x>EPA
United States
Environmental Protection
Agency
EPA/600/R-15/058 | September 2015
www.epa.gov/ord
WATERSHED MANAGEMENT OPTIMIZATION
SUPPORTTOOL (WMOST) v2
Theoretical Documentation
Office of Research and Development
National Health and Environmental Effects Research Laboratory"
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EPA 600/R-15/058| September 2015
www.epa.gov
Watershed Management Optimization
Support Tool (WMOST) v2
Theoretical Documentation
EPA Project Team
Naomi Detenbeck and Marilyn ten Brink
NHEERL, Atlantic Ecology Division
Narragansett, RI 02882
Alisa Morrison
Student Services Contractor at ORD, NHEERL,
Atlantic Ecology Division
Narragansett, RI 02882
Ralph Abele, Jackie LeClair, and Trish Garrigan
Region 1
Boston, MA 02109
Abt Associates Project Team
Viktoria Zoltay, Annie Brown, Brendan Small, and Isabelle Morin, Abt Associates, Inc.
Cambridge, MA 02138
National Health and Environmental Effects Research laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Washington, DC 20460
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WMOST v2 Theoretical Documentation
The development of the tool described in this document has been funded by the U.S. Environmental
Protection Agency (EPA), in part by EPA's Green Infrastructure Initiative, under EPA Contract No.
EP-C-13-039/Work Assignment 07 to Abt Associates, he. Version 2 of WMOST was supported through
funding to an EPA Region 1 RARE project. Versions 1 and 2 of this document have been subjected to the
Agency's peer and administrative review and has been approved for publication. Mention of trade
names or commercial products does not constitute endorsement or recommendation for use.
Although a reasonable effort has been made to assure that the results obtained are correct, the
computer programs described in this manual are experimental. Therefore, the author and the
U.S. Environmental Protection Agency are not responsible and assume no liability whatsoever for any
results or any use made of the results obtained from these programs, nor for any damages or litigation
that result from the use of these programs for any purpose.
Abstract
The Watershed Management Optimization Support Tool (WMOST) is a decision support tool that
facilitates integrated water management at the local or small watershed scale. WMOST models the
environmental effects and costs of management decisions in a watershed context that is, accounting
for the direct and indirect effects of decisions. The model considers water flows and does not consider
water quality. It is spatially lumped with options for a daily or monthly modeling time step. The
optimization of management options is solved using linear programming. WMOST is intended to be a
screening tool used as part of an integrated watershed management process such as that described in
EPA's watershed planning handbook (EPA 2008). WMOST serves as a public-domain, efficient, and
user-friendly tool for local water resources managers and planners to screen a wide range of potential
water resources management options across their jurisdiction for cost-effectiveness and
environmental and economic sustainability (Zoltay et al., 2010). Practices that can be evaluated
include projects related to stormwater, water supply, wastewater, and land resources such as low-
impact development (LID) and land conservation. WMOST can aid in evaluating LID and green
infrastructure as alternative or complementary management options in projects proposed for State
Revolving Funds (SRF). In addition, the tool can enable assessing the trade-offs and co-benefits of
various practices. In WMOST v2, the Baseline Hydrology and Stormwater Hydrology modules assist
users with input data acquisition and pre-processing. The Flood module allows the consideration of
flood damages and their reduction in assessing the cost-effectiveness of management practices. The
target user group for WMOST consists of local water resources managers, including municipal water
works superintendents and their consultants.
Keywords: Integrated watershed management, water resources, decision support, optimization, green
infrastructure
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Preface
Integrated Water Resources Management (IWRM) has been endorsed for use at multiple scales. The
Global Water Partnership defines IWRM as "a process which promotes the coordinated development
and management of water, land, and related resources, in order to maximize the resultant economic
and social welfare in an equitable manner without compromising the sustainability of vital
ecosystems"1. IWRM has been promoted as an integral part of the "Water Utility of the Future"2
in the United States. The American Water Resources Association (AWRA) has issued a position
statement calling for implementation of IWRM across the United States and committed the AWRA
to help strengthen and refine IWRM concepts.3 The U.S. Environmental Protection Agency (EPA)
has also endorsed the concept of IWRM, focusing on coordinated implementation of stormwater and
wastewater management.4
Several states and river basin commissions have started to implement IWRM.5 Even in EPA Region 1
(New England) where water is relatively plentiful, states face the challenge of developing balanced
approaches for equitable and predictable distribution of water resources to meet both human and
aquatic life needs during seasonal low flow periods and droughts. For example, the Commonwealth
of Massachusetts amended the Water Management Act (WMA) regulations6 in 2014 to update the
way water is allocated to meet the many and sometimes competing needs of communities and aquatic
ecosystems.
Stormwater and land use management are two aspects of IWRM which include practices such as
green infrastructure (GI, both natural GI and constructed stormwater best management practices
[BMPs]), low-impact development (LID) and land conservation. In recent years, the EPA SRF
funding guidelines have been broadened to include support for GI at local scales-e.g., stormwater
BMPs to reduce runoff and increase infiltration-and watershed scales-e.g., conservation planning
for source water protection. Despite this development, few applicants have taken advantage of these
opportunities to try nontraditional approaches to water quality improvement.7 In a few notable cases,
local managers have evaluated the relative cost and benefit of preserving GI compared to traditional
1 UNEP-DHI Centre for Water and Environment. 2009. Integrated Water Resources Management in Action.
WWAP, DFfl Water Policy, UNEP-DHI Centre for Water and Environment.
2 NACWA, WERF, and WEF. 2013. The Water Resources Utility of the Future: A Blueprint for Action. National
Association of Clean Water Agencies (NACWA), Water Environment Research Foundation (WERF) and Water
Environment Federation (WEF), Washington, B.C.
3 http://www.awra.org/policy/policy-statements-water-vision.html
4 Nancy Stoner memo: http://water.epa.gov/infrastructure/greeninfrastructure/upload/memointegratedmunicipalplans.pdf
5 AWRA. 2012. Case Studies in Integrated Water Resources Management: From Local Stewardship to National Vision.
American Water Resources Association Policy Committee, Middleburg, VA.
6 For more information on the WMA, see http://www.mass.gov/eea/agencies/massdep/water/watersheds/water-management-
act-program.html
7 American Rivers. 2010. Putting Green to Work: Economic Recovery Investments for Clean and Reliable Water. American
Rivers, Washington, D.C
ill
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WMOST v2
approaches. In those cases, the managers have championed the use of GI as part of a sustainable
solution for IWRM but these examples are rare.8
Beginning with the American Recovery and Reinvestment Act (ARRA) and continued with 2010
Appropriations language, Congress mandated a 20% set-aside of SRF funding for a "Green Project
Reserve (GPR)", which includes GI and land conservation measures as eligible projects in meeting
water quality goals. The utilization of the GPR for GI projects has been relatively limited, and
responses have varied widely across states. According to a survey of 19 state allocations of Green
Project Reserve funds, only 18% of funds were dedicated to GI projects, and none of these projects
were categorized as conservation planning to promote source water protection.8 The state of Virginia
passed regulations banning the use of ARRA funds for GI projects until after wastewater treatment
projects had been funded.8 In New England, states exceeded the 20% GPR mandate and used 30%
of their ARRA funds for the GPR but directed most of the funds (76%) to energy efficiency and
renewables; other uses of ARRA funds included 12% for water efficiency, 9% for GI, and 3% for
environmentally innovative projects.
In order to assist communities in the evaluation of GI, LID, and land conservation practices as part
of an IWRM approach, EPA's Office of Research and Development, in partnership with EPA's
Region 1, supported the development of Version 1 of the Watershed Management Optimization
Support Tool (WMOST). Version 2 of WMOST has been developed with support from a RARE grant
to EPA Region 1 and ORD collaborators, supplemented with funding from US EPA ORD's Green
Infrastructure Initiative research program. Enhancements to WMOST Version 2 include Baseline
Hydrology and Stormwater Hydrology modules to facilitate populating WMOST with the necessary
hydrologic input data pre- and post- Stormwater BMP implementation and a Flood Damage module
to allow consideration of flood-related costs into the optimization analysis.
WMOST is based on a prior integrated watershed management optimization model that was created
to allow water resources managers to evaluate a broad range of technical, economic, and policy
management options within a watershed.9 This model includes evaluation of conservation options
for source water protection and infiltration of Stormwater on forest lands, GI Stormwater BMPs to
increase infiltration, and other water-related management options. The current version of WMOST
focuses on management options for water quantity endpoints. Additional functionality to address
water quality issues is one of the high priority enhancements identified for future versions.
Development of each version of the WMOST tool was overseen by an EPA Planning Team. Priorities
for update and refinement of the original model10 were established following review by a Technical
Advisory Group comprised of water resource managers and modelers. Case studies for two
communities were developed to illustrate the application of IWRM using WMOST vl. These case
studies (Upper Ipswich River and Danvers/Middleton, MA) are available from the WMOST website.
WMOST was presented to stakeholders in a workshop held at the EPA Region 1 Laboratory in
8 http://www.crwa.org/blue.html, http://v3.mmsd.com/greenseamsvideol.aspx
9 Zoltay, V.I. 2007. Integrated watershed management modeling: Optimal decision making for natural and human
components. M.S. Thesis, Tufts Univ., Medford, MA.; Zoltay, V.I., R.M. Vogel, P.H. Kirshen, and K.S. Westphal. 2010.
Integrated watershed management modeling: Generic optimization model applied to the Ipswich River Basin. Journal of
Water Resources Planning and Management.
IV
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Acknowledgements
Chelmsford, MA in April 2013, with a follow-up webinar on the Danvers/Middleton case study in
May 2013. Feedback from the Technical Advisory Group and workshop participants has been
incorporated into the user guide and theoretical documentation for WMOST.
The development of the Baseline Hydrology, Stormwater Hydrology, and Flood Damage modules
in WMOST v2 was assisted by a Technical Advisory Group with expertise in one or more of these
topics. Multiple meetings with stakeholders in the Monponsett Pond watershed (Halifax, MA) were
held to engage the community in a case study application of WMOST v2. Input from the TAG and
community members were incorporated in the final methodology for WMOST v2 and the modeling
case study.
Acknowledgements
WMOST builds on research funded by the National Science Foundation Graduate Research
Fellowship Program and published in "Integrated Watershed Management Modeling: Optimal
Decision Making for Natural and Human Components." Zoltay, V., Kirshen, P.H., Vogel, R.M.,
and Westphal, K.S. 2010. Journal of Water Resources Planning and Management, 136:5, 566-575.
EPA Project Team
Naomi Detenbeck10 and Marilyn ten Brink10, U.S. EPA ORD, NHEERL, Atlantic Ecology Division
Yusuf Mohamoud11, U.S. EPA ORD, NERL, Ecosystems Research Division
Alisa Morrison12, ORISE participant at U.S. EPA ORD, NHEERL, Atlantic Ecology Division
Ralph Abele10, Jackie LeClair,12 and Trish Garrigan12, U.S. EPA Region 1
Technical Advisory Group for WMOST vl
Alan Cathcart, Concord, MA Water/Sewer Division
Greg Krom, Topsfield, MA Water Department
Dave Sharpies, Somersworth, NH Planning and Community Development
Mark Clark, North Reading, MA Water Department
Peter Weiskel, U.S. Geological Survey, MA-RI Water Science Center
Kathy Baskin, Massachusetts Executive Office of Energy and Environmental Affairs
Steven Estes-Smargiassi, Massachusetts Water Resources Authority
Hale Thurston, U.S. EPA ORD, NRMRL, Sustainable Technology Division
Rosemary Monahan, U.S. EPA Region 1
Scott Horsley, Horsley Witten Group
Kirk Westphal, COM Smith
James Limbrunner, Hydrologies, Inc.
Jay Lund, University of California, Davis
10 Versions 1 and 2
11 Version 1
12 Version 2
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WMOST v2
Technical Advisory Group for WMOST v2
Bob Lent, U.S. Geological Survey
Darryl Davis and Chris Dunn, U.S. Army Corps of Engineers, Hydrologic Engineering Center
Matthew Bates, U.S. Army Corps of Engineers, Engineer Research and Development Center
Richard Zingarelli, Massachusetts Department of Conservation and Recreation
Steve Silva, former U.S. EPA and Taunton watershed stakeholder
Tom Johnson, U.S. EPA, ORD, Global Change Research Program
Marisa Mazzotta, U.S. EPA, ORD, NHERRL, Atlantic Ecology Division
Reviewers for WMOST vl
Theoretical Documentation
Marisa Mazzotta, U.S. EPA ORD, NHEERL, Atlantic Ecology Division
Mark Voorhees, U.S. EPA Region 1
Michael Tryby, U.S. EPA ORD, NERL, Ecosystems Research Division
WMOST Tool. User Guide and Case Studies
Daniel Campbell, U.S. EPA ORD, NHEERL, Atlantic Ecology Division
Alisa Richardson, Rhode Island Department of Environmental Management (partial review)
Alisa Morrison, Student Services Contractor at U.S. EPA ORD, NHEERL, Atlantic Ecology Division
Jason Berner, U.S. EPA OW, OST, Engineering Analysis Division
Reviewers for WMOST v2
Theoretical Documentation
Kristen Hychka, ORISE participant at U.S. EPA ORD, NHEERL, Atlantic Ecology Division
Mark Voorhees, U.S. EPA Region 1, Boston, MA
Thomas Johnson, U.S. EPA ORD, NCEA, Washington, D.C.
WMOST Tool. User Guide and Case Studies
Jason Berner, U.S. EPA OW, OST, Engineering Analysis Division
Yusuf Mohamoud, U.S. EPA ORD, NERL, Athens, GA
Steven Kraemer, U.S. EPA ORD, NERL, Athens, GA
Andrea Traviglia, U.S. EPA Region 1, Boston, MA
Previous Contributors
Yusuf Mohamoud, ORD, NERL, Ecosystems Research Division, Athens, GA 30605
Becky Wildner and Lauren Parker, Abt Associates, Inc.
Nigel Pickering, Horsley Witten Group under subcontract to Abt Associates Inc.
Richard M. Vogel, Tufts University under subcontract to Abt Associates Inc.
VI
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Table of Contents
Table of Contents
Abstract ii
Preface iii
Acknowledgements v
1. Background 1
1.1 Objective of the Tool 1
1.2 About this Document 1
1.3 Overview 3
2. Objective Function and Linear Programming 7
2.1 Objective Function 8
2.1.1 Costs 8
2.1.2 Revenue 17
2.2 Constraints 19
2.2.1 Continuity Equations 19
2.2.2 Physical Limits on Watershed Components 25
2.2.3 Constraints Associated with Management Options 26
3. Baseline Hydrology Module 31
3.1 Hydrology Time Series Database 32
3.2 HRU Characteristics Database 37
4. Stormwater Hydrology Module 39
4.1 BMP Selection and Sizing 39
4.2 Linking with SUSTAIN 42
5. Flood-Damage Module 45
5.1 Considerations forthe Flood-Damage Module 45
5.2 Integrating Flood-Damages in WMOST Optimization 46
6. Internal Configuration 49
7. Summary of Input Data 51
8. References 55
VII
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WMOST v2 Theoretical Documentation
Figures
Appendix A- User Support 57
A.I User Error Checks 57
A.2 User Manual, Case Studies and Default Data 57
Appendix B - SUSTAIN Input Cards 58
Appendix C - Future Development 68
C.I Model Components and Functionality 68
C.2 User Interface and User Support 70
Figure 1-1. WMOST Components and Interactions with External Databases or Models 2
Figure 1-2. Schematic of Potential Water Flows in the WMOST 4
Figure 3-1. HSPF Schematic (EPA 2005) 33
Figure 3-2. HSPF Time Series for Two Pervious HRUs 33
Figure 4-1. SUSTAIN Flows With and Without an Aquifer Component (from EPA 2014b) 43
Figure 6-1. WMOST Internal Configuration 50
Table 1-1. Summary of Management Goals and Management Practices 5
Table 3-1. Raw HSPF Time Series 36
Table 3-2. Hydrology Database for WMOST v2 37
Table 4-1. Selected BMPs for WMOST v2 (EPA and MassDEP 2009, EPA 201 la) 41
Table 4-2. BMP Specifications 41
VIM
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Background
1. Background
Objective of the Tool
The Watershed Management Optimization Support Tool (WMOST) is a public-domain software
application designed to aid decision making in integrated water resources management. WMOST is
intended to serve as an efficient and user-friendly tool for water resources managers and planners to
screen a wide-range of strategies and management practices for cost-effectiveness and environmental
sustainability in meeting watershed or jurisdiction management goals (Zoltay et al. 2010).
WMOST identifies the least-cost combination of management practices to meet the user specified
management goals. Management goals may include meeting projected water supply demand,
minimum and maximum in-stream flow targets, and reducing damages associated with flooding.
The tool considers a range of management practices related to water supply, wastewater, nonpotable
water reuse, aquifer storage and recharge, stormwater, low-impact development (LID), and land
conservation, accounting for both the cost and performance of each practice. In addition, WMOST
may be run for a range of values for management goals to perform a cost-benefit analysis and obtain
a Pareto frontier or trade-off curve. For example, running the model for a range of minimum in-
stream flow standards provides data to create a trade-off curve between increasing in-stream flow
and total annual management cost.
WMOST is intended to be used as a screening tool as part of an integrated watershed management
process such as that described in EPA's watershed planning handbook (EPA 2008), to identify the
strategies and practices that seem most promising for more detailed evaluation. For example, results
may demonstrate the potential cost-savings of coordinating or integrating the management of water
supply, wastewater, and stormwater. In addition, the tool may facilitate the evaluation of LID and GI
as alternative or complementary management options in projects proposed for State Revolving Funds
(SRF). As of October 2010, SRF Sustainability Policy calls for integrated planning in the use of SRF
resources as a means of improving the sustainability of infrastructure projects and the communities
they serve. In addition, Congress mandated a 20% set-aside of SRF funding for a "Green Project
Reserve" which includes GI and land conservation measures as eligible projects in meeting water
quality goals.
About this Document
This document provides the theoretical background for WMOST, including the objective, conceptual
framework, mathematical descriptions of the underlying objective function with cost and revenue
components, model constraints associated with the mass balance for water, physical limits on
watershed components and management options, variable definitions, and internal configuration.
Following an overview of the base model available in WMOST version 1, we describe three new
modules available in version 2: 1) a baseline hydrology module, 2) a stormwater hydrology module,
and 3) a flood damage module (Figure 1-1).
