012). These studies advance the
original HAZUS-MH damage functions through the development of new rate curves for pipeline
damage estimation with additional empirical data. The current study uses feature scaling
(Equation 9) to normalize the fragility curve of the empirical data from O'Rourke and Ayala
(1993), which results in a curve similar to Isoyama et al. (1998). Damage percentages are then
directly calculated per discrete cell value, with the assumption that the maximum value can be
taken as the upper bound for the percentage of complete damage:

(9)

This approach also has some intuitive results, as the units of repairs/km are generalized to
a dimensionless measurement scale as the probability of repair to any random pipe per raster cell
is calculated as a result of the percentage of damage per cell. This is founded on the assumption
that the pipelines are more-or-less evenly distributed in the study, proportional to population
density and randomly distributed per cell. The correlation of pipelines to population density can
compensate for the variability of total pipelines per cell as the affected population increases
proportionally to the population density and probability of pipeline damage.
Discrete water pipeline restoration timeline, based on the ShakeOut scenario panel
estimates in Jones et al. (2008), shows: minor (7-days), moderate (14-days), extensive (60-days)
and complete (180-days).
60

The HAZUS-MH loss estimation methodology uses the same damage functions for water
pipes, natural gas and oil pipelines (FEMA 2003). While natural gas pipelines are modeled with
the same damage function as water conveyance in Figure 13, their restoration timelines are
different, as the ShakeOut narrative shows:
For natural gas, damage to main distribution lines is caused by building damage
and ground failure, with 50 percent of gas customers within the MMI VIII+ and in
areas with landslide and liquefaction damage (MMI X) are without gas service for
up to three weeks. Five percent of customers are without gas for between three
weeks and two months (Jones et al. 2008, 148).

Discrete natural gas pipeline restoration timelines, based on the ShakeOut scenario panel
estimates show: minor (7-days), moderate (14-days), extensive (21-days) and complete (60-
days). The “minor” and “moderate” categories are estimated, based on the water pipeline
restoration function, as no other data is available.
Bridge System Damage and Restoration in the ShakeOut Scenario and HAZUS-MH 3.4.5.
The final narrative for the ShakeOut scenario is related to transportation, which includes
rails, roads and bridges. The ShakeOut scenario notes that the Southern California road network
consists of hundreds of thousands of “bridges”, mostly on local roads, with many per square
kilometer (Jones et al. 2008). A bridge is defined as a structure spanning and providing passage
over a gap or barrier, such as a river or roadway. Whenever “a road is not poured literally on the
ground it is considered a bridge” (Jones et al. 2008, 135).
For the ShakeOut scenario, a supplemental study by Werner et al. (2008) for bridge
damage was developed that included a deterministic risk of ground-motion-induced damage and
repair times to 6,719 interstate, national and California highway bridges from the National
Bridge Inventory (NBI) and the National Highway Planning Network (NHPN). For all bridges in
the study region, 92 percent are identified as concrete and 6 percent are steel (Yu 2015). The
61

model in Werner et al. (2008) uses the Spectral Acceleration (1.0 Second) ground-motion
ShakeMap data, with the same damage functions as the HAZUS-MH methodology (FEMA
2003).
Werner et al. (2008) also notes that 24 percent of the major bridges in the region have
completed some seismic retrofitting, while Jones et al. (2008) notes that most of the local bridges
have not been seismically retrofitted and so proportionally more damage is expected to them.
Finally, Werner notes the importance of bridge performance and restoration as an indicator in the
overall resiliency of the transportation system in the region, which is interconnected with
economic, disaster response and other lifeline infrastructure interdependencies in the ShakeOut
scenario. The transportation damage narrative from the ShakeOut scenario continues:
Many roads and highways will be impassable in the first few days after the
earthquake because of debris on the roads, damage to bridges, and lack of power
for the traffic signals. This will have a significant negative impact on the
emergency response. Because of the major highway bridge retrofit program of the
last 20 years, highway bridges are not expected to completely collapse, but some
will not be passable. Many bridges on local roads have not been retrofitted and
more damage is expected on those (Jones et al. 2008, 8).

Shaking-related damage to highway bridges renders most freeways in Los
Angeles, San Bernardino, and Riverside counties impassible at several locations,
with some damages taking as long as 5-7 months to repair (Jones et al. 2008, 94).

Irreparable bridge damage will take 5-7 months to rebuild, and one month to open
the roads beneath the bridges. Extensive damage and moderate damage will take
weeks and days to repair, respectively (Jones et al. 2008, 137).

The results of Werner et al. (2008) identify five zones with a high-degree of “complete”
bridge damage where bridges are irreparably damaged and require total replacement (Figure 14).
62

Figure 14. Complete bridge damage in the ShakeOut scenario. Map from Werner et al. (2008).

The HAZUS-MH Technical Manual uses 1.0 second peak spectral acceleration (SA10)
ground-motion to evaluate structural damage to bridges, based on 28 bridge classes and a
number of other parameters (FEMA 2003). From the literature (e.g. Yu 2015; Werner et al.
2008), more than 92 percent of the bridges in the region are concrete, and 6 percent are steel with
24 percent having been seismically retrofitted. Therefore, parameters are available to create a
proportional weighted averaging model curve for characteristic bridges in the region. The
average “probability of bridge damage” in the hazard component of the risk equation is then
calculated based on the HAZUS-MH Technical Manual loss damage function parameters for
bridge classes.
In the current study, all of the “non-CA” bridge classes were removed and the advanced
HAZUS-MH parameters (e.g. shape, skew and factor shape) set equal to one. The associated
63

parameters for generation of the average impact CDF damage functions are: standard deviation,
σ = 0.6 and mean, µ from the following proportional weighted mean equation:

(10)

This resulted in the following parameters for mean, µ to calculate CDF functions (Figure
15) for: minor, (µ = 0.5, σ = 0.6); moderate, (µ = 0.7, σ = 0.6); extensive, (µ = 0.8, σ = 0.6); and
complete, (µ = 1.2, σ = 0.6);

Figure 15. Probability of bridge damage based on weighted average method

The discrete probability of meeting or exceeding the “complete” damage category was
then calculated as per the HAZUS-MH technical manual and evaluated as (FEMA 2003):
64

[BRIDGE
Damage
] = P[Complete Damage | SA10] (11)

This methodology was validated in Appendix C to ensure that it preserved the five
complete bridge damage areas in its results in comparison to Werner (2008) identified in the
ShakeOut supplemental study. The large numbers of bridges in the study region, too small for
the NBI inventory but still subject to ground-motion-induced damages are assumed more-or-less
evenly distributed in the study region (along with the other NBI bridges) proportional to
population density and randomly distributed within each cell. This method is similar to the
HAZUS-MH loss estimation methodology for averaging damage impacts from power system
components as a general weighting to all of the 2010 U.S. Decennial Census tracts to calculate
impact to the population (as discussed in Section 3.4.1).
Bridge restoration timelines from the Werner et al. (2008) supplemental study indicate:
minor (3-days), moderate (12-days), extensive (49-days) and complete (140-days).
Road and Rail System Damage and Restoration in the ShakeOut Scenario and HAZUS 3.4.6.
Roads and rails are subject to Peak Ground Deformation (PGD), which is associated with
the surficial fault rupture, liquefaction and landslide potential (FEMA 2003). As Werner et al.
(2008) noted, ground deformation data, other than the surficial fault rupture, was not provided
for the study. Similarly, the current study is not able to use PGD, liquefaction and landslide
potential to model these impacts. The Applied Technology Council-13 (1985) study, the seminal
study that forms a core component of the HAZUS-MH loss estimation methodology, does
provide an alternate method based on the Delphi model for expert opinion solicitations (Dalkey
et al. 1970) to develop a road and rail damage curve, using high MMI values (VI+).
ATC-13 (1985) identified “Roadway and Pavements” motion-damage relationships for
“Highways” as Facility Number 48 and “Rails” as Facility Type 47 in Appendix G, Table G.1 of
65

the study. To construct a trend curve based on the MMI levels a maximum, M, value of the best
estimate and weighted standard deviation of the best estimates, σ, for both facility numbers were
required. These are identified as MAXB and SDEVB respectively in the ATC-13 (1985) study.
The road and rail damage probabilities were then directly calculated from the respective trend
functions generated for the MMI values shown in Table 2.
Table 2. MMI based damage probabilities for highways and rails

Source: Data from ATC-13 (1985), Appendix G, Table G.1

Figure 16. Road and rail damage probability from MMI. Data from ATC-13 (1985).
66

The discrete road system restoration timelines, based on the HAZUS-MH damage
categories show: minor (2-days), moderate (7-days), extensive (62-days) and complete (62-
days). Discrete rail system restoration timelines, based on the HAZUS-MH damage categories
show: minor (2-days), moderate (11-days), extensive (49-days) and complete (180-days).
In summary, six damage functions have been identified from the HAZUS-MH Technical
Manual and ATC-13 (1985), along with their associated restoration timelines, which have been
incorporated into the model design (with some extension). These were combined into the hazard
component of the probabilistic risk model, which is investigated in Chapter 4.
Empirical Restoration Curves for Emergency Logistical Resources 3.4.7.
Most of the damage functions from the HAZUS-MH Technical Manual and results from
the Shakeout scenario have restoration timeline curves associated with them. For the current
study, a similar modeled curve for logistical resources requirements over time must be
developed, in order to calculate resource requirements at specific discrete time intervals. From
investigation of the tools used by the United States Army Corps of Engineers (USACE), and
recent events in the commodity mission for Puerto Rico in Hurricane Maria, two very different
restoration curves for resource requirements are found. These were used in the current study, in
the methodology of Chapter 4, to create three possible simulations for resource requirements
over time.
The USACE is identified as the lead agency for the commodity distribution mission, in
coordination with FEMA and the Defense Logistics Agency (DLA) in the event of a catastrophic
event. For the commodity mission, the USACE uses a strategic planning tool based solely on
population impacted by power outage and the expected number of PODS to be activated in an
impacted area (USACE 2008). This tool (an excel spreadsheet) then calculates the decreasing
67

amount of commodities for the entire incident. The model was originally designed to support
emergency planning in suburban, rural and coastal areas in the southeastern United States and
may have a large margin of error in urban areas (UASI 2014). This model also assumes a rapid
timeline for infrastructure restoration, whether by repair or replacement of damage facilities or
augmentation by emergency power generation capabilities—which as recent events have shown,
may not be realistic.
For the current study, the USACE strategic planning tool was experimentally applied to
estimate logistical resource requirements for 143 PODs in the Los Angeles County study area.
The key information from this result are the graph and trend line shown in Figure 17. These trend
equations and associated parameters for the affected categories in the four damage states are
further investigated in Chapter 4 and were used as one simulation for resource requirements over
time.

Figure 17. General resource requirements over time from the USACE model (USACE 2008)
68

The Puerto Rico logistical response for Hurricane Maria can serve as a model for the
worst-case scenario, and so was chosen as a second possible restoration curve for emergency
logistical resource requirements. The Puerto Rico logistical response is the largest commodity
mission ever supported by the United States government, compounded with infrastructure
restoration delayed for an extended period (FEMA 2018b). Figure 18 summarizes Puerto Rico
commodity information from publicly available daily situation reports for six weeks (FEMA
2017). The total population affected is based on power service restoration estimates for an initial
population of 1.5 million, which, it should be noted, is less than half of the population expected
to have emergency logistical resource requirements in the (M) 7.8 San Andreas Earthquake
Scenario.

Figure 18. Puerto Rico commodity mission shortfalls in Hurricane Maria. Data from (FEMA)
2017.

