Prepared in cooperation with National Park Service and U.S. Fish and Wildlife Service

A Decision Framework to Analyze Tide-Gate Options

for Restoration of the Herring River Estuary, Massachusetts

Open-File Report 2019–1115

U.S. Department of the Interior

U.S. Geological Survey
Cover. (Front) Diagram showing fundamental objectives for the restoration of the Herring River estuary: restoration of the hydrography, 

restoration of the ecological function and integrity, minimization of adverse effects, maximization of ecosystem services, and minimization of 

management costs. (Back, top) Aerial view of the Chequessett Neck Road Dike. Image from Google Earth. (Back, bottom) Concept drawing of 

replacement dike with tide gates fully opened. Artwork by Nils Wiberg, Fuss & O’Neill, Inc. Background photo shows the Chequessett Neck 

Road Dike looking upstream. Photograph by Timothy P. Smith, National Park Service.
A Decision Framework to Analyze 

Tide-Gate Options for Restoration of the 

Herring River Estuary, Massachusetts

By David R. Smith, Mitchell J. Eaton, Jill J. Gannon, Timothy P. Smith, 

Eric L. Derleth, Jonathan Katz, Kirk F. Bosma, and Elise Leduc

Prepared in cooperation with

National Park Service and U.S. Fish and Wildlife Service

Open-File Report 2019–1115

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

DAVID BERNHARDT, Secretary

U.S. Geological Survey

James F. Reilly II, Director

U.S. Geological Survey, Reston, Virginia: 2020

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Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Smith, D.R., Eaton, M.J., Gannon, J.J., Smith, T.P., Derleth, E.L., Katz, J., Bosma, K.F., and Leduc, E., 2020, A decision 

framework to analyze tide-gate options for restoration of the Herring River Estuary, Massachusetts: U.S. Geological 

Survey Open-File Report 2019–1115, 42 p., https://doi.org/10.3133/ofr20191115.

ISSN 2331-1258 (online)
iii

Acknowledgments

The authors thank the Herring River Restoration Committee and Cape Cod National Seashore 

for support and active participation. The findings and conclusions in this article are those of 

the author(s) and do not necessarily represent the views of the U.S. Fish and Wildlife Service. 

Any use of trade, firm, or product names is for descriptive purposes only and does not imply 

endorsement by any of the authors’ institutions or affiliations.
iv

Contents

Acknowledgments........................................................................................................................................iii

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

Introduction.....................................................................................................................................................1

Study Area.......................................................................................................................................................2

Structuring the Decision Analysis ..............................................................................................................2

A Statement of the Problem................................................................................................................2

Definitions of the Objectives...............................................................................................................4

Management Options ...............................................................................................................12

Prediction of Option Consequences ...............................................................................................12

Evaluation of Tradeoffs .............................................................................................................15

Implementation of an Option Through Time ...................................................................................15

Prototype Decision Analysis and Results................................................................................................18

Next Steps.....................................................................................................................................................24

Summary........................................................................................................................................................24

References Cited..........................................................................................................................................25

Appendix 1. Conceptual Models ...............................................................................................................27

Appendix 2. Summary of Meeting with Herring River Restoration Committee to Elicit Utility 

Curves...............................................................................................................................................32
v

Figures

1. Maps showing Herring River estuary and subbasins within Cape Cod National 

Seashore and towns of Wellfleet and Truro, Massachusetts...............................................3

2. Objectives hierarchy showing the fundamental objectives and subobjectives 

for restoration of the hydrography, restoration of the ecological function and 

integrity, minimization of adverse effects, maximization of ecosystem services, 

and minimization of management costs .................................................................................10

3. Graphs showing effects of alternative gate operations on mean high water for the 

Herring River estuary, Massachusetts....................................................................................13

4. Example utility curves for selected objectives relating the level of a performance 

metric for hypothetical objectives to a standardized score between 0 and 1 based 

on preferences and risk attitude..............................................................................................18

5. Graph showing the four weighting schemes applied to the fundamental objectives 

to evaluate outcomes.................................................................................................................20

6. Graph showing cumulative utility averaged across a range in prediction 

uncertainty and the four value-weighting schemes in figure 5 to compare seven 

tide-gate options in figure 3 ......................................................................................................21

7. Diagram showing frequencies of ranks based on cumulative utility after 25 years 

for seven options across a range in prediction uncertainty and the four 

value-weighting schemes in figure 5 ......................................................................................21

8. Double-column chart used to evaluate how effectively the tide-gate options 

address all objectives ................................................................................................................22

9. Graphs showing cumulative utility as a function of uncertainty formulated as 

the percentile for which confidence limits were computed for value weights: 

A, balanced, B, ecological, C, equal, and D, socioeconomic..............................................23

Tables

1. Objectives of the Herring River estuary restoration decision support framework ...........5

2. The unweighted consequence table for the pilot tradeoff analysis ..................................16

3. Overall utility from the pilot tradeoff analysis........................................................................19
vi

Conversion Factors

U.S. customary units to International System of Units

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

Area

acre 0.004047 square kilometer (km2)

square mile (mi2) 2.590 square kilometer (km2) 

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F = (1.8 × °C) + 32.

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C = (°F – 32) / 1.8.

Datum

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

Elevation, as used in this report, refers to distance above the vertical datum.

NOTE TO USGS USERS: Use of hectare (ha) as an alternative name for square hectometer 

(hm2) is restricted to the measurement of small land or water areas. Use of liter (L) as a special 

name for cubic decimeter (dm3) is restricted to the measurement of liquids and gases. No prefix 

other than milli should be used with liter. Metric ton (t) as a name for megagram (Mg) should be 

restricted to commercial usage, and no prefixes should be used with it.
vii

Abbreviations

CACO Cape Code National Seashore

CNR Chequesett Neck Road

CYCC Chequesett Yacht and Country Club

DOI U.S. Department of the Interior

EFDC Environmental Flow Dynamics Code

GHG Greenhouse gas

HREC Herring River Executive Council

HRRC Herring River Restoration Committee

MEM Marsh Equilibrium Model

MHW Mean high water

NPS National Park Service

SLAMM Sea Level Affecting Marsh Migration

USFWS U.S. Fish and Wildlife Service

USGS U.S. Geological Survey

T&E Threatened and endangered

WBNERR Waquoit Bay National Estuarine Research Reserve
viii
A Decision Framework to Analyze Tide-Gate Options for 

Restoration of the Herring River Estuary, Massachusetts

David R. Smith1, Mitchell J. Eaton2, Jill J. Gannon3, Timothy P. Smith4, Eric L. Derleth3, Jonathan Katz5, 

Kirk F. Bosma6, and Elise Leduc6

Abstract

The collective set of decisions involved with the restoration of degraded wetlands is often more complex than 

considering only ecological responses and outcomes. Restoration is commonly driven by a complex interaction of social, 

economic, and ecological factors representing the mandate 

of resource stewards and the values of stakeholders. The 

authors worked with the Herring River Restoration Committee 

(HRRC) to develop a decision framework to understand the 

implications of complex tradeoffs and to guide decision making for the restoration of the 1,100-acre Herring River estuary 

within Cape Cod National Seashore, which has been restricted 

from tidal influence for more than 100 years. The HRRC 

represents decision maker and stakeholder interests in the 

restoration process. For a 25-year planning horizon, decisions 

involve the rate at which newly constructed water-control 

structures allow tidal exchange, and the timing and location 

of implementing numerous secondary management options. 

Decisions affect multiple stakeholders, including residents 

of two adjacent towns who value the watershed for numerous benefits and whose economy relies on seasonal activities 

and aquaculture. System response to management decisions 

is characterized by a high degree of uncertainty and risk with 

positive and negative outcomes possible. Decision policies 

will affect biophysical (for example, sediment transport, discharge of fecal coliform bacteria) and ecological (for example, 

vegetation response, fish passage, effects on shellfish) processes, as well as socioeconomic interests (for example, effects 

on property, viewscapes, recreation). The framework provides 

a structured approach for evaluating tradeoffs among multiple 

objectives (ecological and social) while appropriately characterizing relevant uncertainties and accounting for levels of risk 

tolerances and the values of decision makers and stakeholders. 

Consequences of tide-gate management options are predicted 

using a range of methods from quantitative physical process 

models to elicited expert judgement. The decision framework 

is presented, and the software developed to implement the 

tradeoff analysis is introduced. The results from an initial 

prototype analysis using a software application developed 

for analyses of tradeoffs and of sensitivity of the decision 

to risk and uncertainty are presented. The next step is to use 

the decision-support application to analyze options using 

improved predictions.

Introduction

Ecological restoration is challenging, in part, because it is 

not only about ecological endpoints, but also about socioeconomic concerns. The motivations driving our will to restore 

affected systems are based on values, which are complex and 

vary widely among stakeholders. Therefore, the goal of restoring the ecological function of a salt marsh stands alongside the 

need to avoid or at least minimize the adverse effects to stakeholder interests. Stakeholders, who might be affected by the 

restoration or who might affect how the restoration proceeds, 

can have vastly different, and at times conflicting, interests. 

In addition, uncertainty in restoration outcomes and variation 

in attitudes about risk contribute to the challenge of restoration decision making. Thus, restoration success or failure can 

be determined by whether tradeoffs among multiple interests 

and risks associated with uncertain outcomes are suitably 

evaluated.

Decision analysis (Raiffa and others, 2002; Goodwin 

and Wright, 2014) is designed to evaluate tradeoffs and risks. 

Decision analysis examines the available strategies by first 

considering multiple interests in the outcome, based on the 

best available information for predicting the consequences of 

implementing one or more strategies. A large body of literature 

from management science, operations research, and engineering provides the foundation for decision analysis, which represents the “best management practices” for decision making, 

especially for complex problems and group decisions (Raiffa 

and others, 2002). Decision analysis takes a deliberative 

1

U.S. Geological Survey.

2

Department of Interior, Southeast Climate Adaptation Science Center.

3

U.S. Fish and Wildlife Service.

4

National Park Service.

5

University of Vermont.

6

Woods Hole Group.
2 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

approach by providing options rather than advocating for a 

favored option. The process is transparent and explicit, can be 

documented, and is replicable, all of which can contribute to 

stakeholder acceptance of a decision. The decision analysis 

process guides decision makers towards a “good” decision that 

has the best chance of achieving the desired outcomes, while 

at the same time minimizing undesirable effects.

The tide gates at the Chequessett Neck Road (CNR) dike 

at the mouth of the Herring River (fig. 1) severely restrict tidal 

exchange and are the cause of severe ecological degradation to 

the estuary, which has been documented by on-site monitoring 

(Woods Hole Group, 2012; Cape Cod National Seashore and 

Herring River Restoration Committee, 2012). The degradation has motivated resource managers to pursue restoration 

of the Herring River estuary. Decision analysis is appropriate for exploring alternatives for the restoration of Herring 

River because (1) public resources are being used to support 

public decision making, (2) there is a variety of public and 

private interests at stake, (3) there is uncertainty about how 

the system will respond to restoration actions, and (4) restoration will take time thus providing the opportunity to adapt 

through a repeated cycle of prediction, decision making, and 

targeted monitoring.

To develop a decision analysis framework for evaluating 

tide-gate options for the restoration of Herring River estuary, 

the authors worked with the Herring River Restoration Committee (HRRC) to develop the decision framework through a 

series of meetings involving the committee and a workgroup 

formed for framework development. The HRRC represents 

decision maker and stakeholder interests in the restoration 

process. Workshops with stakeholders, science experts, and 

regulators helped those involved to better understand underlying issues, incorporate concerns and interests into the framework, and resolve technical questions. This report includes 

descriptions of the study area and the framework organized 

around the major decision components, followed by a discussion based on results from a prototype application of the decision framework.

Study Area

The 1,100-acre Herring River estuary lies within the 

towns of Wellfleet and Truro and partly within National Park 

Service (NPS) Cape Cod National Seashore (CACO) (fig. 1). 

The full Herring River restoration project area encompasses 

approximately 890 acres that would be affected by monthly 

spring high tide; 80 percent of this area falls under Federal 

stewardship within the CACO boundary, whereas 20 percent 

is outside the boundary in one of these two municipalities. The 

Herring River is the largest river system within the CACO 

and one of the largest tidally restricted estuaries on Cape Cod. 

The estuary has experienced more than 100 years of ecological degradation resulting from construction of the CNR dike 

and up-estuary drainage that began in 1909 and has resulted 

in the almost complete exclusion of tidal exchange to most 

of the estuary. The CNR dike is outside the CACO boundary 

and is managed by the town of Wellfleet. The restoration area 

includes several tributary streams separated into nine subbasins: Herring River (lower, mid, and upper), Mill Creek, 

Pole Dike Creek (lower and upper), Duck Harbor, and Bound 

Brook (lower and upper). The restoration project covers a 

large area encompassing public and private lands and structures, including a nine-hole golf course and an economically 

valuable oyster industry in Wellfleet Harbor. 

Structuring the Decision Analysis

Raiffa and others (2002) and Hammond and others (2015) 

recognized the major components of decisions and developed 

a structured approach for implementation of decision analysis that involves defining the problem, specifying measurable objectives or interests, creating options or alternatives, 

predicting the consequences of these options relative to the 

objectives, and evaluating tradeoffs. The decision analysis for 

the Herring River restoration was structured according to six 

major components: 

1. a clear statement of the problem, 

2. comprehensive and measurable objectives, 

3. a set of discrete tide-gate options, 

4. a means to predict outcomes, 

5. a process to evaluate the implications of these outcomes, 

and 

6. a plan for implementation of a tide-gate option over 

time. 

Monitoring will provide feedback to formally incorporate 

learning, reevaluate options, and possibly adapt management 

as restoration is implemented over time. 