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WMOST v2 Theoretical Documentation
Figure 1-1. WMOST Components and Interactions with External Databases or Models.
Introductory
Worksheet
Baseline
Hydroloi
Database or
'gy external
model output
Output
Worksheets
Management
Option/Co
Table
vs Model
Streamflow
Model
Streamflow
vs Targets
WMOST
componen
External
model or
The rest of this document is organized as follows. The model's theoretical approach (i.e., equations)
is described in detail in Section 2. This section is organized according to the traditional description of
an optimization model: first the objective function (Section 2.1), and then the constraints (Section
2.2). Readers interested in understanding the watershed system first may consider starting with
Section 2.2 where flow balances are presented and then reading Section 2.1 which describes the
management costs that constitute the objective function. Sections 3 through 5 describe the Baseline
Hydrology, Stormwater Hydrology, and Flood-Damage modules, respectively. These modules assist
users with input data acquisition and pre-processing and enable consideration of flood-damage costs
in the optimization function. Section 6 describes the configuration of the software components.
Section 7 summarizes the required input data to run the model. A series of appendices provides
complementary information on common errors, parameter default values, user inputs, and
considerations for future development.
A separate User Guide document provides detailed direction on using WMOST and performing
sensitivity and trade-off analyses. Case study applications are documented individually and are
available on the WMOST website. The WMOST files for the case studies are also available and may
be used as a source of default data, especially for similar watersheds and similar sized water systems.
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Background
Overview
WMOST combines an optimization framework with water resources modeling to evaluate the effects
of management decisions within a watershed context. The watershed system modeled in WMOST
version 1 is shown in Figure 1-2. The figure shows the possible watershed system components and
potential water flows among them.
The principal characteristics of WMOST include:
• Implementation in Microsoft Excel 2010© which is linked seamlessly with Visual Basic for
Applications (VBA) and a free, linear programming (LP) optimization solver, eliminating the
need for specialized software and using the familiar Excel platform for the user interface;
• User-specified inputs for characterizing the watershed, management practices, and management
goals and generating a customized optimization model (see Table 1-1 for a list of available
management practices and goals);
• Use of Lp_solve 5.5, a LP optimization solver, to determine the least-cost combination of
practices that achieves the user-specified management goals (See Section 3 for details on
Lp_solve 5.5, LP optimization, and the software configuration);
• Spatially lumped calculations modeling one basin and one reach but with flexibility in the number
of hydrologic response units (HRUs),13 each with an individual runoff and recharge rate;
• Modeling time step of a day or month without a limit on the length of the modeling period;14
• Solutions that account for both the direct and indirect effects of management practices. For
example, the model will account for the fact 1) that implementing water conservation will reduce
water revenue, wastewater flow and wastewater revenue if wastewater revenue is calculated
based on water flow or 2) that implementing infiltration-based stormwater management practices
will increase aquifer recharge and baseflow for the stream reach which can help meet minimum
in-stream flow requirements during low precipitation periods, maximum in-stream flow
requirements during intense precipitation seasons, and water supply demand from increased
groundwater supply;
• Ability to specify up to ten stormwater management options, including traditional, GI or LID
practices;
• Enforcement of physical constraints, such as the conservation of mass (i.e., water), within the
watershed; and
• Consideration of water flows only (i.e., no water quality modeling yet).
13 Land cover, land use, soil, slope and other land characteristics affect the fraction of precipitation that will runoff, recharge
and evapotranspire. Areas with similar land characteristics that respond similarly to precipitation are termed hydrologic
response units.
14 While the number of HRUs and modeling period are not limited, solution times are significantly affected by these model
specifications.
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WMOST v2 Theoretical Documentation
Figure 1-2. Schematic of Potential Water Flows in the WMOST
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Background
Table 1-1. Summary of Management Goals and Management Practices
Management Practice
Land conservation
Stormwater management via
traditional, green infrastructure
or low impact development
practices
Surface water storage capacity
Surface water pumping
capacity
Groundwater pumping
capacity
Change in quantity of surface
versus groundwater pumping
Potable water treatment
capacity
Leak repair in potable
distribution system
Wastewater treatment capacity
Infiltration repair in
wastewater collection system
Water reuse facility (advanced
treatment) capacity
Nonpotable distribution
system
Action
Increase area of
land use type
specified as
'conservable'
Increase area of
land use type
treated by
specified
management
practice
Increase
maximum storage
volume
Increase
maximum
pumping capacity
Increase
maximum
pumping capacity
Change in
pumping time
series for surface
and groundwater
sources
Increase
maximum
treatment capacity
Decrease
% of leaks
Increase MGD
Decrease
% of leaks
Increase MGD
Increase MGD
Model Component
Affected
Land area allocation
Land area allocation
Reservoir/Surface
Storage
Potable water
treatment plant
Potable water
treatment plant
Potable water
treatment plant
Potable water
treatment plant
Potable water
treatment plant
Wastewater
treatment plant
Wastewater
treatment plant
Water reuse facility
Nonpotable water
use
Impact
Preserve runoff & recharge
quantity & quality
Reduce runoff, increase
recharge, treatment
Increase storage, reduce
demand from other sources
Reduce quantity and/or timing
of demand from other sources
Reduce quantity and/or timing
of demand from other sources
Change the timing of
withdrawal impact on water
source(s)
Treatment to standards, meet
potable human demand
Reduce demand for water
quantity
Maintain water quality of
receiving water (or improve if
sewer overflow events)
Reduce demand for wastewater
treatment capacity
Produce water for nonpotable
demand, ASR, and/or improve
water quality of receiving water
Reduce demand for potable
water
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WMOST v2
Management Practice
Table 1-1 Continued
Aquifer storage & recharge
(ASR) facility capacity
Demand management by price
increase
Direct demand management
Interbasin transfer - potable
water import capacity
Interbasin transfer -
wastewater export capacity
Minimum human water
demand
Minimum in-stream flow
Maximum in-stream flow
Action
Increase MGD
Increase % of
price
Percent decrease
in MGD
Increase or
decrease MGD
Increase or
decrease MGD
MGD
ft3/sec
ft3/sec
Model Component
Affected
ASR facility
Potable and
nonpotable water
and wastewater
Potable and
nonpotable water
and wastewater
Interbasin transfer -
potable water import
Interbasin transfer -
wastewater export
Groundwater and
surface water
pumping and/or
interbasin transfer
Surface water
Surface water
Impact
Increase recharge, treatment,
and/or supply
Reduce demand
Reduce demand
Increase potable water supply
or reduce reliance on out of
basin sources
Reduce need for wastewater
treatment plant capacity or
reduce reliance on out of basin
services
Meet human water needs
Meet in-stream flow standards,
improve ecosystem health and
services, improve recreational
opportunities
Meet in-stream flow standards,
improve ecosystem health and
services by reducing scouring,
channel and habitat
degradation, and decrease loss
of public and private assets due
to flooding
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Mathematical Description
2. Objective Function and Linear Programming
The objective function is defined as minimizing the total, annualized cost of all chosen management
practices. The objective is minimized by selecting the optimal values for decision variables which are
denoted with the prefix b. These decisions determine which management practices are selected to
minimize the objective and meet all the constraints. This section provides the equations for the
objective function and the constraints that define the linear programming (LP) optimization model.
In general, the following naming convention is followed in the equations.
• The first capital letter indicates the type of quantity (e.g., Q =flow, A=area) except for
decision variables which are preceded with the letter "b" (e.g., bQGwPumpAddi = optimal
additional groundwater pumping capacity).
• Primary subscripts provide additional information about the quantity by indicating
o which component the quantity is associated with (e.g., R[/sep=revenue from potable
water use) or
o which components the flow travels between with the source component listed first
and the receiving component listed second (e.g., QusePWwtp=^ow from potable use
to the wastewater treatment plant).
• Additional subscripts indicate elements of a variable. In the optimization problem, an
individual variable exists for each element but for documentation, these subscripts facilitate
brevity and clarity.
o Variables that change with each time step have t subscripts. The number of variables
in the optimization model equals the number of time steps for which data is provided
and the model is optimized (e.g., for one year of data at a daily time step, 365
variables of that parameter exist in the LP model).
o Additional subscripts include u for different water uses (e.g., residential,
commercial), / for different HRU types (e.g., residential/hydrologic soil group
B/slope <5%), s for "sets" of HRU types which include the baseline HRU set and
other sets that have the same HRUs but with management practices implemented
such as stormwater management. The user specifies the number of water uses, HRU
types, and sets of HRU types.
All variables are defined when they are first used in the text. Input variables, their units and
definitions are summarized in Section 7. Units for input variables are based on the units expected to
be used in the most-readily available data sources.
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WMOST v2 Theoretical Documentation
Objective Function
The objective function is defined as minimizing the total, annualized cost of all chosen management
practices. The total, annualized cost includes annualized capital costs and annual operation and
maintenance costs.
(1)
where
Z = total annual cost for all implemented management practices, $
CTjA . = total annualized cost for management option i, $
n = total number of management options
2.1.1 Costs
Total annual costs are calculated for all implemented management practices. In this section, we first
we describe the generic form of cost equations, and then we provide all of the individual equations
used in the model. In general, total annual cost for a management practice is calculated as the
annualized capital cost, CCA , (i.e., incurred once) plus annual O&M costs, C0m.
Capital costs may be annualized using three different approaches with three different annualization
factors, F, depending on the management practice.
CCA = F x Cc (2)
where
CcA = unit annual capital cost, $/year
Cc = unit capital cost, $
Unit construction costs for new facilities or costs for expanding the capacity of an existing facility
(i.e., capital costs) are annualized over the expected lifetime of the new construction (e.g., wastewater
treatment plant, bioretention basin).
i X (1 + l)TNew
where
= interest rate in percent/100, 0-1
= lifetime of new construction, years
-------
Mathematical Description
Replacement costs for an existing facility are calculated as Cc A annualized over the remaining years
in the facility's lifetime, TExist. This annualization factor, (PExist), is defined as follows.
x (1 + i?N™ TPlan - TExist
-- Plan
where
= the planning horizon, years
If Tpian — TExist, then the existing facility will not need to be replaced within the planning period and
CC,A = 0.
One-time implementation costs, such as the initial administrative activities associated with instituting
a price increase, are annualized over the planning horizon.
i X (1 + i)TPlan
Land Management: Land cover, land use, soil, slope, and other land characteristics affect the
fraction of precipitation that will runoff, recharge, and evapotranspire. Areas with similar
characteristics - hydrologic response units (HRUs)15 - respond similarly to precipitation. The user
provides unit runoff and recharge rates (RRRs) for each HRU in the watershed for multiple sets of
HRUs. For example, a 'baseline' set is provided that reflects RRRs without stormwater management.
Additional sets of RRRs may be provided that, for example, represent RRR of HRUs with stormwater
management. For example, a baseline HRU may be defined as low density residential land use with
hydrologic soil group (HSG) B and a stormwater managed HRU may be defined as low density
residential land use with HSG B with a bioretention basin sized to capture a one-inch storm event.
The user provides both the managed RRRs and the cost associated with the management practice.
Recharge and runoff rates may be derived from a calibrated/validated simulation model such as
Hydrological Simulation Program Fortran (HSPF),16 Soil Water and Assessment Tool (SWAT)17
and/or the Storm Water Management Model.18 See Section 2.2. 1 for continuity equations defining
total watershed runoff and recharge based on RRRs and HRU area allocation.
The model provides two land management options as described below.
Land Conservation-reallocating area among baseline HRUs: For a specific scenario, the user may
specify the expected, future areas for each HRU as the baseline values which may include projected
increases in development.19 At the same time, the user can specify the cost to purchase existing,
undeveloped forest land. With this information provided, the model can decide whether it is cost
15 For example, an HRU may be defined as low density residential land use with hydrologic soil group (HSG) B and another
as low density residential with HSG C.
"'http://water.usgs.gov/software/HSPF/
17 http://swat.tamu.edu/
18 http://www.epa.gov/nrmrl/wswrd/wq/models/swmm/
19 If a future scenario is modeled, all input data must be values projected for the future scenario (e.g., water demand must be
the projected demand corresponding to the project development).
-------
WMOST v2
effective to reallocate land from projected developed HRUs to undeveloped forest HRUs.
The cost to reallocate land area among baseline HRUs is defined below.
For s = 1 (i.e., baseline land use),
/"* — \^ (Cf x C ~h C ) X \bA A }\ ((-\\
where
/ = HRU index, 1 to nLu
s = number of HRU sets
CATb = total annual cost of reallocating areas among baseline HRUs from user-specified to model-
chosen values, $/year
nLu = number of HRU types
Q,;,s=i = capital cost associated with land reallocation for each HRU in set 1 (e.g., purchasing forest
land), $/acre
C0m; s=1 = annual O&M cost associated with maintaining, for example, the land preservation, $/acre/yr
AtjS=i = user specified areas for baseline HRU, acres
bAiiS=i = model-chosen, land area for baseline HRUs, acres
Stormwater Management (traditional, GI, low impact development) - reallocating area from
baseline to managed HRUs: The model may choose implementation of Stormwater management
practices based on the available area for each HRU after reallocation for land conservation (i.e.,
bAiiS=i). The user may specify multiple managed HRU sets where for each set the user specifies costs
and runoff and recharge rates. Each set may be a different management practice such as one set for
bioretention basins sized to retain one inch of rain and another set that is a combination of low impact
development practices such as impervious area reduction, bioswales, and bioretention basins to match
predevelopment hydrology.
When the model chooses to place land area under a management practice, additional costs specified
by the equation below are incurred. In addition, the runoff and recharge rates corresponding to that
HRU set are used to calculate total runoff and recharge as shown by equations in Section 2.2.1.
For s = 2 to NLuSet,
NLuSet nLu
X""1 X""1
= 2_, /_l((FPlanXCc,l,s + Com,l,s}xbAljS) (7)
s=2 1=1
where
bAi:S=2to NLuSet = model chosen land area for managed HRUs, acres
NLuSet = number of HRU sets
Section 2.2 details constraints to ensure that area allocation among HRUs meet physical constraints
such as preserving total original land area and user specified constraints such as limits on developable
land based on zoning regulation or the amount of existing forest land which is available for
conservation.
10
-------
Demand Management: There are two demand management options in the model - via pricing and
via other practices such as rebates for water efficient appliances. When acquiring input data for these
practices, the user must be aware of the potential reduction in the individual effectiveness of demand
management practices when multiple practices are implemented simultaneously.20
Pricing change: Costs associated with changing the water pricing structure and/or rates may include
costs for conducting an initial study to determine the appropriate structure and rates and O&M costs
for annual reviews of the rates. The cost to implement changes to the water pricing structure is not
dependent on the percent of change in price or other unit of implementation but is a fixed capital cost
and fixed annual O&M cost. Because the costs are fixed, a binary variable is introduced that is set
equal to one if the price change is implemented and zero for no price change. Therefore, the annual
total cost for a pricing change is defined as:
C-ATPrice = bPriceBin x (FPJan x CCfrice + C0mPriee) (8)
where
^ATPrice = annual cost to implement price changes, $/year
bPriceBin = a binary decision variable, 0 or 1
Cc, price = capital cost of price change, $
Comfrice = annual O&M costs for implementation of price change, $/year
Direct demand reduction: The aggregate cost of various demand reduction practices may be specified
and the initial demand will be reduced by the user specified percentage.
CATDmd = bDmdBin x (Fplan x CCDm + C0mDm) (9)
where
CATD-HICI = annual cost to implement direct demand management practices, $/year
bDmdBin = binary decision variable, 0 or 1
= capital cost of direct demand management, $
= annual O&M costs for direct demand management, $/year
EPA's WaterSense website provides a calculator that together with local or Census data (e.g., number
of households) can be used to determine the total potential reductions in water use with the
installation of water efficient appliances.21
Infrastructure Capacity and Use: Groundwater and surface water pumping facilities, water and
wastewater treatment plants, water reuse facility, aquifer storage and recovery (ASR) facility, and
nonpotable distribution systems follow similar forms for total annual costs.
20 For example, rebates for water low flow shower heads will reduce the gallons per minute used in showering. If an increase
in water rates is implemented at the same time, the anticipated water use reduction may not be as large with a low flow
shower head as with a high flow shower head even if the new water rates induce shorter shower times.
21 http://www.epa.go v/watersense/our_water/start_saving.html#tabs-3
11
-------
WMOST v2
Groun dwater pumping.
^ATGwPump = (fcwPumpExist X CcGwPump X QcwPumpl) + V G
X bQcwPumpAddl) + (f"OmGwPump X /^ "QcwWtpf)
t
where
•wPumpNew X ^CGwPump
(10)
bQc
l annual cost for groundwater pumping, $/year
= annualization factor based on remaining lifetime of existing facilities
= capital costs of new/additional groundwater pumping capacity/facility, $/MGD
= operation and maintenance costs for groundwater pumping, $/MG/year
= initial groundwater pumping capacity, MOD
= annualization factor for new capacity or facilities
= additional groundwater pumping capacity, MOD
= flow from groundwater pump to water treatment plant, MOD
Surface water pumping:
~ \ SwPumpExist
' (.''