69

The underlying trend lines of these empirically based resource requirement curves can be
modeled as decreasing exponential functions, which are solutions to a set of Linear Ordinary
Differential Equations (ODES). Linear ODEs are commonly used in population modeling
(Boyce et al. 2017). These empirical sources and their trend lines are further investigated in
Section 4.4.1 and were used to model emergency logistical resource requirements over time for
three simulations which can provide logistical planning information for the OPLAN commodity
mission.
In conclusion, all of the components of the probabilistic risk model have been presented
and investigated as they are situated within their respective engineering and scientific disciplines.
These components were then implemented in the methodology of the current study to estimate
emergency logistical resource requirements for affected populations in the (M) 7.8 San Andreas
Earthquake Scenario.
70

Chapter 4 Model Implementation
The practical aim of this study was to model the affected “at-risk” populations in the ShakeOut
scenario, at three-days (t = 3) post-event for emergency logistical resource requirements using
the general risk equation and assumptions from the Southern California Catastrophic Earthquake
Response Operational Plan (OPLAN). This was accomplished through computational
implementation of the risk equation from Chapter 3 (per each raster Cell
i,j
) as:

[Risk
Population
] = [HAZARD
Damage
] × [SOVI
Weight
] × [LandScan
Population
] (12)

The Vulnerability component has been established as [SOVI
Weight
]

and the Population
component as [LandScan
Population
] in Chapter 3. The hazard component of the model was
computationally implemented, based on the results of Section 3.4 from the identification of the
six indicators as:

(13)
The components of infrastructure damage indicators, as independent probabilities, were
combined as a “maximum”, for each grid cell (Cell
i,j
). The hazard component should be
represented in a way that includes all the information that is known about the component
functions without assuming anything that is not known. This can be considered a maximum
entropy approach to modeling these infrastructure components in the probabilistic risk model.
A maximum entropy probability distribution is defined as having entropy that is at least as
great as that of all other members of a class of probability distributions, where entropy can be
considered as a measure of information loss (Jaynes 2003). The result is that the probability
71

distribution minimizes entropy subject to certain constraints—the maximum probability of
damage value of the infrastructure indicator component, per cell. In summary, choosing the
“maximum” of the probabilities of the component indicator functions agrees with everything that
is known, avoids loss of information and avoids assuming anything that is not known (Philips et
al. 2005).
Therefore, the “maximum” of the component probabilities has been chosen to
computationally implement the hazard component of the risk equation. The resulting
“maximum” function represents the final result of the probabilistic risk model computations for
the [HAZARD
Damage
] component.
Furthermore, total emergency logistical resources were calculated, and defined as the
initial conditions (t = 3) for the modeling of resource requirements over time as:

[Risk
Population
] × [Meal
Mutiplier
] = X
3
(14)

[Risk
Population
] × [Water
Multiplier
] = W
3
(15)

In these equations, the resource multiplier was established from the OPLAN as 2 meals
per person/day and 3 liters of water per person/day. These initial conditions were then used for
establishing a relative risk ratio (which is investigated in Section 4.3) and for modeling
decreasing resource requirements over time (which is investigated in Section 4.4). The steps for
the development of the probabilistic risk model and its applications are presented in Figure 19
and are explored in the rest of the chapter.
72

Figure 19. Development and applications of the probabilistic risk model

4.1. Global Assumptions
The current study incorporated a number of global assumptions required to develop a
modeling methodology for emergency logistical resource requirements in the (M) 7.8 San
Andreas Earthquake Scenario. Of these, the first set requires limited justification while
individual assumptions that require more detailed justification or validation are provided
immediately following their introduction. The first set of assumptions relate to the ShakeOut
scenario and have already been established:
1. The (M) 7.8 San Andreas Earthquake Scenario has occurred at night and impacted the
73

eight-county Southern California region as identified in the OPLAN
2. A disaster-affected population of between 2.5 million and 3.5 million require emergency
food and water (emergency logistical resources) for a 45 to 90-day period
3. Points of Distribution (POD) sites with associated Areas of Responsibility (AORs) have
been activated along with the emergency logistical resource commodity mission, per the
OPLAN
4. AORs are determined by the Original Gravity Weighted Huff Model for probability of
travel to a site location, bound by Los Angeles County boundaries, at the edges
In Assumption 4, the Original Gravity Weighted Huff Model was used to identify AORs for the
PODs, based on 2010 U.S. Decennial Census block population. These AORs were used to
tabulate total resource requirements per POD and are based on a simple probability of travel
model using the average nearest neighbor distance. This supplemental analysis is documented in
Appendix A. The next two assumptions relate to the specific spatial and temporal resolution of
the study:
5. The populations in the respective LandScan 2015 “global” (~1 km) population database
and the LandScan USA 2012 “conus_night” (~90 m) datasets are randomly dispersed
within each raster grid cell and are represented by proxy at the centroid for calculations
6. The temporal variation between 2010 U.S. Decennial Census-based population, 2015
U.S. Census population estimates, and Landscan populations from 2012 and 2015 do not
significantly affect the model’s results (i.e. this is an acceptable range of uncertainty in
population estimation)
The next set of assumptions relate to calculations and data in the modeling methodology:
7. The total disaster displaced population (from t = 0 to t < 3 days) of 542,000 from the
OPLAN is included in the total (t = 3 day) disaster-affected population of between 2.5
million and 3.5 million (i.e. there is only one characteristic population to model resource
74

requirements for).
The ShakeOut scenario provides estimates for initial displaced populations (t = 0) at 255,251
based on the FEMA Hazards United States (HAZUS-MH) multi-hazard loss estimation
methodology in terms of the HAZUS-MH shelter model. However, it does not estimate
emergency logistical resources or estimate (t = 3) affected populations (Jones et al. 2008). These
estimates for (t = 0) are based on the 2010 U.S. Decennial Census tract population, demographics
indicative of vulnerable populations with associated weighting factors established by the Red
Cross (Harrald et al. 1992) and the damage functions for “extensive” and “complete” damage of
single and multi-family residential occupancy classes represented in the building stock of the
study area (FEMA 2003).
The OPLAN identifies an initial displaced population and estimates (t = 3) disaster-
affected populations at 2.5 million, based on expert panel recommendation (CalOES and FEMA
2011). For this study, it is assumed that these initial displaced populations from (t = 0) of
542,000 are included in the (t = 3) disaster-affected population, which as the literature notes is
affected more by social vulnerability, lifeline utility infrastructure impacts and restoration
timelines.
In consideration of the outcomes over time for the displaced populations, it must be
considered that a disaster emergency housing mission will be activated to stabilize these
displaced populations (CalOES and FEMA 2011). These initial displaced populations are
similarly affected by lifeline utility infrastructure damage and restoration. So, for all intents and
purposes in the model, they are the same—as housing solutions also require full restoration of
lifeline utility infrastructure. The result of this assumption ensures that there is only one
75

characteristic population to model initial resource requirements and resource requirements over
time for, based on the ShakeOut scenario parameters and OPLAN.
8. Infrastructure components and their damages are independent at (t = 3 days), but
increasingly interconnected over time, represented by the averages for their functionality
restoration timelines.
The HAZUS-MH methodology assumes damages are independent when the earthquake occurs at
(t = 0). For example, power infrastructure damage in the HAZUS-MH methodology is not related
to any other factors and can be represented by the damage functions in the HAZUS-MH
Technical Manual without feedback or lag mechanisms from other transportation, water or other
lifeline utility sector components (FEMA 2003). However, as disaster recovery progresses,
transportation impacts may delay infrastructure repair, power loss may delay water restoration,
etc. It is outside the scope of the current study to develop network system analyses of
infrastructure interdependencies. Therefore, these damage functions must be utilized in a
simplified manner without a systems analysis approach to model these interdependencies.
To address this, it is assumed that the infrastructure components in the model, being
independent at (t = 0) remain independent at (t = 3). As the HAZUS-MH loss estimation
methodology uses this simplified approach to model component lifeline utility restoration
throughout the restoration timeline, the current study is justified in applying the same assumption
(FEMA 2003). This assumption is simply stating that at (t = 3) the damage and restoration of one
infrastructure component does not relate to the others and, as such, that they can be
independently combined in the model without consideration for interdependency (i.e. lag and or
feedback mechanisms). The HAZUS-MH methodology recommends systems analysis for more
detailed studies of lifeline utility interdependency.
76

A simplified model of lifeline infrastructure system interaction as increasingly
interconnected over time (t > 3) is then applied, represented by the averages for functionality
restoration timelines of the infrastructure components in the model. Absent any justification for
assigning weights in the averaging of the components, it is assumed they are equally weighted.
The average of the infrastructure components’ restoration timelines is then used to create the
restoration timeline intervals for the resource requirement curve for the associated impact
categories. This assumption requires additional research to establish weights for the components
and is a recommendation in the study’s conclusion for future research.
9. The literature shows that socially vulnerable populations require more resources and for
longer periods of time. The probabilistic risk model represents this observation as a
(±) 22 percent weighting factor, based on the ranked Social Vulnerability Index (SoVI),
as the best available empirical data for social vulnerability’s amplifying effects on
resource requirements
These are the direct conclusions from Section 3.2 which has shown that it is critically important
to represent the effects of social vulnerability in relation to emergency logistical resource
requirements. To be further calibrated, this assumption requires additional research and is a
recommendation in the study’s conclusion for future research.
These next assumptions use results from probability theory and statistical frequentist
inference for applying (n) independent Bernoulli trials (for n = population value of LandScan
cell) to result in the expected value of populations impacted (i.e. this assumption relates the
probability of impact of populations within the grid cell to the proportion of the total population
impacted within it).
10. The total population impacted in a grid cell is the expected value of the probability of
impact per grid cell and the total population impacted in the study area is the sum of the
population impacted in all of the grid cells.
77

This is the method used by the HAZUS-MH loss estimation methodology to calculate
populations exposed to a hazard. Populations subject to outage are calculated directly from the
discrete probability of impact to the substations (FEMA 2003). This is also the method used in
the risk equation and for the other infrastructure indicator variables in the current study. The
approach is based on classical frequentist inference assumption from probability theory to
estimate expected values of indicator variables from the probabilities of success in a binomial
distribution. This expected value is then used as the estimated population impacted per grid cell,
and by the linearity of expectations, for the total population impacted in the study region (Pitman
2006).
The final three assumptions relate infrastructure density to population density and are
simplifications or extensions of the HAZUS-MH loss estimation methodologies.
11. The distribution of electric power system components that occur in each grid cell are
regularly dispersed throughout the study area in proportion to population density and
are randomly distributed within each raster grid cell, represented by proxy at the
centroid
This assumption is investigated in Section 3.4.3. The California Energy Commission substation
data shows on average, there is one substation in every 6 sq. km in Los Angeles County and a
higher density in urban areas. The HAZUS-MH methodology for calculating affected
populations for outages is insufficient and does not account for the MAUP effect. The MAUP
effect can be compensated for through the relationship of infrastructure components to
population density.
As shown in Appendix B, in a sample of the current study region, this assumption and
calculation of population affected by power outage decreases the range of uncertainty (or is at
least as good as the current standard) in the original HAZUS-MH method, as explained in
78

Section 3.4.3. This approach can then be used to calculate the [POWER
Damage
] component of
[HAZARD
Damage
]. The next assumption relates water and natural gas conveyance/pipelines to
population density.
12. The distribution of water and natural gas pipelines in each grid cell are regularly
dispersed throughout the study area in proportion to population density and are
randomly distributed within each raster grid cell, represented by proxy at the centroid
This component in the HAZUS-MH loss estimation methodology is generalized to the census
tract and associated with population density with 80 percent of the pipes assumed to be brittle
(FEMA 2003). Therefore, just as there are more dwellings in areas of higher population density,
there are similarly more residential and community pipelines. Using the equations of Section
3.4.4, the [PIPES
Damage
] component of [HAZARD
Damage
] can then be calculated. The final
assumption is related to transportation infrastructure component distribution.
13. The distribution of transportation infrastructure components (e.g. bridges, roads, rail) in
each grid cell are regularly dispersed throughout the study area in proportion to
population density and are randomly distributed within each raster grid cell, represented
by proxy at the centroid value
It is plausible to associate more roads with a higher population density, similar to the above
methodology for pipe damage. Similarly, in addition to the 6,719 interstate, national and
California highway bridges identified in the ShakeOut supplemental study, Jones et al. (2008)
identifies that there are hundreds of thousands of structures also considered as bridges in the
region, which can be associated with population density.
As shown in Appendix C, the areas of probability of “complete” bridge damage that
dominate the risk equation (Equation 1) fall within the expected regions for complete bridge
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damage in the study by Werner et al. (2008). This approach can then be used to calculate the
[BRIDGE
Damage
] component of [HAZARD
Damage
] using the equations of Section 3.4.5.
To implement the model, the current study used the Esri ArcGIS Desktop 10.6 suite of
software and tools for spatial analysis and database management, MATLAB (2017) and RStudio
ver. 1.1 for statistical analyses and advanced computations.
4.2. Implementation of the Probabilistic Risk Model
For computational implementation of the risk equation, this section focuses on the
translation of the modeling methodology into an Esri ArcGIS 10.6 compatible data structure (e.g.
tables, attributes, relationships, featureclasses and domains) and the development of the
associated database architecture and Entity-Relationship (E-R) schema. To illustrate the steps
used for computational implementation of the probabilistic risk model, process flow diagrams
with descriptions are provided.
Data requirements and preparation 4.2.1.
For the current study, eight GIS raster and vector datasets were identified in Chapters 2
and 3 that are required for developing a model of emergency logistical resource requirements in
the (M) 7.8 San Andreas Earthquake Scenario. These datasets are shown in Table 3.
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Table 3. Eight datasets used for development of the probabilistic risk model

The first step in development of the probabilistic risk model was elementary data
preparation with the creation of an Esri File Geodatabase (FGDB) data structure and loading of
the eight datasets identified above. Elementary data preparation steps for the Entity-Relationship
schema also included:
• Created FGDB: RISK_MODEL_2018.fgdb
• Imported/loaded and projected data sources: WGS 1984 UTM Zone 11S
• Clipped LandScan 2015 “global” to eight-county study area (global.grid)
• Clipped LandScan 2012 “conus_night” to Los Angeles County study area
(conus_night.grid)
• Created subset of Social Vulnerability (SoVI) 2010 U.S. Decennial Census tracts for
study regions
• Created all new attributes in [FINAL_RISK_CALC], [PODS_OPLAN_2011] and
[CA_Tract_SoVI_06_10]
• Created attribute domains and Entity-Relationship (E-R) structure. These data
structures are presented in Figure 20.
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Figure 20. Database Entity-Relationship diagram
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A vector-based (point) approach for analysis was chosen due to the large number of
stored floating-point calculations. The need for interoperability between multiple software
platforms running advanced calculations and statistical analysis made using a vector attribute
table, rather than a raster data structure, a more flexible approach. The spatial resolution for the
model was based on the cell size of the respective LandScan Raster datasets, which were clipped
to the study region and converted to a point centroid dataset for analysis through the “raster-to-
point” function in ArcGIS 10.6. These centroids were converted back to raster through the
“point-to-raster” function in ArcGIS 10.6, without any loss of fidelity, when needed.
As indicated in Figure 19, at the beginning of the chapter, the implementation of the
probabilistic risk model was accomplished in a sequence of six steps. In Step 1 (detailed in
Figure 21), advanced data preparation for the datasets was initiated, with the “raster-to-point”
calculation. This step produced the table [FINAL_RISK_CALC], which was used to store all
risk calculation results. The rescaling of the social vulnerability weighting-factor, which results
in the final vulnerability component of the risk equation, was also calculated. Note that a key for
the color coding used in all process diagrams shown in this chapter is included in Figure 21.