A Statement of the Problem

Representatives of Cape Cod National Seashore and 

the town of Wellfleet compose the Herring River Executive 

Council (HREC) and are responsible for restoring the Herring 

River estuary and minimizing adverse effects over some finite 

length of time (likely less than 25 years). The HREC will have 

ultimate responsibility for managing the new tide control gates 

at CNR, Mill Creek, and Pole Dike Creek and for implementing secondary management actions to achieve overall restoration goals. The HREC will receive decision recommendations 

from the HRRC, whose members are scientific and technical 

experts. The HREC will manage, directly or through contract, 

the project and implement gate operations and secondary 

management actions.
Structuring the Decision Analysis 3

Duck Harbor

Lower Herring River

Upper Bound Brook

Mill Creek

Upper Herring River

Lower Pole Dike Creek

Upper Pole Dike Creek

Lower Bound Brook

Mid Herring River

0 0.5 1 KILOMETER

0 0.5 1 MILE

CAPE COD

BAY

MASSACHUSETTS A T L A N T I C O C E A N

70°20' 70°10' 70° 69°50'

42°10'

42°

41°50'

41°40'

CT

MA

NY

VT

NH

ME

0 10 20 KILOMETERS

0 10 20 MILES

Herring River restoration

project area

Cape Cod National Seashore

(from National Park Service)

Chequessett Neck Road

(CNR) dike

EXPLANATION

Base from Esri, 2014

Base from National Oceanic and Atmospheric Administration

Area of detail

shown above

Town of Truro

Town of Wellfleet

Figure 1. Herring River estuary and subbasins within Cape 

Cod National Seashore and towns of Wellfleet and Truro, 

Massachusetts. Map of Cape Cod with the Cape Cod National 

Seashore boundary is from Kranenburg and others (2017). The 

base layers for the top map and state boundary insert are the 

intellectual property of Esri and is used herein under license. 

Copyright © 2014 Esri and its licensors; all rights reserved.
4 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Broadly, project goals are to restore the natural hydrography (that is, tidal range and marsh surface elevation) and ecological integrity of the Herring River estuary, while minimizing 

adverse economic and social effects, maximizing the estuary’s 

production of ecosystem services, and minimizing management 

costs. The primary management actions adjust the volume of 

tidal flow through of a series of to-be-constructed tide gates at 

CNR, Mill Creek, and Pole Dike Creek; these actions require 

decisions on the number, location, magnitude of opening, and 

flow direction of the individual tide-gate openings at any given 

time. Timing and frequency of gate operations can be periodic or episodic; for example, gate opening can coincide with 

extreme high tides and storm events to facilitate movement of 

sediment farther upstream into the estuary. At each decision 

point, for example annually, gates can be configured to allow a 

greater, lesser, or the same volume of tidal flux into the estuary. 

In addition, project options include secondary management 

actions intended to accelerate the recovery of the estuarine habitat, enhance the benefits of tidal restoration achieved through 

tide-gate management alone, and reduce potential adverse 

ecological and socioeconomic effects of restoring tidal flow. 

Examples of secondary actions include management of floodplain vegetation (for example, vegetation removal or planting), 

modification of marsh surface elevations through management 

of sediment supply and distribution, and restoration of connectivity and natural sinuosity of tidal creeks to enhance the 

circulation of saltwater through the system. Decisions regarding secondary actions involve where and when to implement 

management measures, what techniques to use, and how to 

coordinate the actions with the tide-gate management. 

The operational phase of tide-gate management encompasses the period of time when tidal flow increases until the 

gates are fully open and the maximum tidal range has been 

reached. Tide-gate management will cease after the gates are 

fully open, which is expected to take 25 years or less. The 

rate at which gates are opened varies among alternatives. In 

general, tide-gate management during the operational phase 

could occur 2–3 times a year and could be affected by season 

or tidal cycle. Secondary actions may be implemented before, 

during, and after the period of tide-gate management. Decisions involving management of the tide gates can be spatially 

and temporally divided by the subbasins within the project 

area. Tide-gate management decisions will begin as soon as 

construction of the tide-control structures is complete. Decisions regarding secondary actions may range from simple and 

independent of other decisions to complex and linked to other 

management actions requiring coordination with the tide-gate 

management. For example, removal of vegetation may be 

beneficial to occur prior to restoration of tidal exchange for 

logistical purposes or to minimize effects on the flood plain. 

Tide-gate management decisions and secondary action 

decisions will be made (1) based on predicted outcomes of 

available actions with respect to the multiple project objectives 

and (2) given the uncertainty in system response to the actions 

taken. In general, varying degrees of uncertainty revolve 

around changes in tidal regime and salinity under different 

tide-gate configurations and changes to vegetation, water quality, sediment distribution, and other processes resulting from 

modifications to the hydrodynamics.

Decisions about tide-gate adjustments are subject to regulatory oversight under the U.S. Clean Water Act [33 U.S.C. 

§1251 et seq. (1971)], the Massachusetts Wetlands Protection 

Act (General Laws of Massachusetts Chapter 131, §40) and 

Waterways Regulations (310 CMR 9.00), the Town of Wellfleet wetland by-laws, and the Massachusetts Endangered Species Act (321 CMR 10.00). Tide-gate decisions will be constrained by the management actions required to protect public 

and private structures and property within the project area.

Definitions of the Objectives

Defining the objectives starts with the issues decision makers and stakeholders care about, what they want to 

achieve, and what they want to avoid (Gregory and Keeney, 

2002; McGowan and others, 2015). For Herring River estuary 

restoration, the focus is on achieving ecological and socioeconomic objectives. When the objectives are expressed as 

measurable attributes, the relative achievements of management alternatives can be compared to identify the option 

that best meets the objectives (Keeney and Gregory, 2005). 

Because achieving value for some objectives may come at the 

cost of other objectives, a formalized approach for evaluating 

tradeoffs among these objectives is often required. The manner 

in which the objectives are weighted in that comparison is 

part of the tradeoff analysis discussed below. The fundamental 

and highest-level objectives for Herring River restoration are 

to restore the hydrography, ecological function, and integrity 

of the estuary; minimize adverse effects on the local ecosystem, adjacent landowners, and other stakeholders; maximize 

production of ecosystem services; and minimize management 

costs (table 1, fig. 2). The fundamental objectives are further 

defined by subobjectives. Each subobjective has a performance measure, which serves two purposes. They provide 

a quantitative metric by which (1) predictions are made to 

evaluate how well an alternative is expected to meet each 

of the objectives and (2) observations will be made through 

monitoring to determine the progress towards achieving the 

objectives once an action has been implemented.

In addition, a set of objectives has been specified that 

has to do with strategic goals or the underlying process of 

how decisions are made, implemented, and communicated. 

Examples include maximize long-term collaboration of 

the partnership, maximize access to funding opportunities, 

maximize responsiveness to community concerns, maximize 

public awareness and support for the project, and maximize 

learning about ecological restoration. While these objectives 

are important, they would not be useful in a tradeoff analysis 

to distinguish among different options for gate operation or 

secondary management actions. In other words, process and 

strategic objectives are intended to be met equally, regardless 

of management options, and therefore are not included when a 

tide-gate option is analytically selected. 
Structuring the Decision Analysis 5

Table 1. Objectives of the Herring River estuary restoration decision support framework. There are five fundamental objectives with 

subobjectives within each fundamental objective. Each subobjective is accompanied by the performance measure (that is, metric) to 

be used to measure the current state of the objective, the method to be used to predict the objective of a given tide-gate management 

option, and the method to be used to monitor the objective after implementation of the option.

[EFDC, Environmental Fluid Dynamics Code; MEM, Marsh Equilibrium Model; SLAMM, Sea Level Affecting Marsh Model; WBNERR, Waquoit Bay 

National Estuarine Research Reserve; GHG, Greenhouse Gas; DO, dissolved oxygen; TBD, to be determined; MHW, mean high water; CNR, Chequesett Neck 

Road ; CYCC, Chequesett Yacht and Country Club; T&E, threatened & endangered; h, hour; mg/L, milligram per liter; meTonsCe/ha/yr, metric tons of carbon 

per hectare per year; ft, foot; %, percent, mm, millimeter; psu, practical salinity units; <, less than; >, greater than; >=, greater than or equal to; USGS, U.S. 

Geological Survey ] 

Subobjectives Performance measure Desired 

direction

Spatial 

scale Prediction method Monitoring

Fundamental Objective #1: Restore Hydrography

Restore tidal 

range

Low tide

Minimum water surface 

elevations (ft) averaged 

for subbasins and at key 

locations

Minimize Subbasin EFDC Hydrodynamic 

Model

Electronic waterlevel data loggers 

for subbasins and 

at key locations

High tide

Maximum water surface 

elevations (ft) averaged 

for subbasins and at key 

locations

Maximize Subbasin EFDC Hydrodynamic 

Model

Electronic waterlevel data loggers 

for subbasins and 

at key locations

Restore 

hydroperiod

Flooding extent Marsh area inundated by 

tides (%) Maximize Subbasin EFDC Hydrodynamic Model

Electronic waterlevel data loggers 

for subbasins and 

at key locations

Duration of 

flooding

Duration (h) of inundation 

of marsh surface at key 

locations 

Maximize Subbasin EFDC Hydrodynamic 

Model

Electronic waterlevel data loggers 

for subbasins and 

at key locations

Maximize marsh surface drainage Extent of ponded water at 

low tide (%) Minimize Subbasin EFDC Hydrodynamic Model

Electronic waterlevel data loggers 

in areas of 

predicted ponding

Maximize 

marsh surface 

elevation

Marsh surface 

sediment 

deposition

Accumulation of sediment 

at key marsh surface 

locations (mm)

Maximize Subbasin

EFDC Hydrodynamic 

Model with 

Sediment Module, 

linked with MEM

Deposition/Elevation 

at surface elevation 

tables and markers 

Below surface 

accretion 

(shallow 

subsidence)

Surface elevation (mm) Maximize

Lower 

Herring 

Basin

Baseline data; 

Published values; 

Input from 

SLAMM Model; 

Expert judgment/

elicitation

Soil sampling 

associated with 

marsh surface 

elevation 

monitoring sites
6 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Table 1. Objectives of the Herring River estuary restoration decision support framework. There are five fundamental objectives with 

subobjectives within each fundamental objective. Each subobjective is accompanied by the performance measure (that is, metric) to 

be used to measure the current state of the objective, the method to be used to predict the objective of a given tide-gate management 

option, and the method to be used to monitor the objective after implementation of the option.—Continued

[EFDC, Environmental Fluid Dynamics Code; MEM, Marsh Equilibrium Model; SLAMM, Sea Level Affecting Marsh Model; WBNERR, Waquoit Bay 

National Estuarine Research Reserve; GHG, Greenhouse Gas; DO, dissolved oxygen; TBD, to be determined; MHW, mean high water; CNR, Chequesett Neck 

Road ; CYCC, Chequesett Yacht and Country Club; T&E, threatened & endangered; h, hour; mg/L, milligram per liter; meTonsCe/ha/yr, metric tons of carbon 

per hectare per year; ft, foot; %, percent, mm, millimeter; psu, practical salinity units; <, less than; >, greater than; >=, greater than or equal to; USGS, U.S. 

Geological Survey ] 

Subobjectives Performance measure Desired 

direction

Spatial 

scale Prediction method Monitoring

Fundamental Objective #2: Restore Ecological Function/Integrity

Maximize area 

restored

Appropriate 

salinity 

gradient

Area with practical salinity 

unit (psu)

• <5

• 5 to 18

• >18

Optimize Estuary EFDC Hydrodynamic 

Model

Conductivity data 

loggers for 

subbasins and at 

key locations

Coverage of 

emergent 

vegetation

Area of emergent 

vegetation with psu

• <5

• 5 to 18

• >18

Maximize Estuary

EFDC (salinity 

model results) 

coupled with 

SLAMM wetlandtype results

Transect/Plot cover 

estimates; Habitat 

mapping

Surface-water 

quality

pH % of samples with pH < 5 Minimize

Lower 

Herring 

Basin

Expert elicitation 

informed by EFDC 

Hydrodynamic 

Model and USGS 

model

Continuous surfacewater-quality 

monitoring at key 

locations

DO % of samples with DO < 5 Minimize

Lower 

Herring 

Basin

Expert elicitation 

informed by EFDC 

Hydrodynamic 

Model and USGS 

model

Continuous surfacewater-quality 

monitoring at key 

locations

Habitat quality for estuarine 

community

Species composition of 

benthic invertebrate 

community (similarity 

index 0-1)

Maximize Estuary

Published values; 

expert elicitation 

informed by EFDC 

Hydrodynamic 

Model

Benthic sampling at 

key locations

Maximize connectivity for 

Diadromous fish

Fish passage indicated by 

fish counts Maximize Estuary

Expert elicitation 

informed by EFDC 

predictions of 

flow velocity at 

culverts/crossings 

and current and 

historical fish 

counts

Fish counts at 

crossings
Structuring the Decision Analysis 7

Table 1. Objectives of the Herring River estuary restoration decision support framework. There are five fundamental objectives with 

subobjectives within each fundamental objective. Each subobjective is accompanied by the performance measure (that is, metric) to 

be used to measure the current state of the objective, the method to be used to predict the objective of a given tide-gate management 

option, and the method to be used to monitor the objective after implementation of the option.—Continued

[EFDC, Environmental Fluid Dynamics Code; MEM, Marsh Equilibrium Model; SLAMM, Sea Level Affecting Marsh Model; WBNERR, Waquoit Bay 

National Estuarine Research Reserve; GHG, Greenhouse Gas; DO, dissolved oxygen; TBD, to be determined; MHW, mean high water; CNR, Chequesett Neck 

Road ; CYCC, Chequesett Yacht and Country Club; T&E, threatened & endangered; h, hour; mg/L, milligram per liter; meTonsCe/ha/yr, metric tons of carbon 

per hectare per year; ft, foot; %, percent, mm, millimeter; psu, practical salinity units; <, less than; >, greater than; >=, greater than or equal to; USGS, U.S. 

