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AN ABSTRACT OF THE DISSERTATION OF
Kara N. DiFrancesco for the degree of Doctor of Philosophy in Water Resources Engineering
presented on March 13, 2014.
Title: Development and Application of Climate Risk Assessment Methods for Flood
Management Systems – A Study of Flexibility, Adaptive Capacity, and Robustness
Abstract approved:
______________________________________________________________
Desiree D. Tullos
Discussions around adapting water management systems to climate change often
express the need to increase the flexibility and adaptive capacity of current systems, and to
implement robust strategies going forth. While these topics lie at the center of many climate
change discussions, transforming adaptation recommendations into tangible tools and
information used in decision-‐making has proven difficult. The climate adaptation literature
lacks sufficient concrete examples of how water managers can assess the ability of current
systems to perform under climate change and make decisions regarding potential adaptation
strategies. In this dissertation, I outline a set of complimentary methods for water managers to
assess the climate risk of current systems and potential management strategies. Throughout
this process, I attempt to clarify and redefine climate terminology in terms of water resources
management, with a particular emphasis on the term, flexibility. The developed climate
assessment methods place emphasis on addressing the nonstationary, uncertain nature of
climate change and how this conflicts with traditional water management decision-‐making
methods that assume stationarity.
Within the climate adaptation literature, flexibility is one of the least rigorously explored
terms. Very little work has examined what exactly it means to have a flexible water
management system, what makes one system more flexible than another, or the extent to
which flexibility increases adaptive capacity. In Chapter 2, I review flexibility literature and apply
relevant flexibility concepts from other sectors to flood management systems. Based on this
work, I present a methodology for assessing the flexibility of the structural and non-‐structural
components of water systems using original indicators developed in the categories of: slack,
redundancy, connectivity, adjustability, and compatibility/ coordination. I then apply this
methodology to assess the ability of four proposed flood management strategies to increase
the flexibility of the Sacramento River, CA flood management system (Chapter 3).
In the second portion of this dissertation, I demonstrate a bottom-‐up climate risk
assessment that tailors available climate information to a decision regarding flood management
in the American River basin, CA (Chapter 4). Using historic data and available models, I begin by
evaluating the sensitivity and vulnerability of the flood management system to changes in
climate. In order to incorporate some of the uncertainty associated with General Circulation
Model (GCM) projections in the impact assessment, I use Bayesian methods to stochastically
generate thousands of flood frequency parameters representing a plausible range of future
flood conditions. Lastly, I assess the robustness of proposed management strategies in terms of
their ability to meet flood risk and cost-‐effectiveness thresholds under a large portion of the
plausible future conditions.
The studies presented in this dissertation provide water managers with examples of
how to apply climate adaptation terms to on-‐the-‐ground water systems. I outline example
evaluation techniques for a collection of related adaptation terms, in particular: flexibility,
adaptive capacity, sensitivity, vulnerability, and robustness. While the example case studies are
located in California, USA, the methodological basis used to assess climate risk, has broad
applicability and can be adapted and applied to other water systems around the world.
©Copyright by Kara N. DiFrancesco
March 13, 2014
All Rights Reserved
Development and Application of Climate Risk Assessment Methods for Flood Management
Systems – A Study of Flexibility, Adaptive Capacity, and Robustness
by
Kara N. DiFrancesco
A DISSERTATION
submitted to
Oregon State University
in partial fulfillment of
the requirements for the
degree of
Doctor of Philosophy
Presented March 13, 2014
Commencement June 2014
Doctor of Philosophy dissertation of Kara N. DiFrancesco presented on March 13, 2014
APPROVED:
__________________________________________________________________
Major Professor, representing Water Resources Engineering
__________________________________________________________________
Director of the Water Resources Graduate Program
__________________________________________________________________
Dean of the Graduate School
I understand that my dissertation will become part of the permanent collection of Oregon State
University libraries. My signature below authorizes release of my dissertation to any reader
upon request.
__________________________________________________________________
Kara N. DiFrancesco, Author
ACKNOWLEDGEMENTS
The author expresses sincere gratitude to the many people who have directly or
indirectly contributed to this work. First and foremost, my advisor Desiree Tullos provided
indispensable support throughout my time at Oregon State University. Thank you for
continually asking questions that challenge me to think deeper and identify the broader
implications of my work. To my committee members, Alix Gitelman, Michael Campana, and
David Purkey, I admire your ability to not only understanding complex technical issues, but also
to communicate these issues in a meaningful way to a broad audience. You inspire me to seek
fulfilling work, which contributes positively to the challenges facing the world. In the last four-‐
plus years, the rotating members of the Rivers Lab Group have helped shape and refine my
research from a disjointed list of pre-‐proposal notions to the current state of this document.
Thank you for your most helpful comments and suggestions on several paper and presentation
drafts. In particular, without the company of fellow PhD student Cristina Mateus during
countless hours spent in our office, libraries, and coffee shops, I’m not sure I would have
endured the last four years. Without a doubt, they would not have been nearly as fun – thank
you. Much of the what is presented in this document relies on models and data produced by
others who kindly allowed me to use their work, and for that, I am grateful to: MWH Global,
Inc. (Yung-‐Hsin Sun, Rebecca Guo, and Eric Clyde); US Army Corps of Engineers (Kurt Keilman,
Scott Stonestreet, and John High); California Department of Water Resources (Marill Jacobson);
and Ed Maurer (Santa Clara University). Lastly, words cannot express my appreciation for the
vital role my amazingly supportive friends and family played in shaping who I am and all that
I’ve accomplished. Thank for always reminding me of what is truly important in life.
TABLE OF CONTENTS
Page
Chapter 1. Introduction ............................................................................................................. 1 1.1. Challenges incorporating climate change into water resources management ................ 1 1.2. California flood management case studies ...................................................................... 2
Chapter 2. Flexibility in water resources management: review of concepts and development of assessment measures for flood management systems .............................................................. 5 Abstract ...................................................................................................................................... 5 2.1. Introduction ...................................................................................................................... 6 2.2. Flexibility in water resources systems .............................................................................. 8 2.2.1. Definition and features of flexibility in water resources systems .............................. 8 2.2.2. Characteristics of flexible water resources systems ................................................... 9
2.3. Valuing the costs and benefits of flexibility .................................................................... 18 2.4. Conclusions ..................................................................................................................... 20 References ................................................................................................................................ 27
Chapter 3. Assessment of flood management systems' flexibility with application to the Sacramento River basin, California, USA ...................................................................................... 35 Abstract .................................................................................................................................... 35 3.1. Introduction .................................................................................................................... 36 3.2. Operationalization of the term flexibility ....................................................................... 39 3.3. Data and methods .......................................................................................................... 41 3.3.1. Study area ................................................................................................................ 41 3.3.2. Methods to analyze flexibility in the Central Valley Flood Protection Plan (CVFPP) 42
3.4. Results ............................................................................................................................ 45 3.4.1. Management action contribution to flexibility characteristics ................................ 45 3.4.2. Flexibility of structural and non-‐structural management actions ............................ 45 3.4.3. Flexibility of management strategies proposed in the CVFPP .................................. 46 3.4.4. Relationship between flexibility and cost-‐ and time-‐ effectiveness ......................... 47
3.5. Discussion ....................................................................................................................... 48 3.6. Conclusions ..................................................................................................................... 51 References ................................................................................................................................ 63
Chapter 4. Bottom-‐up assessment of climate risk and the robustness of proposed flood management strategies in the American River, CA ...................................................................... 66 Abstract .................................................................................................................................... 66 4.1. Introduction .................................................................................................................... 68 4.2. Study area: American River Basin, CA ............................................................................ 71 4.3. Data and Methods: Developing the bottom-‐up flood risk assessment .......................... 73 4.3.1. Establishment of the decision context ..................................................................... 73 4.3.2. Sensitivity of current system to flood regime changes ............................................ 74 4.3.3. Vulnerability of system to flood regime changes ..................................................... 77
TABLE OF CONTENTS (continued)
Page 4.3.4. Plausible range of future flood regimes ................................................................... 77 4.3.5. Robustness of current systems and management strategies .................................. 80
4.4. Results ............................................................................................................................ 81 4.4.1. Sensitivity of flood risk (EAD) to changes in flood frequency regimes ..................... 82 4.4.2. Plausible range of future flood impacts ................................................................... 82 4.4.3. Robustness of current system and management strategies .................................... 84
4.5. Discussion ....................................................................................................................... 86 4.6. Conclusions ..................................................................................................................... 90 References .............................................................................................................................. 102
Chapter 5. Conclusions .......................................................................................................... 106
Bibliography ................................................................................................................................ 109
LIST OF FIGURES Figure Page Figure 2.1. Timeline illustrating shift from optimality to flexibility and robustness ..................... 23
Figure 2.2. Flexibility characteristic from domains outside water resources used to develop the characteristics for water resources. ............................................................................................. 24
Figure 3.1. Location map of the Central Valley, CA. ..................................................................... 54
Figure 3.2. Percentage of flexibility characteristics enhanced by each management strategy in terms of: a) number of actions and b) total mid-‐range cost. ...................................................... 55
Figure 4.1. Map of the American River Basin, CA showing major SPFC project works ................. 92
Figure 4.2. Daily hydrograph at Fair Oaks USGS gauge on the American River, CA. .................... 92
Figure 4.3. Basis of the EAD computation used in CVFPP HEC-‐FDA model (modified from CA-‐DWR, 2012).. ................................................................................................................................. 93
Figure 4.4. Gridded FDA model runs (open circles) used in the regression model to develop the flood risk response surface, LN(EAD) = ƒ(µ, σ), under Without Project conditions (shaded background). ................................................................................................................................ 94
Figure 4.5. Observed and modeled daily streamflow used for historic and future flood frequency analysis on the American River at Folsom. ................................................................................... 94
Figure 4.6. Expected value of 30-‐year a) average (μ) and standard deviation (σ) of LN-‐historic observed 3-‐day average peak annual flows. ................................................................................ 95
Figure 4.7. Posterior interval boxplots of: a) mean peak annual flow, μ, and b) standard deviation, σ, of peak annual flow for observed streamflow data (dark gray) and GCMs forced with observed parameters (light gray) from 1950 – 1999.. .......................................................... 95
Figure 4.8. Expected posterior flood frequency curves derived from observed streamflow data and GCMs forced with observed parameters from 1950 – 1999. ................................................ 96
Figure 4.9. Winbugs MCMC parameter output for the historic data (1905-‐2012, light grey circles) and each of the GCMs (2000-‐2099, dark grey circles). .................................................... 97
Figure 4.10. Posterior interval boxplots of: a) mean peak annual flow, μ, and b) standard deviation, σ, of peak annual flow for observed streamflow data from 1905 -‐ 2012 (dark gray box) and GCMs forced with future emissions scenarios (light gray) from 2000 – 2099. .............. 98
Figure 4.11. Benefit-‐cost ratio response surfaces for each of the management strategies: a) Design Capacity, b) Protect Communities, c) Enhance System, d) Combined. ............................. 99
LIST OF TABLES
Table Page
Table 2.1. Definitions of flexibility and inflexibility ...................................................................... 25
Table 2.2. Example metrics to assess flexibility in flood management systems. Unless otherwise noted, larger metric values indicate greater flexibility. ................................................................ 26
Table 3.1. Example metrics to assess flexibility in flood management systems. Unless noted, larger metric values indicate greater flexibility (DiFrancesco and Tullos In review). ................... 56
Table 3.3. Inflexibilities in the SPFC identified in the CVFPP and categorized based on whether the inflexibility relates to structural (S) or non-‐structural (NS) components. .............................. 58
Table 3.4. Impact of management actions on flexibility characteristics, organized by broad flood management elements. Negative numbers indicate actions that reduce system flexibility. ....... 59
Table 3.5. Structural versus non-‐structural diversity in terms of number of projects and expenditure. ................................................................................................................................. 60
Table 3.6. Number of structural versus non-‐structural components that impact each flexibility characteristic. ............................................................................................................................... 60
Table 3.7. Comparison of flood management strategies in the CVFPP based on estimated cost expenditures ($M) for each major flood management element. ................................................. 60
Table 3.8. Number of actions in each CVFPP strategy, which increase or decrease the flexibility metrics. ......................................................................................................................................... 61
Table 3.9. Comparison of strategies by costs, benefits, and implementation time. .................... 62
Table 4.1. Overview of CVFPP management strategies .............................................................. 100
Table 4.2. Low and high cost upfront estimates ($M) for each of the CVFPP management strategies [CA-‐DWR, 2012] ......................................................................................................... 100
Table 4.3. Summary statistics for the linear response function fit to the EAD, mean, and standard deviation, ln𝐸𝐴𝐷 = 𝛽0+ 𝛽1µμ+ 𝛽21𝜎. ................................................................... 101
Table 4.4. EAD robustness indicator, percent of posterior draws of flood frequency parameters that yield an EAD below the threshold. ...................................................................................... 101
Table 4.5. BCR robustness indicator, percent of posterior draws of flood frequency parameters that yield a BCR above the threshold. ........................................................................................ 101
Chapter 1. Introduction
1.1. Challenges incorporating climate change into water resources management
Water is the primary medium through which climate change will impact human societies
and ecosystems. Extensive global efforts have been put forth to study: climate impacts on
water resources; the vulnerability of human systems to those impacts; and strategies to reduce
vulnerability and adapt to changes. Yet, most water management systems remain ill suited to
meet current water resources’ challenges, let alone those lying ahead. As such, incorporating
climate change into water resources management plans often remains a paper based, elusive
goal. Many factors contribute to the lack of inclusion of climate change into on-‐the-‐ground
water resources management and planning (Langsdale et al. 2009; Jantarasami, Lawler, and
Thomas 2010). This dissertation focus on addressing two of those factors in particular, namely:
1) difficulty in translating adaptation recommendations into management and planning
strategies and 2) incongruities between traditional decision-‐making techniques that assume
stationarity and the nonstationarity and uncertainty associated with climate change.
The literature on adapting water resources systems to climate change contains a wide
range of recommendations filled with vague adaptation terminology, which can often be
difficult to decipher. For example, recommendations include the need to increase system’s
flexibility (Pahl-‐Wostl et al. 2007; Gersonius et al. 2013) and adaptive capacity (Folke et al.
2002; Smit and Wandel 2006) and to implement robust strategies (Wilby and Dessai 2010;
Sayers, Galloway, and Hall 2012). While a solid theoretical basis exists to support these
recommendations, it remains difficult to translate the climate adaptation literature into water
resources planning and decision-‐making. In an effort to clarify and operationalize some of the
climate terminology, in this dissertation I present a definition of the term flexibility (Ch. 2) and
develop and apply methods to assess a flood management system’s: flexibility (Ch. 3), climate
sensitivity and vulnerability (Ch. 4), and the robustness of management actions (Ch. 4).
In terms of the second barrier to including climate considerations in water planning,
traditional methods of flood frequency analysis in combination with top-‐down climate impact
2
assessments provide limited opportunities to address the deep uncertainty and nonstationarity
associated with GCM projections. While uncertainty has plagued managers for as long as water
resources have been developed (Hall and Solomatine 2008), the uncertainty associated with
climate change far exceeds anything experienced in the past. Historically, uncertainty
associated with estimation errors in probability density functions and acknowledged faults in
the stationarity assumption were addressed using the ‘precautionary principle.’ For example,
planners oversized dams and added extra height or freeboard to levees above the size
analytically deemed necessary (Stakhiv 2010). However, the current and projected future
hydrologic and socio-‐economic conditions challenge the theory that design conservatism can
adequately address the magnitude and unknowns of climate uncertainties. Also, due to budget
constraints and growing demands for water, energy, and environmental protection, there is no
longer room in many water or economic budgets to allow for operational and economic
inefficiencies associated with the historical conservative approach to designing water resources
systems (Frederick, Major, and Stakhiv 1997).
To date, top-‐down approaches with heavy reliance on Global Circulation Models (GCMs)
have dominated the field of climate risk assessments; however, top-‐down approaches often fail
to provide water resources managers with information useful for planning. Generally speaking,
top-‐down approaches tend to force GCM output into a form compatible with more traditional
hydrologic and decision-‐making models based on assessing impacts under a small number of
future scenarios. In Chapter 4, I detail the issues with taking such an approach, most
prominently the inability to capture the full range of uncertainty of future conditions using a
limited number of scenarios. As an alternative to top-‐down climate assessment, I present a
bottom-‐up approach for conducting an assessment of climate risk and the robustness of
management strategies that intentionally addresses the limitations in using GCM output for
decision-‐making in water resources management.
1.2. California flood management case studies
The topics addressed in the subsequent chapters have broad applicability to water
resources management and climate adaptation more generally. However, the included case
3
studies all apply to flood risk management in California, USA, which provides a unique set of
challenges and advantages. While the impacts of climate change will vary across the globe,
changes in hydrologic extremes, e.g. droughts and floods, present one of the most pressing
concerns for water resources managers. Climate change will result in changes in the frequency,
intensity, spatial extent, duration, and timing of extreme weather and climate events,
potentially resulting in unprecedented events (Field et al. 2012). With these extreme events
comes the potential for large loss of human life and exponentially increasing costs associated
with these events (Karl and Easterling 1999).
California is at risk for catastrophic flooding (CA-‐DWR 2013), which has resulted in
numerous efforts to study floods from a hydrologic, socio-‐economic, and environmental
perspective. The work present in this dissertation builds upon this long line of prior research,
while introducing a novel approach to include climate risk assessment and adaptation into
California’s flood management systems. Although I tailor the subsequent study methodologies
to the regional context, they are broadly applicable outside of California and outside the field of
flood risk management.
4
FLEXIBILITY IN WATER RESOURCES MANAGEMENT: REVIEW OF CONCEPTS AND DEVELOPMENT
OF ASSESSMENT MEASURES FOR FLOOD MANAGEMENT SYSTEMS
Kara N. DiFrancesco, PhD candidate, Water Resources Engineering, Oregon State University, Corvallis, Oregon Desiree D. Tullos, Associate Professor, Biological & Ecological Engineering, Oregon State University, Corvallis, Oregon
Journal of the American Water Resources Association (JAWRA) 350 Main Street Malden, MA 02148 In review
5
Chapter 2. Flexibility in water resources management: review of concepts and development of assessment measures for flood management systems
Abstract:
Discussions around adapting water management systems to climate change often express the
need to increase system flexibility. Yet despite the frequent use of the term flexibility, very little
work has examined what exactly it means to have a flexible water management system, what
features of a system make it more flexible than another system, or when the costs to
implement flexible options outweigh the benefits gained from increased flexibility. To define
and operationalize the concept of flexibility in the field of water resources management, this
article reviews and analyzes concepts of flexibility from the fields of information technology,
manufacturing, management, and adaptive social-‐ecological systems. We identify five
characteristics of flexible water resources systems, namely: slack, redundancy, connectivity,
compatibility/coordination, and adjustability. We then operationalize the assessment of
flexibility for flood management systems by proposing original flexibility metrics and discussing
their application. We conclude with a discussion on the tradeoffs of increasing flexibility.
Keywords: flexibility; adaptive capacity; optimization; climate variability/change; risk
assessment; flood management; water resources flexibility
6
2.1. Introduction
Associated with a need to increase water resources systems’ capacity to cope with and
adapt to climate change, recent literature regarding water resources management increasingly
includes recommendations for more flexible systems (Huang et al., 2010; IPCC, 2007; Johnson
and Lilly, 2009; Pahl-‐Wostl et al., 2007; Richter et al., 2003) Figure 2.1). The need for flexible
systems is driven by uncertainty and changing conditions (Zhao and Tseng 2003), which
influence water resources systems in a number of critical ways. For example, standard risk
analysis methods applied in water resources planning, design, operation, and maintenance
require defining probability distributions on the basis of assuming hydrologic stationarity (U.S.