Figure 21. Step 1: Advanced data preparation
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In Step 2, shown in Figure 22, all unique values in each of the four ground-motion vector
polygon datasets were extracted to look-up tables that could be exported to MATLAB for
calculation of the CDF functions. Once the calculations were completed, the tables were then
joined back to the original ground-motion data sources and new attributes were created. This
resulted in the raw probabilities of damage, which were associated with their respective ground-
motion polygons, available for use in further calculation.

Figure 22. Step 2: Computations in MATLAB for the probabilistic risk model

In Step 3, shown in Figure 23, the results from the calculations in the respective ground-
motion polygon feature classes were each spatially joined to the vector points feature class
[FINAL_RISK_CALC]. At the end of this step, all data for calculation of the probabilistic risk
model were stored as individual columns in the [FINAL_RISK_CALC] attribute table.
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Figure 23. Step 3: Results from the CDF calculations

In Step 4, shown in Figure 24, each of the probability of damage functions for the five
unique infrastructure indicators was calculated within the [FINAL_RISK_CALC] featureclass,
based on the methodologies identified in Chapter 3. Finally, the hazard component of the risk
equation was calculated by a python expression for the “maximum” of each of these damage
functions, per each centroid point.

Figure 24. Step 4: Probabilistic damage functions and maximum probability are computed
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In Step 5, shown in Figure 25, the final calculations of the probabilistic risk model, which
included the weighting for social vulnerability, resulted in the total “at-risk” disaster-affected
population and their emergency logistical resource requirements. Finally, for visualization
purposes, all of these results for the six component probabilities were then converted into raster
grids. At the end of Step 5, the probabilistic risk methodology for modeling emergency logistical
resource of day-three post-event disaster-affected populations was completed.

Figure 25. Step 5: Calculation of “at-risk” populations and their resource requirements, plus
conversion back to raster for visualization purposes

Validation of Results with Regression Analysis 4.2.2.
In order to validate the results of the probabilistic risk model before emergency
management application, the current study quantified the distributions and relationships of the
underlying indicator variables in the model results. Logistic regression analysis and associated
statistical tests was undertaken in Step 6 for analysis of variable contributions in the results and
to determine a confidence interval for these estimates. To do this, generalized linear model
(GLM) regression analysis was applied in RStudio to statistically investigate the resulting risk
86

probability as the dependent variable. The independent variables were the respective five
infrastructure indicator probabilities along with the SoVI weight parameter and ground-motion
data.

Figure 26. Step 6: Validation of the model

The GLM for logistic regression is best specified for models of dependent variables as a
proportion of “successes” using logistic curves as link functions for the family of binomial data
distributions (Cribari-Neto and Achim 2010). R statistics libraries were utilized to run and
evaluate the GLM with the 180,380 raster-cell centroid point data-frame in the eight-county
study region. The Nagelkerke (1991) pseudo R-squared metric was used, along with analysis of
the deviance residuals. These results provided a quantification of the underlying indicators in the
significance of their contribution to the resulting maximum risk probability and provided a range
of uncertainty for the model from each of the components.
This concludes the implementation of the probabilistic risk model for emergency
logistical resource requirements. These results were next applied in calculation of a relative risk
ratio and to estimate the logistical resources needed over time in the Los Angeles County study
area.
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4.3. Methodology for Calculation of the Relative Risk Ratio
In the current study, a methodology similar to Bithell (1990) for estimation of relative
risk to the general population was employed in the eight-county study region. This approach
used the emergency logistical resource requirements as determined from the results of the
probabilistic risk model as the “cases” and the background population from Landscan 2015 as
the “control”. The resulting relative (universal) risk ratio was then directly calculated as the
quotient of the two raster surfaces of population “control” versus resource needs “cases”, which
effectively cancels out the “per-unit of area” term in the numerator and denominator. In general,
a relative risk ratio is the ratio of the probability of an event occurring in an exposed population
to its occurrence in the general population.
The final results were a raster grid based on the cell size from LandScan 2015 “global”
(~ 1 km) that represented the relative risk to any member of the population in the study area.
This can be used by emergency managers for planning purposes and to target resources to
communities with a high probability of emergency logistical resource requirements in support of
mitigation planning and preparedness.
Computational Implementation of the Relative Risk Ratio 4.3.1.
Calculation of the relative risk ratio was accomplished in one step, based on application
of the results from the probabilistic risk model (Figure 27). Two attributes were used to directly
calculate the quotient as the resulting relative risk ratio, per the methodology of Bithell (1990).

Figure 27. The final relative risk ratio calculated for the study area
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The final result was a raster grid based on the cell size of LandScan 2015 “global”
(~1 km) that represents the relative risk of any member of the population in the study area.
4.4. Methodology for Modeling Resource Requirements Over Time
The final part of the methodology investigated modeling emergency logistical resource
requirements over time. The initial resource requirements (t = 3) of at-risk populations resulting
from the probabilistic risk model were used to model recurring resource requirements over a 90-
day period. This provided an estimate of at-risk populations for emergency resource
requirements in Los Angeles County at six future operational periods (e.g. at t = 7, 14, 30, 45, 60
and 90 days) using the high-resolution LandScan USA 2012 “conus_night” (~90 m) population
dataset. Emergency managers can utilize these results in planning for long-term community
resource requirements issues in the commodity mission.
To do this, three factors were investigated which are involved in developing resource
requirements curves, similar to the restoration timelines of the individual infrastructure
components of the probabilistic risk model. The first factor focused on the development of an
equivalent set of four impact categories for the probabilistic risk model’s results and
establishment of a restoration timeline point (i.e. when no further resources are required) for each
of the four impact categories, within the “minor”, “moderate”, “extensive” and “complete”
requirement ranges. These restoration timelines are based on the averages of the respective
components restoration timelines as in Assumption 8.
The second factor was to model the form of the curve based on the empirical curves
found at the end of Chapter 3. The four impact categories and their curves were then fit to the
restoration timeline values where resource requirements are equal to zero on the y-axis for each
of the respective “minor”, “moderate”, “extensive” and “complete” categories (FEMA 2003).
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Curves for three simulations were generated to represent the maximum, mean and
minimum dynamic resource requirement ranges in the current study. Respectively these were:
(1) a minimum decay curve trend, for rapid recovery based on the United States Army Corps of
Engineers (USACE) mission planning tool as Simulation A (Minimum); (2) a maximum decay
curve trend representing long-term infrastructure restoration issues, such as in recent events in
Puerto Rico, as Simulation B (Maximum); and (3) a linear decay curve trend as Simulation C
(Average).
Finally, these curves were computationally implemented and evaluated at specific time
intervals in the study region and summary results per POD site were calculated for emergency
resource requirements in the three simulations, with consideration for social vulnerability per the
probabilistic risk model developed in the current study. This part of the study concluded in
display and summary results of the three simulations and in Appendix D.
Impact Categories and Restoration Timelines 4.4.1.
From the results of the probabilistic risk model, the range of data values for
[HAZARD
Damage
]×[SOVI
Weigtht
] were statistically evaluated to separate the ranked set into four
natural breaks, based on the maximum, minimum and mean. The four damage categories were
defined as: “minor”, as the range from the minimum to the (mean – minimum)/2; “moderate”, as
the range between (mean – minimum)/2 and the mean; “extensive”, as the range between the
mean and the (maximum – mean)/2; and “complete”, as the range between the (maximum –
mean)/2 and the maximum. This is a simple way to define these impact categories using natural
breaks in the data and is similar (within a standard deviation) to a nested means approach. The
only assumption used in the approach is that areas with higher probability of impacts also take
longer to recover, which the ShakeOut scenario indicates (Jones et al. 2008).
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The next step in modeling emergency logistical resource requirements over time was to
establish a restoration timeline point (i.e. the point where 100 percent of resource needs are met)
for each of the four impact categories. From Assumption 8, it was proposed that the average of
restoration timelines for the respective infrastructure indicators can be used to calculate resource
requirement restoration points for each of the four categories. From the ShakeOut scenario
(Jones et al 2008) and the HAZUS-MH Technical Manual (FEMA 2003) in Section 3.3, these
observations have been summarized in Table 2:
Table 4. Average restoration timelines for resource requirements curve

Source: FEMA (2003) and Jones et al. (2008)
These results were used to find the parameter (a) for fitting the resource requirement
curve equations for each of the damage categories to zero values on the y-axis in the three
simulations of the study.
Dynamic Resource Requirements Curves 4.4.2.
The form of the curve in Figure 17 for the USACE resource restoration timeline was
approximated by an exponential trend line. A trend line is created by a modeling function that
represents the behavior of a set of data by identifying its underlying pattern (Dodge 2003).
Equation 16 shows resource requirements over time as a function of time (days) with X
3
as the
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initial conditions resulting from the probabilistic risk model, the parameter (a) as the damage
category, and parameter (b) as the associated SoVI weight in the cell.

(16)

Equation 17 is then the linear ordinary differential equation that is solved by the equation above
(Boyce et al. 2017):
(17)
This was graphed (Figure 28) where X
3
is an arbitrary resource requirement calculated
from the probabilistic risk model, for an arbitrary (Cell
i, j
) in the study area. For the example
below, (b=1) was chosen and can be considered as no social vulnerability amplification.

Figure 28. Simulation A (Minimum)—Dynamic resource requirements curve, based on the
USACE model trend line
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This rapid recovery curve can be considered as Simulation A (Minimum). Similarly,
Figure 18 for the delayed infrastructure restoration in Puerto Rico suggests the following
exponential trend line equation, with the same variables and parameters as the first:

(18)
This equation was split for t = 3, and t > 3 to be computationally implemented in a non-
autonomous fashion (Boyce et al. 2017). Equation 18 is then the solution to the linear ordinary
differential equation below, of the form:

(19)
This was graphed (Figure 29) where X
3
is an arbitrary resource requirement, calculated
from the probabilistic risk model, for an arbitrary (Cell
i,j
) in the study area. For the example
below, (b = 1) was again chosen which can be considered as no social vulnerability
amplification.
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Figure 29. Simulation B (Maximum)—Dynamic resource requirements curve, based on delayed
infrastructure restoration

This delayed restoration curve can be considered Simulation B (Maximum). The constant
decrease scenario is the avaerage rate of the two simulation curves and can be similarly
represented and graphed as:
(20)
Equation 20 is then the solution to the linear ordinary differential equation below, of the form:
(21)
This simple ODE results in linear trend curves, as graphed in Figure 30:
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Figure 30. Simulation C (Average)—Dynamic resource requirements curve, linear trend

This linear trend can be considered Simulation C (Average). Together, three families of
curves for modeling dynamic resource requirements over time have been presented. These three
sets of curves were then implemented as the three simulations and evaluated (as functions) at the
t = 7, 14, 30, 45, 60 and 90-day intervals to determine dynamic logistical resource requirements.
Computational Implementation of the Dynamic Resource Requirements Curves 4.4.3.
The final application of the probabilistic risk modeling methodology was to
computationally implement the resource requirement curves, identified in the previous section, in
ArcGIS 10.6 to calculate resource requirements over time at t = 7, 14, 30, 45, 60 and 90-day
intervals. First, the probabilistic risk model was applied to LandScan USA 2012 “conus_night”
population database in the Los Angeles County study area, and initial conditions for calculating
resource requirements over time (X
3
)

were defined as the (t = 3) day resource requirements
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resulting from the probabilistic risk model. In the tabular data structure this field was stored as
[FINAL_RISK_CALC]![X_3].
These results from the probabilistic risk model were then applied in four steps to
calculate resource requirements over time in three simulations. In Step 1, all of the calculations
as VBScript expressions using the exp() and log() functions were made for t = 7, 14, 30, 45, 60
and 90-days (Figure 31). This resulted in the total resource requirements at the six identified time
intervals for the three simulations, with amplification for social vulnerability. The results of these
18 calculations were stored in the [FINAL_RISK_CALC] point featureclass.

Figure 31. Step 1: Direct calculation of resource requirements over time

In Step 2, the “point-to-raster” tool was applied to generate the final results as 18 raster
surfaces for presentation and display (Figure 32).
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Figure 32. Step 2: Results of the calculations converted to raster surfaces

In Step 3, the results from Appendix A (Figure 33) were applied as the Areas of
Responsibility (AOR) polygon featureclass, modeled from the Original Gravity Weighted Huff
Model for probability of travel to facilities. This data was used to aggregate the results of the
calculations into smaller units for reporting summary resource requirements over time for each
POD throughout the Los Angeles County study area.