Geological Survey ] 

Subobjectives Performance measure Desired 

direction

Spatial 

scale Prediction method Monitoring

Fundamental Objective #3: Minimize Adverse Effects

Prevent effects on wells, property, 

structures, and roads

Number of wells, 

structures, or roads 

affected

Minimize Estuary

Water-surface 

elevation output 

from EFDC 

Hydrodynamic 

Model

Electronic waterlevel data loggers 

for subbasins and 

at key locations

Minimize risk to 

public safety

Risk to public at 

water control 

structures

Number of gates at 

specified heights Minimize Estuary

Calculated from 

gate configuration 

(number of gates at 

specified heights)

Observations of 

activity during 

peak-use periods

Risk to public 

elsewhere

Number of subbasins with 

average water depth at 

MHW of > 1 ft

Minimize Estuary

Calculated from gate 

configuration and 

average depth per 

subbasin at MHW

Observations of 

activity during 

peak-use periods

Prevent adverse 

effects on 

shellfish beds 

in harbor

Ammonium 

export

Concentration in mg/L 

of export from above 

CNR dike to harbor 

(Probability of 

measurable negative 

effect to aquaculture)

Minimize Wellfleet 

Harbor

Expert elicitation 

based on EFDC 

predictions of 

residence time, 

hydroperiod, and 

water surface 

elevation above 

saturated peat 

Surface-water-quality 

monitoring near 

aquaculture areas

Fecal coliform 

levels

Fecal coliform counts near 

aquaculture areas Minimize Wellfleet Harbor

Expert elicitation 

based on EFDC 

predictions of 

Residence Time

Surface-water-quality 

monitoring near 

aquaculture areas

Sediment 

deposition 

onto shellfish 

beds

Change in sediment 

dynamics (categorical) Minimize Wellfleet Harbor

Expert elicitation 

informed by EFDC 

Total suspended 

solids downstream 

from dike; particle 

size & deposition 

near aquaculture 

areas
8 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Table 1. Objectives of the Herring River estuary restoration decision support framework. There are five fundamental objectives with 

subobjectives within each fundamental objective. Each subobjective is accompanied by the performance measure (that is, metric) to 

be used to measure the current state of the objective, the method to be used to predict the objective of a given tide-gate management 

option, and the method to be used to monitor the objective after implementation of the option.—Continued

[EFDC, Environmental Fluid Dynamics Code; MEM, Marsh Equilibrium Model; SLAMM, Sea Level Affecting Marsh Model; WBNERR, Waquoit Bay 

National Estuarine Research Reserve; GHG, Greenhouse Gas; DO, dissolved oxygen; TBD, to be determined; MHW, mean high water; CNR, Chequesett Neck 

Road ; CYCC, Chequesett Yacht and Country Club; T&E, threatened & endangered; h, hour; mg/L, milligram per liter; meTonsCe/ha/yr, metric tons of carbon 

per hectare per year; ft, foot; %, percent, mm, millimeter; psu, practical salinity units; <, less than; >, greater than; >=, greater than or equal to; USGS, U.S. 

Geological Survey ] 

Subobjectives Performance measure Desired 

direction

Spatial 

scale Prediction method Monitoring

Fundamental Objective #3: Minimize Adverse Effects—Continued

Public 

satisfaction

Loss of privacy 

for abutters Number of complaints Minimize Estuary

Expert elicitation 

based on EFDC 

predictions of 

water surface 

elevation and 

salinity, and on 

predictions of 

vegetation change

Documentation of 

incidents

Public 

viewscapes

% of visual field that looks 

bad from key locations 

and visible presence of 

machinery during tourist 

season

Minimize Estuary

SLAMM coupled 

with ArcMap 

viewshed analysis 

and expert 

elicitation

Time series photo 

stations and 

documentation of 

incidents

Appearance of 

dead woody 

vegetation 

% of visual field that 

looks bad from private 

property

Minimize Estuary

SLAMM coupled 

with ArcMap 

viewshed analysis

Time series photo 

stations

Smell Number of complaints Minimize Estuary Expert judgment/

elicitation

Documentation of 

complaints

Community 

conflict Likelihood of litigation (%) Minimize Estuary Expert judgment/elicitation

Documentation 

of conflicts and 

resolutions
Structuring the Decision Analysis 9

Table 1. Objectives of the Herring River estuary restoration decision support framework. There are five fundamental objectives with 

subobjectives within each fundamental objective. Each subobjective is accompanied by the performance measure (that is, metric) to 

be used to measure the current state of the objective, the method to be used to predict the objective of a given tide-gate management 

option, and the method to be used to monitor the objective after implementation of the option.—Continued

[EFDC, Environmental Fluid Dynamics Code; MEM, Marsh Equilibrium Model; SLAMM, Sea Level Affecting Marsh Model; WBNERR, Waquoit Bay 

National Estuarine Research Reserve; GHG, Greenhouse Gas; DO, dissolved oxygen; TBD, to be determined; MHW, mean high water; CNR, Chequesett Neck 

Road ; CYCC, Chequesett Yacht and Country Club; T&E, threatened & endangered; h, hour; mg/L, milligram per liter; meTonsCe/ha/yr, metric tons of carbon 

per hectare per year; ft, foot; %, percent, mm, millimeter; psu, practical salinity units; <, less than; >, greater than; >=, greater than or equal to; USGS, U.S. 

Geological Survey ] 

Subobjectives Performance measure Desired 

direction

Spatial 

scale Prediction method Monitoring

Fundamental Objective #4: Maximize Ecosystem Services

Climate change mitigation Biomass carbon storage 

(meTonsCe/ha/yr) Maximize Estuary

WBNERR GHG 

calculator 

informed by EFDC 

Hydrodynamic 

Model output

Atmospheric 

carbon exchange; 

Soil carbon 

accumulation

Shellfishing opportunities 

Area of available habitat 

(acres) and likelihood of 

closures not exceeding 

current number of 

closures

Maximize

Above 

and 

below 

CNR 

dike

EFDC Hydrodynamic 

Model and expert 

elicitation

Fecal coliform counts 

and documentation 

of incidences

Natural mosquito control

Mosquito species 

composition and 

abundance

TBD TBD

Expert elicitation 

based on EFDC 

output for ponding 

and salinity

Larvae counts in 

breeding areas

Maximize 

recreational 

opportunities

Loss of golfing 

opportunities 

at CYCC

Days/year closed Minimize CYCC Expert elicitation Documentation of 

incidences

Loss of existing 

recreational 

opportunities

Dry land area currently 

used for recreation that 

will be flooded

Minimize Estuary

Expert elicitation 

[based on EFDC 

predictions of area 

flooded]

Documentation of 

loss/gain of access 

points

Newly created 

recreational 

opportunities

Open area with water depth 

>=2 ft at MHW Maximize Estuary

Expert elicitation 

[based on EFDC 

predictions of area 

flooded]

Car counts; 

User surveys; 

Observations of 

activity during 

peak-use periods

Fundamental Objective #5: Minimize Cost

Minimize cost for secondary actions Cost for secondary actions Minimize Estuary Expert judgment/

elicitation

Project timeline/

Financial records

Minimize cost for tide-gate 

operations

Cost for tide-gate 

operations Minimize Estuary Expert judgment/elicitation

Project timeline/

Financial records

Minimize cost for monitoring Cost for monitoring Minimize Estuary Expert judgment/

elicitation

Project timeline/

Financial records

T&E Monitoring Probability that permit 

requirements fully met Maximize Estuary Expert judgment/elicitation

Documentation as 

required by permit
10 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Restore

hydrography

Restore ecological

function and integrity

Minimize adverse

effects

Maximize ecosystem

services Minimize cost

Restore Herring River estuary

Maximize area restored Maximize surface-water

quality

Maximize habitat quality

for estuarine community

Maximize connectivity

for diadromous fish

Restore ecological function and integrity

pH

Dissolved oxygen

Salinity gradient

Vegetation cover

Restore tidal range Restore hydroperiod Maximize marsh surface

drainage

Maximize marsh surface

elevation

Marsh surface

sediment deposition

Below surface

accretion

Restore hydrography

Flooding extent

Duration of flooding

Low tide

High tide

Figure 2. Fundamental objectives and subobjectives for restoration of the hydrography, restoration of the ecological function 

and integrity, minimization of adverse effects, maximization of ecosystem services, and minimization of management costs. (CYCC, 

Chequessett Yacht & Country Club)
Structuring the Decision Analysis 11

Maximize climate change

mitigation

Maximize natural mosquito

control

Maximize shellfish

opportunities

Maximize recreational

opportunities

Minimize loss of

golfing opportunities

at CYCC

Minimize loss of

other recreational

opportunities

Maximize newly

created recreational

opportunities

Maximize ecosystem services

Tide-gate operations Secondary actions Monitoring

Minimize management cost

Prevent effects to structure

and roads Minimize risk to public safety Prevent adverse effectsto harbor shellfish beds Maximize public satisfaction

Minimize loss

of privacy for

abutters

Improve public

viewscapes

Minimize appearance

of dead woody

vegetation

Minimize adverse

smell

Minimize community

conflict

Minimize adverse effects

Prevent ammonium

export

Prevent fecal coliform

Prevent sediment

deposition on

shellfish beds

At water control

structure

Public risk elsewhere

Figure 2. Fundamental objectives and subobjectives for restoration of the hydrography, restoration of the ecological function 

and integrity, minimization of adverse effects, maximization of ecosystem services, and minimization of management costs. (CYCC, 

Chequessett Yacht & Country Club)—Continued
12 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Management Options 

For restoration of the Herring River estuary, there are 

two broad categories of actions: tide-gate management and 

secondary management actions designed to affect the estuary 

by a means other than tidal exchange, such as, mechanical 

removal of woody vegetation within a subbasin. Thus, the 

term “option” denotes a set of actions, including tide-gate 

management or secondary actions, implemented over time. 

The terms “alternatives” and “options” are used synonymously 

in this report.

Options for tide-gate management at the CNR dike are 

defined by the pace of restoring tidal range (fig. 3). Mean high 

water (MHW) in the Lower Herring River subbasin, expressed 

as feet above the North American Vertical Datum of 1988, 

is used to indicate progress towards restoration, and maximum MHW = 4.3 feet (ft) is expected to be reached within a 

25-year period (Woods Hole Group, 2012). In contrast, Woods 

Hole Group (2012) found that MHW in the Lower Herring 

River subbasin is 0.37 ft. Options for tide-gate manipulations 

vary by the pace of reaching a benchmark tidal elevation (for 

example, slow then fast versus fast then slow) or are designed 

for special purposes, such as facilitating sediment deposition 

upstream or enhancing recovery of estuarine vegetation communities. Each tide-gate option identifies a complete sequence 

of manipulations that would occur over time frames of up to 

25 years. 

These policies were developed to achieve full tidal flow 

by a certain time or to address specific hypotheses, objectives, or solutions. The 5-year, 15-year, and 25-year threshold 

options would open the tide gates at a constant rate so gates 

will be fully open by 5, 15, or 25 years, respectively (fig. 3A). 

Variations on these strictly time-based options are designed 

to be precautionary (that is, the 15-year Slow.Fast and the 

15-year Fast.Slow options; fig. 3A), manage vegetation by 

means of tidal flow (that is, the Growing Season option; 

fig. 3B), or enhance upstream sediment transport and deposition (that is, the Sediment option; fig. 3C). The 15-year Slow.

Fast option opens the gates slowly at first and then accelerates 

gate opening to fully open the gates by 15 years. In contrast, 

the 15-year Fast.Slow option initially opens the gates rapidly 

and then opens gates slowly thereafter to fully open the gates 

at 15 years. The Growing Season option opens gates in steps 

to kill invasive reeds (Phragmites) in the lower basin and 

pauses for a growing season to allow emergent native vegetation growth to capture sediment. The Sediment option opens 

gates periodically, closes gates on outgoing tides to allow 

sediment to settle, and then episodically opens the gates during incoming spring or storm tides to allow greater upstream 

sediment deposition.

For the purposes of planning, a management year of 

November–October was assumed, with the indicated gate 

changes occurring at the beginning of the specified year. The 

tide gates, and thus MHW, remain static for the full management year until the next time that a change is scheduled. The 

Sediment option, which periodically opens and closes gates 

to promote sediment deposition (fig. 3C), anticipates a single 

peak occurring in November; however, there may be one or 

more peaks in the specified years that will occur with the highest predicted tide(s) of the year and (or) with an unpredictable storm event, which introduces some uncertainty into the 

within year timing of gate operation. Each peak will last four 

consecutive tidal cycles, centered around the high tide. 

Tide-gate options are referred to as “platform” options 

because they provide the baseline conditions or platform upon 

which secondary actions will be added. Types of secondary 

management actions include vegetation management, sediment management, and channel and marsh surface management. Secondary actions are “added on top of”’ tide-gate management to meet particular objectives. The selection process 

is to identify the best performing tide-gate platform option, 

propose alternative secondary actions, and then select the best 

overall option (tide-gate management plus secondary actions). 

The location and timing where secondary actions are 

needed cannot be anticipated in all cases. Thus, inclusion of 

secondary actions is one way of adapting management as restoration progresses. For example, a given tide-gate option may 

perform well on most objectives but fall short in marsh surface 

drainage. This would indicate very specific secondary actions 

to bolster marsh surface drainage in areas where it is needed 

and would be most effective. 

Secondary actions may range from simple independent 

decisions to complex decisions that are conditionally linked 

to other management actions. The timing of some secondary 

actions may have a temporal relation with the tide-gate operations, thus requiring coordination with the tide-gate management process. For example, removal of vegetation may be beneficial to occur prior to restoration of extensive tidal exchange 

to facilitate work in more conducive, drier conditions.

Prediction of Option Consequences 

Decision making is future oriented; good decisions are 

made after full consideration of What is likely to happen if 

this or that is done? Therefore, predicting the consequences of 

management actions is an important step in decision analysis. Expected performance, in the terms of each objective, is 

predicted under each option. A comparison of the relative predicted performance among alternatives provides the basis for 

selecting an option or, in the case of a multiple-objective problem, the information needed for conducting a tradeoff analysis. 

For Herring River restoration, the conceptual linkages between 

tide-gate and secondary management actions and restoration 

objectives are diagrammed in appendix 1.

Methods for prediction are based on either quantitative 

models or expert judgement. The methods for prediction are 

being developed in a tiered approach and are identified in 

table 1. The first tier (Tier 1) predictions are best professional 

judgments developed by the HRRC. The second tier (Tier 2) 

predictions are those provided through formal elicitation 

methods by subject matter experts and, where appropriate, 

community stakeholders. The third tier (Tier 3) predictions 
Structuring the Decision Analysis 13

3.6 feet

2.6 feet

1.8 feet

0

1

2

3

4

5

0 5 10 15 20 25

Year

Mean high-water mark,

in feet above NAVD 88

A. Threshold options

3.6 feet

2.6 feet

1.8 feet

0

1

2

3

4

5

0 5 10 15 20 25

Year

Mean high-water mark,

in feet above NAVD 88

B. Two growing seasons

3.6 feet

2.6 feet

1.8 feet

0

1

2

3

4

5

0 5 10 15 20 25

Year

Mean high-water mark,

in feet above NAVD 88

C. Sediment capture and deposition

EXPLANATION

Full restoration at

 5 years

 15 years

 25 years

Fast/slow openings at 15 years

Slow/fast openings at 15 years

Figure 3. Effects of alternative gate operations on mean high water (MHW) for the Herring River estuary, 

Massachusetts: A, Threshold options to achieve full restoration (4.5-foot MHW) at 5, 15, or 25 years (yr); deviations in 

the time to reach 4.5-foot MHW are due to constraints on gate openings. Variations of the 15-year option include initially 

slow then fast opening (Slow.Fast 15-year option) and initially fast and then slow opening (Fast.Slow 15-year option). 

B, An option that pauses openings for 2 growing seasons to allow for aquatic vegetation to become established. C, An 

option with timing of openings to allow for upstream sediment capture and deposition. Horizontal lines show reference 

water levels.
14 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

are generated by quantitative models. Typically, accuracy 

and cost increase from Tier 1 to Tier 3; however, the value of 

the information to the selection of the tide-gate option does 

not necessarily indicate that Tier 3 predictions are warranted 

for all objectives. For predicting the percent coverage of 

non-invasive emergent vegetation, expert elicitation using 

available expertise from the HRRC is the Tier 1 method, and 

expert elicitation using a panel of experts is the Tier 2 method. 

In contrast, the model-based Environmental Fluid Dynamics 

Code (EFDC; https://www.epa.gov/ceam/environmental-fluiddynamics-code-efdc; Hamrick, 1996), which predicts hydrology and water-quality dynamics for surface water, coupled 

with the Sea Level Affecting Marshes Model (SLAMM; http://

warrenpinnacle.com/prof/SLAMM/index.html; Warren Pinacle 

Consulting, Inc., 2012), is considered the Tier 3 method for 

predicting the percent coverage of non-invasive emergent 

vegetation. Tier 1 predictions have been compiled but are being used only to assess and develop the decision framework. 

Tier 2 and 3 predictions will be used for the decision analysis. 

Tier 3 predictions can be applied only when a cost-effective 

quantitative model exists for a given objective. Where no 

quantitative model is available, Tier 2 predictions will be 

elicited from technical subject-matter experts and community 

stakeholders through formal elicitation processes.

Planning for expert elicitation is currently underway 

(2019) to develop predictions for objectives where use of a 

quantitative model is not possible or otherwise suitable. Elicitation is a formal process where technical subject-matter experts or stakeholders are asked to provide their own informed 

judgments about how a specific management action, integrated 

within a platform option, may affect a specific objective (McBride and Burgman, 2012; O’Hagan, 2019). There are various 

methods for conducting formal elicitations, but the basis of the 

process is to develop data that allow for quantification of uncertainty and express the range of predictions among multiple 

experts or responders. For the Herring River, two separate 

elicitation processes are currently (2019) being planned: one 

for scientific experts to provide predictions for several measurable attributes for ecological objectives and another for local 

stakeholders to develop information about socioeconomic 

outcomes that are not addressed by existing ecological models. 

We predominately used the four-step question format combined with a modified Delphi format to capture uncertainty 

(Speirs-Bridge and others, 2010).

The foundational quantitative model for the Herring 

River project is a two-dimensional hydrodynamic model 

developed by the Woods Hole Group (2012) using the EFDC 

software package (Hamrick, 1996). The EFDC model spatially 

represents the entirety of the historical Herring River flood 

plain and has been calibrated and validated to a set of tidal 

observations collected over full lunar cycles in 2007 and 2010. 

The model has been used to identify the optimal size of the 

tide gates at the new CNR bridge, the location of the proposed 

Mill Creek dike, and the road culverts to be replaced as part 

of the restoration project. It has also been used to simulate the 

extent of tidal exchange under a range of full and partial restoration scenarios. Outputs from the EFDC model include tidal 

metrics under normal and storm-driven tidal forcing, including 

water-surface elevations, tidal range, water-column salinity, 

flow direction and velocity, and hydroperiod (for example, 

residence time, flood frequency, flood duration). Data outputs 

are available for virtually any Herring River location within 

the model domain and for any time step within the lunar 

tidal cycle.

The EFDC model has been run to simulate 17 different tide-gate configurations at the CNR bridge to understand 

the hydrodynamic effects of incremental tide-gate management. Output from these simulations provides predictions of 

low- and high-tide water-surface elevations and other hydrodynamic metrics, averaged by subbasin and for individual 

and grouped model nodes. In addition to tabular data output, 

spatial data have also been compiled to graphically depict 

the extent of tidal exchange under each of the 17 tide-gate 

configurations. 

In addition to the EFDC hydrodynamic model, other 

computer-based models have been applied to the Herring River project. The Sea Level Affecting Marshes Model (SLAMM) 

is open-source software that was originally developed with 

U.S. Environmental Protection Agency funding in the 1980s 

(Warren Pinnacle Consulting, Inc., 2016). It incorporates 

several input parameters, including Light Detection and Ranging (lidar) survey elevations, existing wetland classifications, 

sea-level-rise rates, tidal range, and accretion and erosion rates 

for various wetland habitat types to simulate the dominant 

processes involved with wetland conversions resulting from 

sea-level rise (Woods Hole Group, 2018).

Although typically utilized to project wetland changes 

owing to sea-level rise, SLAMM was applied in a unique 

approach to advance the understanding of how the changing tidal regimes associated with various tide-gate scenarios 

could potentially affect ecological resources and wetland 

types throughout the Herring River system. Used in combination, land elevation and tidal range are the main drivers of the 

simulated vegetation predictions. Rather than using SLAMM 

to predict water-level increases that are projected to occur 

because of sea-level rise, this application of SLAMM used 

different tidal ranges resulting from various tide-gate configurations at the CNR Dike to project how the vegetation would 

likely respond to changes in tidal conditions. 

Other quantitative models either have been developed 

or are being considered for use for predicting outcomes. The 

U.S. Geological Survey developed a reactive-solute transport 

model of sediment release of nutrients in response to tidal 

flooding based on the Nutrient Flux Model (PHAST; Parkhurst 

and others, 2010). A fully functional version of this waterquality model is not currently available, but in the future, such 

a model could be used to simulate water chemistry change 

as salt marshes are restored. The Marsh Equilibrium Model 

(Morris and others, 2002) is being evaluated for its potential 

use in simulating sediment and marsh accretion processes and 

its ability to be integrated with output from the EFDC hydrodynamic model. Other analytical models are being investigat-
Structuring the Decision Analysis 15

ed to generate quantitative predictions for other water-quality 

variables, sediment deposition, habitat suitability, and vegetation composition.

Evaluation of Tradeoffs

Predicting consequences provides information on the 

expected performance of individual objectives in response to 

available management actions. An analysis of tradeoffs among 

objectives then provides insight into the decision problem and 

helps decision makers and stakeholders deliberate about the 

alternative strategies by considering all objectives and their 

possible interactions. A consequence table is a useful tool for 

integrating the components of a decision analysis (that is, 

objectives, alternatives, and consequences) when conducting 

a tradeoff analysis (table 2). The predicted performance for 

each objective under each option is presented concisely in the 

unweighted consequence table. Relative weights are assigned 

to each objective on the basis of their importance, which can 

vary among stakeholders. Comparison of options is based 

on the overall value-weighted performance considering all 

objectives (Goodwin and Wright, 2014). Software applications 

have been developed within the R programming environment 

(R Core Team, 2018) for use by the HRRC to conduct tradeoff 

analyses for the Herring River restoration. 

There are seven steps in the tradeoff analysis. 

1. Populate the consequence table with predicted outcomes 

for each objective under each alternative action or 

option. 

2. Develop utility curves (described below) for each objective reflecting how the range of possible outcomes are 

valued by stakeholders. Values may not be linear relative 

to outcomes, and utility curves can capture risk attitudes.

3. Use the utility curve to determine the utility value associated with each predicted outcome.

4. Replace the predicted outcomes with the associated utilities in the consequence table.

5. Assign an importance weight to each objective.

6. Calculate a weighted average of the utility values across 

the objectives for each alternative action.

7. Evaluate the sensitivity of the tradeoff analysis to uncertainty and identify options that are robust to uncertainty.

Utility functions transform performance metrics into 

a standardized scale (between 0 and 1) to represent preference for levels of performance and tolerance for levels of risk 

(fig. 4). Utility curves take a variety of shapes depending on 

risk attitude ranging from risk aversion to risk seeking. Risk 

attitude relates to one’s tolerance for accepting the chance of a 

bad outcome for the possibility of better performance. A riskseeking attitude arises when someone is unsatisfied with the 

prospect of low performance for an objective and is willing 

to take chances to achieve a better outcome. A risk-adverse 

attitude applies to someone who is unwilling to trade existing 

performance for the unlikely event of better performance when 

there is also some risk of doing worse than expected. It is 

common that choices involving gains (for example, improved 

ecological function) are risk averse; whereas, choices involving losses (for example, avoid adverse effects) are risk seeking 

(Tversky and Kahneman, 1986). To understand the possible 

range of stakeholder risk attitudes related to the restoration 

of the Herring River estuary, utility curves were elicited from 

the members of the HRRC for a subset of objectives expected 

to cover this range (appendix 2). Default utility curves were 

created for each objective based on the elicitation, but the 

utility curves can be adjusted within the R application prior to 

conducting a tradeoff analysis.

Implementation of an Option Through Time

Opening of the tide gates at the CNR dike will occur over 

a definite period of less than 25 years. Gate operation from 

closed to fully opened has been envisioned as alternative actions composed of incremental tide-gate openings. The HREC 

will select the tide-gate option with secondary actions based 

on recommendations from the HRRC informed by the tradeoff 

and risk analyses. The selected tide-gate option will be implemented followed by monitoring of outcomes. The selected 

tide-gate option will stipulate a schedule for gate operation 

over a 25-year period or until the gates are fully open, whichever occurs first. However, there are two ways the selected 

option can be adapted over time. First, the selected option can 

be reviewed periodically by repeating tradeoff analyses using 

updated or new information. The new information based on 

monitoring data would be used to update predictions based on 

revised estimates of model parameters in EFDC or SLAMM. 

Monitoring locations (table 1) are based on protocols developed under the Cape Cod Ecosystem Monitoring program, 

such as the hydrology protocol developed by McCobb and 

Weiskel (2003), and rely on general guidance provided by 

Buchsbaum and Wigand (2012) (see also https://www.nps.

gov/caco/learn/nature/cape-cod-monitoring-program.htm). 

The tradeoff analysis would be conducted with new baseline 

determined by the current gate openings and hydrology. If indicated, a new option could be selected if the updated tradeoff 

analysis indicates that another option is likely to outperform 

the current option. For the initial 3–5 years, reviews would be 

conducted annually to evaluate short-term responses triggered 

by increases in water-surface elevation; the period between 

reviews can then increase as needed until full restoration is 

achieved. Second, monitoring can indicate the need to change 

secondary management actions. The thresholds that indicate 

secondary management action have not been stipulated. However, deriving thresholds need not be complex because the 

need for action could be evident. For example, monitoring can 

locate where drainage is insufficient to prevent ponded water 

at low tide, and in response, channel modifications can be used 

to increase local drainage. 
Table 2. The unweighted consequence table for the pilot tradeoff analysis. The predictions are the modeled and most likely (expected) elicited valuewere transformed onto a utility scale accumulated over a 25-year period of restoration. The maximum performance on any given objective is indicateyear-specific scores are summed over the 25-year period and maximum performance in any given year is 1. [Subobjectives marked with a single asterisk (*) report the average cumulative utility for the nine subbasins. Subobjectives marked with a double asterisk (**) report the average able areas in each measurement target range. All other subobjectives report the basin-wide cumulative utility. T, threshold option for for 5 (_5), 15 (_15), or 25 (_25) years; FS, fslow.fast 15-year option; MHW, mean high water; MLW, mean low water; DO, dissolved oxygen; WQ, water quality; Veg, vegetation; rec, recreation; TE, threatened & endangegrowing season] Objective hierarchy Tide-gate option (figur

Fundamental objective Objective Subobjective T_5 T_15 FS_15 T_25 S

Hydrography Marsh surface elevation Accretion 8.25 7.25 6.50 6.29 

Deposition* 3.22 2.76 2.66 2.31 

Hydroperiod Flooding duration* 6.43 11.08 16.59 16.91 

Flooding extent* 23.34 22.78 22.54 20.88 

Tidal range MHW* 23.70 21.70 22.23 19.83 

MLW* 4.97 8.58 9.88 12.22 

Marsh surface drainage Ponding* 4.73 12.46 14.27 20.17 

Ecological function/integrity Surface WQ DO 23.50 23.50 21.50 21.50 

Connectivity diadromous fish Fish 11.93 10.12 11.58 9.48 Habitat quality native estuarine animals Invertebrate 18.93 17.91 17.93 15.56 Surface WQ pH 25.00 25.00 25.00 25.00 Area restored Salinity** 23.60 21.54 22.12 19.60 

Vegetation** 21.86 21.82 22.36 21.91 

Adverse effects Harbor shellfish beds Ammonium 24.98 24.97 24.97 24.97 

Harbor shellfish beds Sediment 25.00 25.00 25.00 25.00 

Fecal 23.03 23.94 24.34 23.93 

Public satisfaction Conflict 24.96 24.95 24.96 24.96 

Machine time 25.00 25.00 25.00 25.00 Privacy 17.86 19.23 20.49 20.05 Smell 7.20 12.50 14.05 12.83 Visual field 2.00 5.57 7.19 8.28 Woody veg 1.85 5.11 6.21 7.72 

Public safety Risk at gate 23.04 17.90 11.89 15.11 

Risk elsewhere 4.25 3.75 9.68 10.86 

Damage Private property 2.92 2.92 2.92 2.92 

Private wells 1.86 2.26 2.44 2.83 Public roads 2.92 2.92 2.92 2.92 
Table 2. The unweighted consequence table for the pilot tradeoff analysis. The predictions are the modeled and most likely (expected) elicited valuewere transformed onto a utility scale accumulated over a 25-year period of restoration. The maximum performance on any given objective is indicateyear-specific scores are summed over the 25-year period and maximum performance in any given year is 1.—Continued[Subobjectives marked with a single asterisk (*) report the average cumulative utility for the nine subbasins. Subobjectives marked with a double asterisk (**) report the average able areas in each measurement target range. All other subobjectives report the basin-wide cumulative utility. T, threshold option for for 5 (_5), 15 (_15), or 25 (_25) years; FS, fslow.fast 15-year option; MHW, mean high water; MLW, mean low water; DO, dissolved oxygen; WQ, water quality; Veg, vegetation; rec, recreation; TE, threatened & endangegrowing season]

Objective hierarchy Tide-gate option (figur

Fundamental objective Objective Subobjective T_5 T_15 FS_15 T_25 S

Ecosystem services Climate change mitigation Climate 23.17 22.04 23.00 20.73 

Recreation Existing rec 2.81 2.81 2.81 2.81 

Golf 20.76 20.76 20.76 20.76 New rec 21.94 13.93 16.00 11.31 

Shell fishing opportunities Shellfish acres 18.72 18.69 18.83 18.19 

Shellfish closure 21.44 21.42 18.92 21.41 

Natural mosquito control Mosquitos

Cost Cost of tide-gate operations Gate hours 17.57 18.18 18.80 18.18 

Cost of monitoring Monitoring hours 13.81 12.12 14.10 11.27 Cost of secondary actions Secondary cost 23.93 23.93 23.93 23.93 

Threatened and endangered species Monitoring T&E 19.91 19.91 20.60 19.91 
18 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Objective A Objective B Objective C

Objective D Objective E Objective F

Objective G

Utility

Measured value

Utility

Measured value

Utility

Measured value

Utility

Measured value

Utility

Measured value

Utility

Measured value

Utility

Measured value

-3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 0

0.2

0.4

0.6

0.8

1.0

0 2 4 6 8 10 0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25 0

0.2

0.4

0.6

0.8

1.0

0 50,000 100,000 150,000 0

0.2

0.4

0.6

0.8

1.0

0 20 40 60 80 100 0

0.2

0.4

0.6

0.8

1.0

-1 0 1 2 3 4 5 0

0.2

0.4

0.6

0.8

1.0

0 5 10 15 20 25 0

0.2

0.4

0.6

0.8

1.0

Figure 4. Example utility curves for selected objectives relating the level of a 

performance metric for hypothetical objectives (x-axes) to a standardized score between 

0 and 1 (y-axes) based on preferences and risk attitude. The utility curves are for 

minimized objectives (A–D), maximized objectives (E–G), risk-adverse attitudes (A and E), 

risk-seeking attitudes (C, D, and G), and risk-neutral attitudes (B and F). 

Prototype Decision Analysis and 

Results

A decision analysis was conducted using preliminary 

predictions to serve as a starting point, evaluate the decision 

structure, and identify areas needing improvement. The seven 

steps outlined in the “Evaluation of Tradeoffs” section were 

conducted using predictions from the EFDC model for hydrological objectives, the SLAMM model for certain ecological 

objectives, and preliminary expert-elicited predictions for the 

remaining objectives. Members of the HRRC participated in 

the prototype analysis by providing expert judgment on many 

of the performance measures. To limit the potential for elicitation fatigue, the initial prototype focused on the lower Herring River subbasin for hydrologic and ecological objectives 

and basinwide for socioeconomic objectives. It was assumed 

that the Mill Creek and Upper Pole Dike Creek water-control 

structures were in place to limit the scope of the elicitation. 

The uncertainty comes from the elicited attributes. The numerical models do not yet produce confidence intervals, which 

will be included in future prototypes.

The tradeoff analysis was conducted using a custom 

software application developed in the R programming environment (R Core Team, 2018). The application allowed for selection or specification of utility curves, prediction percentile, 

and importance weighting of the objectives. The prediction 

percentile, which ranged from 0.55 to 0.8, was used to compute confidence limits. For each percentile, the corresponding 

confidence limits represented worst case (pessimistic) and 

best case (optimistic) contingent on whether the objective was 

to be minimized or maximized. Utility curves ranged from 

risk averse to risk seeking options on a continuous scale and 

were used to transform the performance measures to utility 

values between 0 and 1. Some utilities were time specific. For 

example, the utility curve could be differentiated for different 

phases of restoration (for example, specifying risk aversion 

during early restoration and risk neutral or risk seeking late in 

the restoration planning cycle). A discount rate can be set to 

place higher value on performance during the first few years 

relative to performance near full-gate opening. 

The scores in the consequence table, which are cumulative utilities over the 25-year restoration period, range from 

0 to 25 corresponding to performance from poor to excellent 
Prototype Decision Analysis and Results 19

for a given objective and tide-gate option (table 2). Thus, the 

consequence table can be scanned quickly to see how well the 

objectives are being met by comparing the scores to the maximum value of 25 and to the minimum value of 0. 

The overall score for an option is a weighted average 

of the cumulative utilities across all objectives (table 3). The 

objective weights in table 3 were allocated as follows: the 

hydrologic objectives received 30 percent, ecological function objectives received 20 percent, adverse effect objectives 

received 30 percent, ecosystem service objectives received 10 

percent, cost objectives received 5 percent, and threatened and 

endangered species received 5 percent, which is the balancedweighting scenario presented in figure 5. The overall score is 

also scaled from 0 to 25, indicating poor to excellent performance of a given option. The overall scores, along with the 

more detailed objective-specific comparisons, provide a tool 

for comparing options and exploring the predicted outcomes 

of different options to gain a better understanding of the problem and potential management consequences.

Option scores and rankings change depending on choice 

of utility and importance weighting, as well as the level of 

confidence in the prediction. Thus, to complete the tradeoff 

analysis, it is important to determine whether the best-performing option is sensitive to variation in stakeholder values 

or prediction uncertainty as represented by different levels of 

pessimistic and optimistic scenarios; we refer to this as a sensitivity analysis. The goal is to identify options that are robust 

to variation in stakeholder values and prediction uncertainty. 

In other words, the goal is to find an option that is predicted to 

perform well across a wide range of underlying assumptions.

A sensitivity analysis was conducted in which the tradeoff 

analysis was repeated assuming different levels of prediction 

uncertainty and value-weighting schemes. To test the effect 

of uncertainty, the tradeoff analysis was conducted using the 

most likely prediction and again using the limits from the 

confidence interval with a range of percentiles (0.55–0.80). 

The confidence limit to be used depends on whether a best 

case or worst-case scenario is being evaluated and the objective’s direction. If an objective is to be maximized, then the 

upper confidence limit is considered the best-case outcome. 

In contrast, if an objective is to be minimized, then the lower 

confidence limit is the best case. Four weighting schemes were 

included in the sensitivity analysis, and these included either 

(1) a preference for ecological objectives, (2) a preference for 

socioeconomic objectives, (3) a balance between ecological 

and socioeconomic objectives, or (4) an equal weighting of 

each fundamental objective (fig. 5). In an ecological weighting scheme, hydrography and ecological objectives are highly 

valued. In a socioeconomic weighting scheme, the social and 

economic objectives are highly valued. In a balanced weighting scheme, some ecological (hydrography) and some social 

(adverse effects) objectives are highly valued. In the equal 

weighting scheme, all fundamental objectives are equally 

valued. Aspects of the analysis that can be investigated include average performance (fig. 6) and frequency of ranking 

(fig. 7). For example, based on the preliminary predictions, the 

“15-year Fast.Slow” option (fig. 3A) was ranked first more frequently than other options (fig. 7). The predicted performance 

of this option was quite robust to underlying assumptions 

about uncertainty and value weighting because it was ranked 

first more frequently than other options and was never ranked 

below second (fig. 7). The only other option that ranked first 

was the 25-year option (fig. 3A), which was rarely ranked 

below 3rd and never below 4th (figs. 6 and 7). 

Although it is important to identify which option has the 

best and most robust overall performance, it is also important 

to evaluate how well individual objectives and subobjectives 

are being met. A double-column chart shows option performance at the objective level (fig. 8). There are two questions 

that a double-column chart is designed to answer. First, does 

performance among option alternatives vary, or do all options 

perform similarly? Second, is there unmet potential for better 

performance, or does the best performing option achieve full 

or nearly full performance? For example, for the Ponding 

objective there is a wide range in performance among option 

alternatives, but there is only modest room for improvement 

because the option that performs best for this objective nearly 

achieves maximum performance (fig. 8). In contrast, for the 

Deposition objective there is a narrow range in performance 

with all options performing about the same, and there is ample 

room for improvement (fig. 8). Maximizing sediment deposition and accretion, minimizing damage to structures, and 

Table 3. Overall utility from the pilot tradeoff analysis. The cumulative utilities for each objective, which are presented in table 2, are 

value weighted and averaged for an overall performance score for each option. The objective weights in table 3 were allocated as 

follows: the hydrologic objectives received 30 percent, ecological function objectives received 20 percent, adverse effect objectives 

received 30 percent, ecosystem service objectives received 10 percent, cost objectives received 5 percent, and threatened and 

endangered species received 5 percent, which is the balanced-weighting scenario presented in figure 5.

Option score

Options (figure 3)

Threshold 

5 year

Threshold 

15 year

Threshold 

25 year

Fast.Slow 

15 year

Slow.Fast 

15 year

Growing 

season

Sediment

Weighted sum 14.99 15.19 15.67 15.79 14.92 14.92 15.42

Rank 5 4 2 1 6 7 3
20 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

maximizing existing recreation are objectives with potential 

for additional performance. Performance at the individual 

objective level or overall option level is affected by the 

assumed utility curves. For example, the utility for incurred 

damage (fig. 4D) drops off precipitously for incidences greater 

than 0; thus, there is very little tolerance for any occurrence of 

damages. There is high confidence that damage incidences will 

be low (less than or equal to 2 for the life of the project); however, the extreme utility (fig. 4D) penalizes performance even 

for a few such incidences. The 15-year Fast.Slow (P_15_FS) 

option earns the highest cumulative utility after 25 years in all 

four value weight scenarios and at all levels of uncertainty, but 

the rank of the other options, and the difference between the 

P_15_FS option and the other options, vary across weighting 

scenarios (fig. 9). For each level of uncertainty in fig. 9, the 

corresponding confidence limits represented worst-case and 

best-case values contingent on whether the objective was to 

be minimized or maximized. Varying the levels of uncertainty 

and the interval between worst- and best-case outcomes had 

small effect on the range of 25-year cumulative utilities compared to different value weighting scenarios. 

Weight

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

Hydrography

Ecological function/integrity

Adverse effects

Ecosystem services

Cost

Threatened and endangered species

Hydrography

Ecological function/integrity

Adverse effects

Ecosystem services

Cost

Threatened and endangered species

Hydrography

Ecological function/integrity

Adverse effects

Ecosystem services

Cost

Threatened and endangered species

Hydrography

Ecological function/integrity

Adverse effects

Ecosystem services

Cost

Threatened and endangered species

Balanced Equal Socioeconomic Ecological

Figure 5. The four weighting schemes applied to the fundamental objectives to evaluate outcomes. In a balanced scheme 

some ecological (hydrography) and some social (adverse effects) objectives are highly valued. In the equal scheme, all 

fundamental objectives are equally valued. In a socioeconomic scheme, the social and economic objectives are highly valued. 

In an ecological scheme, hydrography and ecological objectives are highly valued.
Prototype Decision Analysis and Results 21

3 4 2 1 5 7 6

Cumulative utility

T_5 T_15 T_25 FS_15 SF_15 GS Sed

16.0

16.5

17.0

17.5

Tide-gate policy option

Figure 6. Cumulative utility averaged across a range in prediction 

uncertainty and the four value-weighting schemes in figure 5 to 

compare seven tide-gate options in figure 3. The numbers inside 

each bar indicate the rank of each option. The average cumulative 

utility for all seven options after 25 years were within 1.5 utility 

points of one another. (T, threshold option for 5 (_5), 15 (_15), or 

25 (_25) years; FS, fast.slow 15-year option; SF, slow.fast 15-year 

option; GS, growing season; Sed, sediment) Rank (Lower is better)

T_5 T_15 T_25 FS_15 SF_15 GS Sed

Policy option

7

6

5

4

3

2

1

0.06

0

0.19

0.23

0.19

0.33

0

0

0

0.02

0.67

0.31

0

0

0

0

0

0.08

0.25

0.56

0.12

0

0

0

0

0

0.12

0.88

0.31

0.19

0.48

0.02

0

0

0

0.13

0.81

0.06

0

0

0

0

0.5

0

0.25

0

0.25

0

0

Figure 7. Frequencies of ranks based on cumulative utility after 

25 years for seven options (figure 3) across a range in prediction 

uncertainty and the four value-weighting schemes in figure 5. 

Frequencies greater than 0 up to the maximum are increasingly 

darker blue. (T, threshold option for 5 (_5), 15 (_15), or 25 (_25) 

years; FS, Fast.Slow 15-year option; SF, Slow.Fast 15-year option; 

GS, growing season; Sed, sediment)
22 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts Points short of maximum | Score range 

Range across options

30 MLW

MHW

Flooding extent

Flooding duration

Ponding

Deposition

Accretion

Salinity

Vegetation

pH

DO

Invertebrate

Fish

Damage

Gate risk

Risk elsewhere

Ammonium

Fecal

Sediment

Privacy

Visual field

Machine time

Woody veg

Smell

Conflict

Climate

Shellfish ac

Shellfish closed

Golf

Existing rec

New rec

Gate hours

Secondary cost

Monitoring hours

TE

20

10

0

10

20

30

Unmet potential, best option

HydrographyEcological function/integrityAdverse effectsEcosystem servicesCostT&E spp

Figure 8. Double-column chart used to evaluate how effectively the tide-gate options address all objectives. 

The upper (dark) columns report the spread in cumulative utility after 25 years between the highest and 

lowest ranking option for each objective. A taller column indicates a greater range among options, whereas 

a shorter column indicates all options were more similar. The lower (light) columns report how much utility 

was unrecovered by the best option. A shorter column indicates the objective was well addressed by the best 

option, and a taller column indicates even the best option did not completely address the objective. (MLW, 

mean low water; MHW, mean high water; DO, dissolved oxygen; Veg, vegetation; ac, acres; TE, T&E Spp, 

threatened and endangered species; rec, recreation)
Prototype Decision Analysis and Results 23

17

16

15

14

17.5

16.5

15.5

14.5

0.55 0.60 0.65 0.70 0.75 0.80

Uncertainty

Cumulative utility

A. Balanced

17

16

15

14

17.5

16.5

15.5

14.5

0.55 0.60 0.65 0.70 0.75 0.80

Uncertainty

Cumulative utility

B. Ecological

17

16

15

14

17.5

16.5

15.5

14.5

0.55 0.60 0.65 0.70 0.75 0.80

Uncertainty

Cumulative utility

C. Equal

17

16

15

14

17.5

16.5

15.5

14.5

0.55 0.60 0.65 0.70 0.75 0.80

Uncertainty

Cumulative utility

D. Socioeconomic

T_5

T_15

FS_15

T_25

SF_15

GS

Sed

EXPLANATION

Figure 9. Cumulative utility as a function of uncertainty formulated as the percentile for which confidence 

limits were computed for value weights: A, balanced, B, ecological, C, equal, and D, socioeconomic. For 

each level of uncertainty, the corresponding confidence limits represented worst-case and best-case values 

contingent on whether the objective was to be minimized or maximized. Varying the levels of uncertainty and the 

interval between worst- and best-case outcomes (x-axes) had a small effect on the range of 25-year cumulative 

utilities compared to different value weighting scenarios (panels). (T, threshold option for 5 (_5), 15 (_15), or 25 

(_25) years; FS_15, fast.slow 15-year option; SF_15, slow.fast 15-year option; GS, growing season; Sed, sediment) 
24 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Next Steps

The decision structure developed for the Herring River 

restoration is complex due to the multiple-stakeholder concerns 

and the importance of the estuary from hydrological, ecological, and socioeconomic perspectives. The tide-gate options are 

structured around restoring the tidal range, which is the ecological basis for restoration. Predicting outcomes is a continuing challenge because of the many and varied objectives. The 

decision structure represents a good-faith effort to include all 

stakeholder concerns and provide decision makers with a transparent approach to incorporate those concerns in comparisons 

of tide-gate options using the best-available science. 

Eventually, the decision structure can be simplified by 

removing objectives that are insensitive to decision choice or 

eliminating dominated alternatives from further consideration. 

However, at this point we do not want to simplify the problem 

for a couple reasons. First, there is a communication value in 

demonstrating that a comprehensive set of objectives is being 

considered, even though some objectives do not affect the 

decision choice. Second, the prediction methods are still being 

developed and improved; thus, the consequences are not finalized. It would be premature to simplify the problem, although 

eventually that is the aim.

Based on the prototype analyses, the 15-year Fast.Slow 

option (fig. 3) performed best among the policies analyzed. 

Secondary management actions could focus on addressing 

objectives not fully met, which can be identified using the 

double-column chart (fig. 8). Opportunities for improvement 

through secondary actions are related to sediment transport, 

damage, and existing recreation. The expected performance of 

the tide-gate option would need to account for updated information because the need for some secondary actions might not 

be foreseen. 

The management process will be implemented over the 

project’s finite time line (that is, less than 25 years before full 

gate opening). As restoration progresses, monitoring will be 

useful to identify additional areas where secondary actions 

are warranted. Also, periodic updating of predictive models 

and tradeoff analysis based on monitoring data can be used 

to determine whether adjustments in the selected option for 

tide-gate management are warranted as managers increase their 

understanding of system dynamics and the response to tidegate manipulations.

Collaborative processes require, at a minimum, a clear 

problem statement, institutional support, an issue that warrants 

significant investment of organizational resources, interdependence among parties to achieve good outcomes, and a zone of 

possible agreement. For a collaborative process to achieve success, the parties need a shared vision and trust in the process. It 

is important that stakeholders and decision makers be explicit 

and transparent about what they care about, engage in creative 

development of tide-gate options, and use best-available science to forecast outcomes.

The next steps are to progress beyond the preliminary 

predictions and to move predictions from first cut (Tier 1) to 

ideal method (Tier 3) wherever possible. Then the applications developed in R programming environment can be used 

to conduct the tradeoff and sensitivity analyses described and 

illustrated in this report to inform discussions within the technical and stakeholder committees and formulation of recommendations to the decision makers.

Summary

Ecological restoration typically involves a complex 

interaction of social, economic, and ecological considerations 

representing the mandate of resource stewards and the values 

of stakeholders. The success of ecological restoration can be 

determined by assessing whether tradeoffs among the multiple 

considerations and risks associated with uncertain outcomes 

are suitably evaluated and incorporated into decision making. 

Decision analysis was devised for evaluating tradeoffs and 

risks to inform management choices. In this report, the authors 

describe a decision analysis framework to evaluate the complex tradeoffs and risks associated with the restoration of the 

1,100-acre Herring River estuary within Cape Cod National 

Seashore in Massachusetts. The tide gates at the Chequessett 

Neck Road (CNR) dike at the mouth of the Herring River have 

severely restricted tidal exchange for more than 100 years and 

caused ecological degradation to the estuary. The degradation 

of the basin and the structural integrity of the dike have motivated resource managers to pursue restoration of the Herring 

River estuary. 

To develop the decision analysis framework, the authors worked with the Herring River Restoration Committee 

(HRRC) through a series of meetings with the full committee and a subgroup tasked with framework development. The 

HRRC represents the decision makers and stakeholders in the 

restoration process. Additional workshops with stakeholders, 

science experts, and regulators helped to elucidate underlying issues, incorporate concerns and interests into the framework, and resolve technical questions. The decision analysis 

for the Herring River restoration was structured according to 

six major components: (1) a clear statement of the problem, 

(2) comprehensive and measurable objectives, (3) a set of 

discrete tide-gate options, (4) a means to predict outcomes, (5) 

a process to evaluate the implications of these outcomes, and 

(6) a plan for implementation of the selected tide-gate option 

over time, including monitoring to provide feedback and to 

formally incorporate learning, reevaluate options, and possibly 

adapt management as restoration is implemented over time.

The decision framework is based on the understanding 

that representatives of Cape Cod National Seashore and the 

town of Wellfleet will be responsible for managing the new 

tide control gates at CNR, Mill Creek, and Pole Dike Creek 

and for implementing secondary management actions to 

achieve restoration goals. The goals are to restore the natural 

hydrography (that is, tidal range and marsh surface elevation) 

and ecological integrity of the Herring River estuary while 

minimizing adverse economic and social effects, maximizing 
References Cited 25

the estuary’s production of ecosystem services, and minimizing management costs. Objectives that fit under the project 

goals define comprehensive performance measures useful 

for predicting and monitoring the consequences of management actions.

The primary management actions are to adjust the volume of tidal flow through a series of to-be-constructed tide 

gates at CNR, Mill Creek, and Pole Dike Creek; the tide-gate 

adjustments can vary by the number, location, magnitude of 

opening, and flow direction of the individual tide-gate openings at any given time. The sequence of tide-gate adjustments 

over the years of restoration form the basis for the management options. In addition, tide-gate options include secondary 

management actions, such as management of flood-plain vegetation or restoration of connectivity, intended to accelerate the 

recovery of the estuarine habitat, enhance the benefits of tidal 

restoration achieved through tide-gate management alone, and 

reduce the potential adverse ecological and socioeconomic effects of restoring tidal flow. Over a planning horizon, decisions 

involve the rate at which newly constructed water-control 

structures allow tidal exchange, and the timing and location of 

implementing numerous secondary management actions.

Performance, in the terms of each objective, is predicted 

for each tide-gate option using a range of methods from quantitative physical process models to elicited expert judgment. 

A comparison of the relative predicted performance among 

options provides the basis for deciding how to manage the tide 

gates. Decisions will affect biophysical (for example, sediment 

transport, discharge of fecal coliform bacteria) and ecological (for example, vegetation response, fish passage, effects 

on shellfish) processes, as well as socioeconomic interests 

(for example, effects on property, viewscapes, recreation). 

The framework provides a structured approach for evaluating 

trade-offs among multiple objectives (ecological and social) 

while appropriately characterizing relevant uncertainties and 

accounting for levels of risk tolerances and the values of decision makers and stakeholders. 

In this project, an initial prototype decision analysis 

was conducted using a software application developed for 

evaluating tradeoffs and sensitivity of the decision to risk and 

uncertainty. The next near-term steps are to progress beyond 

the preliminary predictions, repeat the tradeoff and sensitivity analyses, and inform discussions within the technical and 

stakeholder committees who will formulate recommendations 

for the decision makers. 

The management process is intended to be implemented 

over a finite time line (anticipated to be less than 25 years before full gate opening). As the restoration progresses, monitoring of outcomes can be used to identify additional areas where 

secondary actions are needed. Also, monitoring data can be 

used to update predictions and periodically repeat the tradeoff 

analysis to determine whether adjustments in the selected tidegate management option are warranted as managers increase 

their understanding of system dynamics and the estuary’s 

response to tide-gate manipulations. 

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Appendix 1 27

Appendix 1. Conceptual Models

The description and purpose of the conceptual models 

are presented in this appendix. Five figures (figs 1.1 to 1.5) 

are included, one for each of the fundamental objectives: 

hydrography, ecosystem function, ecosystem services, adverse 

effects, and cost. In each figure, the fundamental objective 

is on the right-hand side of the diagram in a green hexagon. 

Subobjectives that are nested under each fundamental objective are shown to the left of the hexagon in green rectangles, 

with arrows pointing from the nested subobjectives to the 

fundamental objective. There may be multiple layers of nested 

subobjectives, depending on the objective. These, too, will be 

in green rectangles and have arrows from them pointing into 

the upper-level objective. Moving to the left on the diagram, 

things that affect or have influence on the lowest level objectives are shown in purple rectangles. There are arrows from 

the purple rectangles to the lowest-level objective. Continuing 

to move from right to left, things that affect or have influence 

on purple rectangles are also shown in purple rectangles, with 

arrows pointing to the purple rectangle it influences. There 

may be several influences depicted from right to left. Stochastic events or states are shown in red circles, again with an 

arrow pointing directly to the rectangle it affects. Decisions 

that are part of the decision-making process of the restoration are depicted in gray rectangles (that is, gate manipulations and secondary management actions). On the Minimize 

Adverse Effects diagram (fig. 1.3), black rectangles are shown. 

These are actions that can be taken but that are not part of the 

management aspect of the restoration. For example, the Structural Design of the dike will affect the safety of pedestrians, 

fishermen, and boaters; however, it is not part of the decisionmaking process of the restoration. Existing models that make 

predictions regarding the outcome of a given decision (gray 

rectangle) and a resulting state (purple or green rectangles) are 

shown in yellow diamonds. The yellow diamonds are placed 

on the arrow between two shapes: the shape to the left is the 

input to the model, whereas the shape the right is the output 

of the model. Yellow diamonds (that is, predictive models) 

may also be placed between two state rectangles; that is, 

the input to the model does not have to start with a decision 

node. The influence diagrams serve many purposes. They 

Restore 

Hydrography

Marsh surface 

sediment 

deposition

Tidal range

Hydroperiod

Sediment

net upstream flux

Flooding extent

Duration of

flooding

Tide gate 

number, size, 

frequency, timing

Marsh surface 

drainage

Low tide

High tide

Plant cover

Secondary 

mgmt

Weather

(normal v 

storm)

Below surface 

accretion

Marsh surface 

elevation

Channels

Storms

SLAMM

Sheet flow

EFDC

EFDC

MEM

MEM

Figure 1.1. Conceptual model for the hydrography objective. (EFDC, Environmental Flow Dynamics Code; MEM, Marsh 

Equilibrium Model; SLAMM, Sea Level Affecting Marsh Migration; mgmt, management) 
28 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

serve as depictions of conceptual models of how the system 

works regarding the objectives; the decisions we make and 

actions we take; and the effects that those actions have on the 

system, and ultimately, the objectives. The diagrams help to 

communicate our conceptual models. They help elucidate the 

areas where existing models predict outcomes of actions (for 

example, the Environmental Flow Dynamics Code [EFDC]) 

and where predictive models are absent and thus predictions 

are based on expert elicitation. The diagrams will also help 

to identify alternative courses of action, or strategies, whose 

predicted outcomes can be compared with respect to the objectives. The influence diagrams include only as much detail as is 

necessary and useful for understanding the system and making 

predictions of outcome with respect to the objectives (that is, 

the green rectangles and green hexagon).

Area

restored

Temp

EFDC

MEM

Temp

Channels

pH

DO

NH4

Flushing

Recreation

Appropriate

salinity gradient

Cover emergent

vegetation

Plant

composition

Primary

productivity

Benthic

community

Nekton

community

Substrate

conditions Velocity at

structures &

culverts

Surface-water 

quality

Habitat quality

estuarine

community

Maximize

ecosystem

function/

integrity

Connectivity

diadromous fish

Salination of acid

sulfate soil

Sediment 

disturbance

Plant

growth

rate

Marsh

surface

drainage

Porewater

Sslinity

Soil

chemistry

Water column

salinity

Flooding 

frequency & 

duration

Marsh surface

elevation

Sediment 

deposition

Below ground

matter

Fresh water

inputs

Distance 

from

harbor

Tide gates

number, size,

frequency

Secondary

mgmt

Figure 1.2. Conceptual model for the Ecosystem-Function objective. (EFDC, Environmental Flow Dynamics Code; MEM, Marsh 

Equilibrium Model; DO, dissolved oxygen; NH4, ammonium; mgmt, management; Temp, temperature) 
Appendix 1 29

Tide Gates

number, size,

frequency

Secondary

mgmt

Seasonal

heavy

rainfall

EFDC

Channels

Tidal

exchange/

flushing

Fish habitat

(extent/quality)

Marsh surface

drainage

Spring water

table Ponding depth,

residence time,

salinity, acidity

Natural mosquito

control

Mosquito

nuisance

Education/

communication

Education/

communication

Minimize

adverse

effects

Community

conflict

Public viewscapes

Appearance dead

woody vegetation

Smell

Privacy for

abutting

properties

Public

satisfaction

Secondary

mgmt

(timing & type)

Secondary

mgmt

Tide gate

timing & volume

of release

Tide gate

timing & volume

of release

Tide gate

timing & volume

of release

Tide gate

timing & volume

of release

Preemptive

measures

Structural

design

Planning

Surface drainage

Salination of acid

sulfate soils

Flushing frequency

Recreation

Private

property

Debris blockages

at structures

Dead

Fallen

Standing

Decomposing

plant material

Temp

Hypoxia (low

peat oxygen)

Political

incompatibility

Vegetation mgmt

Competing uses

Maxunyn water

surface elevation

Open/closed

areas

Weather

Hydrogen

sulfide

Abundance of

reactive iron

minerals

Vegetation

buffer

Recreation

Surface water

level

Elevation

Pedestrians,

fishers, boaters

Accidents

Road closures

Construction

Naturally

occurring

tides

Congestion and

detours

Emergency access

Control structures

Elsewhere Public safety

Effects on wells,

property, and

structures

Salination of acid

sulfate soils

Ammonium

Temp

Sediment export

from estuary

Grain particle size

Flow velocity

Flow direction

Algal bloom

Sediment

deposition on

shellfish beds

Flushing,

residence time

Animal

fecal inputs

Low DO

Smothering

Fecal coliform

Shellfish

mortality

Shellfish beds

(harbor)

EFDC

EFDC EFDC

EFDC

Figure 1.3. Conceptual model for the Minimize Adverse Effects objective. (EFDC, Environmental Flow Dynamics Code; Temp, 

temperature; DO, dissolved oxygen; mgmt, management; veg, vegetation) 
30 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Seasonal

heavy

rainfall

Tide gates—

number, size,

frequency

Secondary

management

Plant

growth

Temp

Temp

Natural

mosquito

control

Climate

change

mitigation

Pollution

control

Shellfishing

opportunities

Shellfishing

(above and

below)

Fish and

crustaceans

New

Existing

Recreational

opportunities

EFDC

Fish habitat

(extent and quality)

Spring

water table

Channels

Tidal exchange/

flushing

Marsh surface

drainage

Marsh surface

elevation

Plant

cover

Below-ground

organic matter

Storage

(carbon)

Flooding

frequency and

duration

High mean

tide

Marsh surface

drainage Oxygen

Nitrogen

Salinity

Decomposition

Rewetting

of chronically

drained peat

Denitrification

Tidal flow

Salination of

acid sulfate

soils

Fecal

coliform

Water

column

salinity

Water quality

NH4 Algal

bloom

Sediment

deposition

Low DO

Smothering

Mortality

Harvest

Habitat quality

estuarine

community

Abundance

Access

Bed closures

Abundance

Maximize

ecosystem

services

Ponding depth,

residence time,

salinity, acidity

Figure 1.4. Conceptual model for Ecosystem-Services objective. (DO, dissolved oxygen; EFDC, Environmental Flow Dynamics Code; 

mgmt, management; NH4, ammonium; Temp, temperature)
Appendix 1 31

Tide gates—

number, size,

frequency

Secondary

management

Minimize cost

Cost of tide-gate

operations

Time to reach

maximum

tide range

Cost of monitoring

Cost of secondary

management

Permits

Site

conditions

Community

conflict

Rare species

monitoring

requirements

Environmental

conditions

Figure 1.5. Conceptual model for Cost objective.
32 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Appendix 2. Summary of Meeting with Herring River Restoration Committee to 

Elicit Utility Curves

In this appendix we, the facilitators, summarize results of 

an elicitation exercise conducted with the Herring River Restoration Committee (HRRC). The purpose of the exercise was 

to explore stakeholders’ values and risk attitudes for a couple 

key objectives of the restoration project. Elicitation of values 

and risk attitudes is commonly used in decision science to help 

decision makers better understand the nature of tradeoffs and 

make a fully informed decision. This was chiefly a training exercise to verse the HRRC in this form of elicitation; the results 

we show below are not final.

The elicitation was conducted November 4–5, 2015, 

at the National Park Service headquarters during an HRRC 

monthly meeting. The methods are described, and the results 

are summarized chronologically. 

Facilitators: Dave Smith, Jill Gannon, Mitch Eaton (U.S. 

Geological Survey)

Wednesday, November 4, 2015: Elicitation with 

the HRRC

Introduction and Practice 

We introduced three different methods of elicitation: (1) 

setting up a gambling scenario (figs. 2.1 and 2.2), (2) bisection 

method, and (3) direct elicitation. All three methods, when 

followed, can result in a non-linear relation (that is, a curve), 

the shape of which describes the value a stakeholder assigns 

to each level of potential outcome, thus portraying how the 

person feels about risk (that is, risk averse, risk neutral, or 

risk seeking; fig. 2.3). We refer to this curve as a utility curve, 

where “utility” is the value or level of satisfaction a stakeholder feels regarding any potential outcome. All three methods 

have merit, and while theoretically each should produce the 

same relations, because of inherent idiosyncrasies of each 

method, they can result in different curves. We are seeking a 

method the committee understands and feels comfortable with. 

After reviewing the three different methods, the committee 

unanimously agreed that they preferred the first method—the 

gambling scenario. Given this agreement, we approached 

the elicitation exercise the following morning using only the 

first method.

In figure 2.1, you have a choice of either (1) being given 

$100 without risk (“sure thing”) or (2) entering a gamble 

where you might win $200 but risk getting nothing ($0). The 

odds, or probability (p), of this gamble are unspecified. The 

question that needs answering is: What probability of winning the gamble and receiving $200 (that is, the value of x) is 

needed for you to feel indifferent about the choice before you? 

$100

$0

$200

Chance

WIN

LOSE

p = x

p = 1– x

SURE THING

GAMBLE

Choose an

option

e-Value = [$200 × (x)] + [$0 × (1 – x)]

e-Value = $200

Figure 2.1. An introductory example 

of a gambling scenario. 

For example, a value of x = 0.5 means that there is a 50-percent chance you will get $200 and a 50-percent chance you 

will get $0. Thus, the expected value (e-value) of that gamble, 

if repeated many times, would be $100, which is equivalent to 

the expected pay off of choosing the “sure thing” as opposed 

to the gamble. A person who feels indifferent about the choice 

with a probability of 0.5 of winning the gamble would be 

considered risk neutral (fig. 2.3). Of course, this choice is not a 

repeated choice; it is a one-time offer where, if you choose the 

gamble, you will either receive $200 or $0. A risk-adverse individual would require the probability of winning the gamble 

to be higher than 0.5 before that individual would be willing 

to choose the gamble over the sure thing (fig. 2.3). Alternatively, a risk-seeking individual would enter the gamble for the 

chance of winning $200 over taking the sure thing when the 

probability of winning the gamble is less than 0.5 (fig. 2.3). 

In figure 2.3, the x-axis is the dollar amount received. 

The y-axis is the utility, or level of satisfaction, received from 

a specified dollar amount in the given scenario. A minimum of 

three points is needed to plot the utility curve. We automatically set the worst-case scenario (that is, entering the gamble 

and losing) to a utility of 0 and the best-case scenario (that is, 

entering the gamble and winning) to a utility of 1. The elicited 

preference probability is the utility for the third scenario 

(that is, choosing the sure thing). A risk-neutral person would 

require the probability of the winning the gamble to be 0.5 before that person felt indifferent between the choice of entering 

the gamble or taking the sure thing (because in this example 

the amount of the sure thing is the same as the expected value 

of the gamble). The risk-adverse curve shows a person that required the probability of winning the gamble to be greater than 

0.5 (0.875 in this example) before being willing to choose the 
Appendix 2 33

Figure 2.2. The gambling scenario set up for the practice elicitation. This was set up in a spreadsheet so that changing the 

preference probability in the yellow highlighted cell changed the graphs to visually see the effect on the utility curve.

0

0.25

0.50

0.75

1.00

0 50 100 150 200

Value, in dollars

Utility

Risk averse

Risk neutral

Risk seeking

Figure 2.3. Example utility curves resulting from three 

different responses to the gambling question in figure 2.1. 

gamble over the sure thing. The risk-seeking curve shows a 

person that would need the probability of winning the gamble 

to be less than 0.5 (0.125 in this example) before being willing to choose the gamble over the sure thing. Another way of 

looking at these curves is by focusing on the utility. The linear 

curve of the risk-neutral person reveals that this person gains 

equal satisfaction from each dollar won, no matter if that is an 

increase from $10 to $15 or an increase from $75 to $80. In 

comparison, the risk-adverse person is unhappy with the idea 

of receiving less than the amount from the sure thing and thus 

their satisfaction falls steeply below this value. The person is 

more concerned with the possibility of loss than with the potential for gains above this amount, reflected in the relatively 

flat curve between $100 and $200. The risk-seeking person is 

more willing to risk losing (for example, ending up with $0) 

for the chance to win an amount larger than the sure thing; this 

person’s needs are not met by the amount offered by the sure 

thing, and therefore, the person assigns low value to each dollar gained when the dollar amount is below this point (see the 

relatively flat curve between $0 and $100) and higher value to 

each dollar gained when the dollar amount is above this point 

(steep curve between $100 and $200). 
34 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Thursday, November 5, 2015: Elicitation with the 

HRRC

As stated earlier, this was chiefly a training exercise to 

verse the HRRC in this form of elicitation; the results shown 

below are not final. 

The Elicitation

Following the same format as the practice example, we 

posed questions to the group regarding time to reach different 

levels of restoration. First, we discussed the problem to make 

sure everyone had a common understanding and the same 

assumptions. We defined the level restored by the percent area 

inundated by spring tides. We focused on the five subbasins 

affected by the Chequessett Neck Road structure: lower Herring River, mid-Herring River, lower Pole Dike Creek, Bound 

Brook, and upper Herring River. Given this spatial area of 

focus, the maximum acreage that could possibly be restored 

is 800 acres. Quality of restoration was assumed to reach 

a minimal standard; that is, an area was simply considered 

restored (that is, inundated by spring tides) or not restored (not 

inundated by spring tides). Cost of management actions was 

removed from consideration by assuming $30–$60 million had 

been spent. 

We posed a gambling scenario for three different levels of 

restoration (25, 50, 75 percent) at three different time horizons 

(5 years, 15 years, 25 years) for a total of nine questions. We 

started by setting the time horizon to 5 years and setting the 

gambling scenario for 25 percent restored (fig. 2.4A). This 

is the same set up we practiced on Wednesday (fig. 1), but 

instead of money, we focused on percent restoration. The scenario is as follows: You have a choice of either (1) achieving 

25-percent restoration (that is, 200 acres) or (2) entering a 

gamble where you might achieve 100-percent restoration (that 

is, all 800 acres) or you might achieve 0-percent restoration 

(that is, 0 acres). The question posed is, What probability of 

winning the gamble do you require in order to choose the gamble over the sure thing? We asked the same question, again 

given the same 5-year time horizon, but this time setting the 

“sure thing” to 50 percent (400 acres) restored (fig. 2.4B). We 

asked the question a third time, for the same 5-year time horizon, but for the “sure thing” of 75-percent (600 acres) restored 

(fig. 2.4C). We worked to ensure that everyone understood the 

question, posed the three questions to the full group of participants, and allowed the group about 5 minutes to jot down their 

individual answers on a piece of paper. We then went around 

the room, to each participant one by one, and asked them to 

provide their three preference probabilities. We typed the three 

probabilities into a spreadsheet (fig. 2.5), which was projected 

for the group to see; the spreadsheet was set up to show the 

shape of the curve that resulted from a single respondent’s 

three probabilities. As a group, we discussed each response. 

The respondent provided his/her rationale and thought process 

behind his/her choices, and the group provided feedback. We 

continued the process until we recorded the three probabilities from each of the 11 respondents. As a result of the group 

discussion, some respondents modified their answers. Changing of a response occurred for various reasons, some of which 

included (1) gaining a clearer understanding of probability, (2) 

gaining a better understanding of how the shape of the curve 

captures their risk tolerance, and (3) perceiving the situation 

differently after hearing and agreeing or disagreeing with 

another respondent’s rationale. We then repeated the process, 

asking for three probabilities for the three different levels of 

restoration but given the time horizon of 15 years. Lastly, 

25%

(200 acres)

0%

(0 acres)

100%

(800 acres)

Chance

WIN

LOSE

p = x

p = 1– x

SURE THING

GAMBLE

50%

(400 acres)

0%

(0 acres)

100%

(800 acres)

Chance

WIN

LOSE

p = x

p = 1– x

SURE THING

GAMBLE

75%

(600 acres)

0%

(0 acres)

100%

(800 acres)

Chance

WIN

LOSE

p = x

p = 1– x

SURE THING

GAMBLE

Choose an

option

Choose an

option

Choose an

option

A B C

Figure 2.4. The three restoration gambling scenarios. A, You have a choice of either (1) achieving 25-percent (200 acres) 

restoration or (2) entering a gamble where you might achieve 100-percent (800 acres) restoration or you might achieve 

0-percent (0 acre) restoration. The respondent sets the preference probability as in the practice example. B, Same 

question but the sure thing is 50-percent (400 acres) restoration. C, Same question but the sure thing is 75-percent (600 

acres) restoration. (ac, acres; %, percent; p, probability)
Appendix 2 35

Figure 2.5. The restoration gambling scenarios shown to the respondents during the elicitation exercise. (ac, acres; %, percent)

we repeated the process under the scenario of a 25-year time 

horizon. After going through the process three different times, 

some respondents went back and modified earlier responses 

they had provided for different time horizons. These changes 

typically had to do with assessing their risk tolerance and how 

they perceived it changing, given their greater understanding 

of the different time horizons and how they felt about the level 

of restoration achieved at each of these time horizons. We did 

not capture the range of changes that a respondent provided; 

we captured only the final response per respondent. 

In figure 2.5, the screen capture shows the response of a 

single respondent for the 5-year time horizon and the three different levels of restoration: 25, 50, and 75 percent. The worst 

case scenario (that is, entering the gamble and losing) is automatically set to a utility of 0, whereas the best case scenario 

(that is, entering the gamble and winning) is automatically set 

to a utility of 1. The elicited preference probabilities (shown 

in the highlighted cells) are the utility values for each level of 

restoration, which are also plotted in the utility curve. This is 

an example of a risk-adverse utility curve. 
36 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Results of the Elicitation

Responses of participants are shown in table 2.1 and 

figures 2.6–2.9. 