'SwPumpNew
bQswPumpAddl) + (^ OmSwPump X Ljt\"QswWtp,t + "QResWtp.tJ )
(11)
where
^ATSwPump
77
rSwPumpExist
r
'-CSwPump
r
^OmSwPump
^cSwPumpl
77
rSwPumpNew
bQswPumpAddl
bQswWtp.t
= total annual cost for surface water pumping, $/year
= annualization factor based on remaining lifetime of existing facilities
= capital costs of new/additional surface water pumping capacity/facility, $/MGD
= operation and maintenance costs for surface water pumping, $/MG/year
= initial surface water pumping capacity, MOD
= annualization factor for new capacity or facilities
= additional surface water pumping capacity, MOD
= flow from surface water to water treatment plant, MOD
= flow from reservoir to water treatment plant, MOD
Water treatment facility (WTP):
C-ATWtp — (FwtpExist X
/) + (FM
X QwtpMaxl) T VwtpNew
wWtp.t +
X bQwtpAddl^) + (C,
omWtp
(12)
where
wtpExist
wtpMaxl
FwtpNew
bQwtpAddl
total annual costs for water treatment, $/year
annualization factor based on remaining lifetime of existing facilities
capital costs of new or additional water treatment capacity or facility, $/MGD
initial water treatment capacity, MOD
annualization factor for new capacity or facilities
additional water treatment capacity, MOD
annual O&M costs for water treatment, $/MG/year
12
-------
Reducing unaccounted-for water (Uaw), assumed to be leakage out of the potable distribution
system into groundwater):
The cost for repairing unaccounted-for water in the potable distribution system is calculated as:
r - (v vr -t-r x bPwtpGwFix
^ATUaw ~ \rPlan A ^CUaw ' ^OmUawJ A .. (->(->
where
CCATUO.W = total annualized capital cost of reducing unaccounted-for water, $/year
Ccuaw = capital cost of fixing Uaw such as initial survey and initial work to lower Uaw rate, $
Comuaw = annual O&M cost to maintain low Uaw rate, $/year
ix = percent of leakage that is fixed, %
(f-OmWwtp X
Wastewater treatment plant (WWTP):
= (fwwtpExist X C-CWwtp X QwwtpMaxl) + (fwwtpNew X (-CWwtp X bQWwtpAddl
OmWwtp
where
= total annual costs for wastewater treatment, $/year
= annualization factor based on remaining lifetime of existing facilities
= capital costs of new or additional wastewater treatment capacity or facility, $/MGD
IwwtpMaxi = initial wastewater treatment capacity, MOD
= annualization factor for new capacity or facilities
= additional wastewater treatment capacity, MOD
= annual O&M costs for wastewater treatment, $/MG/year
bQusepwwtp,t = flow from potable water use to treatment plant, MOD
bQuseNPwwtp,t = flow from nonpotable water use to treatment plant, MOD
Qcwwwtp,t = groundwater infiltration into collection system, MOD
Reducing infiltration into wastewater collection system:
„ —fee 4- r \ bPGwWwtpFiX
w w p an w w p m w w p ^QQ
where
CATGwWwtp = total annualized capital cost of reducing groundwater infiltration into the wastewater
collection system, $/year
Cccwwwtp = capital cost of fixing infiltration such as initial survey and initial repairs to lower
infiltration rate, $
ComGwwwtp = annual O&M cost to maintain low infiltration rate, $/year
= percent of groundwater infiltration that is fixed, %
13
-------
WMOST v2
Water reuse facility (WRF):
= (fwrf Exist X Qwr/ X QwrfMaxl) + (fwrfNew X Qwr/ X
X /^ "QwwtpWrf.tJ
+ (f
omWrf
where
wrfExist
wrfMaxl
(16)
•OmWrf
bQwrfAddl
bQwwtpWrf
= total annual costs for water reuse, $/year
= annualization factor based on remaining lifetime of existing facilities
= capital costs of new or additional WRF capacity, $/MGD
= existing maximum WRF capacity, MOD
= annualization factor for new capacity or facilities
= annual O&M costs for WRF, $/MG/year
= additional or new WRF capacity, MOD
= flow from WWTP to WRF, MOD
Nonpotable distribution system (Npdist):
^ATNpdist = \FNpdistExist X ^CNpdist X QNpdistl) + (.^NpdistNew X ^CNpdist X ^Q Npdist Addl)
X y bQwrfUseNp,t)
where
LATNpdist
FNpdistExist
QNvdistl
p
r NpdistNew
bQNpdistAddl
r
'-OmNpdist
bQwrfUseNp.t
total annual costs for nonpotable water distribution, $/year
annualization factor for existing capacity or facilities
existing capacity of nonpotable distribution system, MOD
annualization factor for new capacity or facilities
new or additional capacity, MOD
capital costs for maximum capacity Npdist, $/MGD
annual O&M costs for maximum capacity Npdist, $/MG/year
flow from WRF to nonpotable water use, MGD
(17)
Aquifer storage and recovery (ASR):
ASR costs may represent the conveyance and injection infrastructure necessary to operate an ASR
facility or it may also include treatment required by an injection permit or other operational
requirements. In WMOST vl, only one capital and one O&M cost may be specified for ASR. In
future versions, separate costs may be programmed for each source depending on the need for
treatment (e.g., water from a WRF likely does not need treatment while water from surface water or
reservoir likely needs some treatment prior to injection to prevent clogging of the injection well
and/or aquifer and/or to meet permit requirements).
14
-------
'•I
^ _|_ (C V
ixl) ' \rAsrNew
bQswAsr,t + bQRe
(18)
where
QAsrMaxl
77
^srWew
bQAsrAddl
bQwrfAsr.t
bQswAsr,t
bQResAsr.t
total annual costs for ASR, $/year
annualization factor based on remaining lifetime of existing facilities
capital costs of existing facility annualized over the remaining lifetime, $/year
operation and maintenance costs of ASR, $/year
existing maximum capacity, MOD
annualization factor for new or additional capacity
capacity of new or additional capacity, MOD
flow from WRF to ASR, MOD
flow from surface water to ASR, MOD
flow from reservoir to ASR,MGD
Reservoir or surface storage (e.g., storage tank, pond):
(-ATRes = (.^ResExist X CCRCS X 'ResMaxlJ + (rResNew X ^CRes X "'ResAddU + (f-OmRe
x (bV Afifii + V ))
where
= total annual costs for reservoir/surface storage, $/year
= annualization factor based on remaining lifetime of existing facilities
= capital costs of new or additional capacity, $
^ResMaxi = existing capacity, MG
FResNew = annualization factor based on lifetime of new facilities
bVResAddi = additional or new capacity, MG
ComRes = annual O&M cost, $/year
(19)
Interbasin transfer (IBT)for water andwastewater: As shown in Figure 1-2, IBT water is routed
directly to water users and is assumed to be treated, potable water. Therefore, costs should reflect the
total cost of purchasing and delivering IBT water to users. The total annual cost of interbasin transfer
of imported potable water, CATIbtw, is calculated as:
where
C,btw
bQibtwusep,t
bQibtwuseNP,t
/(bQ
lbtWUseP,t
bQ
lbtWUseNp,t
(20)
initial cost of purchasing additional water rights for IBT and construction of necessary
infrastructure, $/MGD
additional water IBT capacity purchased, MOD
cost of purchasing IBT water, $/MGD
fl°w °f IBT water to potable water use, MOD
fl°w °f IBT water to nonpotable water use, MOD
15
-------
WMOST v2
IBT wastewater is transferred directly from users to the service provider outside of the basin;
therefore, costs should reflect the collection and transport of wastewater from users to the out of basin
provider. The total annual cost of exporting wastewater via interbasin transfer, CATibtWw, is calculated
as:
— Fplan X Qr/fetWw X
/(bQ
usePlbtWw,t
bQ
useNplbtWw,t
where
/ www
initial cost of purchasing additional wastewater transfer rights for IBT and construction
of necessary infrastructure, $/MGD
additional wastewater IBT capacity purchased, MOD
cost of IBT wastewater services, $/MGD
flow °f wastewater from potable use to IBT, MOD
flow of wastewater from nonpo table use to IBT, MOD
Flood damages: The annualized cost of damage from flood flow is calculated as the damage times
the inverse of the recurrence interval of the flow:
bQ
usepibtww,t
where
CFAn
CFn
Tn
Qn
n
ATI = CFn X for Qn
annualized cost of damage caused by flood flow n, $/year
cost of damage caused by flood flow n, $
recurrence interval of flood flown, years
flood flow n, ft3/sec
one element of the sets of flood flow data entered by user
(22)
Linear interpolation between flood flow and annualized damage cost provides a linear cost curve for a
specific flow interval. With a minimum of three sets of input data for the flood damage modeling,
there will be at least two equations representing the damages corresponding to possible flows.
Therefore, these equations are programmed in the linear programming solver as "special order sets"
or SOS. The SOS function allows a piece-wise definition so that each equation applies only to the
specific flow interval for which it is valid. Flow below the lowest flood flow specified is assumed to
cause no flood damages. Flow above the largest flood flow specified is assumed to cause the same
damage as the largest specified flood flow. The final total flood damages incurred over the modeling
period is the sum of all flows that cause flood damages as calculated by the appropriate corresponding
cost curve:
CFA = T.t ™-Fni2 X QswRes,t + <&Fni2 forflow between Qn and Qn
(23)
where
CFA = annualized cost of damage caused by flood flows over the modeling time period, $/year
mFnl2, &Fni2 = constants of equation resulting from linear interpolation between Qn and Qn+1
QswRes.t = flow in the stream channel, ft3/sec
16
-------
Penalty for Insufficient Water: WMOST gives the user an option to allow "make up" of water
shortfalls within the watershed system by adding a hypothetic flow of water to the reservoir located at
the outlet of the watershed. This ensures that the system is able to meet the specified in-stream flow
targets and inform the user that available water was insufficient. This option allows for feasible runs
without iterative guessing about flow targets that are feasible.
If this option is enabled, the user specifies a (large) penalty for needing to add this make-up water and
this penalty is included when estimating the total cost.
= )
(24)
where
CATMU = annualized cost of make-up water, $/year
CMUW = penalty for make-up water, $/MGD
= Flow of "made-up" water into the system to balance mass /, MOD
Total costs:
Total annual costs for all services, CAT, is calculated as the sum of all annualized capital and O&M
costs as defined above:
CAT = CArb + CAT-TII + CATPrice + CATDmd + CATGwPump + CATSwPump + CATWtp + CATUaw +
^ATWwtp + C-ATGwWwtp + C-ATWrf + ^ATNpdist + C-ATAsr + ^-ATRes + ^-ATlbtW + ^ATlbtWw^^ATMU + (25)
CFA + CFAn
2.1.2 Revenue
Revenue is calculated and provided for informational purposes. It is not part of the objective function
because most municipalities minimize cost and calculate the rates necessary to cover those costs.
Total revenue, RT, is calculated as the sum of water and wastewater services.
/ \ / PTICG \
RT = ((RusePT + RuseNpr) X ( 1 H )) + RWWT (26)
where
= revenue from delivered potable water, $/year
= revenue from delivered nonpotable water, $/year
= revenue from wastewater services, $/year
= percent price increase for potable and nonpotable water services, %
These quantities are further defined as follows.
RusePT = /^ RusePF ^(.RuseP X /(QwtpUseP,t + "QlbtWUseP.tJJ (27}
m t
17
-------
WMOST v2
RuseNpT — /^RuseNpF + (RuseNp X / ^ "QwrfUseNp.tJ
(28)
where
UsePF
R
RuseNpF
m
RuseP
RuseNp
QwtpUseP,t
bQwtpUseNp,t
bQlbtWUseP,t
bQlbtWUseNp,t
bQwrfUseNp,t
WtpUseNp,t "r uVlbtWUseNp,t)
fixed monthly fee for potable customers, $/month
fixed monthly fee for nonpotable customers, $/month
monthly time steps in period of analysis
original customer price per unit of water for potable water, $/MG
original customer price per unit of water for nonpotable water, $/MG
flow of water from water treatment plant to potable uses, MOD
flow of water from water treatment plant to nonpotable uses, MOD
flow of water from interbasin transfer to potable uses, MOD
flow of water from interbasin transfer to nonpotable uses, MOD
flow of nonpotable water from water reuse facility to nonpotable uses, MOD
Wastewater revenue may be calculated based on water flow into a house or organization or based on
separately metered sewer flow. The user specifies which situation exists in their system or which
situation the user would like to model on the Infrastructure page under Wastewater Treatment Plant
heading.
If wastewater fees are charged based on wastewater flow, then
R ~ Y R + (R
WwT — / WwF ' \ Ww
' /[pQusePWwtp,t ~^~ ®QusePlbtWw,t ~^~ ®QuseNpWwtp,t ~^~ ®QuseNplbtWw,tj)
(29)
where
RWWF
RWW
"QusePWwtp.t
"QuseNpWwtp.t
"QusePIbtWw.t
"QuseNpIbtWw.t
fixed monthly fee for all customers, $/month
customer price for wastewater services per unit wastewater, $/MG
wastewater flow from potable uses to wastewater treatment plant, MOD
wastewater flow from nonpotable uses to wastewater treatment plant, MOD
wastewater flow from potable water uses exported to interbasin transfer, MOD
wastewater flow from nonpotable water uses exported to interbasin transfer, MOD
If wastewater fees are charged based on water flow, then
RWWT = y RWWF + (.Rww
m
X y(QwtpUseP,t + bQlbtWUseP,t
t
+ bQlbtWUseNp,t))
(30)
18
-------
Constraints
The objective in Section 0 must be met subject to constraints. There are three main categories of
constraints: 1) continuity equations that enforce mass balance among watershed components,
2) physical limits on the capacity of watershed components, and 3) constraints associated with
management options. Any constraint or management option can be excluded by entering -9 instead of
an input value as specified on the user interface pages.
2.1.3 Continuity Equations
Land Management - Land Conservation and Stormwater Management: Land area in the
watershed can be reallocated among baseline and managed HRU sets as described in Section 2.1.1 .
The user provides a time series of 'baseline' runoff and recharge rates (RRRs, inches/time step) for
each HRU in the study area for the time period of analysis. The user may also provide multiple,
additional time series of RRRs for managed HRU sets. These managed RRR rates, for example, may
represent the installation of bioretention basins. Recharge and runoff rates may be derived from a
calibrated/validated simulation model such as Hydrological Simulation Program Fortran (HSPF),22
Soil Water and Assessment Tool (SWAT)23 and/or the Storm Water Management Model (SWMM).24
Based on the optimization model's final allocation of area among HRUs, the total runoff and recharge
volumes in the watershed are calculated. Constraints ensure that area allocations meet physical limits
and, as specified by the user, policy requirements.
During the reallocation, the total land area must be preserved according to the following equalities.
These equalities show that managed HRU sets are mutually exclusive; that is, one acre of land may
only be placed under one of the managed HRU sets.
Z AL'S=I = Z bAi's=i = Z Z
L=ltoNLu L=ltoNLu s=2 to NLuSet 1 = 1 to NLu
where
AiiS=i = user specified HRU areas
S=1 = baseline HRU areas after
S=2 to NLuSet = HRU areas under management
jS=1 = baseline HRU areas after reallocation for conservation
In addition, the minimum and maximum areas with respect to conservation must be met, if specified
by the user:
bAij > ^Min,i,s for / = 1 to NLu and 5=1 (32)
where ^Min,(,s = minimum area possible for baseline HRUs
bAiiS < AMaXiiiS for / = 1 to NLu and 5=1 (33)
22 http://water.usgs.gov/software/HSPF/
23 http://swat.tamu.edu/
24 http://www.epa.gov/nrrnrl/wswrd/wq/models/swrnrn/
19
-------
WMOST v2
where AMaXiiiS = maximum area possible for baseline HRUs
If land can be conserved (e.g., forest area), then the minimum (e.g., amount already in land trust) and
maximum (e.g., amount existing or potentially allowed to regrow) can be specified with the
corresponding costs. If an HRU can be reduced in exchange for conserving another land use, the
minimum and maximum areas for the HRU may be entered. If an HRU cannot be decreased or
increased as part of land conservation, the user may enter the same value for baseline, minimum, and
maximum areas under baseline HRU set specifications.
The following additional constraints are added to ensure that HRUs that can be conserved only
increase in area and others only decrease in area. The user indicates which HRUs can be conserved by
indicating the cost for conservation. The user indicates which HRUs can be decreased to
accommodate conservation by entering -9 for costs.
where CCA; <>-9, bAliS=i - AliS=i > 0 (34)
else, bAL,s=1 - AL,S=1 < 0 (35)
When allocating land area from the baseline to the managed condition for any of the land uses, the
area allocated to a managed land use cannot be greater than the area allocated to the corresponding
baseline land use chosen under conservation, bAtiS=1 (e.g., users can not choose to implement
stormwater management on more urban land area than the urban area decided upon by the model). In
addition only one land management practice may be implemented on any given area; therefore, land
management practices are mutually exclusive. However, one "management practice" may represent
the implementation of multiple GI practices to meet a specific stormwater standard.
(36)
where bAts = area allocated to 'managed' HRU in set s
In addition, user specified minimum and maximum areas are used to constrain the amount of land that
may be placed under each management condition, i.e., each set, s. For example, there may be
technical or policy requirements that can be represented with these limits.
bAl-s > AMiriiliS for I = 1 to nLu and s = 1 to NLuSet (37)
where ^Min,(,s = minimum area possible for management for HRU / and management set s
bAliS < AMaXiliS for I = 1 to nLu and s = 2 to NLuSet (38)
where AMaXiiiS= maximum area possible for management for baseline HRU / and management set s
The total runoff (QRUit) and recharge (QR6,t) for each time step are calculated based on the final area
allocations for all HRUs and HRU sets.
Z
NLu NLu
NLuSet
1=1 "— 1=1
20
-------
where QRUiiiSit = runoff rate25 from HRU / in HRU set s for time step t.
x bA (40)
where QRe,i,s,t= recharge rate from HRU / in HRU set s for time step t.
Groundwater (Gw): The groundwater system, or aquifer, has storage. It may receive inflow from
recharge, groundwater from outside of the watershed, point sources, leakage from the potable water
distribution system, recharge from the aquifer storage and recharge (ASR) facility, and septic
systems. Outflow from the groundwater system may discharge to surface water via baseflow, be
withdrawn by the potable water treatment plant via groundwater wells, infiltrate into the wastewater
collection system, and discharge to a groundwater system outside of the basin.
*Gw,t = *Gw,t-l + \QRe,t + QsxtGwIn.t + QptGw.t + QwtpGw.t + QAsrGw,t-l + QsepGw,t-l ~
QcwSw.t ~ bQcwWtp.t ~ QcwWwtp.t ~ bQcwExt.t ~ QcwPt.t) X At
where VGWit= volume of groundwater, QR6:t = recharge from all land areas, QsxtGwin,t = inflow of
external groundwater, Qptcw,t = private groundwater discharges, QwtpGw.t = leakage from potable
water from distribution system, QASTGW.I = recharge from ASR facility to groundwater, QsepGw,t =
inflow from septic systems, QcwSw,t= baseflow, bQGwWtp:t= withdrawal by water treatment plant,
QcwWwtp.t = infiltration into wastewater collection system, bQGwExtt = groundwater leaving the
basin, QcwPt,t = private groundwater withdrawals, and At = time step=l.
Two variables are further defined as
n - n V ("I - bPWtpLeakFix^ (42)
VwtpGw.t VUsePI,u=l,t •*• I1 10Q )
where
QwtPGw,t = unaccounted-for-water flow from distribution system to groundwater
Qusepi,u=i,t = initial, unaccounted-for-water flow
bPwtpLeakFtx = percent of distribution system leakage that is fixed
and
Qcwsw,t = kb • VGw,t-i (43)
where Qcwsw,t is baseflow and kb is the groundwater recession coefficient.
The model assumes that unaccounted-for water infiltrates completely into the groundwater table via
leaks in the distribution system.
Surface Water (Sw): The surface water, or stream reach component, does not have storage, that is, it
is assumed to completely empty with each time step. To model surface water storage such as lakes,
ponds or storage tanks, see the reservoir section below. Wetlands should be modeled as an HRU but
may also be modeled as part of surface storage as described in the next section below.
25 RRRs may be derived from simulation models such as Soil Water Assessment Tool, Hydrological Simulation Program-
Fortran or Storm Water Management Model
21
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WMOST v2
The surface water component may receive inflow from runoff, external surface water sources (i.e., an
upstream reach), point sources, wastewater treatment plant, and a water reuse facility. Flow from
surface water may discharge downstream to a reservoir, be withdrawn by the potable water treatment
plant, and be withdrawn by the ASR facility. Surface water only exits the watershed after passing
through the reservoir. A reservoir with zero storage may be specified.
where
QsxtSwln,t
QptSw,t
QwwtpSw,t
QwrfSw
QswRes,t
bQswWtp,t
bQswAsr,t
QswPt,t
QRU,I + QsxtSwlnf + QptSw.t + QcwSw.t + QwwtpSw.t + QwrfSw.t
= QswRes,t + bQswwtp,t + bQswAsr,t + QswPt,t
(44)
surface water inflow from outside of basin
discharge from surface water point sources
discharge from wastewater treatment plant
discharge from water reuse facility (advanced treatment)
flow from surface water to reservoir
flow to water treatment plant
flow to ASR facility
private surface water withdrawals
Reservoir (Res)/Surface Water Storage: The reservoir may represent a surface water reservoir,
flood control structure, off-stream storage in tanks, and/or ponds. The reservoir component has
storage. It may receive inflow only from the surface water. Water may flow to a downstream reach
outside of the basin, potable water treatment plant, and ASR facility. This routing of flows assumes
that the reservoir is at the downstream border of the study area. The reservoir is at the downstream
portion of the watershed, so off-stream surface storage may be added to the reservoir storage.26
where
VRes,t
QswResf
"QswExt.t
"QResWtp.t
"QResAsr.t
"QwMake.t
\Q
swRes,t
X
(45)
volume of reservoir
inflow to reservoir from surface water bodies
flow to surface water bodies outside of basin
flow to water treatment plant
flow to ASR facility
"make-up" water as needed to compensate for water shortfalls within the watershed system
Water Treatment Plant (Wtp): The water treatment plant treats water to potable standards. It may
receive flow from the reservoir, surface water reach or groundwater aquifer. Water from the plant
26 Future versions of the model may include the option for flow routing that assumes the reservoir is at the upstream end of
the modeled reach segment and models separate off-stream surface storage to represent lakes, ponds and storage tanks.
22
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may be used to meet potable and nonpotable water use demand. In addition, some water is lost to the
groundwater through leaks in the potable distribution system.
+ bQ
swwtpt
+ bQ
cwwtp
t — Q
wtpuse?,t
+
^WtpUseNpt + QwtpGwt
where
QwtpUsePt
= fl°w to potable water use
= flow to nonpotable water use
(46)
Potable Water Use (UseP):
{QwtpUsePt
where
bQlbtWUsePt
p
r ConsUsePAvgt
bQusePWwtpt
QusePSept
QusePSepExtt
bQusePIbtWwt
-L hn ~\ t1 ConsUsePAvg\
t + "VlbtWUseP.t) x I 1 TTTI
= bQusePWwtp.t + QusePSept + QusePSepExt.t + "QusePIbtWw.t
inflow of potable water to water treatment facility via interbasin transfer
flow weighted average of percent consumptive use for potable water uses
flow to wastewater treatment plant
flow to septic systems within the study area
flow to septic systems outside the study area
wastewater flow from potable uses to interbasin transfer wastewater services
(47)
Nonpotable Water Use (UseNp):
(bQ-
WtpUseNpt ~^~ OQwrfUseNpt
ConsUseNpAvg
where
bQwrfUseNp,t
bQlbtWUseNp,t
p
1 ConsUseNpAvg,t
bQuseNpWwtp,t
QuseNpSept
QuseNpSepExt,t
bQuseNplbtWw,t
t^ QuseNpSepExt,t + bQuseNplbtWw,t
(48)
inflow of nonpotable water from water reuse facility
inflow of nonpotable water to water treatment facility via interbasin transfer
flow weighted average of percent consumptive use for nonpotable water uses
flow of nonpotable water to wastewater treatment plant
flow to septic systems within the study area
flow to septic systems outside the study area
flow of nonpotable water to wastewater collection system via interbasin transfer
23
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WMOST v2
Wastewater Treatment Plant (Wwtp):
bQusePWwtpt + bQuseNpWwtp,t + QcwWwtp,t = QwwtpSw,t + b QwwtpWrf ,t
where bQWwtpWrf = outflow to water reuse facility.
One variable, infiltration into the wastewater collection system, is further defined as
(49)
bPwwtpLeakFix^ PwwtpLeakl
(50)
WWuser n
ju=2 VUsePI,u,t
PconsUsePI,u,t
100
Psep.u + PsepExt.u^
TOO ;
where
Qusepi,u,t
Pconsusepi,u,t
PSepiU
PsePExt,u
100
percent leakage of groundwater into the wastewater collection system, as a percent of
wastewater treatment plant inflow
percent of leaks fixed in the wastewater collection distribution system,
initial specified water use (total demand for potable and nonpotable water)
initial percent consumptive use of potable water uses
percent of users serviced by septic systems recharging inside the study area
percent of users serviced by septic systems draining outside the study area
Water Reuse Facility (Wrf):
bQwwtpWrf,t = bQwrfUseNp,t + bQwrfAsr,t + QwrfSw,t
where bQWrfAsTit= flow from the water reuse facility to the ASR facility.
Septic Systems (Sep): Consumptive use and demand management affect the amount of wastewater
that will flow to septic systems. Septic systems may drain inside the area of analysis or outside;
therefore, the user may specify the percent of septic systems draining within and outside of the area of
analysis.
Flows to septic systems within the study area are calculated as
QusePSep,t = (^ QusePI,u,t x (l - ^7^) x ^ ) x (l + ElasPrice x
x (1
useNpMax,u,t\
100 )
CUseNpSep,t
cons
useNpMax,u,t\
100 )
. , „, n .
x 1 + Elasprice x
bPprice\ (53)
24
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Mathematical Description
where
Qusepi,u,t = initial potable water use/demand
PSepjU = percent of users serviced by septic systems draining within the study area
bPomd = percent demand reduction from direct demand management
PuseNPMax,u,t = maximum percent of water demand that can be met by nonpotable water
ElasPrice = flow-weighted average of price elasticities for water user types
bPprice = percent change in price
Consumptive use is assumed to exit the watershed system (e.g., does not runoff or percolate).
Flows to septic systems outside the study area are calculated as
,\" „ i-, pcons(/sep/,u,A ^sepftrt.u, /„,,,, n . bPprice\ (54)
QusePSepExt,t = (2_, QusePl,u,t X ^1 — J X 1QQ ) X ^1 + ElasPriCe X 1QQ j
P \
rUseNpMax,u,t \
100 /
PconsUseNpI,u,t\ PsepExt.u \
u
Septic flows enter the groundwater system:
QusePSep.t + QuseNpSep.t = QsepGw.t (56)
where QsepGw.t = fl°w from septic systems to groundwater.
Aquifer Storage and Recovery Facility (Asr):
bQswAsr,t + bQResAsr,t + ^Qwrf Asr ,t = QAsrGw,t (57)
where QASTGW,I = fl°w from the ASR facility to groundwater.
2.1.4 Physical Limits on Watershed Components
Facility capacity: Flow through a facility must not exceed the pumping or treatment capacity of the
facility. The final capacity of the facility is the initial user specified capacity plus additional capacity
built as part of the solution set (additional capacities are available as management options, see Table
1-1). This constraint applies to surface water pumping, groundwater pumping, water treatment,
wastewater treatment, water reuse, and aquifer storage facilities.
bQswWtpt + bQResWtpj < QswPumpl + bQswPumpAddl (58)
bQcwWtpt S= QcwPumpl + bQcwPumpAddl (59)
+ bQswWtpt + bQcwWtp,t ^ Qwtp,Maxl + bQwtp,Addl (60)
+ QcwWwtp,t S= Qwwtp,Maxl + bQWwtp,Addl (61)
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WMOST v2 Theoretical Documentation
bQswAsr,t
bQwwtpWrf.t — Qwrf.MaxI
•,t — QAST.MUXI
where
bQwtp,Addi
Qwwtp,Maxi
bQwwtp,Addi
Qwrf,Maxi
bQwrf,Addi
QAsr,Maxi
bQAsr,Addi
bQwrfUseNp,t ^ QNpdist,Maxl + bQNpdist,Addl
initial surface water pumping capacity
additional surface water pumping capacity
initial groundwater pumping capacity
additional groundwater pumping capacity
initial water treatment plant capacity
additional water treatment plant capacity
initial wastewater treatment plant capacity
additional wastewater treatment plant capacity
initial water reuse facility capacity
additional water reuse facility capacity
initial ASR facility capacity
additional ASR facility capacity
(62)
(63)
(64)
Limits for groundwater and reservoir storage volumes: For groundwater, the minimum storage
volume, VGwMin, may be specified to reflect the maximum desired drawdown (e.g., to avert land
subsidence). The maximum volume, VGwMax, may also be specified to reflect the size of the aquifer
and the maximum storage capacity. For the reservoir, the minimum storage volume, VResMin, may be
specified to reflect "dead storage" (i.e., what can not be released from the reservoir) or the quantity
that is required to be maintained for emergencies. The maximum volume, VResMaxJ, may be specified
to reflect the physical size of the reservoir (note that additional surface water storage capacity,
bVResAddi, is one of the management options in Table 1-1).
VCw,t > VCW.MIU
VRes,t >
2.1 .5 Constraints Associated with Management Options
(65)
(66)
(67)
(68)
Human demand and demand management: The user may specify the number of water use
categories; however, the first water use category is always unaccounted water. The user only specifies
demand data, QusePi,u=i,t for this water use category; therefore unaccounted water is not affected by
demand management or consumptive use and is assumed to entirely drain to the groundwater.
Initial demand, QusePi,u,t , provided as input, may be reduced by increasing the price of water and
decreasing the demand. A flow weighted average price elasticity, ElasPrice, is calculated based on
each water user's price elasticity and initial demand.
26
-------
„, _ . ..t) (69)
ElasPmce = — v - —
Lu Lt VusePl,u,t
where Eu=price elasticity for water user, u.
The initial demand is reduced based on the percent increase in price, bPprice, chosen in the solution.
In addition, water demand is divided into potable and nonpotable demand based on the percent of
demand that can be met by nonpotable water,
^ (70)
VUsePMin.t ~ \*- 1 Of)
x( QUsePI,u,t x (1 - )) x (1 + ElasPrice x
u=2 to NUse
_ ,„ m^ , „ sepax,u^ ,. , _,, _. .
vseNPMin,t = (1 - --) ( Qt'sew'u't -* ( ElasPrice
p ("71")
100
u=2 to NUse
Minimum demand for potable and nonpotable water uses is set as:
QwtpUseP,t + bQlbtWUseP,t ^ QusePMin,t (72)
bQwtpUseNp,t + bQlbtWUseNp,t + bQwrfUseNp,t ^ QuseNpMin,t (73)
Consumptive water use
The final percent consumptive use for potable water use, Pconsusep,u,t, is calculated based on the
initial percent consumptive use of potable water, PconsUsePi,u,t> maximum percent of potable demand
that may be met by nonpotable water PuseNpMax,u> and the percent consumptive use of nonpotable
water, PconsiiseNp,u,t- This adjustment is necessary because nonpotable use may significantly differ
from potable water use in its consumptive percentage. For example, non-potable use may be all
consumptive such as outdoor watering or agricultural irrigation or almost all non-consumptive such as
toilet flushing. Depending on the intended use of the non-potable water, the user can specify the
appropriate percent consumptive use. We make the assumption that outdoor water use (e.g., watering
lawns) is fully consumptive via evapotranspiration; therefore, it does not enter the groundwater or, in
the case of overwatering, the storm sewer system.
P
rConsUseP,u,t
PconsUsePI,u,t 'UseNpMax.u X 'ConsUseNp,u,t (74)
100 - Py
seNpMax,u
In-stream flow: Minimum and maximum in-stream flows may be specified for the surface water
reach,QSwRest, and for minimum flows exiting the basin, QExtswOut.t- These constraints can be used
to ensure that minimum flow targets are met or that peak flows are reduced.
QswMm.t ^ QswRes,t where QSwMin,t= minimum in-stream flow for subbasin reach (75)
27
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WMOST v2
QswMax,t ^ QswRes,t where QSWMax,t= maximum in-stream flow for subbasin reach (76)
QswExtMin,t < QResExt,t where QSwExtMin,t= minimum flow exiting subbasin (77)
Groundwater flow: If known and desired, the user may set minimum groundwater outflows from
study area, QcwExtMin.t- If the optimization solution chooses unrealistic values for groundwater
exiting the study area (e.g., large flow one time step and no flow next step), then these constraints can
help generate more realistic solutions.
cwExtMin,t
(78)
Management limits: The model user may specify limits on the social and/or physical limits of
implementing four management options-increasing water price, fixing leaks in the water distribution
and wastewater collection systems, and inter-basin transfer.
"Pprice — PpriceMax * "price (' °)
where
PpriceMax = one time, maximum percent change in price
Dprice = a binary decision variable
bPwtpleakFix ^ PwtpLeakFixMax (80)
Where
PwtpLeakFixMax = maximum physical limit of leakage reduction in distribution system (e.g., given
age of system and the repair costs specified)
bPwwtpleakFix ^ PwwtpLeakFixMax (81)
Where
PwwtpLeakFixMax = maximum physical limit of repairing infiltration into the wastewater collection
system (e.g., given age of system and the repair costs specified).
Maximum IBT flows can be specified as daily, monthly, and/or annual limits.
For the daily limit, if the time step is daily, then, for each time step in the period of analysis,
bQibtWUseP,t + bQlbtWUseNp,t ^ QlbtWMaxDay (82)
bQusePIbtWw.t + OQuseNpIbtWw.t — QlbtWwMaxDay (83)
28
-------
For the daily limit, if the time step is monthly, then the limits are multiplied up to a monthly value;
therefore, for each time step in the period of analysis,
bQ,btwusep,t + bQ,btwuSeNP,t < QibtwMaxoay x NDay(month(t)) (84)
bQusepibtww,t + bQUseNpIbtww,t ^ QibtwwMaxDay x NDay(month(t)) (85)
where
= maximum potable water transfers from/to outside the basin for each day in the
optimization period
= maximum potable wastewater transfers from/to outside the basin for each day in
the optimization period
NDay(month(t)) = number of days in the month
Since the period of analysis may start and/or end on a day other than the start or end of a month or
year, limits are prorated to keep the limits accurate for partial months or years. For daily time steps,
monthly limits are prorated for the number of days in the month within the period of analysis. Annual
limits are prorated for the number of days or months in the year within the period of analysis.
For the monthly limit, if the time step is daily, then^or each month in the period of analysis,
ZNdtM (86)
bQibtWUseP,t + bQjbtWUseNp,t ^ QlbtWMaxMonth,m X 777 7 ., ,,^.\
NDay(month(t))
t=ltoNdtM ' ^ ^ JJ
ZNdtM (87)
bQusePlbtWw,t + bQUseNpIbtWw,t ^ QibtWwMaxMonth,m X TTT 7 fhff\\
t=itoNdtM -^ ^ ''
where
QibtwMaxMonth,m = maximum potable water transfers from/to outside the basin for each month, m
QibtwwMaxMonth,m = maximum potable wastewater transfers from/to outside the basin for each month, m
NdtM = number of time steps in the month
For the monthly limit, if the time step is monthly, then^or each month in the period of analysis,
bQibtWUseP,t + bQjbtWUseNp,t ^ QibtWMaxMonth,m
bQusePlbtWw,t + bQUseNpIbtWw,t ^ QibtWwMaxMonth,m
For the annual limit, for each year in the period of analysis,
y bQIbtwUsepj + bQIbtwUseNpj < QibtWMaxYr X
Ndt (90)
NdtYr
t=l to Ndt
ZNdt (91)
bQusePlbtWw,t + bQUseNpIbtWw,t ^ QlbtWwMaxYr X ~,
t=l to Ndt
29
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WMOST v2
where
= maximum potable water transfers from/to outside the basin for a given year in the
optimization period
= maximum potable wastewater transfers from/to outside the basin for a given year in the
optimization period
Ndt = number of time steps in the year
NdtYr = potential number of time steps in the full year (i.e., 365 or 366 for daily and 12 for
monthly time step)
30
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Baseline Hydrology Module
3. Baseline Hydrology Module
WMOST v2 includes three modules that assist users with retrieving and processing required input
data for baseline hydrology, stormwater hydrology, and flood-damage costs. These modules are
described in the next three chapters. The Baseline Hydrology module provides users with pre-
processed hydrology databases and automated functionality to retrieve and process the data and
populate the appropriate WMOST input fields. WMOST requires time series of runoff and recharge
for the hydrologic response units (HRUs)27 in the study area and a groundwater recession coefficient.
Previous applications of WMOST version 1 required obtaining these data from a calibrated/validated
simulation model such as Hydrological Simulation Program—Fortran (HSPF)28, Soil Water
Assessment Tool, or the Storm Water Management Model (SWMM). In version 2 of WMOST, we
provide a database of selected model outputs that the user can select from via the user interface rather
than cutting and pasting model output from an external source. Currently the model library includes
model output from HSPF models but other model types such as SWAT will be included in future
versions.
The pre-processed hydrology databases in WMOST version 2 are comprised of regional data from
calibrated HSPF models from which the user will select the watershed most similar to their study
watershed. Each HSPF model has two associated datasets - one for time series data and one for HRU
characteristics. The time series data include the runoff and recharge time series for each HRU and
precipitation and temperature time series for each watershed. The HRU characteristics data include
groundwater recession coefficients, effective impervious area (EIA)29, and infiltration data for each
HRU. Metadata are compiled for all the HSPF models and may aid the user in selecting the
appropriate watershed and hydrologic time period of interest. Metadata include the location of the
watershed, description of basic watershed characteristics from the HSPF documentation, time period
for available time series, and calibration time period.
The user downloads a zip file called "SupportFiles" which contains a folder by the same name with
database files (.csv files). The user must save this folder in the same folder as the WMOST Excel file.
The hydrology module shows the user the HRUs that exist in the selected HSPF watershed model and
the available time period. The user selects the HRUs that exist in their study area and the time period
of interest. The hydrology module extracts those data and sums the hourly time series data to the
appropriate daily or monthly time step based on user specification. Finally, the module populates the
appropriate WMOST input fields.
The groundwater recession coefficient is calculated based on the hydrology data. On the Groundwater
tab, the user can initiate this calculation by clicking on the "Calculate and Populate the Groundwater
Recession Coefficient" button. The calculation estimates one lumped groundwater recession
27 In WMOST, an HRU is a land area with characteristics (e.g., land cover, soil type) that responds similarly to
precipitation.
28 U.S. Geological Survey (USGS) has developed numerous Hydrologic Simulation Program - Fortran (HSPF) watershed
models that include hourly time series of precipitation, runoff and subsurface flows for the modeled region.
http://water.usgs.gov/software/HSPF/
29 Effective impervious area is impervious area in catchment that is directly connected to stream channels (i.e.,
precipitation falling on that area is effectively transported to the stream). http://www.epa.gov/caddis/ssr_urb_is2.html
31
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WMOST v2
coefficient for the study area by averaging the HRU specific recession coefficients weighted by their
respective areas and annual flows.
Databases are available for the following HSPF models in New England: Ipswich, Taunton,
Blackstone North, Blackstone South, Sudbury, and Pawcatuck. These data serve as generic time
series of land response to precipitation similar to curve numbers or loading coefficients. Therefore,
the user's study area does not need to overlap with the specific watersheds. Rather the modeled time
series of runoff and recharge for an HRU is expected to behave similarly in a comparable watershed
(e.g., similar climate, topography). The derivation of the hydrology databases are described in the
following subsections. Model output for other regions of the country will be included in future
releases.
Hydrology Time Series Database
Here we describe the process of extracting data from HSPF model output to provide the pre-packaged
inputs to WMOST in the Baseline Hydrology module. As we add time series from other model types
(e.g., SWAT), we will provide similar processing information for those models. HSPF defines HRUs
and represents subsurface flow differently from WMOST. In addition, HSPF models are detailed
simulation models run at the hourly time step while WMOST is a screening, optimization tool run at
the daily or monthly time step. As such the following considerations and assumptions are important to
note about the derivation of the hydrology databases.
Runoff from Pervious and Impervious Areas
Within a given HRU, HSPF delineates land into pervious and impervious areas. Different pervious
time series represent different types of developed land uses (e.g., residential) and undeveloped land
uses (e.g., forest). There is only one impervious runoff time series30. WMOST does not have different
runoff time series by impervious and pervious cover within an HRU. Thus, runoff data for developed
WMOST HRUs (e.g., residential, commercial) require combining pervious and impervious HSPF
time series. The percentages of effective impervious area (EIA) for developed land uses provide the
ratio for combining the pervious and impervious time series. For example, medium density residential
land use may be 12 percent EIA and its time series calculated as 12 percent residential impervious
time series and 88 percent low density residential pervious time series. The HSPF model
documentation provides the percent EIA value for each developed land use.
Subsurface Flow under Pervious Areas
HSPF delineates four subsurface storage components for pervious areas: interflow (IFWS), upper
zone (UZS), lower zone (LZS), and active groundwater (AGWS) (Figure 3-1). Two subsurface
components have outflows to the stream reach: interflow outflow (IFWO) and active groundwater
outflow (AGWO). WMOST delineates one subsurface storage component with one outflow to the
stream reach.
Figure 3-lshows the schematic for HSPF storage components and flows and their corresponding
variables' names.
30 Although HSPF models have impervious areas differentiated by name (e.g., residential and
commercial/industrial/transportation), they are hydrologically identical time series. They have been differentiated in case
of future water quality modeling with the HSPF model. This differentiation does not affect WMOST hydrology or future
water quality modeling.
32
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Baseline Hydrology Module
Figure 3-1. HSPF Schematic (EPA 2005)
0
33
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WMOST v2
To develop WMOST input data from HSPF data, we summed subsurface flows to derive one
subsurface flow time series. This process follows methods used by DeSimone et al. (2002) and EPA's
System for Urban Stormwater Treatment and Analysis IntegratioN (SUSTAIN; EPA 2014) where
interflow and active groundwater outflows (IFWO and AGWO) are summed to represent the total
groundwater outflow to the stream reach. The process in WMOST differs in that WMOST models
groundwater storage and outflow to the stream reach; therefore, WMOST requires inflow to the two
subsurface components rather than outflow. Inflow to interflow is represented by one distinct variable
IFWI. Inflow to AGWS must be calculated as the difference between inflow (AGWI) and
evapotranspiration (AGWET). Therefore, the final groundwater recharge for WMOST equals IFWI +
AGWI - AGWET. The external lateral inflows shown in the diagram do not exist in HSPF models
used to derive the WMOST hydrology database; therefore, this variable and associated flow is
excluded from consideration.
The above methodology required confirmation to ensure its applicability given: 1) the change in
variables (subsurface inflow rather than subsurface outflow) and 2) the timing of interflow can
resemble surface flow (SURO) more than groundwater flow depending on the watershed, the model
and the model calibration. Time series are graphed below for three flows (SURO, IFWI, AGWI) for
two HRUs in the Taunton watershed (Figure 3-2). AGWET was zero for both HRUs. The graphs
show that the magnitude and behavior of interflow resembles groundwater flow more than surface
runoff. The results are the same for different soil types. From these results, we conclude that the
approach is appropriate for WMOST.
Subsurface Flow Adjustments
All time series are at an hourly time step. At this scale, five of the six watersheds had negative
recharge values in their recharge time series; the Blackstone watershed has all positive values. When
evapotranspiration is greater than infiltration, negative net flow is the result. However, the linear
solver in WMOST can not accept negative flows. We assessed the magnitude of these negative flows
in the Sudbury watershed and found that they range from 7% in high-density residential HRU to 20%
in forest HRU for daily data as assessed for the entire period of record (50 years). (Impacts at the
monthly time step reduce to only 2-5% because there are fewer instances of negative values.)
Depending on the HRU configuration of a study area and time period selected, these values can have
a significant impact. To accommodate the solver and maintain accuracy, we replaced all negative
recharge values with zero and provide the negative recharge values as separate database files called
"RechargeAdjustment". The user may aggregate these time series to their desired time step and enter
the data under "Other groundwater withdrawal" on the groundwater worksheet. Note that the recharge
adjustment time series contain positive values but since they are used as a withdrawal time series, the
negative value is maintained.
34
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Baseline Hydrology Module
Figure 3-2. HSPF Time Series for Two Pervious HRUs
Taunton River Watershed
Medium Density Residential, Sand & Gravel Deposits
o.o?
0.035 — ' -Interflow
0.03 • • - Surface
Runott
0.025 _
3/1/2006
Taunton River Watershed
Medium Density Residental, Till and Fine-Grained Stratified Deposits
r
| 0.8
a 0.6
— • —Interflow
- Surfarr Runnff
0.8
0.4
iJ
A-A
J/l/2000
3/29/2006
4/26/2006
DIM
S/24/2006
b/n/200C,
35
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WMOST v2
Developed Areas with Public Water and Public Sewer
HSPF models delineate separate pervious areas for developed land uses for various combinations of
public or private water supply and sewered or septic wastewater disposal. Areas with private water
supply (i.e., private wells) assume a specific water withdrawal rate from the subsurface. Areas with
septic disposal assume a specific discharge rate into the subsurface. WMOST accounts for water
withdrawals and septic discharges; therefore, HSPF runoff and recharge time series are used only to
represent the land area's response to precipitation without adjustments for human withdrawals and
discharges. As such, for developed pervious areas, only land use time series that are designated as
public water and public sewer areas were extracted. HSPF time series for developed pervious areas
that are designated other than public water and public sewer (i.e., private water and septic, public
water and septic, private water and public sewer) were not used since use of these time series would
have resulted in double accounting for human use impacts on HRU hydrology.
Overview of Variables in the Hydrology Database
Table 3-1 below shows the time series that we extracted from HSPF. We used these data to:
1) provide metadata to the user when selecting the appropriate watershed and modeling time period
for their analysis, 2) simulate evapotranspiration in SUSTAIN runs as part of the Stormwater Module,
and 3) provide input to future potential climate change and sensitivity modules.
Table 3-1. Raw HSPF Time Series
Variable Type
Calculated
Water Flows
Measured Data
HSPF Variable
TAET
AGWI
AGWET
IFWI
SURO
PET
PREC
TEMP
Description
Total Actual Evapotranspiration
Active Groundwater Inflow
Active Groundwater Evapotranspiration
Interflow Input from Surface
Surface Outflow
Potential Evapotranspiration
Precipitation
Air Temperature
Note: Data Series Numbers (DSNs) are not specified because they vary among models
(e.g., Taunton versus Blackstone HSPF models).
The time series data were extracted, processed and compiled into one .csv file per watershed. The
final times series databases contain the data elements shown in Table 3-2 below. The files are named
according to the watershed name with a suffix of "Timeseries."
36
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Table 3-2. Hydrology Database for WMOST v2
Purpose
For use in WMOST calculations (hydrology
module)
For use in SUSTAIN calculations (stormwater
module) and metadata to aid user with watershed
and time period selection (hydrology module)
For user's reference
WMOST Variable
Runoff
Recharge
Air Temperature
Precipitation
Potential
Evapotranspiration
HSPF Variable
SURO
IFWI + AGWI - AGWET
TEMP
PREC
PET
HRU Characteristics Database
The second hydrology database for a watershed contains information on the following HRU
characteristics: groundwater recession coefficients, percent effective impervious area (EIA), and
infiltration rate. EIA values are provided in the HSPF documentation.
For recession coefficients, the HSPF models have two calibrated recession coefficients - one for
interflow and one for groundwater flow - for each pervious land use. (Impervious areas do not have
infiltration and subsurface flow.) WMOST has one subsurface storage and hence one recession
coefficient. Similar to other hydrology models, WMOST represents subsurface flow as a linear
relationship between groundwater storage and discharge. That is, groundwater discharge is the
product of the groundwater recession coefficient and groundwater storage. To calculate one recession
coefficient, each of the two HSPF recession coefficients were weighted based on their corresponding
average annual flow as fractions of total subsurface flow.
For infiltration, HSPF uses two parameters: INFILT (index to mean soil infiltration rate) and INTFW
(coefficient that determines the amount of water which enters the ground from surface detention
storage and becomes interflow).31 HSPF documentation specifies that the average measured soil
infiltration rate can be calculated as two times INFILT times INTFW. To support data needs of the
Stormwater Hydrology module, we extracted these two parameters from the HSPF UCI files,
calculated infiltration rates for HRUs according to the formula in the HSPF documentation and
included them in the hydrology dataset to serve as default infiltration values for stormwater modeling.
http://water.epa.gov/scitech/datait/models^asins/upload/2000_08_14_BASINS_tecnote6.pdf
37
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-------
Stormwater Module
4. Stormwater Hydrology Module
The Stormwater Hydrology module transforms baseline runoff and recharge time series into
corresponding time series reflecting implementation of Stormwater best management practices
(BMPs) chosen by the user. Previous applications of WMOST that included the assessment of
Stormwater management required the user to derive these data using an external model. The
Stormwater Hydrology Module automates this process by dynamically linking with EPA's SUSTAIN
model to derive the necessary input data for WMOST (EPA 2014a).
BMP Selection and Sizing
SUSTAIN uses input from EPA's Storm Water Management Model (SWMM) or a similar model for
runoff volume and pollutant loads and calculates changes in runoff due to a Stormwater BMP using a
combination of SWMM and HSPF algorithms. It can also calculate BMP costs and select among
BMP configurations to meet an objective such as a load and/ or flow reduction target at minimum
cost. WMOST uses SUSTAIN in simulation, not optimization, mode. WMOST optimizes for one or
more water management objectives utilizing not only Stormwater but other watershed management
practices in drinking water, wastewater, and land conservation programs. (See WMOST User Guide
for complete description of management options.) Therefore, WMOST needs simulation data from
SUSTAIN so that WMOST may optimize across watershed practices.
In the Stormwater Hydrology module, the user selects the type(s) of BMP to consider and specifies
the desired design size(s). If the Baseline Hydrology module is not used, the user must also provide
the percent impervious area and infiltration rate of developed HRUs. Based on the selection and
input, the module runs the selected BMP types and sizes through SUSTAIN in simulation mode.
These setups simulate one type of BMP per HRU. The user may perform sequential runs of the
Stormwater BMP module in WMOST for a defined sequence to simulate multiple BMPs. If more
complex Stormwater modeling with a wider range of BMP options is desired or warranted based on
WMOST results (e.g., pervious pavement plus bioretention basin for remaining impervious areas), the
user may still run a Stormwater model outside of WMOST and manually input those results.
WMOST version 2 has the capability to simulate three of the BMPs included in SUSTAIN; future
versions will include more options. We selected three BMPs from the following BMPs that are
available in SUSTAIN and for which we have default design parameters from the Performance
Analysis study for New England and SUSTAIN case studies (EPA 2010, EPA 2014a). BMPs are
highly flexible and may be parameterized for the following hydrologic processes: evaporation from
standing surface water, transpiration from vegetation, infiltration of ponded water into soil media,
percolation of infiltrated water into groundwater, and/or outflow through an orifice or weir.32
32 HSPF BMP Web Toolkit (http://www.epa.gov/athens/research/HSPFWebTools/) categorizes BMPs according to
hydrologic functions as follows: 1) storage BMPs without infiltration ("grey"), 2) infiltration BMPs with surface
ponding ("green- surface storage") and 3) infiltration BMPs with surface ponding and subsurface storage ("green -
surface and subsurface storage").
39
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WMOST v2
SUSTAIN BMP Options
> Bioretention Area: Depressed area with porous backfill under a vegetated surface. It provides
groundwater recharge and runoff detention. May include an underdrain with subsurface
outflow.
> Gravel Wetland/ Constructed Wetland: Potentially up to three parts to the system - a sediment
forebay and two wetland cells with subsurface discharge.
> Wet Pond: Excavated area that is designed to permanently retain some volume of water at all
times. Wet ponds provide storage detention, infiltration, and biological uptake of nutrients.
> Dry Pond: Excavated area that stores stormwater runoff for a limited amount of time,
providing water storage detention and improved infiltration of runoff.
> Infiltration Basin: Excavated area with gravel backfill and no outlets. Infiltration basins
collect runoff during a storm event and release it into the soil by infiltration.
> Infiltration Trench: Rock-filled ditches with no outlets. Infiltration trenches collect runoff
during a storm event and release it into the soil by infiltration.
> Porous Pavement: Pavement that is an alternative to asphalt or concrete surfaces that allows
stormwater to drain through the porous surface to a stone reservoir underneath. The
pavement's reservoir temporarily stores surface runoff before allowing the runoff to infiltrate
the soil.
> Water Quality Swale/ Grassed Swale: Shallow grass-covered hydraulic conveyance channels
that help facilitate infiltration and slow runoff by providing storage detention.
In selecting the initial set of BMPs to incorporate into WMOST version 2, we considered the
appropriate hydrological soil groups, land use types, hydrologic treatment processes, and unit costs.
We selected the BMPs shown in Table 4-1 for the user to evaluate. These selections are based on
meeting WMOST's two primary application objectives at lowest unit cost: 1) to achieve minimum in-
stream flows for aquatic health while meeting water supply needs (infiltration trench) and 2) to reduce
flooding related damages (detention pond). We included bioretention basins or rain gardens because
of their popularity and aesthetic compatibility with residential and commercial applications33.
33 http://www.epa.gov/regionl/soakuptherain/index.html,
http://www.seattle.gov/util/MyServices/DrainageSewer/Projects/GreenStormwaterInfrastructure/RainWise/
-------
Table 4-1. Selected BMPs forWMOST v2 (EPA and MassDEP 2009, EPA 2011a)
BMPs
Rain garden/
Bioretention basin with
underdrain
Infiltration trench
Detention pond
Land Use
Any
Any
Any
Hydrologic Soil
Group
Any
A,B
Any
Hydrologic Treatment
Infiltration,
Evapotranspiration,
Detention
Infiltration,
Evapotranspiration,
Detention
Evapotranspiration,
Detention
New Development
Unit Cost
$8.64/ft3 treated
$7.78/ft3 treated
$4.24/ft3 treated
BMP unit costs originate from EPA and MassDEP (2009) with an adjustment for retrofit conditions
that includes a cost multiplier of 2 and a 35 percent add-on for engineering and contingencies (EPA
201 la). (Users can substitute their own costs if desired.) The final BMP cost is calculated as follows:
BMP Cost = Volume of Runoff to Manage (ft3) x Retrofit Cost ($/treated ft3)
Design parameters shown in Table 4-2 below are used for BMP specifications and originate from
several sources (MPCA 2014, EPA 2014b, EPA 201 la, EPA 2010, EPA 2009, EPA and MassDEP
2009).
Table 4-2. BMP Specifications
Parameter
Orifice Height (ft)
Orifice Diameter (in)
Weir Height (ft)
Soil Depth (ft)
Soil Porosity (0-1)
Soil Field Capacity (ft/ft)
Soil Wilting Point (ft/ft)
Vegetative Parameter A (0.1-1.0)
Soil layer infiltration rate (in/hr)
Underdrain switch (0-off, 1-on)
Depth of storage media below underdrain (ft)
Underdrain void space (0-1)
Background infiltration rate (in/hr)
Bioretention
Area
0
6
0.5
2.5
0.4
0.3
0.15
0.9
4
1
0.67
0.4
Native soil rate
Infiltration
Trench
0
0
0.5
0.5
0.4
0.3
0.15
1
0.8
1
6
0.45
Native soil rate
Detention
Basin
4
Sized34
4
1
0.4
0.3
0.15
1
Native soil rate
0
0
0
Native soil rate
34 Sized based on 24-hour drainage of runoff through the ponding basin and using the orifice equation Q = C x A x
41
-------
WMOST v2
Based on the user-specified depth, the module calculates the required storage volume for the BMP
following the Massachusetts example for the static method35:
Required storage volume = Impervious area x Runoff depth to be managed
For an acre of soil type B, the required volume for the Massachusetts recharge standard would be
0.35" or approximately 1,271 cubic feet per acre of impervious surface.
The storage volume per square foot of BMP for each type of BMP is calculated as follows:
BMP unit storage volume = Sum of (Depth x Porosity) across all components
For example, a bioretention basin with an underdrain has 6 inches of ponding depth (100% storage
volume), 30 inches of 0.40 porosity soil mix (40% storage volume) and 8 inches of 0.40 porosity
gravel mix (40% storage volume). This results in 1.77 cubic feet of storage volume per square foot
of BMP.
Using the unit storage volume, the module calculates the required BMP area. In this example, the
BMP area must be approximately 719 square feet or 1.7 percent of the total site area of one acre.
Linking with SUSTAIN
In order to automate the calculation of reduction of runoff volumes by stormwater BMPs, WMOST
provides a linkage with one of the modules in EPA's SUSTAIN tool. The stormwater module
prepares input files for SUSTAIN, calls SUSTAIN and retrieves outputs. SUSTAIN requires time
series data at least at an hourly resolution, which are available to the user if the Baseline Hydrology
module is used. Sub-daily modeling for stormwater increases the accuracy of the simulated BMP
performance and resulting changes in runoff and recharge. The Stormwater Hydrology module
aggregates the time series to a daily or monthly time step for final use in WMOST. Further details on
this process are described in the remainder of this section.
The aquifer component in SUSTAIN tracks water infiltrated through BMPs to the aquifer. The
aquifer does not affect the BMP function or performance. Only the aquifer is affected by inflow from
the BMP (Figure 4-1). WMOST has a component that tracks aquifer inflow and storage as well as
baseflow to the stream; therefore there is no need to repeat this modeling in SUSTAIN.
In addition, inputting an external recharge time series into SUSTAIN does not affect the BMP
performance and output. An external recharge time series affects the aquifer component but will not
affect BMP performance. Therefore, only the runoff time series is input to SUSTAIN and the aquifer
component is not utilized.
35 These baseline runoff and recharge time series reflect runoff and recharge from both pervious and impervious areas of an
HRU. However, the BMP sizing will be based on the specified sizing depth and impervious area. This methodology follows
SUSTAIN applications and stormwater regulations. For example, Massachusetts Stormwater Handbook states that "for
purposes of [recharge and solids standards], only the impervious areas on the project site are used for purposes of calculating
the [volumes] (MassDEP 2014)."
42
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Stormwater Module
Figure 4-1. SUSTAIN Flows With and Without an Aquifer Component (EPA 2014b)
Enhanced Network
Original Network
Surface
Baseflow
Runoff
S
1
e
c-
1
J
BMPs
BMP Type
Dimensions
..••• ..> Conduit Pipe/Chann
Baseflow
Surface
Runoff
„
quifer
BMPs
BMP Type
Dimensions
F-Table
I
Conduit
Assessment
Point
T
'
-
, *
Optimization Metrics
Volume
Peak
Mass
Assessment
Point
Legend: Original Updated
New
Dummy Node
Pipe/Channel
F-Table
Optimization Metrics
Volume
Peak
Mass
Exceedance Frequency
Flow-Duration Curve
The module prepares the following input files necessary to run SUSTAIN:
• Runoff time series for each HRU (e.g., HRU1 .txt),
• Temperature time series (e.g., climate.swm), and
• Main input file (e.g., input.inp ) which requires the information shown in Appendix B.
The module prepares the time series files using data from the hydrology time series database, user
specifications, appropriate default BMP characteristics, and HRU infiltration rates/soil types. If the
user does not use the hydrology module, the Stormwater module will request the necessary data
including subdaily HRU runoff time series, temperature time series, infiltration rates, percent
impervious area, and latitude of the study area.
The module calls SUSTAIN from WMOST referencing the input files and the SUSTAIN.dll. The
setup initiates one run of SUSTAIN that simulates all combinations of developed HRUs and BMPs.
This requires setting up each combination as a separate "subbasin" representing the WMOST HRU
routed to one BMP. Each subbasin will be specified as one acre with an appropriately sized BMP.
These specifications will result in output values for runoff, recharge, and BMP costs that are on a "per
acre" basis as required by WMOST. The module will initiate the simulation run by calling
"SUSTAINOPT.dll(strFilePath, strScenario,"")", where the parameters are defined as follows.
• strFilePath indicates the folder location for all input files.
• strScenario specifies which of the following run options to initiate: single run, batch mode,
or run for select solutions. In this case, we will specify a single run.
• " " = selection solutions to run if strScenario = run for select solutions. In this case, we will
leave this blank.
43
-------
WMOST v2
SUSTAIN outputs results into separate files for each subbasin, in this case a combination of HRU and
BMPs. The WMOST Stormwater Hydrology module reads data from these files then deletes them to
keep the user's folder clean.
SUSTAIN provides nine types of outflow in units of cubic feet per second. The module processes
these flows as follows:
• Runoff = Weir outflow + Orifice or channel outflow + Untreated outflow
• Recharge = Underdrain + Seepage to Groundwater
• Evapotranspiration
The following flows are not used because it would lead to double counting:
• Infiltration;
• Total outflow and
• Percolation to underdrain storage.
The module aggregates the hourly time series to a daily or monthly time step of runoff and recharge.
Evapotranspiration is retained for potential future use in climate change sensitivity analyses. Final
Stormwater managed runoff is the runoff from the SUSTAIN simulation as shown above. The
SUSTAIN recharge or infiltration is added to the WMOST baseline recharge, reflecting the additional
recharge due to BMP implementation. Finally, the module populates the runoff and recharge
worksheets with the appropriate time series after post-processing.
44
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Flood-Damaged Module
5. Flood-Damage Module
The goal of the flood-damage module is to provide WMOST with flood-damage costs so that
WMOST can utilize that information when determining the least-cost set of actions to meet watershed
goals. Medina et al. (2011) found that the present value of avoided flood damages was equivalent to
20 percent of the annualized cost of retrofitting a highly urbanized watershed with GI BMPs.
Therefore, including flood damages and their reduction from reduced flood flows provides a more
comprehensive accounting of costs and benefits in the WMOST optimization and may result in
selecting a different mix of practices for meeting water resources management goals.
Considerations for the Flood-Damage Module
The general methodology for modeling flood damages in risk assessments includes the
following steps:
1. Peak flow: Hydrologic analysis is conducted to estimate the peak streamflow for various
recurrence intervals (e.g., 10-year streamflow). Depending on the modeling accuracy desired,
hydrologic modeling may be performed using a watershed simulation model such as
HEC-HMS36 or values obtained from existing statistical analyses (e.g., USGS PeakFQ37).
2. Flooding: Hydraulic analysis is conducted to estimate the extent and depth of water in the
floodplain associated with various recurrence interval flows. This analysis is generally
performed using geospatial data and software such as HEC-RAS38.
3. Damage: Geospatial and economic analysis is applied to determine the location and value
of assets in the floodplain and estimate the direct damages (e.g., flooding of building's
basement) and additional indirect economic damages (e.g., loss of income due to direct
damages) from various recurrence interval floods. The primary software and approach used
to assess damages is FEMA's FfAZUS MH39.
Repeating the three-step process for multiple recurrence intervals provides data for developing a
flow-damage cost curve. The annualized loss (AL) is calculated by multiplying the damages with
their respective probability of occurrence. Data for one or more of these steps may be available from
an existing flood insurance study.
To incorporate flood-damage costs in the optimization module of WMOST, we identified the
following requirements: 1) new input data on flood flows, their recurrence interval and the cost of
associated damages; 2) linear representation of flood-damages in the calculation of total management
costs which is a requirement of the linear programming solver used to solve the optimization
problem; 3) translation between peak flood flows considered in flood-damage modeling and average
daily flow calculated by WMOST; 4) input data and linearization with sufficient accuracy to
determine the relative cost-effectiveness of management actions; and 5) usability without extensive
effort or flood modeling expertise.
36 http://www.hec.usace.army.mil/software/hec-hms/
37 http://water.usgs.gov/software/PeakFQ/
38 http://www.hec.usace.army.mil/software/hec-ras/
39 https://www.fema.gov/hazus
45
-------
WMOST v2
As described above, the standard approach to derive a flood-damage cost curve involves three
analyses. Completing these analyses within WMOST would duplicate existing, publicly available
methods and tools and require considerable programing effort. Therefore, we considered two main
approaches for the flood module. The first approach would accept results from flood-damage
modeling, that is flows and associated damage costs, and construct a linear cost curve based on the
data. The second approach would use a regression equation to relate flow and watershed
characteristics to flood damages. The regression could be programmed in WMOST and the user
would provide values for the required explanatory variables. The criterion to provide an option
without extensive effort or flood modeling expertise initially suggested that a regression approach
would be an ideal match for WMOST. However, existing regression approaches do not meet the
requirement for sufficient accuracy. The project's Technical Advisory Group consistently emphasized
that at the local scale, infrastructure (e.g., culverts and impoundments) has a significant impact on
flooding. Infrastructure is not likely captured in regional or national regression analyses given more
significant explanatory variables at that scale and the lack of data sources for the location of local
infrastructure. A review of two national-scale regression approaches (AECOM 2013 and Medina
201 I/Atkins 2013) found that the explanatory variables did not include consideration of infrastructure
and that assumptions that were valid to make at the national scale are not appropriate for local scale
application. We considered developing new regression equations specific for New England and
including infrastructure among the explanatory variables. Discussion with U.S. Army Corps of
Engineers Institute for Water Resources indicated that a generalized equation for predicting local
flooding damage is a long sought goal by USAGE and FEMA (White and Baker 2015). However,
they did not expect a regional equation to provide sufficient accuracy for local, screening level
decisions, similar to the TAG input cited above regarding existing national regressions.
Integrating Flood-Damages in WMOST Optimization
The two goals of providing accuracy while circumventing the need for a high level of effort or
technical expertise in specific topics are challenges for WMOST development based on its objective
to inform municipal and regional scale decision making without time-consuming or costly studies.
The result has been using output from existing detailed simulation models within the region or in
similar watersheds for input data as done for baseline hydrology and stormwater management which
are facilitated by the Baseline Hydrology and Stormwater Hydrology modules in WMOST v2. The
Flood-Damage module follows a similar approach by accepting input data based on results from
flood-damage modeling within the watershed of interest, constructing a linear cost curve based on
those data and including the cost in the total management cost calculation.40 The User Guide provides
instructions for conducting new flood damage modeling based on publicly available data sources. The
instructions should allow someone without flood modeling expertise to perform the analyses needed
to generate input data for the Flood Module.
The Flood-Damage module in WMOST implements the following steps:
> Input Data: The user provides at least three sets of data points consisting of flows, their return
period and associated flood damage costs. These data points may be based on HEC/HAZUS
modeling or historic flood events. Directions in the User Guide emphasize that additional values
beyond the minimum requirement of three and values for a zero-damage and a maximum-damage
40 Appendix C documents the approaches evaluated for incorporating flood damages in the optimization module and
rationale for the selected approach.
48
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flow will increase the accuracy of results. The minimum requirement for three values follows a
similar requirement in HAZUS and discussion with the TAG.
The requested data points are daily flows for given return intervals and associated damage values
since WMOST calculates daily flows. Users should have access to the daily flow equivalents of
peak or flood flows based on the flood damage analyses. In general, stream gage data are daily
measurements and instantaneous peak flows are estimated based on the daily data. In case the
user does not have access to the daily flow corresponding to the flood damages, the User Guide
refers users to USGS resources such as PeakFQ and state level regression equations to estimate
such flows.
> Linear Interpolation: The flood module fits linear equations between user provided data points.
These equations are used to interpolate flood damage costs for flow values that fall between data
points. Following the methodology of Medina et al. (2011) and Atkins (2013), the module will
calculate the annualized losses from each data point by multiplying the flood damage and the
inverse of the return period. Equations are fit between the data pairs of annual loss and flow. The
module does not perform extrapolation; that is, damages are assumed to be zero for flows below
the lowest flood flow specified. Damages from flows above the highest flood flow are assumed to
be the same as those from the highest flood flow. Changes in streamflow are not linearly related
to resulting changes in flood plain and damages; therefore extrapolating beyond the data points in
either direction may lead to over estimating damages and benefits of avoiding damages41. In
addition, one can not assume a specific form for the flow-damage curve as evidenced in
discussions with the TAG and literature (USAGE 2013, Prettenthaler et al. 2010, Mays 2010).
The model provides a warning to the user if any flows are above the highest flow data point
provided by the user. This will inform the user that some damages and benefit of avoiding those
damages may not be counted.
> Adding to the Objective Function: The linear equations are programmed in the linear
programming problem as piece-wise linear approximation of one equation. This approach
provides limits for the applicability of each equation for the segment of flow values specified.
A limitation of the Flood-Damage module is that WMOST must be run on a daily time step, thus
requiring more memory-intensive processing. In addition, flooding is evaluated for each daily time
step; therefore, each day that streamflow exceeds the smallest flood flow, an individual flooding
event is considered to take place with associated flood damages. If a flood persists for multiple
consecutive days, flood damages will be incurred each day and overestimated. The user may evaluate
if this occurred during the modeling time period by assessing whether daily modeled streamflow
exceeded minimum flood flow within a minimum time period, for example, within a week or month.
Within these time periods, it may be reasonable to assume that a second flood would not cause
additional damage. This limitation may be addressed automatically for users in future versions of
WMOST. Second, the module will only affect results if the modeled time period includes flood
flows. The User Guide suggests that users view the precipitation data available from the Baseline
Hydrology module to identify and run wet years when using the Flood-Damage module. The User
Guide also suggests that the user run the model with and without the flood module. The two results
OO
41 For example, extrapolating below the lowest flow may assume damages when the streamflow is contained in the
channel. Extrapolating above the highest flow may assume damages when little additional assets may be damaged by the
incremental change in flow.
47
-------
WMOST v2
will show any differences in the mix of practices and associated direct costs (direct capital and annual
operations costs versus indirect flood damage costs). Since the cost of flood damages are incurred
across multiple stakeholders, the user may want to consider the difference in direct costs between the
two runs to determine whether to make the additional investment in flood prevention and/or pursue
joint funding with the other beneficiaries of reduced flooding.
48
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Internal Configuration
6. Internal Configuration
WMOST is implemented using Excel as the interface software to provide an accessible and familiar
platform for users. VBA is used to:
1) Automate the setup of input worksheets for different numbers of HRU types, HRU sets, and water
user types per user specifications,
2) Assist users in navigating among input and output sheets,
3) Access and pre-process input data via the Baseline Hydrology, Stormwater Hydrology and Flood-
Damage modules and
4) Initiate optimization runs.
VBA also reads the input data from worksheets and generates a custom linear programming (LP)
optimization model by creating equations based on the input data. Finally, VBA calls the LP solver
called Lp_solve and returns the results to the Excel interface for the user. Figure 6-1 shows the flow
of information and process links between components of WMOST
Lp_solve 5.5 is freely available at http://lpsolve.sourceforge.net/. It is a mixed integer linear
programming solver. The website provides background on LP (e.g "What is Linear Programming?",
"Linear programming basics", and detailed description of the solver and its use with various software.
-------
WMOST v2 Theoretical Documentation
Figure 6-1. WMOST Internal Configuration
WMOST internal Configuration
Excel : User Interface Worksheet*
Excel: Visual Basic Modules
Outiide Ejicel
input Worksheets
Introductory
Worksheet
unki to input jnd output
wGfknneeli
krifluntt running
ojl.i- t.ii.nn
Output Worksheets
Input/Interface Setup
' • Setup input worksheets according user oc*ci1ic jtort1.
Hydrology Module
1 * ;,:::! TunCdf »fld WrWff* c! jnd lime period
Storm water Module
* Pvfrpdrp ringHit lilfi for ilMmwabff rrMrugrrn^n^imulaDCtl
i daU, as n
* Oritnr Inea
babrifie, costi, fevcnucv, & conbl* jinu
Main
', including ptfcewftc approumMkin erf
tcrfmnt
Table Outputs
PtopulHr output wailormts wth uWe of rnults from lp_ioh«
Graphical Outputs
Hydrology Database
Runoff, retrwRC1, jnd olrter HSF1F oertved
Stormwater
Management Tool
Linear Programming Solver
50
-------
Input Data
7. Summary of Input Data
Variables
Units
Description
General
TPlan
i
yrs
%
Planning horizon
Interest rate
Runoff and Recharge Rates
QRu,s,l,t
QRe,s,l,t
inches/time step
inches/time step
Unit runoff for each HRU in each set of
baseline and managed set of HRUs for each
time step
Unit recharge for each HRU in each set of
baseline and managed set of HRUs for each
time step
Point Sources
QptSw,t
QswPt,t
QptGw,t
QcwPt,t
MGD per time step
MGD per time step
MGD per time step
MGD per time step
Flow from private point source to surface water,
i.e., discharge
Flow from surface water to private point source,
i.e., withdrawal
Flow from private point source to groundwater,
i.e., discharge
Flow from groundwater to private point source,
i.e., withdrawal
Land Use: Conservation and Stormwater Management
As,l
Amins ;
Amaxs i
CCASil
COmAs.
Acres
Acres
Acres
S/Acre
S/Acre/yr
Baseline or scenario land areas
Minimum area for each HRU
Maximum area for each HRU
Capital cost to conserve or manage HRU / in
land use set s
O&M cost to conserve or manage HRU / in land
use set s
Groundwater Storage
kb
vcw,,
*Gw,Min
*Gw,Max
VGwExt,t
QcwExtMin,t
QsxtGwt
I/time step
MG
MG
MG
MG/time step
MG/time step
MG/time step
Groundwater recession coefficient
Initial groundwater volume
Minimum volume
Maximum volume
Flow from study area groundwater to external
groundwater
Minimum flow from study area groundwater to
external groundwater
Flow from external groundwater into study area
groundwater
51
-------
WMOST v2
Variables
Units
Description
Surface Water/Stream Reach
QsxtSw,t
QswRes,t
QswResMin.t
QswResMax.t
QswExtMin,t
jf/sec
ft3/sec
jf/sec
ft3/sec
ff/sec
Inflow from external surface water to study area
stream reach
Flow from stream reach to reservoir
Minimum in-stream flow in reach
Maximum in-stream flow in reach
Minimum surface water flow out of study area
Reservoir/Surface Storage
VResJ
*Res,Min
'Res,Max
QExtSwOutMin.t
CC,RCS
r
U0m,fles
MG
MG
MG
ft3/sec
$/MG
$/MG/yr
Reservoir volume
Minimum reservoir volume
Current maximum reservoir volume
Minimum flow
Capital construction cost
O&M costs
Water Users
QusePI,u,t
'ConsUsel,u,t
PuseNpMax,u,t
p
rConsUseNp,u,t
RuseP
"useNp
RWW
p
rSep,u
MOD
%
%
%
S/100ft3
S/100ft3
$/100ft3
%
Demand for each user per time step
Percent consumptive use for each water user for
an average month for each month
Maximum percent demand that can be met by
nonpotable water for each user for an average
month for each month
Percent consumptive use for nonpotable water
for each user for an average month for each
month
Customer's price for potable water
Customer's price for nonpotable water
Customer's price for wastewater
Percent septic use for each user
Demand Management
Eu
r
'-CjPrice
^Om,Price
CcDm
^OmDm
% demand reduction / % price
increase
$
S/yr
S
S/yr
Price elasticity for each user
Capital cost to implement price increase
O&M cost to administer price increase (e.g.,
resurvey for appropriate price etc.)
Capital cost of direct demand management
Annual O&M costs for direct demand
management
Interbasin Transfer
-ClbtW
S/MGD
Initial cost for obtaining rights to and building
infrastructure for interbasin transfer of potable
water
52
-------
Input
Variables
Interbasin Transfer
Qr/fetww
ClbtW
ClbtWw
QlbtWMaxDayt
QlbtWwMaxDay ,t
QlbtWMaxMonth.t
QlbtWwMaxMonth,t
QlbtWMaxYr.t
QlbtWwMaxYr,t
Units
Interbasin Transfer
S/MGD
S/MGD
S/MGD
MGD
MGD
MGD
Description
Interbasin Transfer
Initial cost for obtaining rights to and building
infrastructure for interbasin transfer of
wastewater
Service cost for water interbasin transfer
Service cost for wastewater interbasin transfer
Maximum interbasin transfer flow for water and
wastewater on a daily limit
Maximum interbasin transfer flow for water and
wastewater on a monthly limit
Maximum interbasin transfer flow for water and
wastewater on an annual limit
Nonpotable water distribution system (NpDist)
Q.Wpdist
^Om,Npdist
QNpdistI
'Npdist.Exist
' Npdist,New
$/MGD
$/MGD/yr
MGD
yrs
yrs
Capital construction cost for nonpotable
distribution system
O&M cost for nonpotable distribution system
Nonpotable distribution system: Current max
capacity
Lifetime remaining on existing construction of
nonpotable distribution system
Lifetime for new construction of nonpotable
distribution system
Water Treatment Plant
^C,CwPump
r
'-Om,GwPump
QcwPumpI
T
1 GwPump,Exist
T
1 GwPump,New
r
uC,SwPump
r
^Om,SwPump
^cSwPumpl
T
1 SwPump, Exist
T
1 SwPump,New
Cc,wtp
(•Om.Wtp
Twtpfxist
'wtp,New
Qwtp,Max
Cc.WtpLeak
S/MGD Gw pumping: Capital construction cost
$/MGD/yr
MGD
yrs
yrs
S/MGD
$/MGD/yr
MGD
yrs
yrs
S/MGD
S/MGD/yr
yrs
yrs
MGD
S
Gw pumping: O&M costs
Gw pumping: Current max capacity
Gw pumping lifetime remaining on existing
construction
Gw pumping lifetime of new construction
Sw pumping: Capital construction cost
Sw pumping: O&M costs
Sw pumping: Current max capacity
Sw pumping lifetime remaining on existing
construction
Sw pumping lifetime of new construction
Wtp: Capital construction cost
Wtp: O&M costs
Wtp lifetime remaining on existing construction
Wtp lifetime of new construction
Wtp: Current max capacity
Capital cost of survey & repair
53
-------
WMOST v2
Variables
Units
Description
Water Treatment Plant
Com.WtpLeak
'WtpLeakFixMax
$/yr
%
O&M costs for continued leak repair
Maximum percent of leaks that can be fixed
Wastewater treatment plant
Cc,wwtp
^Om,Wwtp
'Exist, Wwtp
T
1 New, Wwtp
Qwwtp,Max
p
rWwtpLeakFixMax
p
rWwtpleakl
^C,WwtpLeak
r
'-Om,WwtpLeak
$/MGD
$/MGD/yr
yrs
yrs
MOD
%
% of WW Inflow
$
$/yr
Capital construction cost
O&M costs
Lifetime remaining on existing construction
Lifetime of new construction
Current maximum capacity
Maximum percent of leakage that can be fixed
Initial groundwater infiltration into WW
collection system
Initial cost of repairs
O&M costs of repairs
Water reuse facility
Cc.Wrf
Com,Wrf
' Exist, Wrf
TNew,Wrf
Qwrf.Max
S/MGD
$/MGD/yr
yrs
yrs
MGD
Capital construction cost
O&M costs
Lifetime remaining on existing construction
Lifetime of new construction
Current maximum capacity
Aquifer Storage and Recovery
CC,AST
^Om,Asr
T
1 Exist,Asr
T
1 New,Asr
Q 'AST, Max
$/MGD
S/MGD/yr
yrs
yrs
MGD
Capital construction cost
O&M costs
Lifetime remaining on existing construction
Lifetime of new construction
Current maximum capacity
Flood Flows and Damage
QT
T
CQT
ft3/sec
Years
$
Flood flow of recurrence interval T
Recurrence interval of flood flow
Damage associated with a flood flow
54
-------
References
8. References
AECOM. 2013. The Impact of Climate Change and Population Growth on the National Flood
Insurance Program through 2100. Prepared for Federal Insurance and Mitigation Administration and
Federal Emergency Management Administration. June 2013.
Atkins. 2013. Flood Loss Avoidance Benefits of Green Infrastructure for Stormwater Management.
Prepared forthe U.S. Environmental Protection Agency, Office of Water. July 2013.
Burkham, D.E. 1977. A Technique for Determining Depths for T-year Discharges in Rigid Boundary
Channels, pp. 77-83, USGS Water-Resources Investigations Report.
DeSimone, L.A., et al. 2002. Simulation of Ground-Water Flow and Evaluation of Water-
Management Alternatives in the Upper Charles River Basin, Eastern Massachusetts. Water-Resources
Investigations Report 2002-4234. U.S. Geological Survey, Westborough, Massachusetts.
Fill, H.D. and A.A. Steiner. 2003. "Estimating Instantaneous Peak Flow from Mean Daily Flow
Data", Journal of Hydrologic Engineering 8(6): 365-369,
doi: http://dx.doi.org/10.1061/(ASCE)1084-0699(2003)8:6(365)
Lund, J.R. 2002. Floodplain Planning with Risk-Based Optimization. Journal of Water Resources
Planning and Management. 128:3. May/June 2002, pp. 202-207.
Massachusetts Department of Environmental Protection (MassDEP). 2014. Massachusetts
Stormwater Handbook. Accessed November 2014, http://www.mass.gov/eea/agencies/massdep/
water/regulations/massachusetts-stormwater-handbook.html
Mays, L.W. 2010. Water Resources Engineering. John Wiley & Sons, 890p.
Medina, D., J.Monfils, and Z. Baccala. 2011. Green Infrastructure Benefits for Floodplain
Management: A Case Study. Stormwater. November-December 2011.
Minnesota Pollution Control Agency (MPCA). "Design Infiltration Rates". Retrieved on December
16, 2014, http://stormwater.pca.state.mn.us/index.php/Design_infiltration_rates.
Prettenthaler, F., P. Amrusch, and C. Habsburg-Lothringen. 2010. Estimation of an Absolute Flood
Damage Curve Based on an Austrian Case Study Under a Dam Breach Scenario. Nat. Hazards Earth
Syst. Sci., 10,881-894.
U.S. Army Corps of Engineers (USAGE). 2013. Flood Risk Management, IWR Report 2013-R-05.
U.S. Environmental Protection Agency (EPA). 2005. HSPF Version 12.2 User's
Manual, http://water.epa.gov/scitech/datait/models/basins/bsnsdocs.cfm#hspf, accessed 9/30/2014.
U.S. Environmental Protection Agency (EPA). 2008. Handbook for Developing Watershed Plans to
Restore and Protect Our Waters. March 2008. Office of Water, Washington, D.C.
EPA 841-B-08-002.
U.S. Environmental Protection Agency (EPA) and Massachusetts Department of Environmental
Protection (MassDEP). 2009. Optimal Stormwater Management Plan Alternatives: A Demonstration
Project in Three Upper Charles River Communities. Prepared by Tetra Tech, Fairfax, Virginia.
http://www.epa.gov/regionl/npdes/stormwater/assets/pdfs/BMP-Performance-Analysis-Report.pdf
55
-------
WMOST v2
U.S. Environmental Protection Agency (EPA). 2009. "SUSTAIN—A Framework for Placement of
Best Management Practices in Urban Watersheds to Protect Water Quality". Prepared by Tetra Tech,
Inc. in Support of EPA Contract No. GS-10F-0268K.
U.S. Environmental Protection Agency (EPA). 2010. Stormwater Best Management Practices (BMP)
Performance Analysis. Prepared by Tetra Tech, Fairfax, Virginia.
http://www.epa.gov/regionl/npdes/stormwater/assets/pdfs/BMP-Performance-Analysis-Report.pdf
U.S. Environmental Protection Agency (EPA). 201 la. Memorandum to Project File: Methodology for
Developing Cost Estimates for Structural Stormwater Controls for Preliminary Residual Designation
Sites for Charles River Watershed Areas in the Communities of Milford, Bellingham and Franklin,
Massachusetts. August 9, 2011.
U.S. Environmental Protection Agency (EPA). 201 Ib. "Report on Enhance Framework (SUSTAIN)
and Field Applications for Placement of BMPs in Urban Watersheds". Prepared by Tetra Tech, Inc. in
Support of EPA Contract No. GS-10F-0268K.
U.S. Environmental Protection Agency (EPA). 2014a. System for Urban Stormwater Treatment and
Analysis IntegratioN (SUSTAIN). Accessed August 2014. http://www2.epa.gov/water-
research/system-urban-stormwater-treatment-and-analysis-integration-sustain
U.S. Environmental Protection Agency (EPA). 2014b. SUSTAIN Application User's Guide for EPA
Region 10. Prepared by Tetra Tech, Fairfax, Virginia, http://www2.epa.gov/water-research/system-
urban-stormwater-treatment-and-analysis-integration-sustain
Vogel, R.M. and I. Wilson. 1996. Probability Distribution of Annual Maximum, Mean, and Minimum
Streamflows in the United States. Journal of Hydrologic Engineering. 1:2, pp. 69-76.
Vogel, R.M., C. Yaindl, and M. Walter. 2011. Nonstationarity: Flood Magnification and Recurrence
Reduction Factors in the United States. Journal of the American Water Resources Association. 47:3.
Pp. 464-474.
White, K. and B. Baker. 2015. USAGE Institute for Water Resources. Personal communication,
January 29, 2015.
58
-------
Appendix A
Appendix A - User Support
User support is provided by checking user entered data for errors via code in the VBA modules and
providing the WMOST User Guide and case studies as a source of default data.
A.1 User Error Checks
The user is informed with a message box if any of the following are encountered:
• number of HRU types, HRU sets or water users is less than or equal to zero
• warning to user that data will be deleted if new setup is requested for input data tables
• price elasticity values are not negative
• minimum in-stream flow is greater than maximum in-stream flow,
• time series data, that is runoff (and therefore recharge, water demand, point sources) dates,
are not daily or monthly
• stormwater sub-daily time series entered by user (when using manual entry for baseline
hydrology) does not match the time period of the baseline runoff and recharge time series
• baseline hydrology modeling time period requested by user is outside of the data available in the
watershed's time series file
• supporting documentation and data, such as the time series data and watershed map files,
are not found
• stormwater simulation is attempted to be run prior to generating the input files
• when calculating runoff and recharge, dates or watershed have not been selected
• when calculating the groundwater recession coefficient,
o the area in the baseline HRUs is empty,
o data is missing from the recharge table, and
o modeling dates have not been entered.
• user attempts to enter less than 0 or greater than 50 land use sets or water user types
A.2 User Manual, Case Studies and Default Data
Case studies are provided which provide default data that the user may draw on in lieu of other
data sources.
In general, O&M costs may be assumed to be between 1 and 10% of capital costs depending on the
infrastructure or management practice.
Many federal and state websites provide data for spatial data such as land use, soil, slope, zoning,
and protected areas.
Note that the accuracy of the input data will affect the accuracy of the model solutions. Therefore,
as described in the user manual, sensitivity analyses are recommended especially for input data with
the greatest uncertainty.
57
-------
WMOST v2 Theoretical Documentation
Appendix B - SUSTAIN Input Cards
The following table lists and describes the input cards and parameters specified in the main input file
(*.inp) for SUSTAIN runs.
Card No.
700
Parameters
LINE1
LINE2
LINES
LINE4
LINES
LINES
Card No.
705
Parameters
POLLUTJD
POLLUT_NAME
MULTIPLIER
Card Name
Model Controls
Parameter Definitions
Land simulation control (0-external,l-internal)
Land output directory (containing land output timeseries)
Start date of simulation (Year Month Day)
End date of simulation (Year Month Day)
Land Timeseries timestep (Min)
BMP simulation timestep (Min)
CRAAT (The ratio of max velocity to mean velocity under typical
flow conditions)
Model output control (0-the same timestep as land time series;
1-hourly)
Model output directory
ET Flag (0-onstant monthly ET,l-daily ET from the timeseries,2-
alulate daily ET from the daily temperature data),
Climate time series file path
Latitude (Decimal degrees)
Monthly ET rate (in/day) if ET flag is 0 OR
Monthly pan coefficient (multiplier to ET value) if ET flag is 1 OR
Monthly variable coefficient to calculate ET values
Card Name
Pollutant Definition
Parameter Definitions
Unique pollutant identifier
Unique pollutant name
Multiplying factor used to convert the pollutant load to Ibs
Notes
Notes
required if ET flag is 1 or 2
required if ETflag is 2
Notes
Notes
(Sequence number same as in land output
time series)
external control
-------
Appendix B
Parameters
SED_FLAG
SED_QUAL
SAND_QFRAC
SILT_QFRAC
CLAY_QFRAC
Card No.
710
Parameters
LANDTYPE
LANDNAME
IMPERVIOUS
TIMESERIESFILE
SAND_FRAC
SILT_FRAC
CLAY_FRAC
Card No.
712
Card No.
713
Card No.
714
Parameter Definitions
The sediment flag (0-not sediment,l-sand,2-silt,3-clay,4-total
sediment)
The sediment-associated pollutant flag (0-no, 1-yes)
The sediment-associated qual-fraction on sand (0-1)
The sediment-associated qual-fraction on silt (0-1)
The sediment-associated qual-fraction on clay (0-1)
Card Name
Land Use Definition
Parameter Definitions
Unique land use definition identifier
Land use name
Distinguishes pervious/impervious land unit (0-pervious; 1-
impervious)
File name containing input timeseries
The fraction of total sediment from the land which is sand (0-1)
The fraction of total sediment from the land which is silt (0-1)
The fraction of total sediment from the land which is clay (0-1)
Card Name
Aquifer Information
Card Name
Aquifer Pollutant Background Concentration
Card Name
Ftable for BMP Class A, B, and C
Notes
if = 1 then SEDIMENT is required in the
pollutant list
only required if SED_QUAL = 1
only required if SED_QUAL = 1
only required if SED_QUAL = 1
Notes
(required if land simulation control is
external)
Notes
[specify time series input files associated
with each WMOST HRU]
Notes
[will not be used in WMOST setup,
subsurface dynamic modeled in WMOST]42
Notes
[will not be used in WMOST setup,
subsurface dynamic modeled in WMOST]
Notes
Optional for designation of Class A, B and C
BMP parameters, unique table for each
BMP
42 On the basis of the approach used in SWMM, evaporation is subtracted from the rainfall or water storage area prior to
calculating infiltration. A differential equation is solved iteratively to determine/(infiltration) at each time step by using
Newton-Raphson method. Therefore, evapotranspiration is accounted for at each time step in the infiltration values.
59
-------
WMOST v2 Theoretical Documentation
Parameters
FTABLEJD
FLOW_LENGTH
BED_SLOPE
NUM_RECORD
DEPTH
SURFACE_AREA
VOLUME
FLOW_WEIR
FLOW_ORIFICE
BMPSITE
BMPNAME
Card No.
715
Parameters
BMPTYPE
Darea
NUMUNIT
DDAREA
PreLUType
AquiferlD
FtableFLG
FTABLEJD
Card No.
720
Card No.
721
Card No.
Ill
Parameter Definitions
Unique Ftable identifier
Flow length (ft)
Longitudinal bed slope (ft/ft)
Number of layers in the Ftable
Water depth (ft)
Water surface area at the given depth (acre)
Storage volume at the given depth (ac-ft)
Overflow or weir outflow rate at the given depth (cfs)
Channel flow or orifice outflow rate at the given depth (cfs)
Unique BMP site identifier
BMP template name or site name
Card Name
BMP Site Information
Parameter Definitions
Unique BMP Types
Total Drainage Area in acre
Number of BMP structures
Design drainage area of the BMP structure (acre)
Predevelopment land use type
Unique Aquifer ID, 0 — no aquifer
Ftable flag, 0 = no, 1 = yes
Unique Ftable identifier
Card Name
Point Source Definition
Card Name
Tier-1 Watershed Outlets Definition
Card Name
Tier-1 Watershed Timeseries Definition
Notes
(continuous string)
Notes
(BIORETENTION,WETPOND,CISTERN,DRYPO
ND,INFILTRATIONTRENCH,GREENROOF,PO
ROUSPAVEMENT,RAINBARREL,SWALE,CON
DUIT,BUFFERSTRIP,AREABMP)
Notes
(must use the exact same keyword)
(for external land simulation option)
(for external land simulation option)
(for BMP Class A, B, and C)
(continuous string as in card 714)
Notes
[will not be used in WMOST setup,
accounted for within WMOST]
Notes
[will not be used in WMOST setup]
Notes
[will not be used in WMOST setup]
60
-------
Appendix B
Card No.
723
Card No.
725
Parameters
BMPSITE
WIDTH
LENGTH
OHEIGHT
DIAM
EXTP
RELTP
PEOPLE
DDAYS
WEIRTP
WEIRH
WEIRW
THETA
ET_MULT
PUMP_FLG
DEPTH_ON
DEPTH_OFF
PUMP_CURVE
Card No.
730
Card No.
735
Parameters
BMPSITE
Card Name
Pump Curve
Card Name
Class-A BMP Site Parameters (BMPs with storage)
Parameter Definitions
Class A BMP dimension group identifier in card 715
Basin bottom width (ft)
Basin bottom length (ft) / diameter (ft) for rain barrel or cistern
Orifice Height (ft)
Orifice Diameter (in)
Exit Type (1 for C=l,2 for C=0.61, 3 for C=0.61, 4 for C=0.5)
Release Type (1-Cistern, 2-Rain barrel, 3-others)
Number of persons (Cistern Option)
Number of dry days (Rain Barrel Option)
Weir Type (l-Rectangular,2-Triangular)
Weir Height (ft)
(weir type 1) Weir width (ft)
(weir type 2) Weir angle (degrees)
Multiplier to PET
Pump option (0-OFF, 1-ON)
Water Depth (ft) at which the pump is started
Water Depth (ft) at which the pump is stopped
The unique name of pump curve
Card Name
Cistern Control Water Release Curve
Card Name
Class B BMP Site Dimension Groups ("Channel" BMPs)
Parameter Definitions
BMP Site identifier in card 715
Notes
(applies if PUMP_FLG is ON in card 725)
[not applicable to BMPs in WMOST v2]
Notes
(required if BMPSITE is CLASS-A in card
715)
Notes
(continuous string without space)
Notes
(applies if release type is cistern in card
720) [not applicable to BMPs in WMOST v2]
Notes
Notes
61
-------
WMOST v2 Theoretical Documentation
Parameters
WIDTH
LENGTH
MAXDEPTH
SLOPE1
SLOPE2
SLOPES
MANN_N
ET_MULT
Card No.
740
Parameters
BMPSITE
INFILTM
POLROTM
POLREMM
SDEPTH
POROSITY
FCAPACITY
WPOINT
AVEG
FINFILT
UNDSWITCH
UNDDEPTH
UNDVOID
UNDINFILT
SUCTION
IMDMAX
Parameter Definitions
Basin bottom width (ft)
Basin bottom length (ft)
Maximum depth of channel (ft)
Side slope 1 (ft/ft)
Side slope 2 (ft/ft) (1-4)
Side slope 3 (ft/ft)
Manning 's roughness coefficient
multiplier to PET
Card Name
BMP Site Bottom Soil/Vegetation Characteristics
Parameter Definitions
BMPSITE identifier in c715
Infiltration Method (0-Green Ampt, 1-Horton, 2-Holtan)
Pollutant Routing Method (1-Completely mixed, >l-number of
CSTRs in series)
Pollutant Removal Method (0-lst order decay, 1-kadlec and
knight method )
Soil Depth (ft)
Soil Porosity (0-1)
Soil Field Capacity (ft/ft)
Soil Wilting Point (ft/ft)
Vegetative Parameter A (0.1-1.0) (Empirical),
Soil layer infiltration rate (in/hr)
Consider underdrain (1), Do not consider underdrain (0)
Depth of storage media below underdrain (ft)
Fraction of underdrain storage depth that is void space (0-1)
Background infiltration rate, below underdrain (in/hr)
Average value of soil capillary suction along the wetting front,
value must be greater than zero (in)
Difference between soil porosity and initial moisture content,
value must be greater than or equal to zero (a fraction)
Notes
Notes
Notes
required for Holtan
required for Green-Ampt
required for Green-Ampt
62
-------
Appendix B
MAXINFILT
Parameters
DECAYCONS
DRYTIME
MAXVOLUME
Card No.
745
Parameters
BMPSITE
Gli
Card No.
747
Parameters
BMPSITE
WATDEPj
THETAj
Card No.
750
Card No.
755
Card No.
760
Card No.
761
Card No.
762
Parameters
BMPSITE
Maximum rate on the Morton infiltration curve (in/hr)
Parameter Definitions
Decay constant for the Morton infiltration curve (1/hr)
Time for a fully saturated soil to completely dry (day)
Maximum infiltration volume possible (in)
Card Name
BMP Site Holtan Growth Index
Parameter Definitions
BMPSITE identifier in card 715
12 monthly values for Gl in HOLTAN equation where i = Jan, feb,
mar ... dec
Card Name
BMP Site Initial Moisture Content
Parameter Definitions
BMP Site identifier in card 715
Initial surface water depth (ft)
Initial soil moisture (ft/ft)
Card Name
Class C Conduit Parameters
Card Name
Class C Conduit Cross Sections
Card Name
Irregular Cross Sections
Card Name
Buffer Strip BMP Parameters
Card Name
Area BMP Parameters
Parameter Definitions
BMP site identifier in card 715
required for Morton
Notes
required for Morton
required for Morton
required for Morton
Notes
Notes
Notes
Notes
Notes
(required if BMPSITE is CLASS-C in card 715)
[not applicable to BMPs in WMOST v2]
Notes
[not applicable to BMPs in WMOST v2]
Notes
[not applicable to BMPs in WMOST v2]
Notes
(required if BMPTYPE is BUFFERSTRIP in
card 715) [not applicable to BMPs in
WMOST v2]
Notes
(required if BMPTYPE is AREABMP in card
715)
Notes
63
-------
WMOST v2 Theoretical Documentation
Parameters
Area
FLength
D
SLOPE
MANNING_N
SATJNFILT
POLREMM
DCIA
TOTAL_IMP_DA
Card No.
765
Parameters
BMPSITE
QUALDECAYi
Card No.
766
Parameters
BMPSITE
K'i
Card No.
767
Parameters
BMPSITE
C*i
Parameter Definitions
BMP area (ft2)
flow length (ft)
area depression storage (in)
Overland slope (ft /ft)
Overland Manning's roughness coefficient
Saturated infiltration rate (in/hr)
Pollutant Removal Method (0-lst order decay, 1-kadlec and
knight method)
Percentage of Directly Connected Impervious Area (0-100)
Total Impervious Drainage Area (acre)
Card Name
BMP Site Pollutant Decay/Loss Rates
Parameter Definitions
BMP site identifier in card 715
First-order decay rate for pollutant i (hrA-l) where i = 1 to N (N =
Number of QUAL from TIMESERIES FILES)
Card Name
Pollutant K' values
Parameter Definitions
BMP site identifier in card 715
Constant rate for pollutant i (ft/yr) where i = 1 to N (N = Number
of QUAL from card 705)
Card Name
Pollutant C* values
Parameter Definitions
BMP site identifier in card 715
Background concentration for pollutant i (mg/l) where i = 1 to N
(N = Number of QUAL from card 705)
Notes
Notes
Notes
Notes
(applies when pollutant removal method is
kadlec and knight method in card 740)
Notes
Notes
(applies when pollutant removal method is
kadlec and knight method in card 740)
Notes
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Appendix B
Card No.
770
Card No.
775
Card No.
780
Card No.
785
Card No.
786
Card No.
790
Parameters
UniquelD
LANDTYPE
AREA
DS
Card No.
795
Parameters
BMPSITE
OUTLET_TYPE
Card Name
BMP Underdrain Pollutant Percent Removal
Card Name
Sediment General Parameters
Card Name
Sand Transport Parameters
Card Name
Silt Transport Parameters
Card Name
Clay Transport Parameters
Card Name
Land to BMP Routing Network
Parameter Definitions
Identifies an instance of LANDTYPE in SCHEMATIC
Corresponds to LANDTYPE in c710
Area of LANDTYPE in ACRES
UNIQUE ID of DS BMP (0 - no BMP, add to end)
Card Name
BMP Site Routing Network
Parameter Definitions
BMPSITE identifier in card 715
Outlet type (1-total, 2-weir, 3-orifice or channel, 4-underdrain)
Notes
(applies when underdrain is on in card 740)
[not applicable in WMOST v2 because no
water quality modeling]
Notes
(required if pollutant type is sediment in
card 705) [will not be used in WMOST
setup, parameters related to in-channel
transport of sediment]
Notes
(required if pollutant type is sediment in
card 705) [will not be used in WMOST
setup, parameters related to in-channel
transport of sediment]
Notes
(required if pollutant type is sediment in
card 705) [will not be used in WMOST
setup, parameters related to in-channel
transport of sediment]
Notes
(required if pollutant type is sediment in
card 705) [will not be used in WMOST
setup, parameters related to in-channel
transport of sediment]
Notes
(required for external land simulation
control in card 700) [link HRUs with BMPs]
Notes
Notes
Notes
65
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WMOST v2 Theoretical Documentation
DS
Card No.
800
Parameters
Technique
Option
StopDelta
MaxRuns
NumBest
Card No.
805
Parameters
BMPSITE
LinearCost
AreaCost
TotalVolumeCost
MediaVolumeCost
UnderDrainVolum
eCost
ConstantCost
PercentCost
Length Exp
AreaExp
TotalVolExp
MediaVolExp
UDVolExp
Card No.
810
Downstream BMP site identifier in card 715 (0 - no BMP, add to
end)
Card Name
Optimization Controls
Parameter Definitions
Optimization Techniques, 0 = no optimization, 1 = Scatter
Search, 2 = NSGAII
Optimization options, 0 = no optimization, 1 = specific control
target and minimize cost, 2 = generate cost effectiveness curve
Criteria for stopping the optimization iteration
Maximum number of iterations
Number of best solutions for output
Card Name
BMP Cost Functions
Parameter Definitions
BMP site identifier in card 715
Cost per unit length of the BMP structure ($/ft)
Cost per unit area of the BMP structure ($/ftA2)
Cost per unit total volume of the BMP structure ($/ftA3)
Cost per unit volume of the soil media ($/ftA3)
Cost per unit volume of the under drain structure ($/ftA3)
Constant cost ($)
Cost in percentage of all other cost (%)
Exponent for linear unit
Exponent for area unit
Exponent for total volume unit
Exponent for soil media volume unit
Exponent for underdrain volume unit
Card Name
BMP Site Adjustable Parameters
Notes
Notes
(in dollars ($))
(for Option 2)
(for Option 1)
Notes
Notes
Notes
Sets range for decision variables [will not
be used in WMOST setup because running
SUSTAIN as simulation]
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Appendix B
Card No.
814
Card No.
815
Parameters
BMPSITE
FactorGroup
FactorType
FactorVall
FactorVal2
CalcMode
TargetVall
TargetVal2
FactorJName
Card Name
Pre-developed Timeseries at Assessment Point for Flow
Duration Curve
Card Name
Assessment Point and Evaluation Factor
Parameter Definitions
BMP site identifier in card 715 if it is an assessment point
Flow or pollutant related evaluation factor group, -1 = flow
related evaluation factor, # = pollutant ID in card 705
Evaluation Factor Type (negative number for flow related and
positive number for pollutant related)
-1 = AAFV Annual Average Flow Volume (ft3/yr), -2 = PDF Peak
Discharge Flow (cfs), -3 = FEF Flow Exceeding frequency
(tttimes/year)
1 = AAL Annual Average Load (Ib/yr), 2 = AAC Annual Average
Concentration (mg/L), 3 = MAC Maximum ttdays Average
Concentration (mg/L)
if FactorType = 3 (MAC): Maximum ttDays; if FactorType = -3
(FEF): Threshold (cfs); all other FactorType : -99
if FactorType = -3 (FEF): Minimum inter-exceedance time (hr); if
= 0 then daily running average flow exceeding frequency; if = -1
then daily average flow exceeding frequency; all other
FactorType : -99
Evaluation Factor Calculation Mode; -99 for Option 0 (card 800):
no optimization; 1 = % percent of value under existing condition
(0-100); 2 = S scale between pre-develop and existing condition
(0-1); 3 = V absolute value in the unit as shown in FactorType
(third block in this card)
Target value for evaluation factor calculation mode; -99 for
Option 0 (card 800): no optimization; Target value for minimize
cost Option 1 (card 800); Lower limit of target value for cost-
effective curve Option 2 (card 800)
Target value for evaluation factor calculation mode; -99 for
Option 0 (card 800): no optimization; -99 for Option 1 (card
800): minimize cost; Upper limit of target value for cost-
effective curve Option 2 (card 800)
Evaluation factor name
Notes
[will not be used in WMOST setup because
running SUSTAIN as simulation]
Notes
[required to obtain detailed output]
Notes
(user specified without any space)
67
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WMOST v2 Theoretical Documentation
Appendix C - Future Development
The following model enhancements may be implemented in future development efforts. These
suggestions are based on reviewer and stakeholder feedback.
C.1 Model Components and Functionality
• Enhanced detail in modeling watershed components and processes
o Adding a deep aquifer/groundwater storage component
o Building in a time step independent delay between groundwater and septic recharge
and baseflow to stream reach (e.g., as derived from detailed runoff-rainfall model or
calibrated internally)
o Adding option for combined sewer-stormwater collection system (user could specify
percent of each HRU's runoff that drains to sewer system)
o Adding stormwater utility - additional watershed component where stormwater
system is separate from wastewater system fees and associated costs and revenues
(user can specify percent of HRU's runoff that drains to stormwater utility)
o Reservoirs
• Subtracting evaporative losses from reservoir
• Providing option for reservoir to be located at top of reach rather than at
outlet
o Modeling of infiltration/inflow and its management even if all wastewater is handled
via interbasin transfer
o Additional options for specifying pricing structure for water and wastewater services
(e.g., increasing price blocks for water).
• Enhanced or additional management practices
o Construction of a separate stormwater system where combined sewer system exists or
no stormwater collection system exists
o Drought management program where demand reductions are triggered by low-flows
in the stream reach.
o Individual limits on withdrawals from each surface and groundwater source (e.g.,
ability to limit withdrawals to sustainable yield, if known).
o Increased leakage in water distribution and sewer collection systems when funds
have not been allocated to their management
o Non-linear cost function for management of leakage from water distribution system
and infiltration/inflow into sewer collection system 43
o Non-linear price elasticities for demand management via pricing
o Option for interbasin transfer of raw water to water treatment plant (WMOST
version 1 assumes direct transfer of potable water to the user)
43 Non-linear functions can be approximated by a set of linear equations to keep the model a linear programming
optimization problem.
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G
o Option to specify maximum outflow to downstream reach (i.e., maximum "Sw
outflow to external Sw")
o Achievement of pre-development hydrology as management goal by adding ability to
specify constraints for total basin runoff and recharge rates that mimic pre-
development hydrology
o Routing out of basin wastewater to the wastewater treatment plant
• Additional modules/functionality
o Sensitivity and uncertainty analysis module which identifies most critical input data
(i.e., greatest effect on results), most limiting resource, or most impacting human
activity
• Linking the model with climate data from GREAT44 or other climate
projections to facilitate sensitivity and uncertainty analyses
o Setting or module to assist running a 'simulation' scenario without new management
options implemented to assess model performance prior to optimization; this may
include automated calculation and reporting of performance metrics comparing
measured and modeled streamflow
o Provide guidance when the solution is infeasible, e.g., specify which constraint(s)
made the solution infeasible. This can be determined using output from Lp_solve.
o Demand management module as a pre-processing step to facilitate calculating one
estimate for potential user demand reductions and the associated cost (e.g., rebates
for water efficient appliances, monthly metering and billing, water rate changes,
outdoor watering policies)
o Enhanced spatial modeling by optimizing multiple reaches (e.g., running the model
for multiple study areas/subbasins, routing between them and potentially optimizing
for all areas/subbasins not just individually).This option would allow for an optimal
solution across a region without creating 'hot spot' problems in any one basin.
o Option for objective function
• Alternative objective function such as maximizing in-stream flow for a user-
specified budget
• Multi-objective function such as minimizing cost, meeting human demand
and achieving minimum in-stream flow targets with the ability to weight
each objective for their relative priority/importance. The ability to weight
different objectives would also allow prioritization based on social or
political factors/costs.
o Automated generation of trade-off curve between objective and user selected
constraint.
o Development of a water quality module to allow for optimization with water quality
and/or water quantity management goals
• The water quality module would allow for the use of WMOST in EPA's
Integrated Municipal Stormwater and Wastewater Planning45 by screening
44 http://water.epa.gov/infrastructure/watersecurity/climate/creat.cfm
45 http: //cfpub. epa. go v/npdes/integratedplans. cfm
89
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WMOST v2
stormwater and wastewater management practices for the most cost-effective
combination to meet water quality standards.
o User ability to define a generic constraint that is not pre-programmed
o Calculation of co-benefits of solutions
• Avoided costs (e.g., system capacity expansion)
• Savings in compliance costs for stormwater, drinking water and water quality
standards
• Changes in ecosystem services based on changes in-stream flow and land use
(e.g., additional forest area) and their monetized value
• Addition of payment values for flow trading
C.2 User Interface and User Support
• Input features
o Direct linking and interoperability with simulation models for importing baseline
runoff and recharge rate time series (e.g., Hydrological Simulation Program Fortran
(HSPF),46 Soil Water and Assessment Tool (SWAT)47
o Ability to specify additional IBT initial cost as one time fixed cost ($) or based on
capacity ($/MGD)
o Provide alternate setting for entering input using metric units
o When Setup 1 is clicked and the tables are emptied, change the buttons for land use,
recharge and runoff back to blue and uncheck them.
o Only allow optimization when input data boxes are checked
• Output features
o Provide capital and O&M costs for management practices separately in results table
o Provide time series for all flows among components and for storage volumes for
groundwater and reservoir/surface storage as an advanced user option
o Provide initial values for infrastructure capacities and other management practices
• Testing and guidance on appropriate spatial and temporal scales for modeling
• Create a tutorial with simple, idealized example to teach about WMOST and decision making
in a watershed context
• Create a tutorial to teach about optimization (e.g., a simple optimization problem in Excel to
demonstrate optimization concepts).
46 http://water.usgs.gov/software/HSPF/
47 http://swat.tamu.edu/
70
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