Figure 33. Step 3: AORS for summary resource requirements tabulation

In Step 4, the [FINAL_RISK_CALC] featureclass was spatially joined in a “many-to-
one” relationship with the AORS, where all of the calculated resource requirements over time
were summarized. Finally, [AORS_OPLAN_2011] and [PODS_OPLAN_2011] featureclasses
were joined in a “one-to-one” relationship to update summary resource requirement fields
(Figure 34), which were then presented as a report.
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Figure 34. Step 4: Calculated resource requirements over time are summarized by AOR

The output of Step 4 is the Logistical Resource Summary Report, which is shown in its
entirety in Appendix D, is a summary of the modeled resource requirements at each of the 143
Point of Distribution (POD) sites in Los Angeles County identified in the OPLAN (CalOES and
FEMA 2011). For this report, truckloads and pallets of food and water for the seven operational
periods in the recovery timeline were calculated, based on standard shipping formulas and
established metrics used in humanitarian relief (Johnson and Coryell 2016).
The final result of this multi-step process was a comprehensive model for emergency
logistical resource requirements supporting socially vulnerable disaster-affected populations
affected by the (M) 7.8 San Andreas Earthquake Scenario in Los Angeles County.

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Chapter 5 Model Results
The results for this study are presented in three sections. First, an overview of the probabilistic
risk model development and results are provided along with the results from the logistic
regression analysis. Second, results are presented from the application of the probabilistic risk
model to calculate a relative risk ratio in the eight-county study area. Finally, emergency
logistical resource requirements over time in Los Angeles County for the commodity mission in
the Southern California Catastrophic Earthquake Response Operational Plan (OPLAN) are
estimated and summarized by the Point of Distribution (POD) sites, for three simulations. These
results are presented in their entirety in Appendix D.
5.1. Overview of the Probabilistic Risk Model Results
The computational implementation of the probabilistic risk model from Section 4.2.1 was
successful, with a resulting “at-risk” population of 3,352,955 for emergency logistical resource
requirements in the eight-county study region. These results are in alignment with the ShakeOut
earthquake scenario and the OPLAN priority to provide meals and water to support disaster-
affected populations of between 2.5 million and 3.5 million in the eight-county study region,
from three-days post-event. Therefore, the model has produced preliminary results that can be
used by emergency managers and community planners for planning assumptions in the support
of affected population with emergency logistical resource requirements.
Results from the Hazard Components of the Probabilistic Risk Model 5.1.1.
The calculations of the components in the probabilistic risk model were made without
much deviation from the proposed six-step process shown in Figure 19. The hazard components
were individually calculated according to the methodology in Figure 24, as shown in Figure 35.
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Figure 35. Probability of damage calculated for the infrastructure indicators
100

The final hazard damage “maximum” component of the probabilistic risk model, based
on the identified infrastructure indicators, was then calculated as the “proxy” for the probability
of emergency logistical resource requirements. These results are shown in Figure 36.

Figure 36. Results of calculation of the hazard component of the probabilistic risk model

Analysis of these results was performed to determine the contribution of each
infrastructure damage component to the overall hazard in the study. Queries were used to
identify the component that dominated the results of the hazard “maximum” calculation in each
cell. The results of the analysis are presented in Table 5 for all of the grid cells.
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Table 5. Summary of infrastructure component contribution to hazard results

These results using the Isoyama et al. (1998) damage functions for pipeline damage were
also tested and compared with the normalized pipeline damage functions from O'Rourke and
Ayala (1993) used in the current study—with only a small difference in the results. It was also
found that bridge damage dominated the hazard calculation in the five expected areas from
Werner et al. (2008), as shown in Appendix C.
It should also be noted that analysis of the infrastructure component contributions to the
hazard indicated that road damage had a zero percent contribution to the final “maximum”
hazard throughout the study area. This is because both the rail damage and road damage are
based on Modified Mercalli Intensity (MMI). The rail damage curve dominated the road damage
curve in each cell—and so the maximum excluded these values. The individual components of
the model, and their quantitative contribution to the results, are further explored in the next
section through validation with regression analysis.
One unexpected observation of boundary problems in the results required a slight
adjustment to the methodology. Due to the smaller extent of the modeled ground-motion
datasets, the entire eight-county region extent was not covered, so no damage probability values
could be calculated for populations in these areas. However, analysis of the datasets indicated
that there were likely very low ground-motion results in these sparsely populated areas.
Therefore, all of the damage probability values were set to zero outside of the areas with
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modeled ground-motion data, and the model was run with zero values in these regions. It is
assumed this had no significant impact on the results.
The SoVI weight was also calculated as per the methodology, with no issues (Figure 37).

Figure 37. Results for the SoVI amplification factor calculation

The original range of composite factor scores for social vulnerability from the SoVI
index (-15.93 to 14.78) were rescaled, as per the methodology in Chapter 4, to the new range
(0.78 to 1.22) which preserved the ranked social vulnerability relation between census tracts in
the computations. The social vulnerability classes and the resulting weights are presented in
Figure 37 with the same standard deviation ranking as in the original data (HVRI 2018).
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Finally, the computational implementation of the risk equation (Equation 12) was
completed using the result of the hazard component calculations, social vulnerability weighting
and the LandScan 2015 “global” population dataset. The final result, as presented in Figure 38, is
a model of the “at-risk” population with emergency logistical resource requirements in the (M)
7.8 San Andreas Earthquake Scenario, throughout the eight-county study region, at day-three
post event.

Figure 38. Final calculation of “at-risk” population

From these results, a summary of “at-risk” populations by county in the eight-county
study region was calculated as well as the percentage of the total population from Landscan 2015
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“global”. These preliminary results and the percentage of the population “at-risk” versus the total
population can be considered as a preliminary risk assessment by county, pending validation.
Table 6. Summary of “at-risk” populations in eight-county study area

Validation with Regression Analysis 5.1.2.
The model was then validated to quantify the distributions and relationships of the
underlying indicator variables in the model results. Logistic regression and associated statistical
tests were performed for analysis of variable contributions in the results and to determine a
confidence interval for these estimates.
The first step was to analyze the empirical distribution of the results from
[HAZARD
damage
]×[SOVI
Weight
], which is the “proxy” for the probability of emergency logistical
resource requirements calculated in Equation 12. A histogram was generated in RStudio which
showed the distribution and frequency of these results. From this distribution, an empirical
cumulative distribution function (CDF) was calculated, which represented the density (as a
probability) of the modeled data less than or equal to any specific value in the dataset. From
analysis of these results, it was found that the empirical distribution was most closely
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approximated by the beta distribution with alpha = 0.1391879 and beta = .2605410. These graphs
characterize the model results and are represented in Figure 39.

Figure 39. Empirical distribution of model results and beta distribution

The component variable distributions and relationships of the six infrastructure indicators
and the four ground motion parameters were then analyzed individually in comparison to the
model results. This analysis is presented in Figures 40 and 41, with a logistic trend curve
approximating the relationship between each component and the results of the model, as the
logistic curve serves as the link function for many forms of regression analysis with the family of
binomial data distributions. This analysis of the components showed the distribution of each
variable and the overall predictive trend for each variable in relation to the “proxy” for the
106

probability of emergency logistical resource requirements calculated in the methodology of the
current study.

Figure 40. Variable distributions and relationships for model components
107

Figure 41. Variable distributions and relationships for ground-motion parameters

The range of each independent (predictor) variable is representative of independent
conditional probabilities along the y-axis, given the probability on the x-axis, with the striated
linear pattern resulting as an artifact from the discrete data values used in the model. In the
current study, the probabilistic risk model results in a probability of emergency logistical
resource requirements as a proportion of “successes” in the total population (as in Assumption 10
and 11). In this case, regression for a beta distribution is similar to a binomial generalized linear
model (GLM) and so the GLM may provide useful information on the relative strength of the
contribution of the variables in the model results (Cribari-Neto and Achim 2010).
Logistic regression was performed with the GLM for the binomial family using a
“logistic” link function through RStudio core libraries. This was based on the ten independent
variables as identified in Figures 40 and 41 and the dependent response variable as the “proxy”
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for the probability of emergency logistical resource requirements resulting from the current
study. Beta regression and GLM for the quasibinomial family were also tested, as Cribari-Neto
and Achim (2010) indicated, with similar results to the binomial GLM for ranked significance of
dependent variable contributions as measured by z values (or t values). A pseudo R-squared
(Nagelkerke) value of .71774 resulted, which indicated that the binomial GLM model accounts
for approximately 72 percent of the variance. The results are shown in Figure 42, sorted by the z
values to indicate the relative strength of the contribution of the variables in the model results.

Figure 42. Initial binomial GLM regression results

Further investigation of the binomial GLM with the removal of independent variables
with statistical significance below the 95 percent threshold resulted in a similar AIC and pseudo
R-squared value as the initial regression results. Therefore, all of the independent variables were
left in the binomial GLM in the final regression results.
To evaluate these results and the goodness of fit of the binomial GLM regression model,
an analysis of the residuals was performed and the deviance divided by the degrees-of-freedom
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was calculated. Myers et al. (2002) states that lack of fit may be a problem when deviance
divided by the degrees of freedom exceeds one. Deviance divided by the degrees-of-freedom
showed a value of 0.296576, which did not indicate a lack of fit.
Residuals were examined to see if any systematic trends resulted. In summary, residuals
plotted against predicted values showed a strong clustering near zero, with variance decreasing
slightly as the absolute value of the predicted results increased—but overall the fit worked well.
There were no signs of heteroscedasticity and no signs of significant outliers affecting results in
plots of the standardized Pearson residual against the leverage. These results are shown in Figure
43.

Figure 43. Analysis of residuals from the GLM regression results
110

Finally, the residuals were mapped over the study area, which showed some spatial
autocorrelation, which is to be expected, but not a clear systematic trend. These results are shown
in Figure 44.

Figure 44. Mapping of residuals from the GLM regression results

The binomial GLM regression results showed that MMI and power damage were the two
independent variables with the greatest contribution to the explained variance in the model. The
power damage significance in logistical resource requirements was to be expected, as per
USACE (2008) and UASI (2014) and so provided independent validation for the methodology of
the probabilistic risk model—in particular for the choice of the maximum in the hazard
component calculation of the risk equation.
The significance of MMI was an interesting result, as increased logistical resource
requirements should be correlated with higher earthquake intensities—however the MMI data
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cannot be directly related to damage probabilities for the majority of the infrastructure indicators,
and so this is difficult to show. These results independently confirmed that MMI can be
considered a global indicator for emergency logistical resource requirements, which is to be
expected based on the literature (e.g. from NRC 2007; Earle et al. 2009, CalOES and FEMA
2011; CalOES and UASI 2015; UASI 2014). Therefore, the probabilistic risk model has
produced viable results that can be considered validated for application by emergency managers
and community planners.
5.2. Applications of the Probabilistic Risk Model
With the probabilistic risk model validated, the next step was to apply the results of the
model in several applications for use by emergency managers and community planners. The
development of a relative risk ratio in the eight-county study region proceeded according to the
methodology of Chapter 4. The results are presented in Figure 45, where the extent is centered
and scaled to an area that fits most of the relative risk ratio results.
The largest high-risk communities with over 50 percent risk for emergency logistical
resource requirements identified were: El Monte, Baldwin Park, Glendora, Lancaster and
Palmdale in Los Angeles County; San Bernardino, Rialto, Colton, Highland, Redlands and
Yucaipa in San Bernardino County; and Palm Springs, Thousand Palms, Bermuda Dunes, Indio,
Coachella, Thermal, Mecca in Riverside County.
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Figure 45. Results from calculation of the relative risk ratio to the general population

Calculation of Resource Requirements Over Time in Los Angeles County 5.2.1.
To calculate the resource requirements over time in the Los Angeles County study area,
the probabilistic risk model was applied with the LandScan USA 2012 “conus_night” population
dataset, as per the methodology in Section 4.4. The results in Figure 46 show a total “at-risk”
population for emergency logistical resource requirements of 1,421,415 at day-three, post-
event—or approximately 14.7 percent of the population—with a total requirement of 2,832,830
meals and 4,264,245 liters of water. Population counts were calculated for each 90×90 meter
cell.
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Figure 46. “At-risk” population and resource requirements at day-three, in Los Angeles County
114

These results had a small variation in summary population counts in comparison to
LandScan 2015 because of differences in time and scale, as seen in Table 6. Four priority areas
were identified in Figure 46 where the majority of the resource requirements were expected to
arise. These areas are presented in detail in Figure 47 and 48, from the inset maps of Figure 46,
with the same symbology and legend.

Figure 47. “At-risk” population and resource requirements at day-three, in Los Angeles
County—Areas of Detail I
115

Figure 48. “At-risk” population and resource requirements at day-three, in Los Angeles
County—Areas of Detail II

The next step in application of the methodology of Section 4.4 to determine resource
requirements over time was to establish the classification breaks for the four damage categories
from the results of the probabilistic risk model in Los Angeles County. Several methods were
tested, including a quantile approach, equal interval, Jenks natural breaks and nested means, with
varying results. However, natural breaks was chosen as per the methodology in Section 4.4.1 to
best represent the naturally occurring groupings of resource requirements in increasing severity.
The results from [HAZARD
Damage
]×[SOVI
Weight
] were analyzed, and a maximum value of
.8644, minimum of 0 and mean value of .2091 were found. From these values, the four damage
categories were then defined as: “minor”, as the range between 0 (minimum) and .1045;
“moderate”, as the range between .1046 and .2091 (mean); “extensive”, as the range between
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.2092 and .5367; and “complete”, as the range between .5368 and .8644 (maximum) probability
of resource requirements.