In figure 2.6, all respondents show risk aversion at this 

time horizon; that is, the preference probability has to be 

quite high (greater than 75% percent) for a 25-percent level of 

restoration. Stated another way, at 5 years into the restoration 

effort, people would be 75 percent satisfied with having had 

achieved a 25-percent level of restoration. 

In figure 2.7, at a 15-year time horizon, respondents feel 

differently about risk (that is, differently than each other and 

differently than they, themselves, felt at the earlier time horizon); three respondents remain risk adverse, whereas the other 

respondents are more risk neutral, and a couple are tending 

toward risk seeking. 

In figure 2.8, at a 25-year time horizon, a couple of 

respondents are risk adverse, but most respondents have 

shifted to a risk neutral or more risk-seeking behavior. The 

curves of the risk-seeking respondents reveal dissatisfaction 

Table 2.1. Responses provided for the nine elicitation questions.

[%, percent]

Respondent

Time horizon

5 Years 15 Years 25 Years

Percent restored

25% 50% 75% 25% 50% 75% 25% 50% 75%

A 0.75 0.85 0.95 0.1 0.7 0.9 0.05 0.5 0.95

B 0.9 1 1 0.25 0.4 0.8 0.05 0.5 0.95

C 0.8 0.95 0.99 0.25 0.4 0.8 0.1 0.3 0.6

D 0.85 0.95 0.99 0.15 0.6 0.9 0.2 0.95 1

E 0.75 0.85 0.95 0.15 0.6 0.9 0.2 0.6 0.9

F 0.95 1 1 0.8 0.9 0.95 0.2 0.5 0.9

G 0.85 0.85 0.95 0.1 0.5 0.8 0.1 0.4 0.8

H 0.95 1 1 0.7 0.9 1 0.6 0.8 1

I 0.75 0.9 0.98 0.2 0.5 0.95 0.15 0.65 1

J 0.75 0.85 0.95 0.75 0.85 0.95 0.8 0.8 1

K 0.75 0.8 0.95 0.25 0.75 0.8 0.1 0.65 0.95

1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

B

C

D

F

G

H

I

J

K

A E

Respondent identifier

EXPLANATION

Figure 2.6. Responses of all 11 respondents for the first three questions regarding level of restoration achieved (25, 

50, and 75 percent) given a 5-year time horizon. 
Appendix 2 37

1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

B

C

D

F

G

H

I

J

K

A E

Respondent identifier

EXPLANATION

Figure 2.7. Responses of all 11 respondents for the second trio of questions regarding level of restoration achieved 

(25, 50, and 75 percent) given a 15-year time horizon. 

1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

B

C

D

F

G

H

I

J

K

A E

Respondent identifier

EXPLANATION

Figure 2.8. Responses of all 11 respondents for the third trio of questions regarding level of restoration achieved (25, 

50, and 75 percent) given a 25-year time horizon. 
38 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

with having achieved only 25-percent restoration at 25 years 

into the restoration effort. These respondents are so unhappy 

with this level of restoration, that they would be willing to 

gamble at a chance to achieve increased success at very low 

odds (ranging from 5:1 to 20:1 against). Stated another way, at 

25 years into the restoration effort, most respondents are only 

marginally happier with 200 acres restored than they are with 

0 acres restored.

In figure 2.9, all but two of the respondents shift from 

a risk-adverse behavior toward a risk-neutral or more riskseeking behavior from the 5-year to the 25-year time-horizon. 

Two of the respondents remain risk adverse at all three time 

horizons. For the two individuals who are risk adverse at all 

three time horizons, they would rather have something than 

risk having nothing, even after 25 years of working towards 

achieving restoration. The remaining respondents show that 

as the time horizon extends, their expectations of restoration 

levels achieved rise, such that they are dissatisfied with a low 

level of restoration. For most of these respondents, however, 

even at a 25-year time horizon, the risk-seeking behavior is 

confined to the lower levels of restoration (25 percent) and 

switches from risk neutral to risk adverse at higher levels 

of restoration.

Time horizon

 5 year

 15 year

 25 year

EXPLANATION

1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

Response A 1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

Response B 1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

Response C

1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

Response D 1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

Response E 1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

Response F

1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

Response G 1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

Response H 1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

Response I

1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

Response J 1

0.75

0.50

0.25

0

0 25 50 75 100

Percent restored

Utility

Response K

Figure 2.9. Responses to each of the three trios of questions per respondent. 
Appendix 2 39

How this Type of Information Will be Used?

The process would be to elicit this type of information for 

the restoration objectives that would be traded off each other. 

To follow through with this process, we would need to know 

the performance measure, unit, and the full potential range of 

each objective from its lowest to highest performance value. 

We would elicit utility from the decision makers. Depending 

on the objective, it may be appropriate to elicit this information from a stakeholder group. Elicited curves from each 

individual will be kept separate and, if desired, anonymous; 

we will use the range of the elicited values to explore the 

sensitivity of the decision to the differences expressed by each 

individual. A decision is said to be “sensitive” to the differences if one alternative option would be recommended as “best” 

if one utility curve was used, but a different alternative option 

would be “best” if another curve was used. If the decision is 

not sensitive to the differences (that is, the same alternative 

option would be recommended regardless of the different 

curves), then we can decide whether and how to combine the 

responses across individuals for a single objective. If the decision is sensitive to the differences, then some form of negotiation would have to take place to select among the identified 

alternative policies that are in contention.

Values from these curves, which we refer to as “utility,” 

will be used in the consequence table in place of the actual 

predicted outcomes (that is, they represent the “true value” 

of any particular outcome). Imagine a two-step process. In 

the first step, we populate a consequence table with the raw 

predicted values of the outcomes of each objective, in terms 

of its performance measure, for each alternative action/decision that is under consideration. In the second step, we convert 

the raw predicted values into their respective utility, based on 

the curves we elicited. In doing so, the consequence table will 

be capturing two aspects: (1) the prediction, which is based 

on the best available science and (2) values, which are based 

on how decision makers/stakeholders feel about the predicted outcomes. 

Why do we want to use “utility” as opposed to 

the raw predictions in the consequence table? 

Often, our feelings about outcomes are not linear; that is, 

we do not feel the same about an x unit increase in an objective across the full range of the potential outcomes of that 

objective. For example, if the objective is to minimize cost, 

the decision makers may not care that much about a difference in cost of $10 million among alternative actions if one 

decision costs $5 million and the other costs $15 million; 

however, decision makers might feel quite differently about 

the same $10 million difference between alternative actions if 

the costs of the two options were $60 million and $70 million 

(fig. 2.10). When assessing performance of alternative actions 

across an objective, what matters is how the decision maker 

feels about the predicted outcome, not the predicted outcome 

itself. This is part of value-focused decision making; we focus 

on what we care about (objectives), and we focus on the 

level of satisfaction with the predicted outcomes (utility) for 

these objectives. 

How does all the information come together to 

help us identify the decision that performs best 

across the project objectives? 

Imagine a consequence table that is populated with the 

predicted outcomes for all objectives across each of the decision alternatives under consideration. Also, imagine we have 

the utility curves for each of the objectives. We then determine 

the utility of the predicted outcomes of each objective across 

each decision alternative. We then sum the utility values across 

all objectives for each decision alternative. Another step, the 

process of which is not described here, is weighting of the different objectives (stated simply, not all objectives are valued 

equally). The weights for the different objectives will result in 

a weighted sum of the utilities for each decision alternative. 

We compare the weighted sum of utilities for each decision 

alternative; the alternative with the highest weighted sum is 

the alternative that performs best across the objectives. Below 

is a contrived example of the generic description above; to 

keep it simple, the example considers three objectives and two 

decision alternatives.

1

0.75

0.50

0.25

0

0 10 20 30 40 50 60 70 80 90 100

Millions of dollars

Utility

Cost

Figure 2.10. Example non-linear utility curve for cost. In 

this scenario, the decision maker has high satisfaction with 

spending $0–30 million; however, the level of satisfaction 

decreases quickly with spending beyond $30 million, declining 

to 0 at the point of $80 million.
40 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Step 1. Elicit utility curves for the three objectives.

1

0.75

0.50

0.25

0

0 100 200 300 400 500 600 700 800

Acres restored

Utility

Restoration

1

0.75

0.50

0.25

0

100 90 80 70 60 50 40 30 20 10 0

Percent decrease in volume harvested

Utility

Shellfish

1

0.75

0.50

0.25

0

0 10 20 30 40 50 60 70 80 90 100

Millions of dollars

Utility

Cost

Step 2. Populate the consequence table with the raw predicted outcomes.

Objectives Unit Direction Decision 1 Decision 2

Restoration Acres restored Maximize 600 500

Shellfish Percent decrease in volume harvested Minimize 40 10

Cost Millions of dollars Minimize 50 65
Appendix 2 41

Step 3. Determine the utility associated with each predicted outcome. 

1

0.75

0.50

0.25

0

0 100 200 300 400 500 600 700 800

Acres restored

Utility

Restoration

1

0.75

0.50

0.25

0

100 90 80 70 60 50 40 30 20 10 0

Percent decrease in volume harvested

Utility

Shellfish

1

0.75

0.50

0.25

0

0 10 20 30 40 50 60 70 80 90 100

Millions of dollars

Utility

Cost

Predicted outcome and utility

 Decision 1

 Decision 2

EXPLANATION

Step 4. Populate the consequence table with the utilities from the elicited curves. 

Because we are now using utilities as opposed to the raw predictions, we want to maximize utility in all cases. Specifically, 

though we wish to minimize the percent decrease in the volume of shellfish harvested and minimize the cost, we wish to maximize the utility for these objectives.

Objectives Unit Direction Decision 1 Decision 2

Restoration Acres restored Maximize 0.8 0.6

Shellfish Percent decrease in volume harvested Minimize (unit)

Maximize (utility) .025 0.5

Cost Millions of dollars Minimize (unit)

Maximize (utility) 0.6 0.25
42 A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts

Step 5. Calculate a weighted sum of utilities across objectives for each alternative decision.

U1 = wr(ur1) + ws(us1) + wc(uc1)

U2 = wr(ur2) + ws(us2) + wc(uc2)

where

U = sum of utilities across all objectives,

u = utility of individual objectives,

w = weight on the objective,

r = restoration objective,

s = shellfish objective, and

c = cost objective.

Subscripts 1 and 2 are for decision alternatives 1 and 2.

Assuming equal weight for each of the three objectives, the 

calculation for this example would be as follows:

U1 = (0.8) + (0.025) + (0.6) = 0.475 and

U2 = (0.6) + (0.5) + (0.25) = 0.45.

U1 is greater than U2; therefore, Decision 1 performs best 

across the objectives.

Given everyone agreed with the input, the recommendation would be to go with decision alternative 1. Recall, 

the input to arrive at this weighted utility score includes the 

following pieces: (1) choice of objectives, including their 

performance measures; (2) elicitation of utility curves for each 

objective; (3) creation of alternative decisions under consideration; (4) predicted outcomes of each alternative with respect 

to each objective; and (5) weights on each objective. Changes 

to any one of these inputs may result in a different decision 

outcome. In an additional analysis, we can explore the sensitivity of the decision to uncertainty or disagreement regarding 

the utility curves, the predicted outcomes, and the weights on 

the objectives. We can only evaluate the objectives and the 

alternatives that have been developed for consideration; thus, 

it is important that these have been fully vetted beforehand. 

Insights from the Elicitation Exercise

1. Set up matters. Though we spent a fair amount of time 

preparing the elicitation, including choice of objectives 

on which to focus, the spatial scale, the range of potential 

outcomes for the objectives, and the methods of elicitation, once the group convened, discussion regarding these 

choices was essential and affected the procedure. 

2. You can never be too clear. Though we knew that it is 

imperative for everyone to have a common understanding of the assumptions, the process, and the questions, 

despite taking precautions to ensure everyone was on the 

same page, different interpretations cropped up. Thus, it is 

important to be vigilant, in communicating and in listening, to identify potential different interpretations of the 

question that could bias the results.

3. How questions are phrased has potential to introduce bias. 

For example, the primer on Wednesday evoked quite a 

different response from participants depending on how it 

was phrased. If the question was phrased as “You just won 

$100; now you have a choice to keep it or enter a gamble 

where you can either double it or lose it all,” it was 

perceived very differently than if phrased as, “You have 

$100 in your pocket that is your existing, earned money; 

you have a choice to keep your money or enter a gamble 

where you can double it or lose it all.” The distinction 

regarding whether the $100 had been won (that is, essentially free money) versus earned made a big difference in 

participants risk tolerances. It is critical that we are aware 

of these types of biases when phrasing future elicitations 

regarding project objectives. 

4. The shape of participants’ curves may differ because of 

who the person represents. For example, one participant 

explained that he was answering the questions as a representative of the townspeople. He expressed that 25-percent restoration achieved at 25 years into the restoration 

effort would be completely unacceptable to the townspeople; as such, he was willing to risk obtaining 25-percent 

restoration for a small chance at achieving a much higher 

success. 

5. There is a balance between the number of questions we 

ask and the quality of the information we receive. Too 

many questions will quickly lead to fatigue in the participants. Too few questions may not provide the detail 

of information we require. For example, it took about 2 

hours for us to complete the nine questions for the one 

objective with the group. Even so, it was noted by a participant that we needed finer discretization of the percent 

restored to determine more accurately the inflexion point 

of the curves. Finer discretization of either component 

(that is, percent restored or years of restoration effort) 

quickly increases the number of questions we must ask. 

We will always need to keep this balance in mind when 

we develop elicitations in the future for all the objectives.
For additional information, contact:

Director, Leetown Science Center

U.S. Geological Survey

11649 Leetown Road

Kearneysville, WV 25430

or visit our website at: 

https://www.usgs.gov/centers/lsc

Publishing support provided by the 

West Trenton Publishing Service Center
Smith and others—A Decision Framework to Analyze Tide-Gate Options for Restoration of the Herring River Estuary, Massachusetts—Open-File Report 2019–1115

ISSN 2331-1258 (online)

https://doi.org/10.3133/ofr20191115