Water Resources Council 1983). This assumption has been heavily challenged due to land use
and climate change (Frederick, Major, and Stakhiv 1997; Milly et al. 2008), leading to an
increased emphasis on flexibility, robustness, and adaptive capacity (Lempert, Bankes, and
Popper 2003) in water resources planning. Furthermore, the utility and validity of optimization
techniques, used in water resources planning studies since the 1960s for meeting multiple
objectives (Wolman and National Research Council, 1962; Wurbs, 1991), declines as uncertainty
increases (Lempert, Bankes, and Popper 2003) and the future is not constrained to the limited
scenarios examined by optimization (Bonder 1979). With water resources systems facing all of
requirements for conditions of deep uncertainty (Lempert, Bankes, and Popper 2003), planning
and analysis of water resources projects are shifting towards emphasis on adaptive and robust
strategies that perform reasonably well over a wide range of uncertain, yet plausible future
scenarios (Lempert, Bankes, and Popper 2003; Frederick, Major, and Stakhiv 1997).
While it is acknowledged that increased emphasis on adaptive water resources systems
can improve their robustness in the future, clarity is needed regarding how adaptive capacity
can be integrated into water resource systems. The capacity to adapt has been variously
defined in the literature on social-‐ecological systems (SESs) over time (Adger et al., 2005; Adger
et al., 2004; Engle, 2011; Gallopín, 2006; Smit and Wandel, 2006) and generally converges on a
definition that includes: the processes, actions, or resources of a SES that facilitate adjusting to,
coping with, and/or benefitting from a change or hazard (Adger et al., 2005; Carpenter and
7
Brock, 2008). Adaptive capacity is determined by several system features, including: financial,
human, and social assets, governance and institutions, knowledge and information, and
stakeholders (Adger et al. 2004; Jones, Ludi, and Levine 2011; Smit and Wandel 2006). Yet, the
mere existence of these features does not lead to adaptive systems. Rather, certain traits
exhibited by the features, such as the flexibility of governance and institutions (Folke et al.,
2002; Pahl-‐Wostl, 2009; Dietz et al., 2003; Folke et al. 2005; Huitema et al., 2009) and the
engagement of stakeholders (Pettengell 2010), increase adaptive capacity. As such, flexibility
and adaptive capacity are positively related (Engle, 2011).
However, despite the importance and frequency of recommendations for flexibility in
adaptive water resources systems, very little work has examined what exactly it means to have
a flexible water management system and what makes one system more flexible than another.
From the management perspective, the term lacks utility because it is unclear how to assess
and compare the flexibility of proposed management actions. Furthermore, to our knowledge,
no analysis has considered whether the costs to implement flexible options outweigh the
benefits gained from increased flexibility. However, analysis of flexibility from the fields of
Information Technology (IT) (Byrd and Turner 2000; Duncan 1995; Golden and Powell 2000; D.
E. Turner and Lankford 2005); management (Fayol 1916); manufacturing (Pyoun and Choi
1994); planning (Pye 1978); and adaptive social-‐ecological systems (SESs) (Adger, et al., 2005;
Smit and Wandel, 2006) can offer insight on applying the concept of flexibility to the
management of water resources systems.
Thus, the overarching goals of this study are to define the concept of flexibility in water
management systems generally and then to operationalize the concept in the field of flood
management more specifically. We review literature on flexibility in water management by first
conducting a Google Scholar keyword search on “flexibility water management” and then
expand our search to “flexible systems” to review the use of the term in other domains. We
apply and modify the flexibility topology in the literature to define flexibility in water resources
systems. We identify different characteristics of flexible systems and propose a set of metrics
under each characteristic to assess the flexibility of flood management systems. We conclude
8
with a discussion on the costs and unintended consequences of incorporating additional
flexibility into water resources systems.
2.2. Flexibility in water resources systems
2.2.1. Definition and features of flexibility in water resources systems
Despite the proliferation of flexibility recommendations in water resources
management and other sectors, flexibility remains an ambiguous term due to the lack of a
common, operational definition (Golden and Powell 2000; Duncan 1995). Few studies have
been undertaken to directly assess the flexibility of adaptive systems (Engle 2011). This
ambiguity stems from the term’s multidimensional and varied traits (Golden and Powell 2000),
making flexibility difficult to measure and integrate into the planning and decision-‐making
processes (Duncan 1995). Definitions of flexibility (or inflexibility) vary between sources and
often depend on the target of the flexibility or the system being assessed (Table 2.1). We
synthesize the definitions and features of flexibility from other domains to define flexibility in
water resources as:
the inherent ability of the human and physical elements of a system to
cope with, or adapt to, uncertain and changing conditions, in a timely
and cost-‐effective manner.
This definition is based on three features of flexibility derived from the literature. First,
flexibility supports the ability to cope (Gallopín 2006) and adapt (Gallopín 2006) to uncertain,
changing conditions. The IT, management, and manufacturing literature on flexibility focus on
the need to meet new and growing demands (Duncan 1995; Fayol 1916; Golden and Powell
2000; Pyoun and Choi 1994; D. E. Turner and Lankford 2005) under an uncertain future (Golden
and Powell 2000). Water resources flexibility references the capability to adapt to new or
changes in both demands and supply (FAO, 1993; Patel Center, 2011; Gunderson and Holling,
2002; IPCC, 2007). For example, water resources managers face challenges from increasing
demands for residential water supply due to population growth (Falkenmark and Widstrand
9
1992; Holdren and Ehrlich 1974; Vörösmarty et al. 2000), new demands and operational
requirements for which the systems were not designed, such as providing environmental flow
releases (Arthington et al. 2006; Richter et al. 2003; Richter and Thomas 2007), and for
protection from potentially larger and/or more frequent future floods under climate change
(IPCC, 2007).
Second, several definitions of flexibility (Table 2.1), as well as further explanations in the
IT and manufacturing literature, include economic and time benefits of flexibility (Duncan 1995;
Golden and Powell 2000; Pyoun and Choi 1994). Flexibility involves not only the ability to cope
or adapt, but also the ability to do so in a timely and cost-‐effective manner. For example,
flexible IT systems provide a competitive advantage in their capability to quickly respond to
customer demands and keep up with new innovations marketed by competitors (Duncan 1995).
Third, the assessment of flexibility is an absolute characteristic of a system, rather than
relative to a particular hazard or stressor (IPCC, 2007), presenting a snapshot of a single,
specific system at a point in time. In contrast, adaptive capacity, vulnerability, and resilience are
measured in terms of some specific type of disturbance or perturbation, requiring an answer to
the question: Adaptation, vulnerability or resilience of what to what? (Carpenter et al. 2001;
Gallopín 2006). Alternatively, flexibility is an inherent system characteristic that needs no
qualifier. Thus in describing the flexibility of a system, we need not answer the question:
Flexible to what? This makes it possible to assess the flexibility of a system without the need to
fully characterize potential future conditions and uncertainties. However, although
perturbation and uncertainty parameters do not enter into the process of measuring the
flexibility of a system, they do influence the value of flexibility (Huang, Vairavamoorthy, and
Tsegaye 2010; Zhao and Tseng 2003). The value of flexibility increases with the degree of
uncertainty and the projected magnitude of perturbations in future conditions, as further
discussed later in this manuscript.
2.2.2. Characteristics of flexible water resources systems
Following a comprehensive review of literature across scholarly databases and the
references found therein, we find that in-‐depth assessments of flexibility and attempts to
10
operationalize the term appear primarily in the field of IT, which maintains similarities with
water resources management regarding uncertainty and growing demands. We thus apply
concepts from the IT field as a foundation for operationalizing the concept of flexibility in flood
management, along with relevant contributions from other fields. Researchers in the IT field
(e.g. Golden and Powell, 2000; Duncan, 1995; Byrd and Turner, 2000; Turner and Lankford
2005) propose assessing characteristics of flexible systems that relate to 1) the range of options
that an organization has available and 2) how long it takes an organization to adapt. Along
similar lines, we find that the characteristics found in the literature (e.g. efficiency,
responsiveness, versatility, and robustness; Golden and Powell, 2000) relate to water system’s
1) the ability to cope and 2) the ability to adapt. We use these characteristics as the foundation
from which we operationalize the concept of flexibility in water resources systems (Figure 2.2).
We find that the characteristics of slack, redundancy, connectivity, and compatibility/
coordination, increase the range of available options, providing water systems with the
flexibility to cope with changes. The ease of adjusting the aforementioned flexibility
characteristics, adjustability, provides water systems with the flexibility to adapt to changes.
Individually, each of the flexibility characteristics may be insufficient to fully represent the
concept of flexibility, requiring some collective combination of dimensions to adequately
characterize flexible systems (D. E. Turner and Lankford 2005).
We integrate and modify the measureable characteristics of flexible systems provided
by the IT literature to develop a framework for characterizing and assessing flexibility in water
resources management (Figure 2.2). As a starting point to developing a full methodology to
assess the flexibility of water systems, in the following section, we 1) identify and define five
flexibility characteristics in water resources systems, namely: slack, redundancy, connectivity,
compatibility/coordination, and adjustability; 2) propose a set of sample metrics within each of
the characteristics for evaluating the degree of flexibility in a flood management systems (Table
3.); 3) give descriptive examples of actions that may increase flexibility for that characteristic;
and 4) explain the contribution of each flexibility characteristic to increasing flexibility and
informing management decisions.
11
2.2.2.1. Slack
Slack provides surplus capacity to cope with uncertain and changing conditions (D. E.
Turner and Lankford 2005). Intentionally embedding excess capacity into a system provides
increased flexibility for future expansion, helping to ensure it can meet increased demands
and/or changing objectives under a wider variety of conditions (Zhao and Tseng 2003; Hall and
Murphy 2012). For example, Zhao and Tseng (2003) apply a trinomial lattice model to identify
an appropriate foundation size of a parking garage. This analysis balances the upfront costs to
incorporate the slack necessary for future expansion with the potential profit provided by the
option to expand the garage under uncertain future parking demand.
From a flood risk management perspective, evaluating and appropriately incorporating
slack into the design of water resources systems, via dam/bypass sizing, channel/spillway
capacity, etc., may help eliminate the need for costly, retrofit constructions. Flood managers
may evaluate the degree of slack based on the normalized excess capacity of reservoirs to store
(Table 2.2, S1) and release (Table 2.2, S3) flood flows, the downstream channels to convey flood
flows (Table 2.2, S2), and bypasses’ ability to store excess channel flows (Table 2.2, S4). For
example, increasing stream conveyance capacity (Table 2.2, S2) has been identified as a
promising option for mitigating climate change impacts of flooding (Brekke et al. 2009).
Managers may evaluate the magnitude of a future flood of interest and current stream
conveyance capacity (Table 2.2, S4) to evaluate the excess capacity needed for a flood bypass.
Alternately, if flood magnitudes are projected to increase, but the normalized excess reservoir
capacity (Table 2.2, S1) is equal to or less than 1, then the system could likely benefit from
increases in slack related to flood storage.
Unfortunately, the need for additional flexibility in water resources is often only realized
in hindsight when meeting objectives is made difficult by the inflexibility of the current system,
as can be the case when a system lacks slack. For example, a report (CA-‐DWR 2010) on the
current condition of the California flood management system lists a variety of factors
contributing to the inability of the system to meet its designed flood management objectives.
12
These include a lack of slack through insufficient flood storage capacity to regulate flood flows
(Table 2.2, S1 & S4) and inadequate capacity to convey design flows (Table 2.2, S2 & S3) in
approximately half of channels evaluated (CA-‐DWR 2010a).
2.2.2.2. Redundancy
Redundancy generally refers to multiple options performing the same function in a
system, such as multiple species performing a same role (e.g. nitrification) in ecosystems (B. H.
Walker 1992). Redundancy and the substitution or interchangeability of components are critical
to adaptive and robust SESs (Ospina and Heeks 2010) and ecosystems exposed to disturbances
(De Leo and Levin, 1997; Naeem, 1998). Similarly, robust IT systems are defined by the degree
of repetitiveness, labeled in IT analyses as intensity (D. E. Turner and Lankford 2005). In flood
management systems, repetitiveness and diversity of options also increase a water resources
system’s ability to cope or adapt to uncertain, future conditions (Gleick, 2003; IWMI, 2009).
Thus, whereas slack ensures the existence of excess capacity in the system to cope with
changing conditions and demands, redundancy ensures that this capacity is spread amongst a
variety of options. We can then measure redundancy by the number of storage options
available (Table 2.2, R1), the diversity of those options (Table 2.2, R2), and the number of
groups with vested interests and responsibility for managing the water resources (Table 2.2,
R3).
In addition to a larger number of options (e.g. number of reservoirs and bypasses in
each tributary – Table 2.2, R1), distributing capacity across many different management
strategies can also reduce flood risk over the long term. The value of diversity in flood
management strategies in meeting capacity requirements has been emphasized by scientists
and managers (Gleick 2003; Pearce 2004; Brooks, Brandes, and Gurman 2009; Rijsberman 2006;
Hall and Murphy 2012) who critique twentieth-‐century water policies for relying too heavily on
“hard path” approaches to meet human demands, including large dams, aqueducts, and levees,
as opposed to “soft path” approaches. In contrast to large, centrally managed infrastructure,
soft path approaches emphasize lower-‐cost community-‐scale systems, decentralized and open
13
decision-‐making, water markets and equitable pricing, application of efficient technology, and
environmental protection. Thus, assessing the relative number of structural and non-‐structural
options for managing floods (Table 2.2, R2) can identify the balance in a system’s portfolio of
infrastructure that contributes to reducing exposure to flood risk.
Finally, the number of parties invested in a flood management system (Table 2.2, R3)
can contribute to its flexibility, though generally only up to a point. Many resources, including
water, are too complex to be governed effectively by a single agency (Berkes 2009). Instead, co-‐
management of natural resources, defined as the sharing of power and responsibility between
the government and local resource users (Adger et al. 2004; Adger, Brown, and Tompkins 2005;
Armitage et al. 2008; Huitema et al. 2009; Wallace, Acreman, and Sullivan 2003), can be more
effective at achieving management objectives. Different levels of organization, from local to
federal, have comparative advantages in the management of resources (Berkes 2009). In the
flood management context, state and federal agencies may provide financial support and
expertise not available at the local level, while local institutions have a better understanding of
their specific needs and can respond more quickly to flood emergencies. However, the number
of parties involved can also decrease flexibility of a system and the mere existence of multiple
agencies does not always lead to effective and adaptive co-‐management. In some cases (Adger
et al. 2005), individual institutions may simply promote themselves without promoting the
flexibility the overall management structure or its adaptability.
2.2.2.3. Connectivity
Connectivity ensures that a system is capable of fully utilizing its redundancy by
employing the options available to meet system objectives. Connectivity is generally viewed as
a positive attribute of most adaptive systems (but see Fraser et al. (2005) for an alternate
perspective). For example, hydrologic connectivity is essential to functioning ecosystems,
where hydrologic connectivity refers to the water-‐mediated movement of materials, energy,
and organisms down and across rivers and riparian areas (Kondolf et al. 2006). With respect to
water resources management, the term applies to the linkages between infrastructure that
14
promote reliability of moving water across networks (Yang et al. 1996). Increasing connectivity
of water supply infrastructure is considered a mechanism to improve the resilience of existing
resources as well as to provide security from extreme events in the face of climate change
(Wilby and Dessai 2010).
The need for connectivity in a water resources system includes both natural
infrastructure, including rivers, aquifers, and floodplains, and man-‐made infrastructure, such as
reservoirs, constructed bypasses, and irrigation canals. Since a variety of water storage options
exist for flood management, each with strengths and weaknesses, connectivity between these
structures and flexibility in their use can help hedge against the uncertainty associated with
climate change (IWMI, 2009). Connectivity between water system components also allows for
shared utilization between flood management and other operating objectives, such as
ecosystem restoration or agricultural production, resulting in overall increased system
performance.
Connectivity and collective management in the use of surface and groundwater (Table
2.2, C1), called conjunctive use, can increase storage capacity by utilizing underground aquifers
while avoiding the economic, environmental and social costs of dams. A study (USACE, 2002)
conducted in the Central Valley of California found that, via natural replenishment and
anthropogenic aquifer storage during times of high flow, conjunctive use operations generated
between 92,000 and 322,000 acre-‐feet (AF) of newly available annual yield per reservoir. Thus,
managers may evaluate the balance of conjunctive use options relative to reservoirs to identify
whether additional conjunctive use operations can contribute to expanding storage capacity for
flood management.
In addition to leading to more efficient utilization of water supplies, increased
connectivity, particularly between the main river channel and its floodplains (Table 2.2, C2), can
generate space for storing and attenuating flood events, while also providing increased slack,
redundancy, and ecological benefits. Restoring river-‐floodplain connectivity can increase the
ability of the system to cope with the larger and more frequent floods projected under climate
change (IPCC, 2007) by utilizing the natural storage capacity of floodplains, subsurface flow,
15
aquifers, in addition to the human-‐managed storage reservoirs included in the slack
characteristic. For example, reconnection of 8,000 hectares (ha) of floodplain along the Illinois
River to allow peak flood waters to inundate strategically-‐designated farmland could halve the
probability of flooding 26,000 ha of downstream farmland (Akanbi, Lian, and Soong 1999). This
same study found that an alternate management option of raising the levee height (Table 2.2,
S2) could achieve the similar risk reduction goals, but at a significantly lower benefit to cost
ratio (Akanbi, Lian, and Soong 1999). In heavily leveed rivers (Table 2.2, C2), such as the Illinois
River, it may be more cost-‐effective for managers to reduce flood stage by increasing river-‐
floodplain connections over implementing other management options. Restoring connectivity
of floodplains may also allow upstream reservoirs to remain at a higher elevation during the
flood season by increasing downstream flood storage capacity, increasing the available water
supply and hedging against scarcity concerns (Opperman et al. 2009).
2.2.2.4. Compatibility/ coordination
Duncan (1995) emphasizes the ability to share information across any technology
component, termed compatibility, as an important determinant of IT flexibility, since
information sharing provides easy access to relevant data and lowers the cost of innovation. In
order to make informed decisions, water managers need access to hydrologic, operations, and
regulatory information (Table 2.2, CC1). This information includes antecedent, current, and
projected future hydrologic and climate data, water demands and usage, reservoir operations,
and forthcoming policy and regulatory changes. The information is needed in locations and
forms that are accessible and compatible for use by other entities. In addition, compatibility
and coordination are needed between policy makers and water resource planners and
managers to ensure that policy and regulations, such as the structure or priority of water rights,
both inform and are informed by water resources management.
In most cases, a variety of different agencies work within a river basin on different
aspects of water management, and each agency is likely to have access to data that may be
relevant to others. Furthermore, researchers, water users, and other stakeholders outside of
16
water management agencies also possess data (Table 2.2, CC1) and analytical tools (Table 2.2,
CC2) relevant to water managers, and vice versa, requiring a multi-‐dimensional flow of
information. For example, the peer-‐reviewed literature contains many examples of the
potential for ensemble streamflow prediction (ESP) forecasts to improve water system
operations (Faber and Stedinger 2001; Hamlet and Lettenmaier 1999; Hamlet, Huppert, and
Lettenmaier 2002). However, many water agencies lack access to peer-‐reviewed literature and
to the modeling techniques and decision processes to fully exploit ESP forecasts (Faber and
Stedinger 2001). Assessing the sharing of data and tools in a basin is binary (Table 2.2, CC1 &
CC2), but may vary across user groups.
In addition, within-‐basin coordination of water resources management and operations
(Table 2.2, CC3) can significantly contribute to system flexibility and robustness. In their
recommendations for a sustainable future, the Western Governors’ Association (2008)
emphasized that ongoing coordination and information sharing between scientists and water
managers, along with the various levels of government engaged in planning efforts, is critically
needed. Similarly, after the devastating 1997 flood in the Yuba-‐Feather River system in
California, USA, the Yuba County Water Agency (2008) found that sharing weather, water, and
management information and the coordination of operational decisions among agencies
provided one of the most cost-‐effective measures for improved flood management (Table 2.2,
CC1 & CC3). The implementation of Forecast-‐Coordinated Operations in these basins is
expected to reduce peak flows of the rivers and the risk of exceeding river channel capacity, as
well as improve the notification processes and advance flood warning and preparation times
(Yuba County Water Agency 2008). Similarly, the National Hydrologic Warning Council reported
in 2013 that lives were saved during Colorado floods of 2013 by the coordinated flood warning
and management systems that were implemented following flash floods that killed over 140
people in 1976 (Curtis 2013). Such coordination, both of information and agencies, can be
assessed by the number of coordinated agreements in a basin (Table 2.2, CC3), normalized for
example, relative to the number of reservoirs. The normalized metric allows managers to
17
evaluate potential operational gains by determining the relative number of reservoirs operating
in isolation.
2.2.2.5. Adjustability
Khosrowpour (2006) takes a broad interpretation of Duncan's (1995) definition of
modularity to include the: ability to add, modify, and remove any software, hardware, or data
components of the infrastructure with ease and with no major overall effect. Since the use of
the term modularity in the IT context usually takes on a specific meaning associated with
isolating and standardizing business and system processes (Duncan 1995), we modify the
definition given by Khosrowpour (2006) and rename this flexibility characteristic adjustability,
or the ability to add, modify, and remove any component of the system and/or its operations
with ease and with no major overall effect. In essence, adjustability describes the ease with
which managers can modify the formally described flexibility characteristics – slack,
redundancy, connectivity, and compatibility/ coordination – to adapt to changing conditions.
Relative to adjustability, one of the most widely-‐cited inflexibilities in water
management systems refers to the inability to modify system operations in a timely and cost-‐
effective manner due to legal or other regulatory constraints (CA-‐DWR, 2009; Hamlet and
Lettenmaier, 1999; Johnson and Lilly, 2009). At a workshop in 2009, western water managers
emphasized the need to “evaluate and revise the legal framework for water management to
the extent allowable to ensure sufficient flexibility exists to anticipate and respond to climate
change” (A. M. A. Johnson and Lilly 2009). In particular, these managers stressed the
importance of the ability to revise dam operations (Table 2.2, A1) based on new information
without going through costly and time consuming Congressional re-‐authorization and/or
completing an Environmental Impact Statement (EIS) every time a change is needed (A. M. A.
Johnson and Lilly 2009).
The ability to modify reservoir operations and storage allocations (Table 2.2, A1) is one
key characteristic of a flexible flood management system. For example, in response to much
larger floods in the American River Basin after the completion of Folsom Dam, the initial
18
operations manual and rule curves have been changed three changed times (Ferreira and CA-‐
DWR, 1982; NRC, 1999; Platt, 1995). The current rule curve allows for annually varying flood
storage space (Table 2.2, A2), based on an allowance to utilize upstream reservoir space to
store flood waters (Table 2.2, A1) (Platt 1995). However, the number and extent of changes to
Folsom’s operations serves as a unique case. Adjusting the water appropriation policies that
evolved over the past 100 years in the Western US and other areas of the western world (CBO,
1997) is often not politically or socially acceptable and presents a prohibitive financial and time
expense. Thus, an assessment of the ability to modify reservoir operations (Table 2.2, A1 & A2)
can help identify potential sources of flexibility through areas lacking adjustability.
Alternately, managers can assess the adjustability of the existing levee footprints by
calculating the proportion of levees sufficiently distanced from infrastructure (Table 2.2, A3).
High values for metric A3 indicate a greater potential and lower cost to adjust the system and
enhance future flexibility characteristics, through efforts to set back levees to increase
floodway conveyance capacity (Table 2.2, S2), reconnect the floodplain (Table 2.2, C2), and/or
construct a bypass to increase slack (Table 2.2, S1) and possibly redundancy (Table 2.2, R1).
2.3. Valuing the costs and benefits of flexibility
There may be a point at which more flexibility is no longer desirable and/or the costs
outweigh the benefits (Byrd and Turner 2000; Duimering, Safayeni, and Purdy 1993; Nemetz
and Fry 1988). Too much flexibility can introduce unintended, negative impacts on systems,
particularly if individual flexibility characteristics are considered in isolation from others. For
example, oversizing reservoir capacity without taking precautions to preserve slack for future
times of need may lead to the classic overshoot and collapse problem (Meadows et al. 1972).
Alternately, a large number of agencies involved in water resources management and funding,
reflective of high intensity and redundancy, can delay and complicate decision-‐making if there
is not proper collaboration and communication between the agencies and a formal governance
structure in place (National Research Council, 2012). Inconsistencies between federal and state
flood risk policies are not uncommon (USACE, 2009) and can complicate project permitting.
19
Connectivity can introduce negative human interventions into historically and genetically
isolated systems through inter-‐basin transfers or river restoration activities (Fausch et al. 2009).
Flexible dam operations and rule curves, reflecting the characteristic of adjustability, provides
planners and operators with discretion that could lead to unintended impacts on ecosystems or
water supply.
Furthermore, flexibility comes at a price, and flexible technologies tend to cost more
than traditional, less flexible equipment and products (Nemetz and Fry 1988; Duimering,
Safayeni, and Purdy 1993; Byrd and Turner 2000). Retrofitting flood management infrastructure
to incorporate more flexibility can require considerable financial investments. For example,
increasing the storage capacity, and thus slack, in the American River Basin, California by raising
Folsom Dam will cost an estimated $314 million (State of California 2010). It cost $41-‐55 million
to increase adaptability at Cougar Dam, Oregon by installing a selective withdrawal structure
for managing downstream temperatures (Learn 2011; Palmer 2010) and $800M to modify
Hoover Dam to improve operations under lower flow conditions (Brean 2012). Increased
flexibility may also come with increased technological complexity, which requires advanced
management and support staff at additional costs (Byrd and Turner 2000).
The value of flexibility relates to the uncertainties and changes the system faces (Huang
et al. 2010; Zhao and Tseng 2003). Thus, qualitatively, the value of flexibility is lower in more
stable, predictable conditions, whereas the value of flexibility increases with the degree of
uncertainty and the projected magnitude of perturbations in future conditions. Furthermore,
identifying the appropriate level of flexibility in a system will depend upon the risk tolerance
level of decision-‐makers, planners, and other stakeholders and the extent to which they are
willing to accept the inability of the system to fully meet objectives for all plausible conditions
(Galloway 2011). Thus, alternative decision-‐making models, such as Robust Decision-‐making
(Lempert et al. 2013), Real Options theory (Hertzler 2007; Leary 1999; Heal and Kriström 2002),
and optimization that maximizes robustness and/or adaptability, may be needed to guide
valuation of flexibility in uncertain future conditions. For example, despite the limitations of
optimizing to an uncertain future, a manager might implement actions that maximize the range
20
of plausible futures under which the system could meet a performance threshold with
secondary objectives or constraints associated with financial costs, creation or elimination of
real options, maintaining a balanced portfolio of flexibility characteristic, etc. Alternately,
potential management actions could be evaluated based on the extent to which they increase
the range of conditions under which the system could meet a performance target per unit cost
for the action. For a flood management scenario, an example action might maintain flood risk
below a target Expected Annual Damage (EAD) for a 10% larger range of plausible futures than
the baseline system at a cost of $1M. This is equivalent to a 1% increase in operational range
for every $100,000 invested.
2.4. Conclusions
Given the contribution of flexibility to the adaptive capacity of water resources systems,
and the increasing uncertainty in future hydrologic conditions, flexible water resources
management systems are likely to perform well over a wide range of conditions. However,
flexibility as a concept requires definition and characterization within the context of water
resources systems. We define flexibility for the field of water resources management as the
inherent ability of the human and physical elements of a system to cope with, or adapt to,
uncertain and changing conditions, in a timely and cost-‐effective manner. Given that, unlike the
related characteristic of adaptive capacity, flexibility of a system is determined by its inherent
characteristics that are independent of future conditions, we propose metrics that are
assessable using system specifications, plans, and management structures, rather than deeply
uncertain future projections. Lastly, we identify some potential methods for comparing
management strategies for their contribution to flexibility and for making decisions of how to
incorporate flexibility into water management systems.
Water resources managers have a wide array of infrastructure, operational, and
regulatory options for meeting objectives of water resources systems. Each option has different
performance characteristics, including its contribution to the system’s ability to adapt as the
severity and uncertainty of climate change materialize. In support of others’ recommendations
21
for increased flexibility in water resources systems, as well as the clear benefit of flexibility in
other domains, this work contributes to incorporating flexibility in the performance evaluation
of the different options available to water resources managers. However, we emphasize that
the proposed framework and metrics do not provide direct guidance regarding how much more
slack, or other flexibility characteristics, are needed. The manager and public must determine
the degree of flexibility in a water resources system based on their acceptable level of risk and
the cost of achieving reduced risk. Furthermore, additional investigation of flexibility is
warranted to fully understand its role in the planning, design, operations, and management of
adaptive water resources systems. In particular, further studies are needed to: a) apply and
evaluate the flexibility metrics in existing water resources management systems (DiFrancesco et
al. in review); b) conduct case studies to quantify the relationship between system flexibility
and adaptive capacity; c) demonstrate valuation of flexibility; and d) develop flexibility metrics
for other operating objectives (e.g. hydropower generation, water supply, environmental
benefits, recreation, etc.).
The conclusions and remaining research gaps reported herein highlight the urgent need
for synthesis, dialogue, and comparative analysis to progress towards implementation of
adaptive, flexible water resources systems. For example, given the important but largely
assumed connection between flexibility and adaptive capacity, a critical next step is to assess
the value of flexibility in terms of its relationship with climate risk reduction, uncertainty, and
adaptive capacity. Comparing the flexibility and adaptive capacity of case study systems would
allow for assessment of the extent to which overall system flexibility contributes to adaptive
capacity, as well as the relative contributions of each of the flexibility characteristics to adaptive
capacity. From such a study, one may synthesize general principles regarding flexibility and
adaptive capacity. For example, it may be the case that a subset of the proposed flexibility
metrics or characteristics disproportionally relates to a system’s adaptive capacity.
Alternatively, such study may identify other flexibility metrics not included in this manuscript.
Further, the finding of a weak relationship between flexibility and adaptive capacity may
indicate that other factors play a larger role in determining a system’s ability to adapt and
22
perform under uncertain, changing conditions. It is through these types of multi-‐disciplinary
and rigorous analysis that we will understand best strategies for establishing robust water
resources systems in an uncertain future.
23
Figure 2.1. Timeline illustrating shift from optimality to flexibility and robustness
1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
First flexibility reference in literature -‐ Fayol (1916) advocates for flexible management principles
Operations research becomes a recognized activity by US military, 1940-‐45, and continues to be used today (Bonder 1979)
Operations research in water resources -‐ NRC first notes potential application to water resources (Wolman and NRC 1962)
Bonder (1979) describes the limitations of operations research and need to consider more scenarios
Modern flexibility -‐ Slack (1987) describes “Flexibility as a manufacturing objective”
Watkins and McKinney (1995) describe robust optimization in water resources
RAND publishes 2003 book advocating large ensembles, robust & adaptive strategies
Shift to nonstationary analysis in water resources -‐ Milly et al. (2008) declare, “Stationarity is Dead”
24
Figure 2.2. Flexibility characteristic from domains outside water resources used to develop the characteristics for water resources in the bottom row. The four left columns of characteristics ease the system’s ability to cope with uncertainty and change, while adjustability on the bottom right eases the system’s ability to adapt.
25
Table 2.1. Definitions of flexibility and inflexibility Target system/
sector Definition References Contribution to water resources’
flexibility
General Characterized by a ready capability to adapt to new, different, or changing requirements
(Merriam-‐Webster, Inc
2003)
Relationship to adaptation
Information Technology
Ability of a resource to be used for more than one end product; Degree to which [IT infrastructure’s] resources are sharable and
reusable (Duncan 1995)
Redundancy and connectivity characteristics
`The capacity to adapt' across four dimensions, or areas within which flexibility can be achieved: temporal, range, intention and
focus
(Golden and Powell 2000)
Relationship to adaptation; time
component Represented by three dimensions or influences, defined as: 1)
slack, the degree of excess capacity, underutilization or salability, 2) adaptability, the degree of versatility, openness, robustness, and 3) intensity, the degree of repetitiveness and frequency of
changes in a parameter
(D. E. Turner and Lankford
2005)
Slack, adjustability, and
redundancy characteristics
Management Ability to be adapted to changing circumstances. (Fayol 1916) Relationship to adaptation
Management (inflexibility)
Physical resources of a firm are characterized by fixed capacity. Also, they are usually useful in a few very similar industries
(Chatterjee and
Wernerfelt 1991)
Slack, redundancy, and adjustability characteristics
Manufacturing
Capability of a manufacturing system to: increase or decrease its capacity when needed; produce new or improved parts; support interchange between stations or their tooling and functions when needed; and handle the system control software in the above
cases
(Pyoun and Choi 1994)
Slack, adjustability, and
redundancy characteristics
Planning
The amount of uncertainty which the decision maker retains concerning the future choices he will make...Unforeseeable
uncertainty can only be dealt with if the decision-‐maker's response to nature's moves is not fixed in advance but is itself uncertain. Flexibility is then defined as the entropy of that uncertainty.
(Pye 1978) Emphasis on uncertainty
Social-‐ecological systems
Degree to which a system is pliable or compliant (similar to adaptability, but more absolute than relative).
Adaptability is defined as: the ability, competency, or capacity of a system to adapt to (to alter to better suit) climatic stimuli
(essentially synonymous with adaptive capacity)
(IPCC 2007)
Relationship to adaptation; adjustability characteristic; absoluteness;
Social-‐ecological systems
(inflexibility)
Rigid social-‐ecological systems are those that are highly connected and self-‐ reinforcing, with low potential for change
(Gunderson and Holling
2002)
Adjustability characteristic
Water management
Allocations between users, uses, regions and sectors can be changed at a low cost in relation to benefits; changes in demand are accommodated easily by reallocating water to higher-‐valued uses as they emerge; Certainty is also necessary: water-‐use rules
must be easy to discover and to understand
(FAO 1993)
Compatibility and adjustability
characteristics; cost component
Limited possibilities to introduce change based on new insight (Pahl-‐Wostl 2007)
Adjustability characteristic
Ability to cope with uncertainties and … capability to adapt to new or changing requirements
(Patel Center 2011)
Relationship to adaptation
Ability to respond to uncertainties in the future (Suttinon and Nasu 2010)
Emphasis on uncertainty
26
Table 2.2. Example metrics to assess flexibility in flood management systems. Unless otherwise noted, larger metric values indicate greater flexibility.
1 Structural components: dams and reservoirs, levees, walls, diversion channels, bridge modifications, channel alterations, pumping, and land treatment; Nonstructural measures: flood warning and preparedness; temporary or permanent evacuation and relocation; land use regulations including floodway delineation, flood plain zoning, subdivision regulations and building codes; flood proofing; area renewal policies; and conversion to open space (USACE 1999). 2 Structural components: dams and reservoirs, levees, walls, diversion channels, bridge modifications, channel alterations,
ID Metric description
Slack
S1 Excess reservoir capacity: calculated as a dam’s flood storage capacity in excess of the amount of water stored in the reservoir to attenuate an x-‐year flood event.
S2 Excess stream capacity: calculated as the stream conveyance capacity in excess of the expected discharge during an x-‐year flood event.
S3 Excess capacity to release and convey flood waters: calculated as the stream conveyance capacity in excess of an upstream dam’s outlet and spillway capacity.
S4 Excess bypass capacity: calculated as the capacity of the bypass to store water in an x-‐year flood event that exceed the stream conveyance capacity
Redu
ndan
cy R1 Surface storage options: number of reservoirs and bypasses per major tributary
R2 Structural vs. non-‐structural diversity1
R3 Delegation of management responsibility: number of agencies committed to flood management
Conn
ectiv
ity
C1 Ground-‐ and surface water connections: percent of reservoirs operated conjunctively with groundwater
C2 Potential for floodplain connection: percent of river length without levees
Adjustab
ility A1
Ability to revise operations plans: level of governmental approval needed to adjust reservoir operations plans (rule curves) or storage allocation (lower level is more flexible)
A2 Opportunities to annually vary flood storage space: calculated as the percent of the maximum flood storage space which can be varied
A3 Ability to expand storage and conveyance capacity with levee setbacks: calculated as the percent of levees with greater than an x m. buffer to infrastructure the length of
Compa
tibility/
Coordina
tion CC1
Access to data: water managers have access to future hydrologic projections at relevant temporal and spatial scales
CC2 Access to data analysis tools: water managers have tools and ability to analysis and use hydrologic projections for reservoir planning and operations
CC3 Intra basin coordination of operations: percent of reservoirs with coordinated operating agreements
27
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ASSESSMENT OF FLOOD MANAGEMENT SYSTEMS' FLEXIBILITY WITH APPLICATION TO THE
SACRAMENTO RIVER BASIN, CALIFORNIA, USA
Kara N. DiFrancesco, PhD candidate, Water Resources Engineering, Oregon State University, Corvallis, Oregon Desiree D. Tullos, Associate Professor, Biological & Ecological Engineering, Oregon State University, Corvallis, Oregon
International Journal of River Basin Management (JRBM) Taylor & Francis 4 Park Square, Milton Park Abingdon, Oxfordshire OX14 4RN, UK
In review
35
Chapter 3. Assessment of flood management systems' flexibility with application to the Sacramento River basin, California, USA
Abstract:
Water resources managers and researchers have concluded that increasing system flexibility
will provide flood management systems advantages in meeting objectives under uncertain
future hydrologic conditions. However, despite the frequent use of the term flexibility,
demonstration of the concept to analysis and design of flood management systems has yet to
be conducted. Building upon previous studies of flexibility in other fields, we outline an
approach to investigate how structural and non-‐structural flood management actions relate to
system flexibility. We assess flexibility using metrics within five characteristics: slack,
redundancy, connectivity, adjustability, and compatibility/ cooperation. We apply this flexibility
assessment to four proposed flood management strategies, each with a unique suite of
management actions, for the Sacramento River Basin in California, USA. The foci of benefits
differ between the four different flood management strategies, with varying emphasis on
protecting urban communities, rural and agricultural improvements, and ecosystem
restoration. The flexibility assessment reveals a disproportionate emphasis in all strategies on
increasing slack in the current system as well as a concentration of expenditures towards
structural versus non-‐structural components. Only two of the assessed strategies improve all
five flexibility characteristics, and these two strategies also include the greatest number of
actions that provide flexibility benefits. We do not find a clear link between more flexibility
strategies and their time and cost-‐effectiveness in terms of reduction in damages. The outlined
method provides a useful tool for comparing the flexibility of potential management strategies,
and further application can provide more insight into broader thinking on flood management
under uncertainty.
Keywords: Flexibility, flood risk management, adaptive capacity, climate change, robustness,
uncertainty
36
3.1. Introduction
With water resources under increasing pressure from population growth and climate
change, scientists and managers frequently assert the need for additional flexibility in the
systems and infrastructure that retain, divert, and deliver water. The need for flexibility is
fundamentally driven by uncertainty and changing conditions (Zhao and Tseng 2003). For water
resources systems, including the human and physical components that contribute to managing
water within a river basin, the recent rise in flexibility recommendations relates to substantial
changes in hydrologic and socio-‐economic conditions. Although uncertainty has plagued
managers for as long as water resources have been developed, the deep uncertainty in
hydrology under climate change far exceeds any uncertainty flood managers confronted in the
past (Hall and Solomatine 2008). Faced with a wide range of uncertain and changing future
hydrologic conditions, flexible systems that can adapt to change quickly and effectively are
thought to provide advantages over inflexible systems (Pahl-‐Wostl et al. 2007; Wilby and Dessai
2010).
Furthermore, changes in attitudes towards risk and uncertainty coincide with the call for
more flexibility in water resources management. For example, through the present day, flood
managers primarily use risk analysis in planning and evaluating water resources systems and
projects. Risk is most commonly analyzed in relation to the ability of the system or components
to withstand a probabilistic flood size (NRC 2000). However, increased uncertainty due to
climate change and other future changes calls into question our ability to describe performance
outcomes of future flood managements strategies with probability distributions, a requisite for
risk-‐based analysis (Frederick, Major, and Stakhiv 1997; Milly et al. 2008). As such, addressing
climate change in water resources planning has led to an increased emphasis on uncertainty
analysis, utilization of large ensembles of future scenarios, and a rise in recommendations for
flexibility, resilience, adaptive capacity, and robustness (Lempert, Bankes, and Popper 2003). In
line with this shift in the framing of future conditions and uncertainty, the overarching goals of
the water resources management analyses shift from seeking an optimal strategy for a limited
set of future expectations, to seeking flexible, robust, and adaptive strategies that perform
37
reasonably well over a wide range of uncertain, but plausible future scenarios (Lempert,
Bankes, and Popper 2003; Frederick, Major, and Stakhiv 1997).
The contribution of flexibility to the performance of water resources systems in an
uncertain future is embedded in its relation to concepts of resiliency and adaptive capacity
from the study of social-‐ecological systems. For example, resilience in human systems has been
defined (B. Walker et al. 2004) as, “the capacity of a system to absorb disturbance and
reorganize while undergoing change so as to still retain essentially the same function, structure,
identity, and feedbacks.” We (DiFrancesco and Tullos In review) define flexibility of water
resources systems as “the inherent ability of the human and physical elements of a system to
cope with, or adapt to, or alter to better suit uncertain and changing conditions, in a timely and
cost-‐effective manner.” A key distinction in these concepts is the reference to an external
disturbance. Both resilience and adaptive capacity are defined in terms of a stress or
disturbance and an answer to the question: Adaptation or resilience of what to what?
(Carpenter et al. 2001; Gallopín 2006). In contrast, a system’s flexibility can be assessed without
classification of an external disturbance, as we do in this manuscript. Yet, flexibility none-‐the-‐
less provides a means for the system to respond to the changes generated by a disturbance.
Flexibility is thus thought to contribute to a system’s resiliency and capacity to adapt, as well as
to the system’s robustness, which describes the capacity to perform over a large range of
uncertain, but plausible future scenarios (Lempert et al. 2006).
However, while it is generally agreed that flexibility contributes to long-‐term resiliency
and robustness, it is less clear how the broad collection of management actions and
infrastructure available to water resources managers contributes to a system’s flexibility. In
particular, it is unclear how best to prioritize maintenance of, and improvements to, flood risk
management systems, which can be achieved though actions aimed towards both structural,
physical components (S) of the system as well as the non-‐structural, operations and
management components (NS) (Byrd and Turner 2000; Pyoun and Choi 1994; Wang and De
Neufville 2004). Structural flood management components include dams, levees, diversions,
etc., whereas non-‐structural components refer to laws and regulations, zoning, flood forecast-‐
38
warning systems, and awareness raising. For a variety of reasons, recent discussions of flood
risk management have shifted away from a reliance on a few large structures to consideration
of the complete spectrum of both structural and nonstructural solutions (Galloway 1997;
Werritty 2006). One predominant reason for this shift is that non-‐structural actions generally
provide more reversible and less expensive mechanisms to reduce flood risk than structural
actions. This reversibility represents higher flexibility in the system, ensuring that future options
remain open and thus supports adaptive management strategies (Kundzewicz 2002). Along
similar lines, (Sayers, Galloway, and Hall 2012) recommends increasing flexibility, used
interchangeably with adaptability, by implementing solutions that can be modified if the future
should turn out to be different from expectations. Often non-‐structural solutions provide more
adaptability and real options than non-‐structural actions (Paul B. Sayers, Galloway, and Hall
2012). However, characteristics of flexible systems go well beyond reversibility and adaptability
(DiFrancesco and Tullos, in review), and it is currently unclear how structural and nonstructural
management actions contribute to the broad range of characteristics that comprise a flexible
flood management system.
The goal of this study is thus to investigate how structural and non-‐structural flood
management actions relate to system flexibility in the Sacramento River basin, California. More
specifically, we ask these key questions:
• How do individual management actions contribute to the different flexibility
components?
• How are structural and non-‐structural actions different in their impacts on flexibility?
• How do different management objectives, represented in the four CVFPP management
strategies, lead to different outcomes for flexibility characteristics?
• Is there a relationship between flexibility and cost/time effectiveness of management
strategies?
Following (DiFrancesco and Tullos In review), we examine five characteristics of flexibility –
slack, redundancy, connectivity, adjustability, and compatibility/ cooperation – to identify areas
in which flood management systems exhibit inflexibilities or can achieve increased flexibility.
39
Using the Sacramento River Basin, California, USA as a case study, we apply an approach to
assess the impact of proposed management actions on system flexibility. For this analysis we
use information provided in the 2012 Central Valley Flood Protection Plan (CVFPP) regarding
the current Sacramento flood management system. This plan includes four proposed flood
management strategies, each comprised of more specific flood management actions (CA-‐DWR
2012). The following analysis examines the number, type, and cost of proposed actions that
would affect each of the five flexibility characteristics.
3.2. Operationalization of the term flexibility
The few in-‐depth examinations of flexibility and attempts to measure flexibility,
primarily come from the fields of: Information Technology (IT) (Byrd and Turner 2000; Duncan
1995; Golden and Powell 2000; D. E. Turner and Lankford 2005); adaptive capacity of social-‐
ecological systems (SESs) (Adger, Arnell, and Tompkins 2005; Smit and Wandel 2006);
management (Fayol 1916); manufacturing (Pyoun and Choi 1994); planning (Pye 1978); and
water resources (Paul B. Sayers, Galloway, and Hall 2012; Gersonius et al. 2013). Studies from IT
fields represent the first and most thorough attempts to assess the flexibility of a system (Byrd
and Turner 2000; Duncan 1995; Golden and Powell 2000; D. E. Turner and Lankford 2005). Each
of these studies in the IT field delineates between different characteristics of flexible systems
that represent areas in which flexibility can be gained or lost. (DiFrancesco and Tullos In review)
adapt these delineations, identifying five characteristics of flexible water management systems:
• Slack: degree of excess capacity or underutilization;
− Example: reservoir flood storage capacity in excess of design flood volume
• Redundancy: degree of repetitiveness and diversity of options available to meet
objectives;
− Example: number of flood storage facilities within the system
• Connectivity: ability of any component to attach to any of the other components inside
and outside the system;
− Example: number of conjunctive use operations in place
40
• Adjustability: ability to add, modify, and remove any component of the system and/or
its operations;
− Example: level of governmental approval needed to adjust reservoir operations
plans (rule curves) or storage allocation;
• Cooperation: ability to utilize and share available information across components.
− Example: Use of Decision Support Tools (DSS) in planning and operations
These flexibility characteristics can be mapped to structural and nonstructural
components within a flood management system or actions that enhance or degrade flexibility.
We summarize the relationships between flexibility characteristics and flood risk management
actions using a set of metrics (Table 3.1, adapted from DiFrancesco and Tullos (In review)).
Examining these relationships highlights a few key points related to assessing flexibility. First,
while the assessment of system flexibility can occur in isolation, in general, more meaning can
be gained if flexibility is used as a relative assessment, such as comparison between different
systems or management actions. Second, similar to adaptive capacity (O’Brien and Leichenko
2000; B. L. Turner et al. 2003; Luers 2005), flexibility is not a steady feature of a system as it can
change over time in response to changes in human and physical system components. For
example, one metrics to assess system slack examines reservoir capacity in excess of a
probabilistic flood (Table 3.1, S1). Larger floods, a common climate projection in many regions
(Cameron, Beven, and Naden 2000; Milly et al. 2002; IPCC 2007; Das et al. 2011), would
consume slack in the system, decreasing flexibility in this regard. As such, the assessment of
flexibility at any given time is a snapshot of the system and must be reassessed when internal
or external physical or human components change. Third, some actions contribute to multiple
flexibility characteristics and may impact flexibility characteristics differently. For example, new
levees can increase conveyance capacity and thus slack (Table 3.1, S3), while also decreasing
connectivity (Table 3.1, C2) and potentially adjustability (Table 3.1, A3). Finally, all of the
flexibility metrics can be assessed for individual management actions, with the exception of the
redundancy metric R2 a. and b. (Table 3.1). When evaluating redundancy in terms of the
41
diversity of the suite of structural versus non-‐structural options or management actions (Table
1, R2 a. and b.), we assess the combination of system components or management actions.
Additional discussion on the derivation of the flexibility characteristics and metrics, as well as
the features of flexible water resources systems, is presented by (DiFrancesco and Tullos In
review).
3.3. Data and methods
3.3.1. Study area
The Central Valley of California, USA contains areas with some of the highest flood risk
in the country (USACE 2002). The 70,500 km2 Sacramento River system, the focus of this study,
drains the northern portion of the Central Valley, while the San Joaquin River system drains the
39,000 km2 southern portion (Figure 3.1). These two river systems meet in the Sacramento-‐San
Joaquin Delta (Delta), the largest estuary on the west coast of the United States. Prior to land
reclamation and the construction of upstream dams, the low-‐lying valley floor flooded regularly
during large, seasonal storms. The first European explorers to reach the valley in the early 19th
century estimated that high flows north of the Delta covered distances greater than eight km
on the eastern side of the river and five km on the western side (Kelley 1989). Researchers
believe that these events are related to the influence of atmospheric rivers across the
Sacramento basin, narrow corridors of concentrated moisture traveling over the Pacific Ocean
from near Hawaii (Dettinger et al. 2011). These atmospheric river storms can drop most of the
region’s annual precipitation totals over the course of a few days.
In the Sacramento and San Joaquin basins, efforts to regulate floods began
simultaneously with settlement and continue to this day. Currently, the State Plan of Flood
Control (SPFC), administered by the California Department of Water Resources (CA-‐DWR),
guides flood management planning in the basin, in coordination with many other state, federal
and local entities. The SPFC includes: facilities (levees, weirs, dams, pumping plants, bypass
basins, etc.); lands (fee title, easements, and land use agreements); operations and
maintenance requirements of SPFC facilities, conditions (terms, Memorandums of
42
Understanding, regulations, etc.); and programs and plans. Although the SPFC has prevented
billions of dollars in flood damages since its inception, some SPFC facilities currently face an
unacceptably high chance of failure (CA-‐DWR) 2010b). In addition, an unintended consequence
of the long-‐term effort to reduce flooding is that development and population growth behind
levee-‐protected areas have increased flood damages over time (CA-‐DWR 2012). Thus, although
the probability of flooding has decreased, the damages generated when floods do occur are
much greater, resulting in a net long-‐term increase in flood risk (CA-‐DWR) 2012).
3.3.2. Methods to analyze flexibility in the Central Valley Flood Protection Plan (CVFPP)
In response to increasing flood damages, highlighted during flooding in the 1990s, the
California State Legislature directed CA-‐DWR to prepare the CVFPP along with other supporting
documentation (CA-‐DWR 2012). The primary goal of the CVFPP is to improve flood risk
management, but the plan also includes supplemental goals to: improve operations and
maintenance; promote ecosystem functions; improve institutional support; and promote multi-‐
benefit projects. The CVFPP and associated documents contain information regarding the
current state of the SPFC, as well as proposed actions for addressing the primary and
supplemental goals now and into the future. Several factors contribute to managers’ concerns
about the SPFC, including some factors that refer to specific inflexibilities in system components
(CA-‐DWR 2010a). We compile and categorize the deficiencies in system flexibility noted in the
CVFPP (Table 3.2) based on their relationship to the flexibility characteristics and metrics in
Table 3.1. For example, managers’ noted insufficient storage capacity indicates that the current
system lacks sufficient slack in terms of metric S1 (reservoir capacity) and/ or S4 (bypass
capacity).
In total, the CVFPP analyzed four strategies to address the identified inflexibilities (Table
3.2) and other deficiencies in the SPFC, which we also use in this study. The CVFPP began its
initial analysis by outlining three preliminary strategies. Each of the three strategies emphasizes
different overarching goals. The first strategy, henceforth referred to as “Design Capacity,” aims
to re-‐establish the original Design Capacity of the SPFC facilities, primarily through levee
43
improvements throughout the system. The second strategy henceforth referred to as “Protect
Communities,” focuses on protecting high-‐risk Protect Communities through physical
improvements to levees around urban areas and small communities. The third strategy,
henceforth referred to as the “Enhance System” strategy, aims to enhance the flood
management system storage and conveyance capacity through widening floodways,
reconnecting floodplains, and increasing floodwater storage. The Enhance System strategy
incorporates all of the management actions of the first two strategies, along with other multi-‐
benefit actions. After assessing the costs and benefits of these three strategies, the CA-‐DWR
developed a fourth strategy to pursue, which combines the strengths of each preliminary
strategy, termed the “Combined” strategy. It includes both regional actions to improve levees
and reduce flood risk in urban areas, small community and rural-‐agricultural areas, as well as
large system improvements, such as bypass expansion.
Each of the strategies developed for the CVFPP contains a suite of management actions
aimed at addressing the overarching goals of the strategy. The CVFPP identified eight broad
classes of flood management system elements that address the key types of improvements
needed to meet the 2012 CVFPP plan’s goals, including: 1) bypasses, 2) ecosystem restoration,
3) flood structure improvements, 4) residual risk, 5) rural-‐agriculture improvements, 6) small
community improvements, 7) storage and operations, and 8) urban improvements. The CVFPP
further divided each element into more specific flood management actions. To maintain
consistency with the CVFPP, in this manuscript we retain the same categorization of
management actions under the eight classes of system elements.
We assess our first study question regarding the contribution of each proposed
management action towards system flexibility by determining the impact of each of the 29
proposed actions listed in the CVFPP (CA-‐DWR 2012) on the flexibility metrics in Table 3.1. Due
to the lack of specificity regarding the outlined actions, we could not calculate the absolute
system flexibility under each management strategy. Rather, for each management action we
determine whether it would: increase (1), have no effect (0), or decrease (-‐1) each flexibility
metric. Actions can impact more than one metric and characteristic. For example, a new flood
44
bypass would increase storage capacity, a component of the slack measurement (Table 3.1, S4),
as well as the number of storage facilities, a measure of redundancy (Table 3.1, R1). Under each
of the eight major elements, we summed the number of actions that would enhance flexibility
characteristics, as well as the number of actions that may reduce flexibility. Some of the
included actions seem to have little relevance for flood management (e.g. improved fish
passage), but they still address at least one of the supplemental goals in the CVFPP. In addition,
actions that integrate ecosystem improvements early in the planning stage may allow for a
more holistic approach to restoration, rather than traditional project-‐by-‐project compensatory
mitigation (CA-‐DWR 2012).
Second, we assess the structural and non-‐structural diversity of the suite of proposed
actions and the impact of structural and non-‐structural management actions on flexibility. We
first categorize the suite of proposed actions based on whether they apply to structural or non-‐
structural elements in the flood management system. We then assess structural diversity (Table
3.1, R2 a. and b.), based on number of projects and expenditures, and the extent to which
structural and non-‐structural actions impact each of the five flexibility characteristics.
Thirdly, we assess how different management goals, represented in the four CVFPP
management strategies, lead to different outcomes for flexibility characteristics. We summarize
the expenditures for each management strategy to illustrate the relationship between
management goals and actions. We also compare the four management strategies based on
the number of included actions that increase each of the flexibility characteristics, as well as the
expenditures dedicated towards increasing each of those characteristics.
Lastly, we conduct a cursory analysis of the relationship between flexibility and cost-‐
and time-‐ effectiveness of each management strategy. We assess cost-‐effectiveness using the
mid-‐range expected cost of each strategy in comparison to the strategy’s ability to improve
flood risk management, the primary goal of the CVFPP. We use the CVFPP’s estimate of each
strategy’s potential to reduce expected annual damages (EAD) as a measure of the its ability to
meet the primary flood risk reduction goal (CA-‐DWR 2012). Similarly we assess time
45
effectiveness as the reduction in EAD per year of strategy implementation. We compare these
simple efficiency measures to the flexibility of each strategy.
3.4. Results
3.4.1. Management action contribution to flexibility characteristics
The management actions proposed in the CVFPP have significant potential to address
the identified inflexibilities in the system. All but two of the 29 proposed actions have the
potential to increase one or more of the flexibility characteristics (Table 3.3). Four of the actions
increase more than one flexibility characteristic. The actions disproportionately address slack in
the system, with 55% of the actions contributing to increased slack and only 21%, 21%, and 17%
of the actions contributing to adjustability, compatibility/ cooperation, and redundancy,
respectively (Table 3.3). Only one action increases connectivity, via improvements to fish
passage structures that increase the movement of floodwaters and aquatic species into and out
of the bypass system, i.e. longitudinal connectivity (Table 3.1, C3). Furthermore, another 21% of
the actions reduce connectivity, through levee improvements that further limit lateral river-‐
floodplain connections (Table 3.1, C2). Notably, the proposed management actions also focus
more frequently on modifying the existing components rather than introducing new
components, as evident by the relatively few individual actions that increase the redundancy,
or number of options in the system. Of the 18 actions that increase slack in the system, only
three also increase system redundancy through introducing new components to the system.
The remaining 15 actions increase slack by enlarging the capacity of components in the existing
system.
3.4.2. Flexibility of structural and non-‐structural management actions
Assessment of the redundancy of the suite of management actions in terms of the
diversity of the number of structural versus non-‐structural actions (Table 3.1, R2a) and
redundancy in terms of expenditure (Table 3.1, R2b) yields different results. The CVFPP contains
almost an even split in the number of proposed structural versus non-‐structural actions (Table
46
3.4). As such, calculating diversity in the number of proposed actions (Table 3.1, R2a) yields a
value extremely close to the optimum 0.5, with 1 indicating no diversity. Despite the relatively
balanced number of structural and non-‐structural actions, structural actions require
significantly greater investment. Implementing the structural actions would cost seven times
more than the cost of the non-‐structural actions yielding an R2b value of 0.78 (Table 3.4).
Structural rural-‐agricultural levee improvements require the greatest expenditure of all
elements. This action includes repairs and improvements to 21 km of levees in order to provide
rural communities protection from a 100-‐year flood.
The structural versus non-‐structural elements also impact the flexibility characteristics
differently (Table 3.5). The structural actions overwhelmingly increase slack in the system, with
12 of the 15 actions contributing to flexibility attributed to slack. In contrast, only one structural
action increases connectivity and only two increase adjustability. None of the structural actions
increase redundancy or compatibility/ cooperation. Alternately, the contributions of non-‐
structural actions to flexibility are spread across the range of characteristics, with four or more
non-‐structural actions increasing slack, redundancy, adjustability, and compatibility/
coordination. Furthermore, although the suite of actions contains less non-‐structural than
structural actions, the number of non-‐structural actions that provide positive impacts on the
flexibility characteristics is greater (Table 3.5, row totals).
3.4.3. Flexibility of management strategies proposed in the CVFPP
The different objectives of the four CVFPP management strategies, represented through
the suite of management actions and elements in each strategy, leads to different outcomes for
flexibility characteristics. In all strategies, the greatest portion of expenditures is allocated to
either rural-‐agricultural improvements or urban improvements, depending on the strategy
objective (Table 3.6). The strategies that focus on Protect Communities and Design Capacity
only contain management actions in three or four of the eight flood management elements,
respectively. Alternatively, the Enhance System and Combined strategy include a more diverse
array of management actions that address all eight of the broad elements. While none of the
47
metrics in Table 3.1 explicitly consider the diversity of elements, this diversity is consistent with
increased flexibility in terms of the redundancy characteristic.
To further compare the impact of the different strategies on flexibility, we assess the
number of actions in each strategy that impact each flexibility characteristics (Table 3.7 and
Figure 3.2a), as well as the expenditure on strategy actions that increase each of the flexibility
characteristics (Figure 3.2b). In every strategy, slack represents the flexibility characteristics
impacted by the largest number of actions. In addition, the majority of costs for each strategy
address slack in the system, ranging from 82% of project costs in the Combined strategy to 94%
for the costs for the Design Capacity strategy (Figure 3.2b). While the Enhance System and
Combined strategies include actions that address every flexibility characteristic to some extent,
the Design Capacity and Protect Communities strategy do not include any investments towards
improving the connectivity or adjustability of the system. Further, the Enhance System and
Combined strategies include management actions that increase the greatest number of
flexibility metrics (Table 3.7).
3.4.4. Relationship between flexibility and cost-‐ and time-‐ effectiveness
We also compare each strategy in terms of absolute and relative costs and benefits,
based on financial cost, implementation time, and reduction in EAD. In absolute terms, the
Enhance System strategy has the highest reduction in EAD at $246M but also costs the most
and takes the longest time to implement (Table 3.8). In contrast, the Protect Communities
strategy provides a comparable reduction in EAD by $202,504,000, but costs considerably less
and takes the least amount of time to implement (Table 3.8). The Protect Communities strategy
also reduces EAD most efficiently in terms of reduction in EAD per dollar spent and reduction in
EAD per implementation time (Table 8). The Combined approach ranks second to Protect
Communities in terms of implementation time, EAD reduction / cost, and EAD reduction/ time,
while providing a greater absolute reduction in EAD (Table 3.8).
The flood management strategies can be compared based on the cost-‐effectiveness,
time effectiveness, and contribution to flexibility, (Table 3.8). The relationship between these
48
three factors that may contribute to selection of a flood management strategy is not clear and
it is not immediately evident that strategies emphasizing flexibility lead to more time and cost-‐
effective solutions over the short term. Flexibility and implementation time appear to be
inversely related, primarily because the more flexible approaches take more time to enact.
There also appears to be a contrary relationship between flexibility and cost-‐effectiveness. This
is due to the high cost of implementing flexible solutions. Finally, while establishing the Protect
Communities is the most effective strategy from the time and cost perspective, it is not
effective from the perspective of increasing flexibility.
3.5. Discussion
The 2012 CVFPP and associated documents identify critical inflexibilities and deficiencies
in the current Sacramento Valley flood management system (Table 3.2). The CVFPP outlines
four overarching strategies, each containing a suite of structural and non-‐structural
management actions to address the identified deficiencies. Each strategy emphasizes different
objectives and approaches to achieving those objectives, yielding different impacts on system
flexibility.
Overwhelmingly, the actions proposed in the CVFPP address slack in the system over
other flexibility characteristics. This emphasis on increasing slack may be of concern, since
other characteristics can be important. For example, while slack ensures that sufficient excess
capacity exists in the system, redundancy ensures that the capacity of the system is spread
amongst a variety of options, similar to the resilience that diversity offers in ecosystems subject
to disturbance (Elmqvist et al. 2003; Folke et al. 2004). The CVFPP management actions
emphasize modifying existing infrastructure over introducing new components to the flood
management system that would increase redundancy. To some extent this may reflect the
notion that all of the best storage sites are already taken (Minton 2001). However, it also
reflects a lack of openness to implement actions that may deviate from how floods have been
managed in the past. Furthermore, public comments at the Central Valley Flood Protection
Board meeting (24 February 2012, Sacramento, CA) on the draft 2012 CVFPP revealed
49
opposition by the agricultural community to any actions that increase slack and redundancy of
flood storage capacity at the perceived expense of agricultural lands. Opposition was
particularly focused on the proposed new bypass on the Feather River and new Sacramento
River easements.
Examination of the ratio of structural to non-‐structural actions, a measure of the
system-‐wide redundancy, leads to different conclusions depending on whether we examine the
relative number or relative cost of structural and non-‐structural actions. The legislation guiding
the 2012 CVFPP requires CA-‐DWR to consider both structural and non-‐structural methods for
improving flood management (CA-‐DWR 2012). This mandate is in line with the shift away from
a reliance on large flood structures to more of an integrated flood management strategy
(Galloway 1997; Werritty 2006). While the plan meets this criterion with a balanced number of
structural and non-‐structural actions under consideration, the proposed structural actions
would cost nearly seven times more than the non-‐structural actions. It may be the case that
non -‐structural actions cost less than structural actions to achieve the same level of flood risk
reduction. Alternately, the higher cost of structural actions may indicate that the plan still relies
more heavily on the structural system over non-‐structural actions. Because the CVFPP only
provides EAD estimates for each flood management strategy, and not individual actions, we are
not able to eliminate either of the explanations as possible reasons why structural actions have
such higher emphasis from the investment perspective.
The contribution to flexibility varies across the CVFPP strategies. Strategies that
emphasize Protect Communities and restoring the Design Capacity of the system use fewer
elements and contribute to fewer flexibility characteristics than strategies (e.g. Enhance System
and Combined) that have broader management goals. Based on our analysis, the Enhance
System and Combined strategies contribute to larger increases in flexibility in the Sacramento
flood management system than do the Design Capacity or Protect Communities strategies. The
former two strategies include a more diverse portfolio of flood management actions (Table
3.6), which in turn leads to improvements in a wider range of flexibility characteristics (Table
3.7 and Figure 3.2). Alternately, by focusing almost entirely on physical levee improvements
50
and residual risk, the Design Capacity and Population Center strategies omit actions that could
increase connectivity and adjustability in the system (Table 3.7).
As noted by researchers outside of the water resources field (Nemetz and Fry 1988;
Duimering, Safayeni, and Purdy 1993; Byrd and Turner 2000), flexibility comes at a price.
Flexible technologies tend to cost more than traditional, less flexible equipment and products.
The Enhance System strategy is the most expensive but also generates the greatest reduction in
EAD. Furthermore, the Enhance System strategy represents the greatest number of
opportunities to increase system flexibility (Table 3.7), as well as a more diverse number of
actions (Figure 3.2a) and expenditures (Figure 3.2b) dedicated to increasing the five flexibility
characteristics. Alternately, the Protect Communities strategy is the least expensive, and most
cost efficient in terms of EAD reduction (Table 3.8), yet also one of the least flexible strategies
(Table 3.7). The Combined strategy, as CA-‐DWR intended, represents a middle ground in terms
of cost, increased flexibility, reduction in EAD, and time to implement (Table 3.8).
Importantly, this simple economic analysis neglects to consider the benefits each
strategy provides in terms of the supplemental goals, namely to: improve operations and
maintenance; promote ecosystem functions; improve institutional support; and promote multi-‐
benefit projects. These omissions may represent significant factors that influence decision-‐
making. For example, the explicit inclusion of promoting ecosystem functions as a goal of the
CVFPP represents a unique and controversial element of the plan. The legislation guiding the
CVFPP requires that ecosystem restoration be included as a goal of the plan in response to the
degradation of riverine habitats and ecosystem functions through changes in land use,
construction of dams and levees, water pollution, and other causes (CA-‐DWR 2012). However,
ecosystem enhancement features were only included in the Enhance System and Combined
strategies and not the Design Capacity or Protect Communities strategies. The actions listed
under the ecosystem restoration element, as well as ecosystem enhancements integrated into
other flood management elements, would increase lateral and longitudinal connectivity in the
system. Interestingly, connectivity is also the only flexibility characteristic that the management
actions have the potential to decrease by improving levees and thus further limiting floodplain-‐
51
river connectivity. By omitting ecosystem enhancement actions, the Design Capacity and
Protect Communities strategies only include actions that would decrease connectivity. Broadly
speaking, it appears as though the ecosystem restoration projects included in the Enhance
System and Combined strategies have the potential to provide connectivity benefits that
counteract the negative impact on connectivity resulting from other management actions.
3.6. Conclusions
Flexibility is often given as a critical component to reliably managing water resources in
an uncertain hydrologic future. Particularly with respect to flood management, when a wide
range of future conditions is anticipated, flexible water resources systems are expected to
outperform fixed, optimized solutions, based on stationary conditions. However, limited
examples exist for how to assess and measure the flexibility of water management systems and
proposed management actions. In this study we develop and apply an approach to assess the
inflexibilities in an existing flood management system, as well as the flexibility of proposed
management actions in the Sacramento River basin, CA. We investigate a set of characteristics
within which flood management systems can increase flexibility and categorize management
actions based on their contribution to system flexibility.
Key findings of this analysis include those related to the CVFPP specifically and more
broadly to the management of floods and floodplains. Regarding the CVFPP, we find a
disproportionate emphasis on increasing system slack over other characteristics of flexibility.
Slack in the system provides surplus capacity to cope with uncertain and changing conditions.
The need for these improvements at the present time indicates that the original SPFC did not
include enough slack to keep up with changing hydrological and socio-‐economic conditions in
the region.
We find that very few individual management actions increase the redundancy of the
system by increasing the number of tools available to managers. This indicates that managers
are choosing to emphasize improvements in the current system, particularly related to
increasing capacity, over introduction of new system actions. In terms of system-‐wide
52
redundancy, we find evidence of a general relationship between the diversity of major
elements represented in management actions and the number of flexibility characteristics
enhanced. The Enhance System and Combined strategies include a diverse array of actions
representing all eight of the broad flood management system elements, and also contribute to
increasing flexibility under all five characteristics. On the contrary, the strategies that include
fewer broad elements address, at most, three of the five flexibility characteristics.
The CVFPP strategies appear to equally emphasize structural and non-‐structural
management options when the number of actions is considered. However, when costs of the
management actions are considered, the emphasis on structural options is far greater than
non-‐structural options. It is not clear whether this discrepancy between number of actions and
the cost of actions is due to higher costs associated with structural options for flood
management or to a disproportionate prominence of structural options in the CVFPP portfolio
based on projected expenditures.
Finally, it appears that tradeoffs exist between cost-‐effectiveness, time effectiveness,
and contribution to flexibility. Focusing on Protect Communities results in the cheapest and
quickest solution to reducing flood damages, but contributes little to the flexibility of the
system and excludes benefits to some areas of the basin. Strategies that increase flexibility
appear to cost more and take longer to implement, but also provide the greatest overall
reduction in flood damages and benefits to the range of basin residents and ecosystems. Thus,
management strategies that balance cost-‐effectiveness, time effectiveness, and contribution to
flexibility are likely to have the greatest benefits over the long term.
Future work should investigate several systems to see if the trends found in our
assessment of the CVFPP are consistent across systems, and thus representative of broader
thinking on flood management. Additional work is also needed to a) assess the magnitude of
management actions impact on flexibility; b) examine the relative contributions of the flexibility
characteristics to adaptive capacity; and c) develop flexibility metrics for other operating
objectives (e.g. hydropower generation, water supply, environmental benefits, recreation, etc.).
Furthermore, we note that the benefits of flexibility may not be fully realized under present
53
conditions, as it is primarily advocated as a tool to improve system performance under
uncertain, changing future conditions.
54
Figure 3.1. Location map of the Central Valley, CA.
55
Figure 3.2. Percentage of flexibility characteristics enhanced by each management strategy in terms of: a) number of actions and b) total mid-‐range cost.
a)
b)
56
Table 3.1. Example metrics to assess flexibility in flood management systems. Unless noted, larger metric values indicate greater flexibility (DiFrancesco and Tullos In review).
ID Metric description Metric evaluation Units
Slack
S1 Excess reservoir capacity in a 100 year flood
m3/ m3
S2 Excess stream capacity in a 100 year flood cms/cms
S3a Dam capacity to release and convey flood waters
cms/cms
S3b Weir capacity to intake flood waters into bypass
cms/cms
S4
Bypass capacity to store discharge in excess of stream capacity
m3/ m3
S5 Excess funding in relation to expected damages
$/$
Redu
ndan
cy
R1 Surface storage options (reservoirs and bypasses)
# / #
R2a Structural vs. non-‐structural diversity (by number, R2a, and by
cost R2b)2
Where s is number/ cost of structural components; ns is number / cost of non-‐structural elements; and N is total number/ cost of components
(lower value is more flexible)
# / #
R2b $/$
R3 Delegation of management responsibility
Number of agencies committed to flood management #
Conn
ectiv
ity
C1 Ground-‐ and surface water connections # / #
C2 Potential for floodplain connection km/km
C3 Longitudinal connectivity #/#
2 Structural components: dams and reservoirs, levees, walls, diversion channels, bridge modifications, channel alterations, pumping, and land treatment; Nonstructural measures: flood warning and preparedness; temporary or permanent evacuation and relocation; land use regulations including floodway delineation, flood plain zoning, subdivision regulations and building codes; flood proofing; area renewal policies; and conversion to open space (United States Army Corps of Engineers (USACE) 1999).
maximum reservoir flood storage capacity
(3day 100 yr flood inflow volume - 3day objective release outflow volume)
stream conveyance capacity
100 yr flood discharge
stream conveyance capacity downstream of dam
outlet + spillway capacity
weir intake capacity
100 yr flood discharge
flood bypass storage capacity
(3day 100 yr flood volume - 3day stream conveyance capacity volume)
annual flood funding
Expected Annual Damages (EAD)
number of surface storage facilities (reservoirs and bypasses)
number of major tributaries
s
N( )2
+ns
N( )2
number of conjunctive use operations
number of reservoirs
total river length
leveed river length with ≥ 100 yr protection
number of dams/ weirs with safe fish passage
number of dams/ weirs
57
ID Metric description Metric evaluation Units Ad
justab
ility
A1 Ability to revise operations plans
Level of governmental approval needed to adjust reservoir operations plans (rule curves) or storage allocation (lower level is more flexible)
Federal / state / local
A2 Opportunities to annually vary flood storage space
m3/ m3
A3
Ability to expand storage and conveyance capacity by levee set backs
km/km
Compa
tibility/
Coordina
tion
CC1 Access to data Water managers have access to future hydrologic projections at relevant temporal and spatial scales Binary
CC2 Access to data analysis tools
Water managers have tools and ability to analysis and utilize essential data for reservoir planning and operations Binary
CC3 Intra basin coordination of operations
#/#
(maximum flood storage space - minimum flood storage space)
maximum flood storage space
length of levees with > x m. buffer to infrastructure
total levee length
number of reservoirs with coordinated operating agreements
number of reservoirs
58
Table 3.2. Inflexibilities in the SPFC identified in the CVFPP and categorized based on whether the inflexibility relates to structural (S) or non-‐structural (NS) components of the flood system. Characteristic Example inflexibilities Metrics
(Table 3.1)
Slack − Insufficient flood storage capacity to regulate flood flows (S) S1, S4
− Inadequate capacity to convey design flows in approximately half of channels evaluated (S)
S2
− Accumulation of sediment in bypasses (NS) S4
− Current federal, State, and local funding mechanisms are not adequate to sustain effective flood management (NS)
S5
− Insufficient funding for: • Maintenance and improvements (NS) • Flood fight (NS)
S5
Redundancy − Flood management is often made difficult by the large number of agencies and entities involved (NS) (NOTE: too much flexibility)
R3
Connectivity − Loss and fragmentation of habitat and lack of connectivity between floodplains and river systems (S)
C2, C3
Adjustability − Water control manuals based on a limited period of record (NS) A1
− Existing flood management system does not provide the level of protection desired and/or required because of the following: • System designed for different uses and levels of protection, and • New legislation increased protection req. for urban and urbanizing
areas.
A1
Compatibility / Coordination
− Water control manuals not designed to accomplish system wide coordinated operations (NS)
CC3 (and
A1)
− Lack of coordination (planning and implementation) (NS) CC3
− Lack of comprehensive mutual aid agreements covering flood response (NS) CC*
− Inconsistent and/or conflicting federal, State, and local maintenance standards, practices and implementation (NS)
CC*
− Limitations of emergency response capabilities to flood threats include the following: • Institutional capacity, resources, and coordination • Not using available forecasting technology in operations decisions (NS) • Inadequate snow and flow sensor data (NS) • Poor or outdated flood risk information and maps (NS) • Conflicts between maintenance practices and ecological processes (NS)
CC1, CC2,
CC3
* There is currently not a metric specifically dedicated to measuring this inflexibility, but it fits within the flexibility characteristic’s definition.
59
Table 3.3. Impact of management actions on flexibility characteristics, organized by broad flood management elements. Negative numbers indicate actions that reduce system flexibility.
Major elements and management actions Structural (S
)/ Non
-‐Structural (N
S)
Slack
Redu
ndan
cy
Conn
ectiv
ity
Adjustab
ility
Compa
tibility/
Coordina
tion
Bypasses 2 3 1 -‐2 2 Agricultural conservation easements NS 0 0 0 0 1 Land acquisition for bypass expansion NS 0 1 1 0 1 Levee improvements for new and expanded bypasses S 1 1 0 -‐1 0 New levee construction S 1 1 0 -‐1 0
Ecosystem restoration 1 0 0 1 0 Ecosystem restoration and enhancement (habitat development) NS 0 0 0 0 0 Fish passage collaboration NS 0 0 0 0 0 Fish passage structures S 1 0 0 1 0
Flood system structures 1 2 0 0 0 Improvements to weir, bypass, and dam outlet structures S 1 1 0 0 0 System erosion and bypass sediment removal projects NS 0 1 0 0 0
Residual risk 4 1 2 0 2 Additional flood information collection and sharing NS 0 0 0 0 0 Additional forecasting and notification NS 0 0 0 0 0 Develop enhanced O&M programs and regional maintenance NS 0 0 1 0 0 Identification and repair of after event erosion S 1 0 0 0 0 Land use and floodplain management integration NS 0 0 0 0 0 Local flood emergency response planning NS 0 0 1 0 0 Purchasing and relocating homes in the floodplain S 1 0 0 0 1 Raising and waterproofing structures and building berms S 1 0 0 0 1 Sacramento channel / levee management and bank protection S 1 1 0 0 0
Rural-‐agricultural improvements 4 4 0 0 0 Achieve SPFC levee design capacity in non-‐urban areas S 1 1 0 0 0 Non-‐urban levee erosion repair S 1 1 0 0 0 Setback levees S 1 1 0 0 0 Site-‐specific rural/agricultural levee improvements S 1 1 0 0 0
Small community improvements 1 1 0 -‐1 0 100-‐year protection levee improvements S 1 1 0 -‐1 0
Storage and operations 0 2 2 -‐1 2 Easements for flood water storage NS 0 1 1 0 1 Forecast-‐Coordinated Operations/ Forecast-‐Based Operations NS 0 0 0 0 0 Allocate new reservoir flood storage/enlarge flood pool NS 0 1 1 -‐1 1
Urban improvement 3 3 0 -‐3 0 200-‐year protection levee improvement S 1 1 0 -‐1 0 Achieve SPFC levee design capacity in urban areas S 1 1 0 -‐1 0 Non-‐SPFC urban levee improvements S 1 1 0 -‐1 0
GRAND TOTAL 16 16 1 (-‐6) -‐6 6
60
Table 3.4. Structural versus non-‐structural diversity in terms of number of projects and expenditure.
Number of actions
Expenditure for actions ($M)
Structural 16 18,892 Non-‐Structural 13 2,678
Total 29 21,571
Metric R2 0.51 0.78
Table 3.5. Number of structural versus non-‐structural components that impact each flexibility characteristic.
Slack
Redu
ndan
cy
Conn
ectiv
ity
Adjustab
ility
Compa
tibility /
Coordina
tion
Total
Structural 12 0 1 (-‐6) 2 0 15 (-‐6) Non-‐Structural 4 5 0 4 6 19
Total 16 5 1 (-‐6) 6 6
Table 3.6. Comparison of flood management strategies in the CVFPP based on estimated cost expenditures ($M) for each major flood management element.
Flood management element Design Capacity
Protect Communities
Enhance System
Combined
Bypasses 0 0 3,132 3,132 Ecosystem Restoration 0 0 335 801 Flood Storage and Operations 80 0 2,820 80 Flood System Structures 0 0 605 605 Residual Risk 812 1,494 724 1,695 Rural-‐Agricultural Improvements 11,073 0 14,731 896 Small Community Improvements 0 1,003 345 555 Urban Improvements 6,093 5,527 5,527 5,527
GRAND TOTAL 18,058 8,024 28,218 13,290
61
Table 3.7. Number of actions in each CVFPP strategy, which increase or decrease the flexibility metrics.
ID Metric description Design Capacity
Protect Communities
Enhance System Combined
Slack
S1 Excess reservoir capacity in a 100 year flood 0 1 3 1
S2 Excess stream capacity in a 100 year flood 4 4 9 9
S3a Dam capacity to release and convey flood waters
0 1 2 2
S3b Weir capacity to intake flood waters into bypass
0 0 1 1
S4 Bypass capacity to store discharge in excess of stream capacity
0 0 1 1
S5 Excess funding in relation to expected damages 0 0 0 0
Slack Total 4 6 16 14 14
Redu
ndan
cy
R1 Surface storage options (reservoirs and bypasses) 0 0 3 1
R2a Structural vs. non-‐structural diversity (# of actions) 0 0 0 0
R2b Structural vs. non-‐structural diversity (cost, $, of actions) 0 0 0 0
R3 Delegation of management responsibility 2 2 2 2
Redundancy Total 6 2 2 5 3
Conn
ectiv
ity C1 Ground-‐ and surface water connections 0 0 -‐1 0
C2 Potential for floodplain connection -‐2 -‐3 -‐5 -‐5
C3 Longitudinal connectivity 0 0 1 1
Connectivity Total -‐2 -‐2 -‐3 1 (-‐6)
Adjustab
ility A1 Ability to revise operations plans 0 0 0 0
A2 Opportunities to annually vary flood storage space
0 0 3 1
A3 Ability to expand capacity by levee set backs
0 0 2 3
Adjustability Total 0 0 5
Compa
tibility/
Coordina
tion
CC1 Access to data 2 3 3 4
CC2 Access to technology and data analysis tools 1 1 2 2
CC3 Intra basin coordination of operations 4 4 5 5
Compatibility/ Coordination Total 3 7 8 10 GRAND TOTAL 18 (-‐2) 22 (-‐3) 13 (-‐2) 16 (-‐3)
# increase # increase (# decrease)
# decrease
62
Table 3.8. Comparison of strategies by costs, benefits, and implementation time.
Units Design Capacity Protect
Communities Enhance System Combined
Cost $ $9,114,450,000 $6,727,850,000 $17,312,800,000 $10,037,600,000 EAD reduction $ $128,404,000 $202,504,000 $246,565,000 $213,144,000
Implementation time yrs. 33 18 38 23
EAD reduction / cost $/ $M $14,000 $30,000 $14,000 $21,000
EAD reduction/ implementation time $ / yr $3,951,000 $11,572,000 $6,575,000 $9,473,000
63
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Chapter 4. Bottom-‐up assessment of climate risk and the robustness of proposed flood
management strategies in the American River, CA
Abstract:
The hydrologic nonstationarity and uncertainty associated with climate change requires new
decision-‐making methods to incorporate climate impacts into flood frequency analysis. Further,
water resources managers currently lack planning approaches to assess how uncertain climate
impacts might affect the performance of flood risk management strategies under future
hydrologic conditions. In this manuscript, we develop a bottom-‐up approach for assessing of
flood management systems and management actions under uncertainty and nonstationarity.
Using the developed approach we characterize the vulnerability of the current American River
flood management system and potential management actions to changes in flood frequency
and flood risk. We first identify the sensitivity and vulnerability of the American River flood
system to different climates. This information is mapped as climate response surfaces of
Expected Annual Damages (EAD, $/yr) under different flood regimes. Next, we determine
potential changes in flood frequency and flood risk under a climate change. By applying
Bayesian statistical methods to projected future flows, we stochastically generate a wide range
of plausible future flood frequency scenarios. Using the climate response surfaces, we identify
the portion of plausible future scenarios under which the current flood system can maintain
damages below a threshold EAD, a measure of robustness. Using this approach, we then
evaluate the robustness of four proposed management strategies in the 2012 Central Valley
Flood Protection Plan in terms of both flood risk and cost-‐effectiveness, to assess the
performance of the strategies in the face of climate risks. Results indicate that the high
sensitivity of the expected damages to changes in flood regimes makes the system extremely
vulnerable to a large portion of the plausible range of future flood conditions. While the
proposed management strategies all offer the potential to increase system robustness in terms
of maintaining EAD below an acceptable risk threshold, they would still leave the system
vulnerable to a wide range of future conditions. Further, as flood frequency regimes increase in
67
intensity from the current conditions, the cost-‐effectiveness of the management strategies
increases, to a point. However, under the most extreme flood conditions projected by global
climate models, the benefits in terms of reduction in EAD begin to decline. This bottom up
analysis demonstrates a viable decision-‐making approach for water managers in the face of
uncertain and changing future conditions. Neglecting to use such an approach and omitting
climate considerations from water resource planning could lead to strategies that do not
perform as expected or which actually lead to mal-‐adaptations, increasing vulnerability to
climate change.
Keywords: Flood frequency analysis, flood risk, bottom-‐up risk assessment, climate change
adaptation, Bayesian statistics, nonstationarity
68
4.1. Introduction
Scientists and managers currently lack reliable climate projections at the temporal and
spatial resolution required to perform traditional flood risk analyses. Furthermore, there is no
consensus on methods to incorporate multiple, uncertain future scenarios into such analyses.
Climate model output has served as the starting point and basis of most studies of climate risk
(Hamlet and Lettenmaier 2007; Das et al. 2011; Willis et al. 2011). However, the output from
climate models is often ill-‐suited for this role for several interrelated reasons that include:
misalignment with designed purpose of GCMs, to evaluate global policies concerning
greenhouse gases, and their application to regional planning and decision-‐making (Mote et al.
2011; Brown and Wilby 2012); incompatible spatial and temporal resolution between reliable
General Circulation Model (GCM) output and water resource specialists’ needs (Prudhomme,
Reynard, and Crooks 2002; Hallegatte 2009); and cascading of uncertainty through bias
correction and downscaling to achieve desired spatial and temporal resolution (Wilby and
Dessai 2010). Importantly, advances in modeling and downscaling techniques will not
ameliorate the concerns listed above. While new generations of GCMs, Regional Climate
Models (RCMs), and downscaling techniques all possess the potential to better characterize
uncertainty, these new models and techniques will by no means eliminate uncertainty, and
instead may increase uncertainty in future climate projections (Roe and Baker 2007; Knutti and
Sedláček 2013). Current approaches to flood frequency analysis (e.g. Bulletin 17B (US Water
Resources Council 1982)), that rely on a single, reliable, long-‐term hydrologic record and
assume stationarity are ill-‐suited for assessing flood risk using multiple, highly uncertain climate
change projections.
To date, top-‐down, scenario-‐led impact assessments have dominated thinking on
climate change impacts and evaluation of potential adaptation measures (e.g. Hamlet and
Lettenmaier, 2007; Das et al., 2011; Willis et al., 2011). However, the dependence of these
approaches on a small set of deeply uncertain, downscaled GCM output limits their ability to
reliably assess the full range of future flood risk. Currently, there exists no agreement on a
universally appropriate method to temporally and spatially downscale GCM output to the
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resolution required for flood frequency analysis (e.g. catchment scale and daily or sub-‐daily
time step) (Xu 1999; Fowler, Blenkinsop, and Tebaldi 2007). At the same time, the choice of
downscaling method can have significant implications for a flood frequency analysis
(Prudhomme, Reynard, and Crooks 2002). Alternatively, RCMs can be used to indirectly derive
regional climate from GCM output, though RCMs have their own issues (Laprise et al. 2008). In
either case, calculating the resulting streamflow requires further modeling efforts to force
hydrologic models with the output from the climate models. As a result, uncertainty is cascaded
down the various steps reaching the point where the streamflow impacts can span wide,
confounding ranges, which may even include opposite signs (Prudhomme et al. 2010; Wilby and
Dessai 2010). Few studies take the additional step of combining the hydrologic projections with
damage projections in order to assess vulnerability and flood risk (Prudhomme et al. 2010),
which adds another layer of uncertainty to the results.
Approaching flood risk assessment and decision-‐making from the bottom-‐up can
overcome some of the limitations of top-‐down decision-‐making. With bottom-‐up approaches,
assessments are tailored to address a specific flood management decision within the limitations
of the available data. Bottom-‐up approaches take several names and forms, including: scenario-‐
neutral approaches (Prudhomme et al. 2010), decision scaling (Brown and Wilby 2012; Brown
et al. 2012), climate informed decision analysis (Hallegatte et al. 2012), and robust decision-‐
making (Lempert, Bankes, and Popper 2003; Wilby and Dessai 2010). These approaches reverse
the order of typical impact and vulnerability assessment used in top-‐down approaches, as well
as the order in which projected hydrologic information is used to inform decision-‐making. Top-‐
down approaches first generate a limited set of downscaled GCM scenarios from which to
assess impacts and then vulnerability to those limited scenarios. In contrast, bottom-‐up
assessments generally start with an identified management concern, around which system
sensitivity and vulnerability to climate are characterized. Bottom-‐up approaches acknowledge
the limits of uncertain GCM output and downscaling approaches, and as such they only
consider GCMs in the later stages of the risk assessment process, alongside other available
climate data including observations and paleontological data.
70
We present a methodology for bottom-‐up assessment of flood damages based on
existing frameworks (e.g. T. E. Johnson and Weaver 2009; Brown et al. 2012) that require first
defining the decision context for assessing climate impacts on water systems. The decision
context refers to identifying the assessment goals and relevant parameters in the context of a
specific management or policy decision, and it is established before choosing and analyzing
models and data (T. E. Johnson and Weaver 2009). Focusing on the specific management
decision or policy at hand, bottom-‐up approaches scale and tailor climate information to inform
that decision, usually through a sensitivity and vulnerability analysis. We begin our analysis with
a sensitivity and vulnerability assessment that does not consider climate projections, but is
intended to help water managers better understand the hydrologic conditions that push the
system into a vulnerable state. For this bottom-‐up flood risk assessment, sensitivity is defined in
terms of how much Expected Annual Damages (EAD) change under different climatic
conditions. A system’s vulnerability to exceeding an acceptable flood risk is defined by the
extent to which a system is unable to maintain EAD below a threshold risk level. As part of the
sensitivity and vulnerability analyses, several studies (Prudhomme et al. 2010; Brown et al.
2011; Brown et al. 2012) develop functions to describe climate response (e.g. increase in peak
flows) as a function of different climate states, where a climate state is represented by changes
in mean annual precipitation and seasonal variation. We take this work a step further and
describe climate response in terms of flood risk, a function of both changes in peak flows and
the damages associated with those flows (NRC 2000).
The climate response surfaces, describing sensitivity and vulnerability, in combination
with plausible climate impacts, can then be used to compare the performance of different
management actions in the future and determine the climate scenarios that favor certain
management strategies over others. The criteria used for assessment are also different
between bottom-‐up and top-‐down approaches. Top-‐down approaches tend to seek an
optimum solution based on the probability of future scenarios occurring and the expected
value of different decisions under those scenarios. However, in the face of uncertain climatic
changes, a growing body of literature advocates for seeking robust strategies that perform
71
reasonably well over a wide range of uncertain, yet plausible future scenarios (Frederick, Major,
and Stakhiv 1997; Lempert, Bankes, and Popper 2003; Dessai and Hulme 2007; Hallegatte 2009;
Wilby and Dessai 2010). Using robustness criterion in combination with a vulnerability and
impact assessment, as is common with bottom-‐up assessments, managers can evaluate:
whether actions towards adaptations are needed (Brown et al. 2012), the conditions that cause
a particular decision to be favored over another (Brown et al. 2011), or the robustness of a
policy (Prudhomme et al. 2010).
We present analyses on the hydrology and flood management system in the American
River, California with the objectives of: 1) developing a bottom-‐up methodology for the
assessment of flood management decisions in which uncertainty and nonstationarity of flood
frequencies are directly considered and 2) applying the methodology to the flood management
system in the American River to characterize its vulnerabilities to flood damages under
different climate and management scenarios. Using a bottom-‐up approach, we begin by
framing the decision context around a key question water resources managers have been
investigating (CA-‐DWR 2012): Given climate change, what is the most robust strategy to take
for managing flood risk in the American River basin? To inform this decision, we 1) identify the
sensitivity of the American River flood system to different climates, defined in terms of changes
in EAD; 2) identify a vulnerability range of flood regimes under which the current system cannot
maintain flood risk (EAD) below an acceptable threshold; 3) determine potential changes in
flood frequency and flood risk by stochastically generating a set of plausible future flood
regimes; and 4) evaluate the robustness of the flood management scenarios under plausible
future conditions in terms of their ability to maintain flood risk below a threshold EAD and
maintain a cost-‐effective benefit-‐cost ratio above a threshold.
4.2. Study area: American River Basin, CA
From its headwaters in the western slopes of the Sierra Nevada mountain range in
Northern California, the American River flows southwest towards its confluence with the
Sacramento River at the City of Sacramento (Figure 4.1). This study focuses on flood risk in the
highly populated portion of the basin to the south of the American River. The American River
72
drains an area of 4,975 km2, from elevations of 3,170 m. along the Sierra crest to 7 m. above
sea level at the confluence with the Sacramento River. Forty percent of the basin lies above the
snowline, which occurs at an elevation of approximately 1,500 m. The basin has a
Mediterranean climate, with 90% of annual precipitation falling in 2-‐3 winter months sometime
between November and April (Willis et al. 2011). Wintertime rainfall and snowmelt runoff
comprises about two-‐thirds of the American River streamflow, with less than one-‐third derived
from springtime snowmelt runoff (Dettinger et al. 2004). The American River experiences large
variations in annual precipitation and streamflow (Figure 4.2). Much of this variation results
from water years that include a few large storms fueled by the landfall of atmospheric rivers.
Known informally as Pineapple Express storms in the Pacific region, these events produce a
narrow corridor of concentrated moisture that travels northeast over the Pacific Ocean from an
area near Hawaii to California. As the moist air and orography interact over land, the events can
generate substantial portions of a basin’s annual precipitation and runoff (e.g. up to 50% for
California; Dettinger et al., 2011) over the course of a few days, often leading to substantial
flood hazards.
The history of flooding on the American and Sacramento Rivers pre-‐dates European
settlement, as, in 1808 the Spanish explorer Ensign Gabriel Moraga knowingly observed
evidence that the rivers created “one immense sea, leaving only scattered eminences which art
of nature have produced, as so many islets or spots of refuge” (in Kelley, 1989). Attempts to
control the floodwaters of the American River necessarily coincided with settlement and
continue to this day. The State Plan for Flood Control (SPFC) represents California’s first large-‐
scale coordinated effort to manage floods at the state level. The SPFC is comprised of: facilities
(levees, weirs, dams, pumping plants, bypass basins, etc.); lands (fee title, easements, and land
use agreements); operations and maintenance (O&M) requirements of SPFC facilities,
conditions (terms, Memorandums of Understanding, regulations, etc.); and programs and
plans. Major SPFC works in the American River basin include Folsom Reservoir and Dam,
located at the confluence of the American River’s two main tributaries (Figure 4.1); levees on
both banks of much of lower portions of the river below Folsom; and three pumping plants (CA-‐
73
DWR 2010a). About the SPFC, the California Department of Water Resources (CA-‐DWR) (2010)
has concluded that: 1) it has prevented billions of dollars in flood damages since its inception;
2) some SPFC facilities face an unacceptably high chance of failure; and 3) an unintended
consequence of the long-‐term effort to reduce flooding is that development and population
growth behind levee-‐protected areas have increased flood damages over time. Thus, although
the probability of flooding has decreased, the damages when floods occur are much higher,
resulting in a net long-‐term increase in flood risk (CA-‐DWR, 2012). The City of Sacramento faces
some of the highest flood risk in the United States and the developed world (USACE, 2002),
which is one of the reasons many prior research efforts (Ferreira and CA-‐DWR, 1982; Platt,
1995; NRC, 1999; Dettinger et al., 2004) and financial investments have attempted to help
manage flood risk in the American River basin. In this study, we expand upon previous flood
management work in the basin to include a bottom-‐up climate impact assessment.
4.3. Data and Methods: Developing the bottom-‐up flood risk assessment
To develop the methodology for a bottom-‐up risk assessment, we adapted each of the
steps in the general approach to the retrospective decision regarding a future flood
management strategy for the American River basin. We expand and quantify the CVFPP analysis
through a climate risk assessment to investigate how the management strategies vary in their
robustness under climate change. The importance of tailoring the impact assessment to the
decision context requires that every situation be treated individually. As such this manuscript
presents a methodology in line with other bottom-‐up studies, but with specific aspects uniquely
tailored to the decision context and using models and data in the American River basin.
4.3.1. Establishment of the decision context
In response to increasing flood damages, highlighted during flooding in the 1990s, the
California State Legislature directed the CA-‐DWR to prepare a Central Valley Flood Protection
Plan (CVFPP) and supporting documentation (CA-‐DWR, 2012). The primary goal of the 2012
CVFPP is to improve flood risk management, though the plan also includes supplemental goals
to: improve operations and maintenance of project facilities; promote ecosystem functions;
74
improve institutional support; and promote multi-‐benefit projects. The plan developed for the
CVFPP outlines three preliminary strategies for addressing the problems identified in the
current Without Project SPFC as well as a fourth strategy that combines the strength of each of
the preliminary strategies, described below (Table 4.1). The CVFPP assessed each of the
strategies, along with the baseline Without Project conditions, based on effectiveness in
contributing to the CVFPP goals and other quantitative and qualitative performance measures,
including: level of flood protection, population with less than 100-‐yr protection, EAD and
reduction in EAD, capital costs, O&M requirements, opportunity for ecosystem restoration,
opportunity for multi-‐benefit projects, ability to meet objectives in flood legislation, social
sustainability, and climate change adaptability. The CVFPP analysis concluded that the Enhance
System strategy best meets CVFPP goals, but it also requires the highest level of investment and
significant institutional changes. Thus, CA-‐DWR adopted the Combined strategy to incorporate
many of the beneficial features included in the three preliminary strategies at a more
reasonable cost and implementation time. We assess the robustness of the management
strategies in terms of their ability to meet the primary goal of flood risk reduction in terms of
EAD, as well as the cost-‐effectiveness in terms of the Benefit-‐Cost Ratio (BCR).
While the CVFPP did not include a full climate assessment, the plan does include a
description of potential climate change effects on flood management and a discussion of a pilot
Climate Change Threshold Analysis Approach (CA-‐DWR, 2012). The Threshold Analysis
Approach includes aspects of both top-‐down and bottom-‐up climate impact analysis; however
it was only applied to a pilot study of the Oroville Dam on the Feather River. Despite the lack of
a full climate assessment, the CVFPP concluded that Enhance System is the only preliminary
strategy that substantially improves resiliency to climate change by the fact that it enhances
storage and conveyance. Although the CVFPP did not assess the resiliency of the Combined
strategy, a subset of the storage and conveyance projects that improve resiliency in the
Enhance System strategy are also included in the Combined strategy (CA-‐DWR, 2012).
4.3.2. Sensitivity of current system to flood regime changes
75
We assess current system sensitivity to climate change by evaluating the relationship
between flood risk and changes in the hydrologic flood regime. Flood risk is a function of the
probability of a flood event occurring multiplied by the damages expected to result from such
event (NRC, 2000). Integrating flood damages over the probability of all possible flood events in
a given year yields EAD:
Equation 1: Expected annual damages EAD = D p 𝑑𝑝!!! !
where D(p) is the expected damages, D, in dollars, based on the probability of event (p).
Consistent with the CVFPP analysis and the USACE evaluation procedures for flood risk
management plans (USACE, 1996, 2006), we base our climate risk metrics on EAD and reduction
in EAD. Our assessment only includes hydrologic changes and does not incorporate changes in
the damage function, D(p), which could result, for example from development and landuse
changes in the floodplain.
For flood risk management, the most important input to characterize hydrology is the
probability distribution of annual peak flows, known as the flood-‐frequency curve (Faber 2010).
In the U.S., flood forecasting by federal agencies follows the analysis techniques outlined in the
Guidelines for Determining Flood Flow Frequency Bulletin 17B, commonly referred to as
“Bulletin 17B.” Bulletin 17B recommends fitting a log-‐Pearson type III (LP3) distribution to
observed annual maximum streamflow data using the method-‐of-‐moments to estimate the
mean (μ), standard deviation (σ), and the skew coefficient (ϒ) (US Water Resources Council
1982). In terms of potential changes to the flood frequency curve: higher values of μ indicate
larger expected values of flood magnitudes in any given year; higher values of σ indicate larger
inter-‐annual variability in flood magnitude; and higher values of ϒ steepen upper tail of the
distribution, resulting in larger extreme events.
We base our initial flood frequency curve analysis on historic observations of daily
streamflow gauge records collected on the American River at Fair Oaks gauge (USGS 11446500),
located 11 km downstream of Folsom Dam, from 1905-‐2012. However, direct gauge data after
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the construction of Folsom Dam in 1955 represents regulated flow. Thus, we replaced the
gauge data with estimated natural flows for the 1955-‐2012 period (Northwest River Forecast
Center (NWRFC), unpublished data), which were calculated based on upstream gauges, storage
volume, and release rates at Folsom. In this study we assume a skew parameter of zero for the
LP3 distribution, which is a reasonable assumption for the historic period at considering that
the calculated station skew at Fair Oaks gauge is -‐0.035 with a standard deviation of 0.233
(Parrett et al. 2011). While this assumption may not hold into the future, limited historical
records already result in unstable skew parameters (Griffis and Stedinger 2007), and projections
of future skew are even more uncertain than mean and standard deviation. In addition, the
zero skew assumption simplifies the Bayesian analysis and does not detract from the
methodological focus of the study.
To assess the sensitivity of the current flood management system to different climates,
we first develop a climate response function that describes the relationship between EAD and
log-‐normal flood frequency curve parameter sets of μ and σ for the peak 3-‐day average
discharge at Fair Oaks gauge. We calculate EAD with the USACE Hydrologic Engineering Center’s
Flood Damage Assessment software (HEC-‐FDA) (USACE, 2002; CA-‐DWR, 2012). Using HEC-‐FDA,
we use stage-‐exceedance probability curves and damage-‐stage curves to estimate EAD (Figure
4.3). For the CVFPP, the stage-‐exceedance probability curves are determined in HEC-‐FDA by
inputting the stage associated with 99.9-‐, 10-‐, 4-‐, 2-‐, 1-‐, 0.5-‐, and 0.2-‐percent exceedance
events derived from historical gauge data (CA-‐DWR, 2012] (Figure 4.3a). We then assess EAD
across a gridded range of parameter sets representing flood frequency curves; for each
parameter set, we calculated the probability (Figure 4.3b) of exceeding the river stage
associated with the historic discrete exceedance events (Figure 4.3b). Combining these figures
results in a damage-‐exceedance plot (Figure 4.3c).
After shifting the historic stage-‐exceedance curves using the gridded parameter sets, we
use the damage exceedance plots from HEC-‐FDA to calculate EAD values for each gridded
parameter set (Figure 4.4). Due to the stepwise nature of the damages functions, where
flooding and damages only occur after a certain flood magnitude, low (μ, σ) combinations
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produce EAD values of $0, or no damage. We concentrate on the portion of the EAD functions
that produce damages, i.e. those with σ values of 0.8 and above. To assess how EAD responds
to changes in the flood frequency curve, we develop a continuous climate response surfaces for
the Without Project conditions by fitting a linear climate response function to the discrete flood
frequency curve parameter sets (Equation 2).
Equation 2: ln 𝐸𝐴𝐷 = 𝛽! + 𝛽!µμ+ 𝛽!!!
where: EAD is Expected annual damages ($); μ is the mean of the 3-‐day peak flow; σ is the standard deviation; and βi are regression coefficients. We develop climate response surfaces using Equation 2 to examine the sensitivity of changes in
EAD to changes in μ and σ (Figure 4.4).
4.3.3. Vulnerability of system to flood regime changes
After developing the climate response surfaces, we identify the range of flood frequency
regimes under which the system is vulnerable to exceeding an acceptable flood risk. We define
a threshold for acceptable flood risk as the EAD ($38 million/year) under the Combined strategy
that was selected as the CVFPP management strategy moving forward [CA-‐DWR, 2012]. As
such, the system is considered vulnerable when mean and standard deviation combinations
yield EAD above the threshold of $38 million. We term the region above the threshold the
“vulnerability range” and below the threshold the “coping range” (Smit and Wandel 2006), and
use historical gauge data to assess the extent to which the current system is vulnerable to
exceeding the threshold EAD (Figure 4.4).
4.3.4. Plausible range of future flood regimes
After assessing the sensitivity and vulnerability of the current system based on historic
data, we then develop a plausible range of future flood regimes based on GCM simulations of
future peak flow. We also use historic observations and historic GCM simulations to inform our
confidence in the future simulations (Figure 4.5). In addition to the historical Fair Oaks gauge
dataset, we assess GCM-‐derived projections based on daily streamflow output from a Variable
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Infiltration Capacity (VIC) model of the Sacramento Basin, forced with Bias Corrected Spatially
Downscaled (BCSD) output from two runs each of six GCMs (Maurer and Hidalgo 2008; Maurer
et al. 2010). We use streamflow simulations at a VIC index point on the American River at
Folsom Dam, 11 km upstream of Fair Oaks and without significant inflow/outflow between the
two locations. VIC output from 1950 to 1999 represent a forcing of the GCMs with observed
atmospheric variables, downscaled and input into the hydrologic model. For the future time
period (2000-‐2100), each GCM was forced with two climate change emissions scenarios (A2 and
B1), totaling twelve sets of daily streamflow projections from 1950 to 2099.
We evaluate flood frequency parameters for each of the historic and future flow
datasets to both characterize plausible climate impacts on flood regimes and to qualitatively
assess the reliability and uncertainty in the climate projections. This analysis includes: 1)
examining trends in flood frequency parameters based in the observed historic data (1905-‐
2012); 2) comparing flood frequency parameters based on historic observations and historic
GCM simulations (1950-‐1999); and 3) comparing flood frequency parameters based on historic
observations (1905-‐2012) and future GCM simulations (2000-‐2100).
In conducting the flood frequency analyses, we incorporate two major modifications to
the methods outlined in Bulletin 17B. The first is the inclusion of future projections in addition
to historic observations in the analysis. Secondly, we use Bayesian statistical techniques to
develop plausible ranges of historic and future flood regime projections rather than Frequentist
techniques. Bayes Theorem (Bayes and Price 1763) treats the parameters of the probability
distribution as variables themselves, which allows for describing the parameters of fitted flood
frequency curves (μ, σ) in terms of their own probabilistic distributions, conducive to
developing our desired range of plausible impacts. For this analysis, using WinBUGS (Lunn et al.
2009) we fit a log-‐normal Bayesian model with non-‐informative priors to the observed and
simulated peak annual 3-‐day average flood discharge datasets. For each dataset, we use a
Gibbs sampling Markov Chain Monte Carlo (MCMC) algorithm to produce 11,000 iterations,
with the first 1,000 used for burn in, to determine posterior intervals of the flood frequency
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parameters. To check convergence we ensure that the Gelman-‐Rubin diagnostic results in 𝑅
values less than 1.05.
4.3.4.1. Trends in mean and standard deviation of flood flows for the historic period (1905 – 2012)
We examine trends in the historical data and projections based on those trends to help
establish a level of confidence in the future GCM-‐based projections. Studies examining climate
trends often describe the factor of interest (e.g. precipitation, temperature, streamflow, etc.) in
terms of the mean and variability over a period of time, typically 20 to 40-‐year intervals (e.g.
Bengtsson, Hagemann, and Hodges 2004; Lins and Slack 2005). As such, we fit log-‐normal flood
frequency curves to moving 30-‐yr time periods and examine trends in the fitted parameters
over the historic period. Since flood frequency methods in Bulletin 17B generally only use the
peak flow in any given year, the number of data points is low and equivalent to the number of
years analyzed. The small sample size associated with extreme events makes conclusive trend
analysis difficult (Easterling et al. 2000). As a result, while we examine a 30-‐year moving
average of the μ and σ of the peak discharge to investigate historical trends, results remain
highly uncertain.
4.3.4.2. Comparison of historic observations and historic GCM simulations (1950 – 1999)
To assess the reliability of the GCM projections in projecting observed conditions, we
compare the posterior intervals of the Bayesian flood frequency parameters (μ and σ) fit to the
gauge observations and those fit to the GCM projections forced with observed historical
emissions scenarios from 1950-‐1999.
4.3.4.3. Comparison of historic observations (1905 – 2012) and GCM projections (2000 – 2099)
Lastly in developing the plausible impact range, for the historic observed and twelve
future projected peak flow datasets (Figure 4.5), we generate 10,000 Markov chain samples of
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(μ, σ) combinations representing flood frequency curves. The resulting 120,000 parameter sets
derived from the future GCM projections define our plausible range of future flood regimes. We
compare the posterior intervals of the parameter sets derived from future GCMs to those
derived from the historic record to assess potential hydrologic responses to climate change.
4.3.5. Robustness of current systems and management strategies
In the last step of the bottom-‐up decision-‐making approach, we combine the
vulnerability and impact assessment to determine the robustness of the current system and
proposed management strategies. Consistent with Lempert, Bankes, and Popper (2003), we
define robust strategies as those that perform reasonably well compared to the alternatives
across a wide range of plausible scenarios. As an indicator of the robustness, we calculate the
percentage of the draws from the posterior flood frequencies parameter sets below an
established vulnerability threshold:
Equation 3:
Robustness indicator = Number of posterier draws below threshold
Total number of posterier draws ∗ 100
A robustness value of one indicates that the full range of flood regimes lies below the
threshold, and thus the system is not vulnerable to exceeding the decision threshold. On the
other end of the spectrum, a robustness value of zero indicates that the system is vulnerable to
exceeding the vulnerability threshold for all potential combinations of the parameter sets.
We use two different robustness metrics, one a measure of flood risk (EAD) and the
other a measure of cost-‐effectiveness (BCR). We assess the robustness of the current system
and management strategies in terms of the EAD threshold of $38 million, by first developing
EAD response functions for each of the management strategies using the same methods
described in Section 3.1.1. We then determine how many MCMC parameter sets lie above and
below the threshold. In addition, we develop climate response surfaces of the BCR (Equation 4:)
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for each of the management strategies under different flood regimes, to assess their cost-‐
effectiveness.
Equation 4:
BCR = EAD!" − EAD!"#"$% ∗ 1− 1− r !!
r 𝑐𝑜𝑠𝑡
Where BCR is the Benefit Cost Ratio ($/$), EADWO is the EAD under Without Project conditions, EADmanage is the EAD under one of the management strategies, r is the discount rate, t is life of the project, and cost is the cost of the management strategy.
Assessment of the BCR presents difficulties when trying to align the spatial extent of
costs and benefits. We measure benefits in terms of EAD reduction within the American River
Basin, however the cost estimates (CA-‐DWR, 2012) include all projects located within the lower
Sacramento region, of which the American River is a sub-‐basin. As such, the cost estimates
includes projects outside of the American basin, some of which influence EAD within the
American basin (e.g. expansion of Yolo Bypass) and some of which only produce benefits
outside the American basin (e.g. mainstem levee improvements downstream of the confluence
of the American). In addition, the projects included in the costs produce benefits outside of the
American Basin, which are not included in the benefits calculation. To roughly address the
incongruence with costs and benefits, similar to the EAD threshold, we set the BCR decision
threshold to the BCR of the Combined strategy under historical flood conditions, namely 0.2
(California Department of Water Resources (CA-‐DWR) 2012).
We set the discount rate to 7% as recommended by the Federal Emergency
Management Agency for public investments (FEMA, 2001) and the life of the project to 50 years
based on the CVFPP planning horizon (CA-‐DWR, 2009). Further, we conservatively use the high
cost estimate for each strategy (Table 4.2).
4.4. Results
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We present the results of the bottom-‐up analysis by first discussing the sensitivity and
vulnerability of the current system, based on historic data. We then present a range of plausible
future potential climates and finally an assessment of the robustness of the current and
possible future flood management strategies.
4.4.1. Sensitivity of flood risk (EAD) to changes in flood frequency regimes
The climate response equation provides a good fit (Table 4.3) to the gridded sets of (μ,
σ), providing useful insight into the sensitivity of the current system to changes in the flood
regime. The sensitivity of EAD to the flood frequency parameters is represented by β1 and β2
(Table 4.3). Small increases in the mean and standard deviation of peak annual floods yield large
changes in EAD, indicating a high sensitive to flood regime changes (Figure 4.4). For example, an
increase in μ from 6.3 to 6.4 (540 to 600 m3/s, 11% increase) with σ = 0.9, yields a 27% increase
in EAD from approximately $55M to $70M. EAD increases logarithmically from the lower left
corner of the climate response surfaces to the upper right corner (Figure 4.4). We note that the
linear model exhibits some heteroscedasticity, with larger residuals at high μ and σ. We discuss
potential implications of this in Sections 4.4.3.2 and 4.5.
4.4.1.1. Vulnerability above threshold EAD
The Without Project system currently operates in the vulnerability range, with EAD
above the threshold of $38M (Figure 4.4). posterior median of μ and σ (6.49, 0.89) based on
historic data from 1905-‐2012, yields an EAD of $79 M, shown with the black diamond in Figure
4.4. In Section 4.4.3, we describe the results of combining the vulnerability assessment with the
impact assessment (Section 4.4.2) to determine the robustness of each management strategy.
4.4.2. Plausible range of future flood impacts
4.4.2.1. Trends in historical gauge data (1905-‐2012)
Calculating a simple 30-‐year moving μ and σ for the historic period reveals an increasing
trend in the σ and a smaller increasing trend in μ (Figure 4.6). For the historic period (1905-‐
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2012), the 30-‐year mean of the LN-‐peak annual flood flow ranges from 6.33 to 6.64, and the
standard deviation ranges from 0.68 to 1.10. Projecting the linear trend into 2050 indicates an
E[μ] = 6.55 (1,670 m3/s) and E[σ] = 1.32 (3,630 m3/s). By 2100, and with less certainty, the linear
trend indicates an E[μ] =6.60 (2,644 m3/s) and E[σ] = 1.60 (9,134 m3/s). Furthermore, a short-‐
term cyclic trend in the moving averages is apparent (Figure 4.6) and described with good fit by
fourth degree polynomial functions. This simple analysis demonstrates that the mean and
standard deviation of the flood frequency parameters appear to exhibit short-‐term increasing
and decreasing cycles with some evidence of increasing long-‐term trends, particularly for σ.
4.4.2.2. Comparison of historic observations and historic GCM simulations (1950 – 1999)
In comparing the downscaled GCM output to the historic observed data from 1950-‐99,
the GCM output more accurately estimates the historic mean (μ) of peak annual flood flows
than the historic standard deviation (σ) of flood flows (Figure 4.7). The posterior median of μ
from all of the GCM simulations (Figure 4.7a) fall within the quartiles around the posterior
median of μ based on historical observed peak flows. However, the posterior median of σ for
only two of the 12 GCMs fall within the quartiles around the posterior median of σ based on
historical observed peak flows (Figure 4.7a). All of the GCMs underestimate σ over the historical
time period (Figure 4.7b). These differences in posterior parameters produce substantially
different flood frequency curves, particularly for estimations of more extreme events (e.g. 100-‐
yr, 200-‐yr floods) (Figure 4.8). The parameter μ represents the 50% exceedance probability
event, whereas σ determines the slope of the flood frequency curve (Figure 4.8). The lower σ
values of the GCM simulations result in flood frequency curves with gentler slopes, leading to
underestimations of extreme events compared to the curve fit to the historic gauge data. For
example, based on the historic data, the expected magnitude of a 100-‐yr flood is approximately
7,500 m3/s, while the expected magnitude based on the GCMs ranges from 4,400 – 7,900 m3/s.
Considering the sensitivity of EAD to changes in μ and σ, the differences in flood frequency
curve parameters derived from GCM simulations versus historic observations can lead to widely
different estimates of EAD. The GCMs’ lack of skill in capturing the mean and variation in the
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historic data, even after bias correction, is indicative of the uncertainty associated with the
downscaled model projections. To capture some of this uncertainty, we present climate impact
(Section 4.4.2.3) and robustness (Section 4.4.3) results in terms of the full distribution of flood
frequency parameters, rather than only using the posterior median of the parameters.
4.4.2.3. Future climate impact assessment
The plausible range of the flood frequency parameters developed from the posterior
samples fitted with the GCM output, encapsulates the range of historic hydrologic conditions
while extended into much higher ranges of μ and σ (Figure 4.9). The lower bound of the future
plausible range for the mean and standard deviation projected with the GCMs resembles the
lower bound of the parameter estimates based on the historical data (Figure 4.9). However the
upper bound on the plausible ranges developed from the GCMs extends far beyond the
posterior samples based on the historical data. As such, the historic output occupies the lower
left quadrant of the GCMs projections, the region of the lowest flood risk (Figure 4.9). Ten of
the twelve GCMs project a larger posterior median μ for the future peak annual flood discharge
than the historic peak (Figure 4.10a), and eleven of the twelve GCMs project a higher posterior
median σ than under historical conditions (Figure 4.10b). These projected increases in μ and σ
are consistent with the results identified previously in the historic data (Section 4.3.1).
4.4.3. Robustness of current system and management strategies
We assess robustness in terms of flood risk (EAD) and cost-‐effectiveness (BCR), which
yield related, but different results.
4.4.3.1. Robustness in terms of flood risk, EAD
Under historic hydrologic conditions, the current Without Project system exhibits the
lowest robustness in terms of EAD, though this is greatly improved under the proposed
management strategies (Table 4.4). Eighty-‐two percent of the draws from the posterior
distributions of the flood frequency parameters derived from the historic observations lie in the
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vulnerability range above the Without Project threshold (Figure 4.9). This indicates that the
current system is predominantly operating outside of its’ coping range. However, each of the
proposed management strategies increases system robustness. Under the Enhance System
strategy, 93% of the draws from the posterior distributions under historic hydrologic conditions
lie below the EAD threshold (Table 4.4, Figure 4.9), making it the most robust strategy. The
Combined and Protect Communities strategies demonstrate very similar robustness, with
overlapping contour EAD threshold lines (Figure 4.9). Lastly, the Design Capacity strategy
exhibits the least robustness over the Without Project scenario.
While the management strategies perform well in terms of robustness based on
historical conditions, the robustness of all of the strategies critically declines under the
plausible range of future conditions. Under the future simulations and Without Project flood
management, only 1% of the draws from the posterior distributions lie below the EAD
threshold (Table 4.4, Figure 4.9). While the most robust Enhance System strategy performs very
well under historic conditions, under the future simulations only 22% of the draws from the
future posterior distributions lie below the threshold.
4.4.3.2. Robustness in terms of cost-‐effectiveness, BCR
As μ and σ increase from historic conditions, the reduction in EAD and the BCR of each
of the management strategies initially increases, but then begins to decrease at higher μ and σ
(Figure 4.11). In contrast to the EAD robustness, the robustness of each of the management
strategies increases under future conditions (Table 4.5). In other words, the cost-‐effectiveness
of the management actions increases under higher μ, σ combinations and more extreme flood
regimes. The Protect Communities exceeds the BCR threshold under the largest portion of
plausible future conditions, while the Design Capacity strategy does not meet the threshold BCR
under any of the historic or future scenarios. Furthermore, under the Design Capacity strategy
very high μ, σ combinations yield EAD that are actually higher than under the Without Project
conditions. This also occurs to a lesser extent under the Enhance System strategy, leading to
negative BCRs in the upper right-‐hand corner of Figure 4.11 b and c.
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4.5. Discussion
The potential for changes in flood regimes due to climate change in combination with
the deep limitations of climate projections, necessitate rethinking how we make flood risk
management decisions. While bottom-‐up climate assessments hold promise as a new way to
view water resources management under climate change, few studies have carried out a full
bottom-‐up approach to flood risk management in practice. In addition, many options exist
within the broadly outlined approaches in the literature (Lempert, Bankes, and Popper 2003;
Prudhomme et al. 2010; Brown and Wilby 2012; Brown et al. 2012) that need to be explored
further. In developing a bottom-‐up climate assessment of flood risk for the American River
flood management system, we identify several key points both about the bottom-‐up
methodology and about flood risk within the American River system, with the goal of
establishing a methodology that will aid water managers everywhere to better understand the
hydrologic conditions that push a flood management system into a vulnerable state. We begin
our discussion around the methodology employed, and then discuss the results for the
American River basin in particular.
The methods used for the sensitivity and vulnerability assessment allow water managers
to identify the hydrologic conditions that shift the system into a vulnerable state, using only the
historic data and models currently available in the American River basin. Our method of fitting
EAD response curves to a grid of flood frequency curve parameters (μ, σ) provides a
computationally efficient method to assess the sensitivity of a system to a large range of
potential flood regimes. However, this method does have limitations. Some accuracy is lost in
fitting a linear model to a relatively small number of HEC-‐FDA runs, particularly at the lowest
and highest range of μ, σ combinations. However, the R2 value for these equations fitted to the
FDA model runs, ranges from 0.79 to 0.87, providing an adequate fit for a reconnaissance level
pre-‐project planning analysis, such as presented in the 2012 CVFPP.
We use the EAD under the CVFPP strategy moving forward as a simple, justifiable
method to determine the EAD vulnerability threshold, but many bottom-‐up approaches
emphasize the importance of including stakeholders in process, particularly the vulnerability
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assessment (Kloprogge and Van Der Sluijs 2006; Few, Brown, and Tompkins 2007).
Unfortunately, the time required to collaboratively establish acceptable risk thresholds is
beyond the scope of our work. We acknowledge the lack of stakeholder participation as a
shortcoming in our case study.
To capture some of the uncertainty associated with the future projections and
incorporate it into the decision-‐making process, we use Bayesian techniques to develop a wide
range of plausible flood frequency regimes characterized by their statistical parameters, μ and
σ. Using draws from the posterior parameter sets in combination with the climate response
surfaces enables us to quickly calculate the EAD under thousands of plausible future flood
regimes. The Bayesian analysis also lends itself to a variety of techniques to combine the
historical and future data depending on its uncertainty and the decision at hand. For example,
while we used non-‐informative priors throughout the study, it is possible to inform future flood
frequency parameters with prior information based on the historical data. Determination of the
plausible range of future scenarios would then incorporate, and place weight on, the historical
record. In addition, rather than examining the 12 sets of future projections in isolation, we
could use a hierarchical Bayesian model to combine the projections from different GCMs and
emissions scenarios, and then examine the hyper-‐parameters that guide μi and σi, the posterior
flood frequency parameters for each set of future projections. Furthermore, adding the skew
parameter, ϒ, to the Bayesian analysis in order to fit LP3 distributions to the historic and future
data, could improve the fit of the distribution, but it could also add more uncertainty with the
additional parameter.
Assessing the proposed management strategies based on two different robustness
parameters demonstrates how the climate response surfaces can be adjusted for different
metrics, as well as the importance of examining all pertinent criteria for decision-‐making. Our
assessment based on EAD demonstrates the extent to which the management strategies
increase the robustness of the systems, but it only examines flood risk benefits without
examining cost of the strategies. Adding costs into the analysis, as well as the net benefits over
the life of the project, rather than average damages (EAD), provides an alternate perspective on
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the cost-‐effectiveness of the projects. Nonetheless, these two metrics only address the primary
goal of the CVFPP, to reduce flood risk, and neglect to consider the three sub-‐goals, namely to:
improve operations and maintenance; promote ecosystem functions; improve institutional
support; and promote multi-‐benefit projects. Similar climate response surfaces could be
developed for metrics to assess the three sub-‐goals of the CVFPP.
Our case study demonstration of a bottom-‐up methodology also reveals interesting
points regarding flood risk within the American River system and the robustness of proposed
management actions. We find that the EAD of the American River flood management system is
highly sensitive to small changes in the flood frequency parameters, which brings up two points
of concern. First, real changes in the flood regime due to nonstationarity could result in very
different damage scenarios for the basin. Secondly, considering the uncertainty associated with
flood frequency parameters, even those calculated with observed gauge records, water
managers must use caution in basing decisions on the median or mean EAD without considering
the uncertainty of the calculation and sensitivity of EAD to the frequency parameters.
In terms of vulnerability, we find that the current system operates in a vulnerable state
with a median EAD above the threshold EAD, as expected. The vulnerability of the flood
management system to current conditions provides the impetus to invest in improving the
system through the CVFPP management strategy.
To increase the utility of the vulnerability assessment, we use historic observed and
future project hydrologic data to develop a plausible range of future flood regimes and our
confidence in that range. Our results demonstrate poor skill in ability of GCM model runs forced
with observed parameters to capture to statistical parameters of the observed historic flood
regime of the American River. Some correlation is found between future model projections and
trends in the historic data. However, trends based on the historic data exhibit a high degree of
uncertainty due to the limited length of the gauge record. Further, we in no way demonstrate
that the historic trend in increased flood regime intensity is linked to anthropogenic climatic
changes. Nonetheless, both the future GCM projections and historic data trends indicate a
similar increase in the flood frequency mean and standard deviation over time. These results
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are also in agreement with the physical science governing floods under climate change and
direct output from the GCMs, which suggest warmer winters with more precipitation in the
Sierra Nevada mountain range (IPCC, 2007, 2012; Das et al., 2011).
Our results also highlight differences in the robustness of different flood management
strategies in the CVFPP, depending on whether robustness is measured in terms of flood risk
(EAD) or cost-‐effectiveness (BCR). The Enhance System strategy provides the greatest
robustness in terms of EAD, and is also the most expensive strategy. Taking project costs into
consideration, the Protect Communities strategy exhibits the greatest robustness in terms its
ability to maintain a BCR above the threshold for the largest portion of the plausible future
range. The Combined strategy exhibits the second highest robustness indicator values for both
metrics, and is also the second most expensive strategy.
The results of the robustness assessment lead to important planning considerations.
While all of the proposed strategies offer substantial gains in EAD robustness under historic
hydrological conditions, the robustness drops drastically when considering the plausible range
of future climate impacts. As such, decision-‐making processes that neglect to consider future
impacts run the danger of implementing strategies that do not reduce risk as much as expected.
Alternatively, the cost-‐effectiveness of the management strategies initially increases in value
under more extreme flood conditions. As such, some management strategies may become
more financially appealing when future hydrologic conditions are taken into consideration.
While our results describe the conditions that may favor one strategy over another, the
uncertainty associated with climate change and the wide plausible range of future conditions
say little to nothing about which conditions we expect to occur in the future. However, over the
course of the long implementation time (15-‐40 years) for the CVFPP strategies, advances in
modeling, data, and analysis methods may allow us to: track changes in observed flood
frequency; narrow the plausible range of future conditions by decreasing uncertainty; and/or
better describe uncertainty and associate probabilities with future conditions. As we gain such
knowledge we can adapt our decision-‐making process and management strategies to the
expected future conditions.
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4.6. Conclusions
The bottom-‐up methodology addresses arguably the two largest challenges facing
future flood management, namely, the lack of: 1) climate projections that can reliably represent
historic conditions at the temporal and spatial resolution required for flood frequency analysis,
and 2) methods to tailor climate projections into information useful to flood managers.
Beginning the climate assessment process from the bottom-‐up enables us to describe the
sensitivity and vulnerability of the system to changes in flood regime, using only historic data.
The climate response surfaces provide flood mangers with a visual representation of the
sensitivity and vulnerability of the system. On their own, these response surfaces can be used
to assess: whether the current system is operating above or below vulnerability thresholds;
how flood risk might change under different flood regimes; as well as how different
management strategies might affect system vulnerabilities. Furthermore, by combining the
response surfaces with future climate projections, we can assess the robustness of the current
system and management strategies in terms of their ability to meet a performance threshold
under a large portion of the plausible range of future conditions.
Our case study of the CVFPP in the American River basin provides an opportunity to
demonstrate the utility of bottom-‐up methods, while yielding insight into the sensitivity,
vulnerability, and robustness of the American River basin and management strategies proposed
in the CVFPP. Our analysis intentionally uses limited data sources and models outside those
already included in the 2012 CVFPP, making it relatively easy to expand to the larger Central
Valley planning region for inclusion in the forthcoming 2017 CVFPP. The 2017 CVFPP builds
upon the decision made in the 2012 CVFPP to pursue the Combined strategy and focuses on
Basin-‐Wide Feasibility Studies, Regional Flood Management Planning, and the Central Valley
Flood System Conservation Strategy (CA-‐DWR, n.d.). As the planning process for the CVFPP
moves forward and more money is at stake, the importance of considering climate impacts
increases, along with the consequences of not considering climate impacts.
While bottom-‐up approaches hold promise for future water resources decision-‐making,
very few applications exist in practice and many questions remain regarding the specific
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methods to use. This leads the way for many potential avenues of future work related
specifically to this study and bottom-‐up climate assessment more generally. In relation to
climate risk assessment for the CVFPP, we recommend further work to: a) include public
participation in identifying threshold metrics and levels; b) include other metrics besides those
focused on EAD (i.e. those that address the sub-‐goals of the CVFPP); c) consider different
methods to combine historic and future data (i.e. informative priors of future projections based
on historical data); and d) consider other sources of uncertainty and nonstationarity (e.g.
population growth, land change, etc.). More generally, the field of climate adaptation could
benefit tremendously from more on-‐the-‐ground examples of climate risk assessment and
adaptation planning.
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Figure 4.1. Map of the American River Basin, CA showing major SPFC project works
Figure 4.2. Daily hydrograph at Fair Oaks USGS gauge on the American River, CA.
Folsom Dam
93
Figure 4.3. Basis of the EAD computation used in CVFPP HEC-‐FDA model (modified from CA-‐DWR, 2012). a) Stage-‐damage curve, where the solid line indicates the curve calculated in HEC-‐FDA from discrete exceedance events calculated using historical gauge data; b) Stage-‐exceedance curves, where the solid line indicates the stage-‐exceedance curve calculated in HEC-‐FDA from the 99.9-‐, 10-‐, 4-‐, 2-‐, 1-‐, 0.5-‐, and 0.2-‐percent exceedance events calculated using historical gauge data (closed points). The dashed lines and open points indicate how the stage-‐probability curves were shifted to assess the sensitivity of EAD to different climates. c) Damage-‐exceedance curves calculated in FDA by combining a) and b).
Stage (ft)
Dam
age
($)
EAD = DdF(D)0
∞
∫
Exceedance Probability 1 0
Dam
age
($)
p
p
Sta
ge (f
t)
Exceedance Probability 1 0
94
Figure 4.4. Gridded FDA model runs (open circles) used in the regression model to develop the flood risk response surface, LN(EAD) = ƒ(µ, σ), under Without Project conditions (shaded background). The system is vulnerable to flood regimes above the white threshold line where EAD = $38M.
Figure 4.5. Observed and modeled daily streamflow used for historic and future flood frequency analysis on the American River at Folsom.
1900 2000 2100
CNRM CM3 GFDL CM2.1
CCSR MIROC3.2 MPI ECHAM5
NCAR CCSM3 NCAR PCM1
CNRM CM3 GFDL CM2.1
CCSR MIROC3.2 MPI ECHAM5
NCAR CCSM3 NCAR PCM1
Observed - gauge
A2
B1
*
Year
Historic observed Historic simulations Future simulations
Climate projections
(12)
1905-2012 Gauge data
Vulnerabili
ty range
Coping
Coping range
Vulnerability range
95
0.3
0.5
0.7
0.9
1.1
1.3
1.5
1.7
σ, 3
0-da
y S
D L
N(D
isch
arge
)
30 previous yrs MA
b)
30 yr. MA Linear (R-sq = 0.80) Poly (R-sq = 0.96)
6.1
6.2
6.3
6.4
6.5
6.6
6.7
µ, 3
0-da
y m
ean
LN(D
isch
arge
)
30 previous yrs MA
a)
30 yr. MA Linear (R-sq = 0.10) Poly (R-sq = 0.74)
Figure 4.6. Expected value of 30-‐year a) average (μ) and standard deviation (σ) of LN-‐historic observed 3-‐day average peak annual flows. The solid lines represent long term linear trends fit to the moving average (MA), with fourth degree polynomial trends, displayed with the dashed lines.
Figure 4.7. Posterior interval boxplots of: a) mean peak annual flow, μ, and b) standard deviation, σ, of peak annual flow for observed streamflow data (dark gray) and GCMs forced with observed parameters (light gray) from 1950 – 1999. The whiskers signify the 95% posterior interval, with quartiles around the median value (black line) indicated with the boxes.
0.4
0.6
0.8
1.0
1.2
1.4
Stan
dard
dev
iatio
n, m
Observed and modeled historic record
6.0
6.2
6.4
6.6
6.8
7.0
7.2
LN(M
ean
annu
al p
eak
disc
harg
e, c
ms)
, µ
Observed and modeled historic record
a) b)
96
Figure 4.8. Expected posterior flood frequency curves derived from observed streamflow data and GCMs forced with observed parameters from 1950 – 1999.
97
Figure 4.9. Posterior distribution draws for the historic data (1905-‐2012, light grey circles) and each of the GCMs (2000-‐2099, dark grey circles). The contour lines represent the EAD threshold under Without Project conditions and the four management strategies outlined in the 2012 CVFPP. The percentage of posterior distribution draws below the threshold represents the coping range for both historic and future conditions, while the system remains vulnerable to conditions above the threshold lines.
98
Figure 4.10. Posterior interval boxplots of: a) mean peak annual flow, μ, and b) standard deviation, σ, of peak annual flow for observed streamflow data from 1905 -‐ 2012 (dark gray box) and GCMs forced with future emissions scenarios (light gray) from 2000 – 2099. The whiskers signify the 95% posterior interval, with quartiles around the median value (black line) indicated with the boxes.
6.2
6.4
6.6
6.8
7.0
7.2
LN(M
ean
annu
al p
eak
disc
harg
e, c
ms)
, µ
Observed historic and modeled future
0.6
0.8
1.0
1.2
1.4
Stan
dard
dev
iatio
n, m
Observed historic and modeled future
a) b)
99
Figure 4.11. Benefit-‐cost ratio response surfaces for each of the management strategies: a) Design Capacity, b) Protect Communities, c) Enhance System, d) Combined. The strategy exceeds the cost-‐effectiveness threshold for flood regimes between the black threshold lines where BCR = 0.2. BCR below -‐3 are displayed in white.
a) b)
d) c)
a)
c)
100
Table 4.1. Overview of CVFPP management strategies Short name CVFPP name
[CA-‐DWR, 2012] Strategy description [CA-‐DWR, 2012]
Without Project
No Project Continuation of existing conditions and inclusion of projects that are currently authorized, funded, permitted, and/or under construction.
Design Capacity
Achieve SPFC Design Capacity (SPFC)
Focuses on improving existing SPFC facilities, primarily urban and rural levees, so that they can convey their design flows outlined in the USACE 1957 Design Profile and Operations and Maintenance Manuals of the SPFC.
Protect Communities
Protect High Risk Communities (PHRC)
Focuses on levee improvements to protect life, safety, and property for high risk population centers, in particular the city of Sacramento.
Enhance System
Enhance Flood System Capacity (EFSC)
Seeks opportunities to achieve multiple benefits through enhanced flood system storage and conveyance capacity, to protect high risk communities, and to fix levees in place in rural-‐agricultural areas. This approach combines most of the features of the above two approaches, with additional features and functions for ecosystem restoration and enhancements.
Combined State Systemwide Investment Approach (SSIA)
Combines the strengths of above three strategies by including significant capital investment to strengthen levees protecting urban areas and small communities, while also expanding flood conveyance capacities, coordinating reservoir operations, and restoring floodplains.
Table 4.2. Low and high cost upfront estimates ($M) for each of the CVFPP management strategies [CA-‐DWR, 2012]
Cost estimate Design Capacity
Protect Communities
Enhance System Combined
Low 3,065 3,965 6,669 6,391
High 3,833 4,460 8,110 6,502
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Table 4.3. Summary statistics for the linear response function fit to the EAD, mean, and standard deviation, ln 𝐸𝐴𝐷 = 𝛽! + 𝛽!µμ+ 𝛽!
!!.
Regression coefficients Goodness of fit
𝜷𝟎 𝜷𝟏 𝜷𝟐 Multiple R2
8.08*** 2.53*** -‐5.45*** 0.87
Significance Codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Table 4.4. EAD robustness indicator, percent of posterior draws of flood frequency parameters that yield an EAD below the threshold.
Input data Without Project
Design Capacity
Protect Communities
Enhance System Combined
Observed (1905-‐2012) 15% 27% 84% 93% 86%
Modeled (2000-‐2099) 1% 3% 15% 22% 17%
Table 4.5. BCR robustness indicator, percent of posterior draws of flood frequency parameters that yield a BCR above the threshold.
Input data Design Capacity
Protect Communities
Enhance System Combined
Observed (1905-‐2012) 0% 15% 2% 3%
Modeled (2000-‐2099) 0% 86% 69% 75%
102
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Chapter 5. Conclusions
Despite widespread recognition that climate change will reveal its most profound
effects through changes in hydrology, the incorporation of climate change into water resources
management lags behind the climate literature. Water managers face considerable barriers in
incorporating climate considerations into planning and management. In particular, status quo
flood frequency analysis and top-‐down climate risk assessment are ill-‐suited for addressing
deeply uncertain, nonstationary conditions. To address these issues, I develop a set of
complimentary methods to assess climate risk and potential adaptation strategies. These
include methods to assess a current system’s flexibility, sensitivity, and vulnerability, as well as
the robustness of management actions and their impact on system flexibility.
We find that flexibility is an inherent ability of the human and physical elements of a
water system to cope with, or adapt to, uncertain and changing conditions, in a timely and cost-‐
effective manner. Given that the flexibility of a system is determined by its inherent
characteristics, we propose metrics that are assessable using system specifications,
components, and institutions, rather than deeply uncertain future climate projections. These
metrics provide the most utility when applied in a comparative manner, such as by assessing
the additional flexibility provided by a management action in comparison to baseline
conditions. Further application of the metrics to a larger range of case studies can provide more
insight into broader thinking on flood management flexibility and its relationship to adaptive
capacity.
In addition to the flexibility assessment, we also present a bottom-‐up climate risk
assessment as an alternative to more traditional top-‐down approaches. The outlined approach
provides a viable method for flood managers to assess the sensitivity and vulnerability of
systems, without the need to use deeply uncertain climate projections. From this assessment,
water managers can identify the climate conditions that push the system into a vulnerable state
in which it is unable to meet performance thresholds. Combining this information with historic
flow data and future projections, allows us to assess the robustness of the current system and
107
management strategies. While we compare management strategies based on flood risk and
cost-‐effectiveness robustness metrics, other metrics could and should be developed to more
holistically compare the benefits and costs of each strategy (e.g. metrics related to the CVFPP
secondary goals).
Application of the flexibility and bottom-‐up climate assessment reveal interesting points
regarding the existing flood management system, as well as the proposed management actions
in the Sacramento River basin, CA. In terms of flexibility, the proposed strategies place a
disproportionate emphasis on increasing slack in the current system as well as a concentration
of expenditures towards structural versus non-‐structural components. Strategies that have
broader management goals (e.g. Enhance System and Combined) use a larger variety of
management elements and contribute more to increasing the flexibility characteristics than
more narrowly focused strategies (e.g. Protecting Communities and restoring the Design
Capacity of the system). The Enhance System and Combined strategy also costs the most and
require the longest implementation time, indicating that flexibility comes at a price.
The robustness assessment for the four CVFPP management strategies compliments the
flexibility assessment, yielding related, but slightly different results. Strategies that most
increase flexibility also perform well in terms of the robustness indicator for flood risk and cost-‐
effectiveness. On the other end of the spectrum, the Design Capacity strategy performed the
poorest in all flexibility and climate risk assessments. Not as clearly in line with the other
results, the Protect Communities approach performs well under the robustness metrics, but it
ranks as one of the least flexible strategies. As such, we cannot make any conclusive statement
about the relationship between flexibility and robustness of management actions from this
limited case study.
In examining the management strategy moving forward, CA-‐DWR adopted the
Combined strategy to incorporate many of the beneficial features included in the three
preliminary approaches at a more reasonable cost, and it appears to fill that role well. The
Combined strategy ranks slightly behind the top performing strategy in terms of flexibility,
robustness in maintaining flood risk below the threshold, and robustness based on cost-‐
108
effectiveness. Thus, it appears as though a management strategy that balances cost-‐
effectiveness with flexibility and flood-‐risk robustness appeals most to decision-‐makers.
In this dissertation I demonstrate the utility of a set of methods to assess climate risk in
practice. As a new field, full of unknowns, much work remains undone in the realm of climate
risk assessment and adaptation. The presented studies in California offer a starting point for
collecting a suite of climate risk assessment case studies as reference material for water
managers. The resources available in California, along with extensive previous research,
provides a wide breadth of existing data and models for the studies presented here. However,
we intentionally designed our methods to be applicable in data poorer regions, and to provide
valuable information even in the absence of uncertain GCM output. It remains essential that
future studies modify the assessment methods around the decision context and appropriate
data and models. We intend our studies to provide water managers with a methodological
basis to assess climate risk, which can be adapted and applied to other water systems around
the world.
109
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