Figure 49. Establish classes for resource requirements over time

The next step was to fit the dynamic resource requirements curves from the three
recovery simulations in Section 4.4.2 to a zero value on the y-axis (where no more resources are
required) from Table 4. This resulted in values for computation of the resource requirements and
their restoration timelines—identified as parameter (a) in Equations 16, 18, and 20. This was
completed in MATLAB and using the online Wolfram Alpha calculator with no issues.
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Table 7. Calculated results for the restoration timeline parameter

The parameter (b) in Equations 16, 18, and 20 was also calculated, for example, as shown
in Figure 50 for recovery Simulation B (Maximum). This parameter increased or decreased the
restoration timeline curve proportionally to the social vulnerability weighting based on
[SoVI
Weight
]. Results for the other two equations were similar for parameter (b).

Figure 50. Equation 18 with social vulnerability weighting

Finally, resource requirements over time were directly calculated in ArcGIS 10.6 at t = 7,
14, 30, 45, 60 and 90-day post-event intervals for each of the three simulations. Equations 16, 18,
and 20 were applied in ArcGIS 10.6 for direct calculation in each of the three simulations for
resource requirements over time based on the four damage levels as per the methodology in
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Chapter 4. The initial resource requirement level for each cell was based on the day-three post-
event resource requirements as determined from application of the probabilistic risk model. The
results are presented for each of the simulations in a summary table (Table 8), graph (Figure 51),
and in three time series map compilations (Figures 52 to 54).
Table 8. Summary results for resource requirements over time for three simulations

Figure 51. Summary resource requirements over time for three simulations
119

Figure 52. Resource requirements over time for Simulation A (Minimum)
120

Figure 53. Resource requirements over time for Simulation B (Maximum)
121

Figure 54. Resource requirements over time for Simulation C (Average)
122

It should be noted that there can be memory issues when processing the results of
Simulation B in ArcGIS 10.6 in Windows 10 Enterprise 2016. From the formulation of Equation
18, the model results in a temporary memory allocation for calculation of all values, including
those less than zero. These negative values are not in the range of valid results and in the final
step are all mapped to “0” as the global minimum for the model. However, these artificial
negative values become astronomical as the curves become asymptotic when values approach
infinity, causing the computer to reach maximum memory limits.
To address this, the original “long integer” values were converted to “double” and the
database was compressed. The small number of “null” values resulting from exceeding the
“double” storage limits were then manually updated to “0” through the field calculator in ArcGIS
10.6 with no further issues.
Summary Resource Requirements by Point of Distribution (POD) Sites 5.2.2.
In order to operationalize these results to support logistical planning in the commodity
mission of the OPLAN, a summary of resource requirements by POD site was calculated, based
on the methodology shown in Figure 34. These results included summary meal requirements by
person, by pallet, and by truckload—which can then be used to prioritize resource distribution
and support the ordering and shipping of commodities to the impacted POD sites. The final
results for day-three are presented below in Figure 55, and the results for the three simulations
for t = 7, 14, 30, 45, 60 and 90-days post-event are presented as a summary report in Appendix
D. Summary calculations for bulk water storage and shipping requirements over time are also
included the results of Appendix D, but summary information past day-three has been omitted.
123

Figure 55. Summary of resource requirements by Point of Distribution (POD) sites at day-three
124

The results of the model and the three simulations provided each POD with a profile of
their respective predicted resource requirements over time. Several characteristic POD sites and
their summary resource requirements over time, taken from the data in Appendix D, are shown
in Figure 56. The location of emergency logistical resource requirements at a community level is
important for emergency managers, as these communities can be directly associated with a
servicing POD site for ordering, shipping and distribution planning.

Figure 56. Characteristic POD sites and their modeled resource requirements

In conclusion, the development and application of the probabilistic risk model for
emergency resource requirements in the (M) 7.8 San Andreas Earthquake Scenario and OPLAN
was successful. The results can be used to enhance the OPLAN through supporting emergency
management decision making and situation awareness in the commodity mission.
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Chapter 6 Discussion
While Chapter 5 has provided an in-depth summary of the model results, this chapter provides a
general summary of the results for application by emergency managers, along with an
investigation into some of the issues and the potential for calibration and validation of the model
in further research. Model-based uncertainty is summarized in an error budget analysis, which
serves as the main instrument for investigation of these issues. Finally, several approaches for
generalization of the model are proposed for supporting emergency logistical resource missions
in global earthquake events both before and after the event occurs.
6.1. Summary of Results
In summary, the probabilistic risk model has predicted the total resource requirement at
(t = 3) of 6,705,910 meals in the eight-county study region for a total “at-risk” population of
3,359,955, and 2,842,830 meals in Los Angeles County for a total “at-risk” population of
1,421,415. Similarly, requirements for 10,058,865 liters of water in the eight-county study region
and 4,264,245 liters in Los Angeles County are also predicted. These estimates are in alignment
with the Southern California Catastrophic Earthquake Response Operational Plan (OPLAN)
assumption of supporting resource requirements for between 2.5 million and 3.5 million people
(2 meals per person/day and 3 liters of water per person/day) in the eight-county study region, at
three-days post-event. Therefore, the model results are a realistic estimate for total resource
requirements.
Additionally, the model has provided a plausible estimate for the actual geographic
locations of where these logistical resource requirements originate—which the OPLAN does not
address. This is invaluable information for emergency managers, which can be used to help plan
for and prioritize resource distribution in the commodity mission. In the applications of the
126

probabilistic risk model, three simulations of resource requirements over time up to (t = 90 days)
have been provided, based on this initial data. This is a novel approach to long-term planning for
the commodity mission, which has been identified as a gap in the current emergency
management capabilities. A relative risk ratio has also been developed to estimate the relative
risk for any random member of the general population, based on these results. This can be used
in disaster preparedness and mitigation planning to address community vulnerability before an
event occurs.
The resulting probabilistic risk model and its applications provide a systematic and
comprehensive methodology to evaluate risks associated with the (M) 7.8 San Andreas
Earthquake Scenario in estimation of “at-risk” populations for emergency logistical resource
requirements. These results address several gaps in current emergency management capabilities
including incorporating social vulnerability, identifying community locations for emergency
logistical resource requirements and estimating resource requirements over time.
Error Analysis 6.1.1.
No discussion of model results is complete without a discussion of model-based
uncertainty and error analysis. As George Box has noted, “models, of course, are never true, but
fortunately it is only necessary that they be useful” (Box 1979, 2). Because deterministic
knowledge of a complex system (such as the emergency logistical resource requirements in the
OPLAN) is not possible, evaluation of model-based uncertainty in the results can focus on
measurement of the analysis of error in the model as a function of uncertainty associated with
each parameter input to the model (O’Sullivan and Perry 2013).
To do this, an error budget matrix, which summarizes the estimation of error introduced
in the model as a function of uncertainty in each parameter, was compiled. A formulation of the
127

error in the probabilistic risk model can be described as the error “delta” for each parameter,
defined as the difference between the “actual” damage or value that occurs in the event and the
“estimate” provided through the modeling methodology. Table 9 shows the error budget matrix
for this model. Several types of errors are identified, based on definitions from O’Sullivan and
Perry (2013).
Table 9. Error budget matrix from the model results

Many of these error deltas are “process” errors inherent within the science and
engineering methodologies from which the components and parameters of the model are taken.
These have been investigated in Chapter 3 and 4, and where appropriate assumptions have been
identified and validated to support their use in the current study or their justification is cited in
128

the literature. However, like all models, they fall short of deterministic knowledge of a complex
system and so are accounted for in the error budget matrix. Research in these areas is ongoing
and can be found in the literature. In general, the best available methods for modeling these
components are incorporated into the current study.
Other “measurement” errors are inherent within the computational implementation
methodology behind development of the probabilistic risk model and its applications. These have
been reduced as much as possible. For the purposes of the current study, these “process” and
“measurement” errors are not further reducible, but instead address the inherent variability and
epistemic uncertainty in the modeling of these processes (O’Sullivan and Perry 2013). From the
error budget matrix, five “reducible” errors have been identified that can benefit from further
research. Addressing these “reducible” errors can improve the results of the model and extend its
applications. These are investigated in the next section.
6.2. Issues and Further Research
Several components of the model can be improved with further research and
development. One of the major gaps in the ShakeOut scenario was the failure to perform a
network system analysis to model electric power system damage and outages. Similarly, the
ShakeOut scenario was not able to perform a network system analysis to model water pipe
system damage and outages. Both of these lifeline infrastructure components are intricately
interconnected with business restoration and food insecurity issues, as the literature has shown in
Chapter 3. Therefore, more accurate estimates of damage and restoration timelines for these
infrastructure indicators in the Shakeout scenario can have great potential to improve the model
results.
129

In the current study, from Table 7, the errors for “ΔPipes” and “ΔPowerInit” can be
reduced through incorporating the results of network system analyses. This will provide more
robust initial parameters for the model and therefore decrease the uncertainty in the results.
Additionally, if that is not possible, the simplified methodology in the current study for modeling
water conveyance can be improved through incorporation of Peak Ground Deformation (PGD)
data, which was not available for the current study.
It was also noted that the current study used a simplified averaging method to determine
the timeline for resource requirements over time. This resulted in equal weights for each of the
six infrastructure indicator restoration times, for each of the four damage categories, when used
to calculate the resource requirement timeline in Table 4. Further research is needed to establish
a weighting scheme that emphasizes infrastructure damage indicators with the highest correlation
to resource requirements. This may be included in post-event validation of the model, as
discussed below. Validation and calibration of the weightings for the infrastructure indicator
restoration timelines will reduce the uncertainty associated with “ΔWeights” and improve the
model results.
Finally, social vulnerability plays an important role in the model—however, there is little
quantitative research on social vulnerability’s effects on the amplification of resource
requirements. For the current study, the ranked social vulnerability index from SoVI was fitted to
a (±) 22 percent range of amplifications from community recovery rates in New Orleans for
Hurricane Katrina over a 13-year period. This basic approach can serve as a first step toward
more detailed studies on the subject. This will address a critical gap in the literature addressing
the application of social vulnerability indices for resource planning in emergency management.
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A range of amplifications based on this research agenda and published in the literature can
reduce the uncertainty associated with “ΔSVAmp” and improve the model results.
Several approaches for further development of the modeling methodology to include
validation of the model, generalization for global earthquake applications and extension of its
applications are presented in the next section.
Further Development of the Model 6.2.1.
While it is noted that we can never verify this model, we can validate and calibrate the
model with data from actual events (O’Sullivan and Perry 2013). Model validation is the process
of evaluating a model’s predictions against independent observational data from an actual event.
In consideration of the current scenario, the model can be calibrated and validated after a
large earthquake occurs, with summary logistical resource distribution information provided by
emergency management authorities. Machine learning algorithms such as Maxent (Philips et al.
2006) can be used to determine the probability of suitable conditions for the distribution of the
observed resource requirements. These results can then be correlated to the probabilistic risk
model’s results, and a calibration factor can be introduced into the model to align the predictions
with the observed data and associated distribution. This approach will also reveal infrastructure
damage indicators with the highest correlation to resource requirements, and as mentioned in the
previous section, can be used to establish a suitable weighting scheme. Previous earthquake
events can also be used to calibrate the model, if logistical summary information is available.
The results from the model can also be immediately integrated into an interactive Web
application for presentation, through ArcGIS 10.6 Server services and the ArcGIS Portal using
Esri Web AppBuilder for ArcGIS. Widgets can be customized to allow the user to identify a
point, line or area and determine the average underlying risk or summary resource requirements
131

from each raster surface within the selected area. The user can also query the model results at the
nearest cell or by address. Graphs of resource requirements over time at each POD site can also
be developed using the default “graph” widget in the Esri Web AppBuilder. This web application
will allow emergency managers to interactively explore the results of the model and to
investigate community vulnerability at any user defined scale.
The methodology introduced in the current study can be easily generalized for any
domestic earthquake event, if the modeled ground-motion data and social vulnerability index are
available. Several catastrophic earthquake plans, similar to the OPLAN and ShakeOut scenario,
that can immediately benefit from the results of the current study include the New Madrid
Seismic Zone Catastrophic Earthquake Plan (MAE 2009), the HayWired earthquake scenario in
the San Francisco Bay Area (Detweiler et al. 2018) and the Cascadia Earthquake Plan in the
Pacific Northwest. Application of the model for global earthquake events and international
humanitarian response is also possible with further generalization of the methodology similar to
the work in Hansen and Bausch (2007) in applications of HAZUS-MH for international
applications. Further research can also investigate expansion of the modeling methodology to
support additional types of catastrophic disaster response events.
Finally, the error associated with “ΔSimulation” can be seen in the broader context of the
development of a mathematical model for predicting resource requirements over time. The
probabilities associated with the initial resource requirements (once the model has been
successfully validated and calibrated) and the curves in Equations 16, 18, and 20 suggest a more
general model of the process as a Stochastic Partial Differential Equation (SPDE). In this
formulation, Simulation A (Minimum) and Simulation B (Maximum) can be seen as boundary
conditions over time (t) for a single model, and the concavity or convexity of any curve between
132

this range can be seen as an unknown parametric function of time, f(t). From this function, any
one of multiple potential curves can then be used to predict resource requirements over time
based on the best fit to actual observations during the event.
Further research and development in this area can lead to a web-based computational
implementation of this algorithm into a decision support tool for resource ordering. This tool can
be used to predict future resource requirements per POD—from within the event—based on
actual observations of resource requirements from the previous operational period. In its present
form, the current study’s applications are limited by the initial ground-motion data, as post-event
damage and restoration data are not incorporated into the current modeling methodology. This
further research will give emergency managers the capacity to predict the next operational
period’s ordering requirements, adjusting as necessary to the varying “burn-rates” of resource
requirements as the event unfolds, in a further extension of the model’s applications.
6.3. Conclusion
In conclusion, the probabilistic risk model and its applications provide a systematic and
comprehensive methodology to evaluate risks associated with the (M) 7.8 San Andreas
Earthquake ShakeOut Scenario in estimation of “at-risk” populations for emergency logistical
resource requirements. These estimates are in alignment with the OPLAN assumption of
supporting resource requirements for between 2.5 million and 3.5 million people (2 meals per
person/day and 3 liters of water per person/day) in the eight-county study region, at three-days
post-event. Therefore, the model results are a realistic estimate for total resource requirements.
These results address several gaps in current emergency management capabilities
including incorporating social vulnerability, identifying community locations for emergency
logistical resource requirements and estimating resource requirements over time. In so doing, this
133

study provides a public service and social benefit to disaster response planning by providing
tools to mitigate impacts to those populations most vulnerable to disruptions in life-sustaining
food and water supplies in the event of a catastrophic incident.
Further research and development with the model can lead to a decision support tool for
the logistical commodity mission in all domestic earthquake response efforts in the United
States. This logistical resource support tool, or LOGRESC
®
, as it will hereafter be known, based
on the methodology and the nascent results of the current study, can then be generalized to
address the gaps in current emergency management capabilities for logistical planning in global
humanitarian relief efforts.
134

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141

Appendix A The Original Gravity Weighted Huff Model
Appendix A provides an overview of the “Original Gravity Weighted Huff Model”, which was
applied to develop the Areas of Responsibility (AORs) used to summarize logistical resource
requirements resulting from the probabilistic risk model.
The Original Gravity Weighted Huff Model is based on the principle of distance decay,
where the probability of a population choosing one site over another is a function of the distance
to the site from their current location and the distance to a finite number of other sites.
Attractiveness is another parameter in the Original Gravity Weighted Huff Model, where sites
that are more attractive are provided an additional weighting. The Original Gravity Weighted
Huff Model is defined by the following equation (Esri 2017a):

(22)

P
ij
= The probability of total population in cell (j), at centroid, receiving support at POD (i)
W
i
=

The attractiveness weighting for each (i) POD, set to “1” in this study
D
ij
= The distance from total population in cell (j), at centroid, to POD site (i)
a = An exponent applied to distance so that the probability of distant sites is dampened. This is set to a = 2 in this
study, as it is assumed that travel throughout an affected area is more difficult after the event occurs.

In the current study, a probability of travel model was appropriate to represent the
populations served by a Point of Distribution Site (POD), as this approach can represent true
probability of travel of affected populations in disaster areas. The inverse distance weighting in
the model can represent the impedance of travel that occurs in the scenario due to areas impacted
by damage and emergency response activities (Jones et al. 2008). The number of sites considered
in the model can also be controlled, which represents the limited knowledge of community PODs
sites to be expected from the public.
142

Therefore, AORs in the current study were determined by the Original Gravity Weighted
Huff Model for probability of travel to a site location and were bound by the Los Angeles
County boundary. The Original Gravity Weighted Huff Model is available for download, and
through Esri Business Analyst 10.6 toolbox. The Original Gravity Weighted Huff Model was
adapted for the current study and implemented through Esri ArcGIS 10.6 model builder, with the
following parameters:
Table 10. The Original Gravity Weighted Huff Model parameters

To determine the search radius, the “calculate distance band from neighbor count” tool
was run in ArcGIS 10.6, which resulted in a maximum distance for three PODs as 49.8
kilometers. The following Python script was then implemented through ArcGIS 10.6 model
builder (Figure 57):
143

Figure 57. The Original Gravity Weighted Huff Model python script

The final results from the “Generate Market Areas” step were converted to polygons, and
validated to ensure there is a unique POD per AOR polygon. The final results are presented in
Figure 7, and were used in subsequent summary calculations in the study and in summary of the
results in Appendix D.

144

Appendix B HAZUS-MH Power Outage Methodology Extension
Appendix B investigates the direct calculation of populations impacted by power outage in the
current study, which is an extension of the HAZUS-MH loss estimation methodology. An
extension of the HAZUS-MH loss estimation methodology was required to estimate populations
affected by power utility outage, as the current methodology is subject to a large range of
uncertainty. This is, in part, due to the modifiable areal unit problem (MAUP) in the variation of
real world service area extents for the substations. Service area data are not generally available to
the public.
The standard methodology—even without consideration for the MAUP effect—still
cannot identify the distribution of populations sufficiently for making decisions for emergency
logistical resource requirements. This is because the HAZUS-MH methodology multiplies the
average probability of damage for all substations in the study area by the population of the entire
region to estimate the impacted population. Populations in the most severely impacted regions
are systematically underestimated and those in the least impacted regions are overestimated
based on that method and variably sized service areas as an additional weighting factor are not
even considered.
To extend and improve this methodology for the current study, Assumption 11 was
validated, which supposes that the substations in the study area can be assumed to be more-or-
less evenly distributed at the LandScan cell resolution, proportional to population density. This
approach is then equivalent to directly calculating populations impacted by power outage based
on the individual Landscan raster cell populations, where the probability of damage is calculated
as the HAZUS-MH Technical Manual suggests.
145

To validate this assumption, a 198 sq. km study region was chosen in Los Angeles
County to investigate the possible scenarios for populations impacted by power outage. This
rectangular region extended from the city of Baldwin Park, in the north to Whittier in the south,
Hacienda Heights in the east and Rosemead in the west. The study region included a total
population of 425,017. This area was chosen as the ShakeOut scenario indicates a large range of
ground-motion and damages in the vicinity (Jones et al. 2008).
To estimate the location of operational substations, the California Energy Commission
electric substation data was investigated. While the data does not identify coordinates for the
substation locations, it does identify their zip code. From this, the location of 22 operational
substations were estimated as evenly distributed through each zip code that intersected the study
region (Figure 58).

Figure 58. Study area for validation of power outage methodology extension

The probability of damage for each substation was then calculated based on the CDF
damage function for the probability of complete damage to medium voltage substations with
seismic components (see Figure 12). The following calculations resulted: average probability of
146

damage .081; maximum probability of damage, .288; and minimum probability of damage, 0.
Based on the standard HAZUS-MH loss estimation methodology, the expected value for
population impacted by power outage using the average was: 34,213 individuals impacted.
In consideration of the MAUP effect, three additional scenarios were investigated to
extend this methodology. These three scenarios can be considered as a plausible “real-world”
range of uncertainty for estimating the populations impacted by power outage. The “maximum”
scenario used larger service areas for the substations in areas farther north. The “minimum”
scenario estimated larger service areas in the south. The Voronoi scenario represented the
average, where service areas between substations were a function of distance (Figure 59)

Figure 59. Substation service areas and the MAUP effect

From these results, it can be seen that the HAZUS-MH loss estimation methodology's
total population impacted was most closely compared with the “minimum” scenario from the
MAUP effect—which seems arbitrary and unlikely. In addition, as all impacted populations in
the HAZUS-MH approach were calculated through the average “yellow” probability values,
populations in the most severely impacted regions were systematically underestimated and those
in the least impacted regions were overestimated. The result was that the population distribution
147

is arbitrary and varied significantly from the MAUP “minimum” scenario, even while the total
population differed by only a small amount.
For the current study, a direct calculation approach is proposed to mitigate these issues as
an extension to the HAZUS-MH loss estimation methodology. Applying the direct calculation
methodology with the assumption that the substations are more-or-less evenly distributed in the
study region at the LandScan cell resolution, proportional to population density, resulted in the
following:

Figure 60. Direct calculation of populations subject to power outages.

This direct calculation resulted in a total population subject to power outage of: 40,358
impacted, using the CDF damage function for the probability of complete damage to medium
148

voltage substations with seismic components. These results were most closely compared with the
Voronoi scenario, where service areas between substations were a function of distance.
The Voronoi scenario is a plausible best available estimate of “real world” substation
service areas, absent actual data on the service area boundaries. In consideration of the MAUP
effect, the direct calculation approach results were close to the mean of the “maximum” and the
“minimum” scenarios, similar to the Voronoi scenario. Both the HAZUS-MH loss estimation
results and the direct calculation approach fell within the range of uncertainty demonstrated by
the MAUP scenarios.
As the affected populations were directly calculated, impacts from the variability in the
service areas (and the MAUP effect) were minimized. The distribution of populations subject to
power outage, which is closely tied to the impacts of nearby servicing substations, was also
preserved—even without actual service area data—which is an improvement on the HAZUS-
MH loss estimation methodology.
Therefore, it was validated that this assumption for a direct calculation approach of
affected populations subject to power outage decreased uncertainty in comparison with the
original HAZUS-MH method. Estimation of population distribution was improved and the
estimation of total population subject to power outage was closer to the mean of the MAUP
scenarios, and so was at least as good (and likely better) than the current standard. This approach
was then used to calculate the [POWER
Damage
] component of [HAZARD
Damage
] in the
probabilistic risk model.

149

Appendix C Complete Bridge Damage Validation
The result from calculation of the probability of complete bridge damage, as the
component [Bridge
damage
] in the current study, was shown to persist and dominate [Hazard
damage
]
in the five areas of “complete” bridge damage in the ShakeOut earthquake scenario (Figure 8) as
identified in Werner et al. (2008). To demonstrate this, the results of the calculation of the
[Hazard
damage
] component of the probabilistic risk model were compared to the [Bridge
damage
]
component to find areas where the two datasets had equal values and the probability of complete
bridge damage was greater than 50 percent.

Figure 61. Validation of probability of complete bridge damage calculation

150

This result indicated that bridge damage dominated the hazard component calculation of
the probabilistic risk model in these areas. These values were compared with Figure 14, with a
near identical match in Figure 61 to the five areas of “complete” bridge damage in the ShakeOut
scenario supplemental study (Werner et al. 2008).
Therefore, [Bridge
damage
] as defined in the current study aligned with the findings from
the ShakeOut scenario supplemental study in Werner et al. (2008) and was sufficient for
calculation of the [Hazard
damage
] component.

151

Appendix D Logistical Resource Summary Report

152
POD ID POP (2012) AT RISK POP DAY-3 (MEALS)
DAY-3
(MEALS/PALLET)
DAY-3
(MEALS/TRUCK
LOADS)
DAY-3 (WATER)
DAY-3 (BULK
WATER/TANKERS)
DAY-3
(WATER/TRUCK
LOADS)
118 371,694 240,185 480,370 834 21 720,555 21 44
76 208,014 96,784 193,568 336 8 290,352 9 18
133 167,136 88,280 176,560 307 8 264,840 8 16
117 185,071 63,282 126,564 220 5 189,846 6 12
92 243,516 47,133 94,266 164 4 141,399 4 9
81 154,654 42,898 85,796 149 4 128,694 4 8
111 182,306 42,447 84,894 147 4 127,341 4 8
109 206,499 42,441 84,882 147 4 127,323 4 8
38 323,622 39,691 79,382 138 3 119,073 3 7
102 117,610 32,842 65,684 114 3 98,526 3 6
106 97,358 27,456 54,912 95 2 82,368 2 5
146 121,241 27,134 54,268 94 2 81,402 2 5
108 119,321 25,848 51,696 90 2 77,544 2 5
89 111,576 25,142 50,284 87 2 75,426 2 5
101 42,887 23,237 46,474 81 2 69,711 2 4
115 97,117 22,488 44,976 78 2 67,464 2 4
52 87,753 14,762 29,524 51 1 44,286 1 3
87 100,600 14,702 29,404 51 1 44,106 1 3
107 76,121 14,527 29,054 50 1 43,581 1 3
39 88,059 14,027 28,054 49 1 42,081 1 3
29 83,282 13,593 27,186 47 1 40,779 1 3
10 85,995 12,467 24,934 43 1 37,401 1 2
66 79,651 12,301 24,602 43 1 36,903 1 2
4 104,008 11,793 23,586 41 1 35,379 1 2
56 109,685 10,662 21,324 37 1 31,986 1 2
121 93,239 10,291 20,582 36 1 30,873 1 2
59 92,704 10,231 20,462 36 1 30,693 1 2
15 67,726 10,192 20,384 35 1 30,576 1 2
55 43,685 9,943 19,886 35 1 29,829 1 2
113 39,978 9,736 19,472 34 1 29,208 1 2
51 46,378 9,642 19,284 33 1 28,926 1 2
17 87,144 8,978 17,956 31 1 26,934 1 2
34 80,903 8,834 17,668 31 1 26,502 1 2
53 44,914 8,494 16,988 29 1 25,482 1 2
64 41,517 8,458 16,916 29 1 25,374 1 2
63 43,055 8,392 16,784 29 1 25,176 1 2
36 62,037 8,295 16,590 29 1 24,885 1 2
11 64,304 8,182 16,364 28 1 24,546 1 2
9 43,674 7,996 15,992 28 1 23,988 1 1
86 58,808 7,989 15,978 28 1 23,967 1 1
44 168,695 7,948 15,896 28 1 23,844 1 1
110 61,454 7,878 15,756 27 1 23,634 1 1
32 49,450 7,210 14,420 25 1 21,630 1 1
37 141,373 7,049 14,098 24 1 21,147 1 1
48 82,237 7,038 14,076 24 1 21,114 1 1
99 178,123 6,756 13,512 23 1 20,268 1 1
105 36,071 6,618 13,236 23 1 19,854 1 1
33 152,436 6,617 13,234 23 1 19,851 1 1
77 85,954 6,076 12,152 21 1 18,228 1 1
21 67,298 6,066 12,132 21 1 18,198 1 1
114 24,089 5,601 11,202 19 0 16,803 0 1
30 88,857 5,347 10,694 19 0 16,041 0 1
120 62,806 5,130 10,260 18 0 15,390 0 1
130 84,226 4,778 9,556 17 0 14,334 0 1
143 69,868 4,750 9,500 16 0 14,250 0 1
68 77,869 4,733 9,466 16 0 14,199 0 1
119 131,238 4,728 9,456 16 0 14,184 0 1
72 19,120 4,725 9,450 16 0 14,175 0 1
7 50,595 4,690 9,380 16 0 14,070 0 1
85 39,060 4,412 8,824 15 0 13,236 0 1
47 28,551 4,374 8,748 15 0 13,122 0 1
135 69,174 4,313 8,626 15 0 12,939 0 1
124 38,713 4,294 8,588 15 0 12,882 0 1
90 56,615 4,264 8,528 15 0 12,792 0 1
8 61,453 4,201 8,402 15 0 12,603 0 1
35 85,267 4,193 8,386 15 0 12,579 0 1
40 79,747 4,138 8,276 14 0 12,414 0 1
DAY-3 SUMMARY
153
POD ID POP (2012) AT RISK POP DAY-3 (MEALS)
DAY-3
(MEALS/PALLET)
DAY-3
(MEALS/TRUCK
LOADS)
DAY-3 (WATER)
DAY-3 (BULK
WATER/TANKERS)
DAY-3
(WATER/TRUCK
LOADS)
DAY-3 SUMMARY
45 71,541 4,040 8,080 14 0 12,120 0 1
74 74,990 4,000 8,000 14 0 12,000 0 1
42 22,390 3,988 7,976 14 0 11,964 0 1
123 77,585 3,682 7,364 13 0 11,046 0 1
91 22,486 3,519 7,038 12 0 10,557 0 1
61 76,475 3,518 7,036 12 0 10,554 0 1
116 70,961 3,428 6,856 12 0 10,284 0 1
132 80,198 3,339 6,678 12 0 10,017 0 1
103 39,191 3,331 6,662 12 0 9,993 0 1
88 21,363 3,276 6,552 11 0 9,828 0 1
43 30,535 3,157 6,314 11 0 9,471 0 1
139 30,069 3,118 6,236 11 0 9,354 0 1
70 36,974 3,068 6,136 11 0 9,204 0 1
94 77,552 2,868 5,736 10 0 8,604 0 1
60 29,759 2,818 5,636 10 0 8,454 0 1
27 43,681 2,750 5,500 10 0 8,250 0 1
31 47,290 2,723 5,446 9 0 8,169 0 1
54 52,595 2,718 5,436 9 0 8,154 0 1
49 43,875 2,539 5,078 9 0 7,617 0 0
122 32,035 2,481 4,962 9 0 7,443 0 0
144 39,100 2,413 4,826 8 0 7,239 0 0
22 95,321 2,389 4,778 8 0 7,167 0 0
104 12,678 2,388 4,776 8 0 7,164 0 0
125 47,400 2,339 4,678 8 0 7,017 0 0
28 27,704 2,314 4,628 8 0 6,942 0 0
128 62,653 2,240 4,480 8 0 6,720 0 0
137 45,078 2,212 4,424 8 0 6,636 0 0
79 69,230 1,991 3,982 7 0 5,973 0 0
46 43,190 1,977 3,954 7 0 5,931 0 0
26 33,596 1,927 3,854 7 0 5,781 0 0
82 28,491 1,859 3,718 6 0 5,577 0 0
67 11,697 1,807 3,614 6 0 5,421 0 0
57 46,573 1,804 3,608 6 0 5,412 0 0
78 36,377 1,792 3,584 6 0 5,376 0 0
20 18,048 1,657 3,314 6 0 4,971 0 0
80 40,996 1,625 3,250 6 0 4,875 0 0
84 20,163 1,585 3,170 6 0 4,755 0 0
71 10,694 1,459 2,918 5 0 4,377 0 0
23 39,996 1,422 2,844 5 0 4,266 0 0
83 13,741 1,421 2,842 5 0 4,263 0 0
73 32,643 1,367 2,734 5 0 4,101 0 0
24 31,635 1,278 2,556 4 0 3,834 0 0
141 38,812 1,271 2,542 4 0 3,813 0 0
19 34,623 1,257 2,514 4 0 3,771 0 0
25 28,104 1,254 2,508 4 0 3,762 0 0
2 22,107 1,250 2,500 4 0 3,750 0 0
16 27,661 1,205 2,410 4 0 3,615 0 0
75 30,906 1,195 2,390 4 0 3,585 0 0
131 34,322 1,189 2,378 4 0 3,567 0 0
134 26,364 1,174 2,348 4 0 3,522 0 0
12 16,246 1,158 2,316 4 0 3,474 0 0
95 33,361 1,119 2,238 4 0 3,357 0 0
65 5,901 1,030 2,060 4 0 3,090 0 0
41 25,494 995 1,990 3 0 2,985 0 0
136 30,084 935 1,870 3 0 2,805 0 0
112 33,249 903 1,806 3 0 2,709 0 0
145 15,178 879 1,758 3 0 2,637 0 0
140 20,050 827 1,654 3 0 2,481 0 0
127 23,834 819 1,638 3 0 2,457 0 0
58 25,846 798 1,596 3 0 2,394 0 0
126 20,736 715 1,430 2 0 2,145 0 0
6 17,056 705 1,410 2 0 2,115 0 0
18 18,761 693 1,386 2 0 2,079 0 0
62 8,469 657 1,314 2 0 1,971 0 0
98 22,959 639 1,278 2 0 1,917 0 0
93 12,838 583 1,166 2 0 1,749 0 0
69 10,658 564 1,128 2 0 1,692 0 0
154
POD ID POP (2012) AT RISK POP DAY-3 (MEALS)
DAY-3
(MEALS/PALLET)
DAY-3
(MEALS/TRUCK
LOADS)
DAY-3 (WATER)
DAY-3 (BULK
WATER/TANKERS)
DAY-3
(WATER/TRUCK
LOADS)
DAY-3 SUMMARY
13 6,093 521 1,042 2 0 1,563 0 0
5 10,152 450 900 2 0 1,350 0 0
129 9,125 449 898 2 0 1,347 0 0
1 5,256 330 660 1 0 990 0 0
3 15,246 296 592 1 0 888 0 0
100 9,338 223 446 1 0 669 0 0
50 78 3 6 0 0 9 0 0
TOTALS 8,992,637 1,421,415 2,842,830 4,931 110 4,264,245 125 263
155
POD ID MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS
118 370,344 643 16 238,626 414 10 94,108 163 4 41,208 72 2 17,228 30 1 1,071 2 0
76 125,790 218 5 66,865 116 3 21,061 37 1 9,046 16 0 3,960 7 0 346 1 0
133 115,873 201 5 62,276 108 3 20,121 35 1 8,577 15 0 3,762 7 0 519 1 0
117 68,077 118 3 26,353 46 1 3,660 6 0 1,512 3 0 654 1 0 34 0 0
81 43,785 76 2 13,847 24 1 826 1 0 0 0 0 0 0 0 0 0 0
111 32,833 57 1 10,397 18 0 206 0 0 0 0 0 0 0 0 0 0 0
101 32,514 56 1 18,886 33 1 6,750 12 0 2,903 5 0 1,252 2 0 116 0 0
102 29,892 52 1 9,528 17 0 91 0 0 0 0 0 0 0 0 0 0 0
109 29,479 51 1 9,422 16 0 87 0 0 0 0 0 0 0 0 0 0 0
92 28,791 50 1 9,170 16 0 65 0 0 0 0 0 0 0 0 0 0 0
106 28,590 50 1 9,132 16 0 390 1 0 0 0 0 0 0 0 0 0 0
146 20,136 35 1 6,423 11 0 126 0 0 0 0 0 0 0 0 0 0 0
89 19,338 34 1 6,182 11 0 183 0 0 4 0 0 1 0 0 0 0 0
115 19,228 33 1 6,018 10 0 134 0 0 0 0 0 0 0 0 0 0 0
108 17,341 30 1 5,451 9 0 110 0 0 0 0 0 0 0 0 0 0 0
38 11,972 21 1 3,685 6 0 58 0 0 3 0 0 0 0 0 0 0 0
107 8,667 15 0 2,626 5 0 92 0 0 0 0 0 0 0 0 0 0 0
113 7,835 14 0 2,486 4 0 34 0 0 0 0 0 0 0 0 0 0 0
55 7,203 13 0 2,260 4 0 105 0 0 0 0 0 0 0 0 0 0 0
29 6,144 11 0 1,967 3 0 27 0 0 0 0 0 0 0 0 0 0 0
51 5,786 10 0 1,796 3 0 31 0 0 0 0 0 0 0 0 0 0 0
53 5,742 10 0 1,850 3 0 63 0 0 0 0 0 0 0 0 0 0 0
64 5,250 9 0 1,580 3 0 67 0 0 0 0 0 0 0 0 0 0 0
63 4,893 8 0 1,468 3 0 31 0 0 0 0 0 0 0 0 0 0 0
114 4,316 7 0 1,383 2 0 13 0 0 0 0 0 0 0 0 0 0 0
9 3,999 7 0 1,299 2 0 15 0 0 0 0 0 0 0 0 0 0 0
72 3,734 6 0 1,194 2 0 71 0 0 0 0 0 0 0 0 0 0 0
15 3,671 6 0 1,008 2 0 11 0 0 0 0 0 0 0 0 0 0 0
39 2,780 5 0 610 1 0 11 0 0 0 0 0 0 0 0 0 0 0
66 1,654 3 0 207 0 0 12 0 0 0 0 0 0 0 0 0 0 0
47 1,424 2 0 436 1 0 0 0 0 0 0 0 0 0 0 0 0 0
52 1,411 2 0 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0
105 1,331 2 0 301 1 0 0 0 0 0 0 0 0 0 0 0 0 0
36 1,249 2 0 331 1 0 8 0 0 0 0 0 0 0 0 0 0 0
10 1,182 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 1,118 2 0 257 0 0 8 0 0 0 0 0 0 0 0 0 0 0
104 985 2 0 299 1 0 0 0 0 0 0 0 0 0 0 0 0 0
87 845 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
34 775 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 642 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
48 624 1 0 180 0 0 0 0 0 0 0 0 0 0 0 0 0 0
121 619 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
56 591 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 423 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
4 392 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
86 355 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
42 355 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
110 334 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
59 326 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
43 254 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
139 249 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 247 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
88 242 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
60 218 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
103 207 0 0 43 0 0 0 0 0 0 0 0 0 0 0 0 0 0
67 198 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
91 121 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
71 118 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 92 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 81 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
65 81 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
85 69 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
70 62 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 49 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 47 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
SIMULATION A (MEALS)
DAY-7 DAY-14 DAY-30 DAY-45 DAY-60 DAY-90
156
POD ID MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS
SIMULATION A (MEALS)
DAY-7 DAY-14 DAY-30 DAY-45 DAY-60 DAY-90
8 45 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
130 40 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
90 35 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 29 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
124 27 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
143 25 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
62 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
77 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
135 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
37 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
122 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
125 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
119 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
40 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
120 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
83 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
144 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
TOTALS 1,083,300 1,881 47 525,889 913 23 148,575 258 6 63,253 110 3 26,857 47 1 2,086 4 0
*Note: All PODS with 0 resource requirements at Day-7 and later are not shown.
157
POD ID MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS
118 450,298 782 20 446,573 775 19 414,443 720 18 367,515 638 16 344,525 598 15 245,465 426 11
76 186,401 324 8 180,882 314 8 152,400 265 7 84,450 147 4 79,744 138 3 59,104 103 3
133 171,321 297 7 166,605 289 7 142,382 247 6 80,856 140 4 76,594 133 3 57,375 100 2
117 116,127 202 5 107,722 187 5 76,673 133 3 13,523 23 1 12,710 22 1 9,404 16 0
81 82,910 144 4 78,081 136 3 58,229 101 3 0 0 0 0 0 0 0 0 0
111 75,261 131 3 56,168 98 2 40,033 70 2 0 0 0 0 0 0 0 0 0
92 74,215 129 3 47,878 83 2 32,597 57 1 0 0 0 0 0 0 0 0 0
109 65,504 114 3 48,769 85 2 32,811 57 1 0 0 0 0 0 0 0 0 0
102 58,020 101 3 50,972 88 2 34,821 60 2 0 0 0 0 0 0 0 0 0
106 52,734 92 2 49,995 87 2 36,779 64 2 0 0 0 0 0 0 0 0 0
101 45,003 78 2 44,182 77 2 39,323 68 2 26,861 47 1 25,333 44 1 18,702 32 1
108 44,507 77 2 28,972 50 1 20,130 35 1 0 0 0 0 0 0 0 0 0
89 42,856 74 2 32,958 57 1 23,697 41 1 26 0 0 25 0 0 15 0 0
146 42,084 73 2 34,788 60 2 24,063 42 1 0 0 0 0 0 0 0 0 0
115 41,770 73 2 33,058 57 1 24,139 42 1 0 0 0 0 0 0 0 0 0
38 37,753 66 2 20,021 35 1 13,709 24 1 45 0 0 43 0 0 12 0 0
107 24,312 42 1 14,290 25 1 10,546 18 0 0 0 0 0 0 0 0 0 0
52 22,526 39 1 254 0 0 173 0 0 0 0 0 0 0 0 0 0 0
39 22,233 39 1 3,347 6 0 2,348 4 0 0 0 0 0 0 0 0 0 0
87 19,961 35 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
66 19,750 34 1 1,155 2 0 859 1 0 0 0 0 0 0 0 0 0 0
10 19,163 33 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
55 18,160 32 1 12,078 21 1 8,991 16 0 273 0 0 0 0 0 0 0 0
29 17,956 31 1 10,122 18 0 6,910 12 0 0 0 0 0 0 0 0 0 0
113 17,384 30 1 13,330 23 1 9,409 16 0 0 0 0 0 0 0 0 0 0
51 16,151 28 1 9,589 17 0 6,769 12 0 0 0 0 0 0 0 0 0 0
15 15,060 26 1 5,472 10 0 3,896 7 0 0 0 0 0 0 0 0 0 0
64 15,037 26 1 8,661 15 0 6,390 11 0 0 0 0 0 0 0 0 0 0
63 14,275 25 1 7,905 14 0 5,710 10 0 0 0 0 0 0 0 0 0 0
4 13,718 24 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
34 13,468 23 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
53 13,224 23 1 9,632 17 0 6,813 12 0 0 0 0 0 0 0 0 0 0
121 12,141 21 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
9 11,695 20 1 6,334 11 0 4,092 7 0 0 0 0 0 0 0 0 0 0
86 11,094 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 10,815 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
11 10,797 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
36 10,787 19 0 1,626 3 0 1,074 2 0 0 0 0 0 0 0 0 0 0
110 10,731 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
56 10,528 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 10,431 18 0 1,395 2 0 984 2 0 0 0 0 0 0 0 0 0 0
105 9,932 17 0 1,640 3 0 1,034 2 0 0 0 0 0 0 0 0 0 0
114 9,401 16 0 7,250 13 0 4,848 8 0 0 0 0 0 0 0 0 0 0
59 9,108 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
72 8,606 15 0 6,270 11 0 4,854 8 0 6 0 0 0 0 0 0 0 0
47 6,474 11 0 2,168 4 0 1,401 2 0 0 0 0 0 0 0 0 0 0
42 6,361 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 5,280 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
88 5,042 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
91 4,838 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
48 4,405 8 0 875 2 0 549 1 0 0 0 0 0 0 0 0 0 0
43 4,153 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
139 3,804 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
104 3,607 6 0 1,634 3 0 1,043 2 0 0 0 0 0 0 0 0 0 0
21 3,595 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
60 3,539 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
124 3,473 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
67 2,778 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
77 2,688 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
SIMULATION B (MEALS)
DAY-7 DAY-14 DAY-30 DAY-45 DAY-60 DAY-90
158
POD ID MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS
SIMULATION B (MEALS)
DAY-7 DAY-14 DAY-30 DAY-45 DAY-60 DAY-90
85 2,606 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
71 2,173 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 2,089 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
90 1,836 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
103 1,818 3 0 224 0 0 157 0 0 0 0 0 0 0 0 0 0 0
8 1,755 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
65 1,614 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
70 1,486 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
130 1,480 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
20 1,109 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
120 1,062 2 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0
84 935 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
83 789 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 696 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
143 643 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 570 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 536 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
135 507 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
62 486 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
119 322 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
37 241 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
122 207 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
125 178 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
74 167 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
40 131 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 108 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
144 58 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
145 20 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
82 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
TOTALS 2,090,919 3,630 91 1,552,876 2,696 67 1,255,080 2,179 54 573,555 996 25 538,974 936 23 390,077 677 17
*Note: All PODS with 0 resource requirements at Day-7 and later are not shown.
159
POD ID MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS
118 462,393 803 20 424,456 737 18 348,771 606 15 272,494 473 12 218,552 379 9 113,891 198 5
76 180,369 313 8 156,878 272 7 103,776 180 5 59,309 103 3 47,681 83 2 24,285 42 1
133 164,745 286 7 143,574 249 6 95,814 166 4 56,395 98 2 45,321 79 2 23,019 40 1
117 114,663 199 5 92,967 161 4 46,815 81 2 9,737 17 0 7,779 14 0 4,071 7 0
81 76,596 133 3 60,922 106 3 26,996 47 1 0 0 0 0 0 0 0 0 0
111 67,410 117 3 45,420 79 2 20,256 35 1 0 0 0 0 0 0 0 0 0
92 66,685 116 3 39,945 69 2 17,647 31 1 0 0 0 0 0 0 0 0 0
109 61,030 106 3 41,205 72 2 18,554 32 1 0 0 0 0 0 0 0 0 0
102 55,309 96 2 42,170 73 2 18,516 32 1 0 0 0 0 0 0 0 0 0
106 49,427 86 2 39,810 69 2 17,937 31 1 0 0 0 0 0 0 0 0 0
101 43,852 76 2 39,060 68 2 28,372 49 1 19,071 33 1 15,293 27 1 7,863 14 0
146 39,593 69 2 28,343 49 1 12,338 21 1 0 0 0 0 0 0 0 0 0
108 38,954 68 2 23,881 41 1 10,537 18 0 0 0 0 0 0 0 0 0 0
89 38,924 68 2 26,742 46 1 12,186 21 1 22 0 0 17 0 0 10 0 0
115 36,995 64 2 26,240 46 1 11,693 20 1 0 0 0 0 0 0 0 0 0
38 33,068 57 1 16,393 28 1 7,302 13 0 45 0 0 39 0 0 31 0 0
107 20,352 35 1 11,384 20 0 5,160 9 0 0 0 0 0 0 0 0 0 0
113 15,758 27 1 10,883 19 0 4,939 9 0 0 0 0 0 0 0 0 0 0
29 15,594 27 1 8,456 15 0 3,692 6 0 0 0 0 0 0 0 0 0 0
39 15,497 27 1 2,704 5 0 1,175 2 0 0 0 0 0 0 0 0 0 0
55 15,355 27 1 9,603 17 0 4,384 8 0 86 0 0 0 0 0 0 0 0
52 14,999 26 1 207 0 0 93 0 0 0 0 0 0 0 0 0 0 0
51 13,975 24 1 7,838 14 0 3,525 6 0 0 0 0 0 0 0 0 0 0
87 13,603 24 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
66 13,004 23 1 915 2 0 418 1 0 0 0 0 0 0 0 0 0 0
10 12,766 22 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
64 12,295 21 1 6,854 12 0 3,078 5 0 0 0 0 0 0 0 0 0 0
53 12,086 21 1 8,020 14 0 3,498 6 0 0 0 0 0 0 0 0 0 0
63 11,971 21 1 6,430 11 0 2,921 5 0 0 0 0 0 0 0 0 0 0
15 11,730 20 1 4,433 8 0 1,977 3 0 0 0 0 0 0 0 0 0 0
9 10,735 19 0 5,644 10 0 2,437 4 0 0 0 0 0 0 0 0 0 0
4 9,965 17 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
114 8,857 15 0 6,086 11 0 2,641 5 0 0 0 0 0 0 0 0 0 0
34 8,771 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
121 8,355 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
36 8,190 14 0 1,417 2 0 626 1 0 0 0 0 0 0 0 0 0 0
86 7,990 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
110 7,677 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
32 7,601 13 0 1,124 2 0 486 1 0 0 0 0 0 0 0 0 0 0
72 7,536 13 0 4,981 9 0 2,359 4 0 0 0 0 0 0 0 0 0 0
105 7,399 13 0 1,392 2 0 585 1 0 0 0 0 0 0 0 0 0 0
11 7,398 13 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
17 7,166 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
56 6,934 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
59 6,320 11 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
47 5,316 9 0 1,891 3 0 795 1 0 0 0 0 0 0 0 0 0 0
42 4,225 7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
7 3,726 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
91 3,519 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
48 3,368 6 0 763 1 0 328 1 0 0 0 0 0 0 0 0 0 0
88 3,299 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
104 3,122 5 0 1,372 2 0 572 1 0 0 0 0 0 0 0 0 0 0
43 2,804 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
124 2,662 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
139 2,632 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
21 2,624 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
60 2,363 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
77 2,155 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
67 1,918 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
85 1,886 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
71 1,519 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
28 1,385 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
90 1,360 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
103 1,330 2 0 185 0 0 84 0 0 0 0 0 0 0 0 0 0 0
8 1,300 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
70 1,105 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
130 1,072 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
65 1,034 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
SIMULATION C (MEALS)
DAY-7 DAY-14 DAY-30 DAY-45 DAY-60 DAY-90
160
POD ID MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS MEALS PALLETTS
TRUCK
LOADS
SIMULATION C (MEALS)
DAY-7 DAY-14 DAY-30 DAY-45 DAY-60 DAY-90
120 878 2 0 2 0 0 1 0 0 0 0 0 0 0 0 0 0 0
20 761 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
84 757 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
83 632 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
143 486 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
12 474 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
27 384 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
135 353 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
62 348 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30 347 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
119 238 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
37 159 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
122 150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
74 142 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
125 119 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
13 100 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
40 96 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
144 49 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
19 38 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
145 19 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
23 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
82 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
TOTALS 1,912,160 3,320 83 1,350,590 2,345 59 843,284 1,464 37 417,159 724 18 334,682 581 15 173,170 301 8
*Note: All PODS with 0 resource requirements at Day-7 and later are not shown.

Abstract (if available)

Abstract Federal, state and local officials are planning for a (M) 7.8 San Andreas Earthquake Scenario in the Southern California Catastrophic Earthquake Response Plan that would require initial emergency food and water resources to support from 2.5 million to 3.5 million people over an eight-county region in Southern California. However, a model that identifies locations of affected populations—with consideration for social vulnerability, estimates of their emergency logistical resource requirements, and their resource requirements over time—has yet to be developed for the emergency response plan. ❧ The aim of this study was to develop a modeling methodology for emergency logistical resource requirements of affected populations in the (M) 7.8 San Andreas Earthquake Scenario in Southern California. These initial resource requirements, defined at three-days post-event and predicted through a probabilistic risk model, were then used to develop a relative risk ratio and to estimate resources requirements over time. The model results predict an “at-risk” population of 3,352,995 in the eight-county study region. In Los Angeles County, the model predicts an “at-risk” population of 1,421,415 with initial requirements for 2,842,830 meals and 4,264,245 liters of water. The model also indicates that communities such as Baldwin Park, Lancaster-Palmdale and South Los Angeles will have long-term resource requirements. ❧ Through the development of this modeling methodology and its applications, the planning capability of the Southern California Catastrophic Earthquake Response Plan is enhanced and provides a more effective baseline for emergency managers to target emergency logistical resources to communities with the greatest need. The model can be calibrated, validated, generalized, and applied in other earthquake or multi-hazard scenarios through subsequent research.

Linked assets

University of Southern California Dissertations and Theses

Asset Metadata

Creator Toland, Joseph Charles (author)

Core Title A model for emergency logistical resource requirements: supporting socially vulnerable populations affected by the (M) 7.8 San Andreas earthquake scenario in Los Angeles County, California

School College of Letters, Arts and Sciences

Degree Master of Science

Degree Program Geographic Information Science and Technology

Publication Date 09/11/2018

Defense Date 08/06/2018

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag commodity,critical infrastructure,differential equations,disaster,earthquake,emergency management,Food,food security,GIS,HAZUS,humanitarian,LandScan,logistical,logistics,LOGRESC,Los Angeles,Model,OAI-PMH Harvest,POD,Power,probabilistic model,relief,requirements,resource,response,risk,San Andreas,ShakeOut,social vulnerability,Water

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Kemp, Karen K. (committee chair), Oda, Katsuhiko (committee member), Swift, Jennifer N. (committee member)

Creator Email j.c.toland@att.net,jctoland@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-73249

Unique identifier UC11669381

Identifier etd-TolandJose-6773.pdf (filename),usctheses-c89-73249 (legacy record id)

Legacy Identifier etd-TolandJose-6773.pdf

Dmrecord 73249

Document Type Thesis

Format application/pdf (imt)

Rights Toland, Joseph Charles

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA