EPA 600/R-13/151 | August 2013
www.epa.gov/ord
United States
Environmental Protection
Agency
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EPA 600/R-13/151 | August 2013
Watershed Management Optimization
Support Tool (WMOST) vl
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 and Jackie LeClair
Region 1
Boston, MA 02109
Yusuf Mohamoud
ORD, NERL, Ecosystems Research Division
Athens, GA 30605
Abt Associates Project Team
Viktoria Zoltay, Becky Wildner, Lauren Parker and Isabelle Morin, 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.
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WMOST v1 Theoretical Documentation
The information 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-07-023/ Work
Assignment 32 to Abt Associates, Inc. It has been subjected to the Agency's peer and administrative review,
and it 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 screening model that is
spatially lumped with options for a daily or monthly time step. It is specifically focused on modeling
the effect of management decisions on the watershed. The model considers water flows and does not
consider water quality. The optimization of management options is solved using linear programming.
The tool 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).: The objective of
WMOST is to serve 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 watershed or jurisdiction for cost-effectiveness as well as environmental and economic
sustainability (Zoltay et al., 2010). Examples of options that could be evaluated with the tool
potentially include projects related to stormwater, water supply, wastewater and water-related
resources such as low-impact development (LID) and land conservation. The tool is intended to aid in
evaluating the environmental and economic costs, benefits, trade-offs and cobenefits of various
management options. In addition, the tool is intended to facilitate the evaluation of LID and green
infrastructure as alternative or complementary management options in projects proposed for State
Revolving Funds (SRF). 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
1 EPA. 2008. Handbook for Developing Watershed Plans to Restore and Protect Our Waters. March 2008. US
Environmental Protection Agency. Office of Water. Nonpoint Source Control Branch, Washington, B.C. EPA 841-B-
08-002.
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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"2. IWRM has been promoted as an integral part of the "Water Utility of the Future"3 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.4 The U.S. Environmental Protection Agency (EPA) has
also endorsed the concept of IWRM, focusing on coordinated implementation of stormwater and
wastewater management.5
Several states and river basin commissions have started to implement IWRM.6 Even in EPA Region 1
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. The state of Massachusetts recently spearheaded the
Sustainable Water Management Initiative (SWMI) process to allocate water among competing human
and aquatic life uses in a consistent and sustainable fashion.7
Stormwater and land use management are two aspects of IWRM which include practices such as
green infrastructure (GI, both natural GI and constructed stormwater BMPs), low-impact
development (LID) and land conservation. In recent years, the EPA SRF funding guidelines have
been broadened to include support for green infrastructure at local scales-e.g., stormwater best
management practices (BMPs) to reduce runoff and increase infiltration-and watershed scales-e.g.,
2 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.
3 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.
4 http://www.awra.org/policy/policy-statements—water-vision.html
5 Nancy Stoner memo: http://water.epa.gov/infrastructure/greeninfrastructure/upload/memointegratedmunicipalplans.pdf
6 AWRA. 2012. Case Studies in Integrated Water Resources Management: From Local Stewardship to National Vision.
American Water Resources Association Policy Committee, Middleburg, VA.
7 MA EAA. 2012. Massachusetts Sustainable Water Management Initiative Framework Summary (November 28, 2012);
http://www.mass.gov/eea/agencies/massdep/water/watersheds/sustainable-water-management-
initiative-swmi.html
III
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WMOST '..1 T^=*ocetical
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.8 In a few notable cases, local managers have evaluated the relative cost and benefit of
preserving green infrastructure compared to traditional approaches. In those cases, the managers have
championed the use of green infrastructure as part of a sustainable solution for IWRM but these
examples are rare.9
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 green infrastructure and land conservation measures as eligible
projects in meeting water quality goals. The utilization of the GPR for green infrastructure 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 green
infrastructure 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 green infrastructure 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 green infrastructure, 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 the Watershed Management Optimization Support Tool (WMOST).
WMOST is based on a recent 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.10 This model includes evaluation of conservation options for
source water protection and infiltration of stormwater on forest lands, green infrastructure stormwater
8 American Rivers. 2010. Putting Green to Work: Economic Recovery Investments for Clean and Reliable Water. American
Rivers, Washington, D.C
9 http://www.crwa.org/blue.html, http://v3.mmsd.com/greenseamsvideol.aspx
10 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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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 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 each of three communities
were developed to illustrate the application of IWRM using WMOST; two of these case studies
(Upper Ipswich River, and Danvers/Middleton, MA) are presented here. WMOST was presented to
stakeholders in a workshop held at the EPA Region 1 Laboratory in 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.
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WMOST v1 Theoretical Documentation
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 Detenbeck and Marilyn ten Brink, U.S. EPA ORD, NHEERL, Atlantic Ecology Division
Alisa Morrison, Student Services Contractor at U.S. EPA ORD, NFIEERL, Atlantic Ecology Division
Ralph Abele and Jackie LeClair, U.S. EPA Region 1
Yusuf Mohamoud, U.S. EPA ORD, NERL, Ecosystems Research Division
Technical Advisory Group
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
Reviewers
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
VI
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Table of Contents
Notice ii
Abstract ii
Preface iii
Acknowledgements vi
1. Background 1
1.1 Objective of the Tool 1
1.2 Overview 1
2. Mathematical Description 6
2.1 Objective Function 7
2.1.1 Costs 7
2.1.2 Revenue 15
2.2 Constraints 17
2.2.1 Continuity Equations 17
2.2.2 Physical Limits on Watershed Components 24
2.2.3 Constraints Associated with Management Options 25
3. Internal Configuration 29
4. Summary of Input Data 30
5. Future Development 35
5.1 Model Components and Functionality 35
5.2 User Interface and User Support 37
6. Appendix A- User Support 39
6.1 User Error Checks 39
6.2 User Manual, Case Studies and Default Data 39
VII
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WMOST v1 Theoretical Documentation
Figures
1-1. Schematic of Potential Water Flows in the WMOST 2
3-1 WMOST Internal Configuration 29
1-1 Summary of Management Goals and Management Practices 4
VIM
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Background
1. Background
1.1 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 and
minimum and maximum in-stream flow targets. 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 the 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
green infrastructure 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 green infrastructure and land conservation
measures as eligible projects in meeting water quality goals.
1.2 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 1-1. The figure shows the possible watershed system components and
potential water flows among them.
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WMOST v1 Theoretical Documentation
Figure 1-1. Schematic of Potential Water Flows in the WMOST
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Background
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),11 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;12
• Solutions that account for both the direct and indirect effects of management practices (e.g., since
optimization is performed within the watershed system context, 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 fifteen stormwater management options, including traditional, green
infrastructure or LID practices;
• A sustainability constraint that forces the groundwater and reservoir volumes at the start and end
of the modeling period to be equal;
• 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).
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. Section 3 describes the configuration of the
software components. Section 4 summarizes the required input data to run the model. We list
considerations for future model development in Section 5.
11 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.
iVhile the numbc
specifications.
12 While the number of HRUs and modeling period are not limited, solution times are significantly affected by these model
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WMOST '
l
A separate User Guide document provides detailed direction on using WMOST and performing
sensitivity and trade-off analyses, and includes two case studies. 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.
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
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
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
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
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Management Practice
Water reuse facility (advanced
treatment) capacity
Nonpotable distribution
system
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 MOD
Increase MGD
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
Water reuse facility
Nonpotable water
use
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
Produce water for nonpotable
demand, ASR, and/or
improve water quality of
receiving water
Reduce demand for potable
water
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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WMOST v1 Theoretical Documentation
2. Mathematical Description
This section provides the equations for the objective function and the constraints that define the linear
programming (LP) optimization model. 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.
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^0^ 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 baseline HRU set and other
sets that have the same HRUs but with management practice 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 4. Units for input variables are based on the units expected to
be used in the most-readily available data sources.
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2.1 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.
Z = O CTiA) (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. First, we describe the
generic form of cost equations, and then we provide all of the individual equations 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.
CC,A = F X Cc (2)
where
CCjA = unit annual capital cost
Cc = unit capital cost
Unit construction costs for new facilities or expanding the capacity of an existing facility with new
construction are annualized over the expected lifetime of the new construction (e.g., wastewater
treatment plant, bioretention basin).
i X (1 + i)TNew
NeW (1 + t
where
i = interest rate in percent/ 100
TNBW = lifetime of new construction in years
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WMOST v1 Theoretical Documentation
Replacement costs for existing facility are calculated as CCA adjusted for the remaining years in the
facility's lifetime, TExist.
_ i X (1 + iY^ew Tplm _ TEx.st
FExist ~
iT"- - 1 TPlan
where
= the planning horizon
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
Pl™ (1 + i)Tplan - 1
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)13 - 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),14 Soil Water and Assessment Tool (SWAT)15 and/or Storm Water
Management Model.16 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.17 At the same time, the user can specify the cost to purchase existing,
13 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.
14 http://water.usgs.gov/software/HSPF/
15 http://swat.tamu.edu/
16 http://www.epa.gov/nrmrl/wswrd/wq/models/swmm/
17 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).
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undeveloped forest land. With this information provided, the model can decide whether it is cost
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),
Lu
=) X (^I.s=l ~ ^I,s=l)) (6)
nu
= y
1=1
where
s = number of HRU sets
CATb = total annual cost of reallocating areas among baseline HRUs from user-specified to model-
chosen values
nLu = number of HRU types
QM,S=I = capital cost associated with land reallocation for each HRU in set 1 (e.g., purchasing forest land)
Com,i,s=i = annual O&M cost associated with maintaining, for example, the land preservation
AiiS=i = user specified areas for baseline HRU
bAi:S=i = model-chosen, land area for baseline HRUs
Stormwater Management (traditional, green infrastructure, low impact development) - reallocating
area from baseline to managed HRUs: The model may choose to implement Stormwater management
based on the available area for each HRU after reallocation for land conservation (i.e., M( s=1). 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 2.1.1.
For s = 2 to NLuSet, where CCjJjS=1 * -9,
NLuSet nLu
CATm= ^ ^((Fplan * CC,l,s + C0m,ltS) X bAltS) (7)
s=2 1=1
where
bAi:S=2to NLuSet = model chosen land area for managed HRUs
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.
-------
WMOST v1
Demand Management: There are two demand management options in the model - via pricing and
via other practice 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.18
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 equals
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:
CAT Price = bPriceBin X (Fpian X CCDmPrice + C0mDmPrice) (g)
where
Cxrprice = annual cost to implement price changes
bPriceBin = a binary decision variable
= capital cost of price change
= annual O&M costs for implementation of price change
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.
^ATDrnd = ^ X (fplan X ^CDm + QlmDm) (9)
VDmRedMax
where
^ATDrnd = annual cost to implement direct demand management practices
bQomRed = quantity of direct demand reduction
Max = maximum demand reduction available
ice = capital cost of direct demand management
rice = annual O&M costs for direct demand management
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.19
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 system follow similar forms for total annual costs.
18 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.
19 http://www.epa.gov/watersense/our water/start saving.html#tabs-3
10
-------
Groundwater pumping.
^ATGwPump — (fcwPumpExist X Q:GwPump X QcwPumpl) + V <
X "QcwPumpAddU + (fomGwPump X M'rs X /^
GwPumpWew X Q:GwPump
(10)
where
rCwPumpExist
C
u CGwPump
VGwPumpI
77
rGwPumpNew
bQcwPumpAddl
rYrs
bQ,
GwWtp,t
= total annual cost for groundwater pumping
= annualization factor based on remaining lifetime of existing facilities
= capital costs of new/additional groundwater pumping capacity/facility
= initial groundwater pumping capacity
= annualization factor for new capacity or facilities
= additional groundwater pumping capacity
= factor to maintain annual value for O&M costs
= flow from groundwater pump to water treatment plant
where one variable, FYrs, is further defined as inverse of the number of days or months in the
modeling period divided by the total number of days or months in all years modeled even if the
modeling period includes only part of a year. Therefore, it is the inverse of the fraction of years, or
partial year(s) modeled which allows the scaling of the O&M costs accrued over the modeling period
to an average annual cost.
FYTS -
number of time steps modeled
total number of time steps in all years modeled
(11)
Surface water pumping:
r —
'-ATSwPump ~
(FswPumpExist X CcSwPump X QswPumpl) + (fswPumpNew X
X ivvc X ,
where
'-ATSwPump
FwtpExist
^CSwPump
rSwPumpNew
bQswPumpAddl
"QswWtp.t
"QResWtp.t
Pump X bQswPumpAddl)
total annual cost for surface water pumping
annualization factor based on remaining lifetime of existing facilities
capital costs of new/additional surface water pumping capacity/facility
initial surface water pumping capacity
annualization factor for new capacity or facilities
additional surface water pumping capacity
flow from surface water to water treatment plant
flow from reservoir to water treatment plant
(12)
Water treatment facility (WTP):
(-ATWtp = (fwtpExlst X Ccwtp X QwtpMaxl) + (fwtpNew X
X FYrs X )(t>QswWtp,t +
X "Q
wtpAdd
+ (f-OmWtp
(13)
11
-------
WMOST '..
where
l
total annual costs for water treatment
annualization factor based on remaining lifetime of existing facilities
capital costs of new or additional water treatment capacity or facility
initial water treatment capacity
annualization factor for new capacity or facilities
additional water treatment capacity
annual O&M costs for water treatment
Reducing unaccounted-for water (Uaw), assumed to be leakage out of the potable distribution
system into groundwater):
wtpExist
Ccwtp
QwtpMaxl
wtpNew
bQ
wtpAddl
The cost for repairing unaccounted-for water in the potable distribution system is calculated as:
~ .Plan
"WtpGwFix
100
(14)
where
r
'-OmUa
w,
WtpGwFix
total annualized capital cost of reducing unaccounted-for water
capital cost of fixing Uaw such as initial survey and initial work to lower Uaw rate
annual O&M cost to maintain low Uaw rate
percent of leakage that is fixed
Wastewater treatment plant (WWTP):
C-ATWwtp — (fwwtpExist X
X QwwtpMaxl) + (fwwtpNew
/\ f^Yfc
x bQWwtpAddi)
JseNpWwtpf^QcwWwtpf))
(15)
where
^ATWwtp
FwwtpExist
QwwtpMaxl
^WwtpNew
bQwwtpAddl
bQusePWwtp.t
bQuseNpWwtp.t
QcwWwtpf
total annual costs for wastewater treatment
annualization factor based on remaining lifetime of existing facilities
capital costs of new or additional wastewater treatment capacity or facility
initial wastewater treatment capacity
annualization factor for new capacity or facilities
additional wastewater treatment capacity
annual O&M costs for wastewater treatment
flow from potable water use to treatment plant
flow from nonpotable water use to treatment plant
groundwater infiltration into collection system
Reducing infiltration into wastewater collection system:
(•ATGwWwtp = (fplan X ^CGwWwtp + Co
bP,
GwWwtpFix
Too
(16)
12
-------
where
^CATGwWwtp
CcGwWwtp
r
'-OmUaw
b'WwtpGwFix
total annualized capital cost of reducing groundwater infiltration into the wastewater
capital cost of fixing infiltration such as initial survey and initial repairs to lower infiltration
annual O&M cost to maintain low infiltration rate
percent of groundwater infiltration that is fixed
Water reuse facility (WRF):
r ~ = (fwrf Exist X
where
wrfExist
wrfMaxl
•OmWrf
bQwrfAddl
bQwwtpWrf
X FYrs X
X QwrfMaxl) + (FwrfN
>^ bQWwtpWrf t)
X
X bQwrfAddl) + (fomWrf
(17)
total annual costs for water reuse
annualization factor based on remaining lifetime of existing facilities
capital costs of new or additional WRF capacity
existing maximum WRF capacity
annualization factor for new capacity or facilities
annual O&M costs for WRF
additional or new WRF capacity
flow from WWTP to WRF
Nonpotable distribution system (Npdist):
^ATNpdist ~ (fNpDistExist X ^CNpDist X QNpDistMaxl) + (.^NpdistNew X ^CNpdist
X QNpDistAddl) + (fomNpdist X ^Vrs X } '
where
LATNpdist
^NpdistNew
bQNpdistAddl
CcNpdist
ComNpdist
(18)
= total annual costs for nonpotable water distribution
= annualization factor for new capacity or facilities
= new or additional capacity
= capital costs for maximum capacity Npdist
= annual O&M costs for maximum capacity Npdist
= total maximum potential capacity need for nonpotable distribution system
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 injection well and/or
aquifer and/or to meet permit requirements).
13
-------
WMOST '..
l
~ (fA
where
^AsrExist
(•CAsr
QAsrMaxl
77
^srWew
bQAsrAddl
bQwrfAsr.t
bQswAsr,t
bQfiesAsr.t
Asr ~ AsrExlst
X
X COAST X QAsrMaxl) + (.^AsrNew X
Fyrs X y(bQwrfAsr,t + bQswAsr,t
(Q)
m,4sr
(19)
total annual costs for ASR
annualization factor based on remaining lifetime of existing facilities
capital costs of existing facility annualized over the remaining lifetime
existing maximum capacity
annualization factor for new or additional capacity
capacity of new or additional capacity
flow from WRF to ASR
flow from surface water to ASR
flow from reservoir to ASR
Reservoir or surface storage (e.g., storage tank, pond):
"" — ff v r v i/ ^ 4- ff
~ V ResExist ^ uCfles ^ 'ResMaxU ~ V ResNew
X (bVResAddi + ^fiesMaz/))
where
p
1 R
esExist
X bV
ResAdd
(20)
-OmRes
total annual costs for reservoir/surface storage
annualization factor based on remaining lifetime of existing facilities
capital costs of new or additional capacity
existing capacity
annualization factor based on lifetime of new facilities
additional or new capacity
annual O&M cost
Interbasin transfer (IBT)for water and-waste-water:
As shown in Figure 1-1, 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
bQ
ibtWAddl
bQlbtWUseP
bQlbtWUseNp
X
X
X
X M'
/(pQlbtWUseP,t + bQlbtWUseNp,t)
(21)
= initial cost of purchasing additional water rights for IBT and construction of necessary
infrastructure
= additional water IBT capacity purchased
= cost of purchasing IBT water
= flow of IBT water to potable water use
= flow of IBT water to nonpotable water use
14
-------
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:
(•ATIbtWw = Fplan X CdbtWw X "QlbtWwAddl + QfcttVw X *Yrs
+ "QuseNpIbtWw.tJ
where
= initial cost of purchasing additional wastewater transfer rights for IBT and construction of
necessary infrastructure
= additional wastewater IBT capacity purchased
= cost of IBT wastewater services
= fl°w °f wastewater from potable use to IBT
bQuseNpibtww = fl°w °f wastewater from nonpotable use to IBT
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 = CATb + CATm + CATPrice + CATDmd + CATGwPump + CATSwPump + CATWtp + CATUaw
+ CATWwtp + CATGwWwtp + CATWrf + CATNpdist + CATAsr + CATRes (23)
+ ^ATlbtW + ^ATIbtWw
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.
RT = ((RUsePT + RuseNpr) X 1 1 H J) + RWWT (24)
where
RuseFT = revenue from delivered potable water
RuseNpT = revenue from delivered nonpotable water
= revenue from wastewater services
= percent price increase for potable and nonpotable water services
These quantities are further defined as follows.
X y^i/sePF +C^l/seP X FYTS X ) (QwtpUseP,t
m t
15
-------
WMOST '
where
/W
RuseNpT — Fyrs X y^ RuseNpF
m
QwtpUseP
bQwtpUseNp
b Qihtwusep
k QibtwuseNp
b QwrfuseNp
X
RuseNp X Fyrs X / "QwrfUseNp.tJ '
t
WtpUseNp.t + "QlbtWUseNp.tJJ
fixed monthly fee for potable customers
fixed monthly fee for nonpotable customers
monthly time steps in period of analysis
original customer price per unit of water for potable water
original customer price per unit of water for nonpotable water
flow of water from water treatment plant to potable uses
flow of water from water treatment plant to nonpotable uses
flow of water from interbasin transfer to potable uses
flow of water from interbasin transfer to nonpotable uses
flow of nonpotable water from water reuse facility to nonpotable uses
(26)
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
FYTS x y RWWF + (Rww x FYTS
m
X y (bQusePWwtpt + bQusePlbtWw,t + bQuseNpWwtp,t (4')
where
RWWF
RWW
"QusePWwtp
"QuseNpWwtp
"QusePIbtWw
"QuseNpIbtWw
fixed monthly fee for all customers
customer price for wastewater services per unit wastewater
wastewater flow from potable uses to wastewater treatment plant
wastewater flow from nonpotable uses to wastewater treatment plant
wastewater flow from potable water uses exported to interbasin transfer
wastewater flow from nonpotable water uses exported to interbasin transfer
16
-------
If wastewater fees are charged based on water flow, then
/^
/(QwtpUseP,t + bQlbtWUseP,t + bQwrfUseNp,t~^~bQwtpUseNp,t ^ '
t
OQlbtWUseNp.t))
2.2 Constraints
The objective in Section 2.1 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.
2.2.1 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, ft /acre/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),20
Soil Water and Assessment Tool (SWAT)21 and/or Storm Water Management Model.22
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.
bAl:S (2g)
1 = 1 to NLu 1=1 to NLu s=2 to NLuSet 1=1 to NLu
where
AiiS=i = user specified HRU areas
bAiiS=i = baseline HRU areas after reallocation for conservation
bAi:S=2 to NLuSet = HRU areas under management
20 http://water.usgs.gov/software/HSPF/
21 http://swat.tamu. edu/
22 http://www.epa.gov/nrmrl/wswrd/wq/models/swmrn/
17
-------
WMOST '..1 T^=*ocetical
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 (30)
where ^Min,(,s = minimum area possible for baseline HRUs
bAls < AMaXils for / = 1 to NLu and 5 = 1 (31)
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 can not 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 (32)
else, bAlf=i - Alf=i < 0 (33)
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 can not be greater than the area allocated to the corresponding
baseline land use chosen under conservation, bAi:S=1 (e.g., 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 green infrastructure practices to meet a specific stormwater standard.
,s AMiTl:l:S for I = 1 to nLu and s = 2 to NLuSet (35)
where AMiniiiS = minimum area possible for management for HRU / and management set s
bAijS < AMaXjijS for / = 1 to nLu and s = 2 to NLuSet (36)
where AMaXiliS= maximum area possible for management for baseline HRU / and management set s
18
-------
The total runoff and recharge for each time step are calculated based on the final area allocations for
all HRUs and HRU sets.
1\ LiLL
QRu,t = 2_,(bAi
1=1
NLu
Wflu.ut - QRu,i,s=i,t)
where QRU,i,s,t23 = runoff rate from HRU / in HRU set s for time step t.
QRe,t = I^"(^^=i x QRe,i,s=^ + Z^Set I™"((<2Be,ut - QRe,i,s=^ x bAlf) (38)
where QR6,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.
Vcw,t = Vcw,t-l + (QRe,t + QsxtGwln,t + QptGw.t + QwtpGw ,t + QAsrGw.t-1 + QsepGw ,t-l ~ QcwSw,t ( '
~ bQcwWtp,t ~ QcwWwtp ,t ~ bQcwExt,t ~ QcwPt,t) X &t
where VGw= volume of groundwater, QRe = recharge from all land areas, Qsxtcwin = inflow of
external groundwater, Qptcw = private groundwater discharges, QwtpGw = leakage from potable
water from distribution system, QASTGW = recharge from ASR facility to groundwater, QsepGw =
inflow from septic systems, QcwSw= baseflow, bQGwWtp= withdrawal by water treatment plant,
QcwWwtp = infiltration into wastewater collection system, bQGwExt = groundwater leaving the basin,
QcwPt = private groundwater withdrawals, and At = time step=l.
Two variables are further defined as
n =n x n - bp^p^akFix^ (40)
VwtpGw.t VUsePI,u=l,t A l^-1- 10Q )
where
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 (41)
where 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.
23 RRRs may be derived from simulation models such as Soil Water Assessment Tool, Hydrological Simulation Program-
Fortran or Storm Water Management Model.
19
-------
WMOST '..1 T^=*ocetical
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. The
surface water component may receive inflow from runoff, external surface water sources (i.e., an
upstream reach), point sources, wastewater treatment plant, and 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.
QRU,I + QsxtSwIn.t + QptSw.t + QcwSw.t + QwwtpSw.t + QwrfSw.t (42)
= QswRes,t + bQswWtpt + bQswAsr,t + QswPt,t
where
Qsxtswin = surface water inflow from outside of basin
Qptsw = discharge from surface water point sources
Qwwtpsw = discharge from wastewater treatment plant
Qwrfsw = discharge from water reuse facility (advanced treatment)
QswRes,t = fl°w fr°m surface water to reservoir
bQswwtp = flow to water treatment plant
bQswAsr = flow to ASR facility
Qswpt = 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.24
^Res,t = ^Res,t-l + (QswRes,t ~ bQswExt,t ~ ^ResWtp.t ~ bQResAsr,t) X At (43)
where
VRes = volume of reservoir
QswRes = inflow to reservoir from surface water bodies
bQswExt = flow to surface water bodies outside of basin
bQResWtp = flow to water treatment plant
bQReSAsr = flow to ASR facility
24 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.
20
-------
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 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.
bQfiesWtp.t + "QswWtp.t + "QcwWtp.t = QwtpUseP.t + "QwtpUseNp.t + QwtpGw.t (44)
where
Qwtpusep = flow to potable water use
p = flow to nonpotable water use
Potable Water Use (UseP):
Zrrn a. hn *\ v ^1 _ ^>ConsUsep^t\ v r- -, (45)
\WwtpUseP,t + "(-llbtWUseP,t) X I -1 77J7J I X *VseP,u,t)
u
= bQusePWwtpt + QusePSept + QusePSepExt,t + bQusePlbtWw,t
where
bQibtwusep = inflow of potable water to water treatment facility via interbasin transfer
Pconsusep,u,t = percent consumptive use for potable water uses
bQusepwwtp = flow to wastewater treatment plant
Qusepsep = fl°w to septic systems within the study area
QusepsepExt = fl°w to septic systems outside the study area
= wastewater flow from potable uses to interbasin transfer wastewater services
One variable is further defined as
QuseP,u,t (46)
n
u VuseP,u,t
where
Qusep,u,t = potable water use by user u at time t
Nonpotable Water Use (UseNp):
Zffhn -L hn -L hn \ d *ConsUseNp,u,t\ ,., . (47)
(\PQwtpUseNp,t + "VwrfUseNpJ + "VlbtWUseNp,t) x I 1 7T77J I x ^(/seWp,u,t)
u
= bQuseNpWwtp,t + QuseNpSep,t+ QuseNpSepExt,t + bQuseNplbtWw,t
where
21
-------
WMOST '..1 T^=*ocetical
One variable is further defined as
_ QuseNp,u,t (48)
~~
LuQuseNp,u,t
where
QuseNP,u,t = nonpotable water use by user u at time t
Wastewater Treatment Plant (Wwtp):
"QusePWwtp.t + "QuseNpWwtp.t + QcwWwtp.t = QwwtpSw.t + "QwwtpWrf.t (49)
where bQWwtpWrf = outflow to water reuse facility.
One variable, infiltration into the wastewater collection system, is further defined as
,. — f-l OPwwtpLeakFix^ PwwtpLeakI (50)
Vcwwwtp,t - (i 77^7;)X :j7j7j
n (* _ PconsUsePl,u,t\ v /-i _ Psep,u + PsepExt,u
VUsePI,u,t I -1 100 I \ 100
(1 _ "wwtpLeakl\
1 Too )
where
Pwwtpieaki = percent leakage of groundwater into the wastewater collection system, as a percent of
wastewater treatment plant inflow
bPwwtpieakFix = percent of leaks fixed in the wastewater collection distribution system,
Qusepi,u,t = initial specified water use (total demand for potable and nonpotable water)
Pconsusepi,u,t = initial percent consumptive use of potable water uses
PSepiU = percent of users serviced by septic systems recharging inside the study area
PsepExt,u = percent of users serviced by septic systems draining outside the study area
Water Reuse Facility (Wrf):
"QwwtpWrf.t = "QwrfUseNp.t + "QwrfAsr.t + QwrfSw.t (51)
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 of are calculated as
ZNWuser / p \ / /j \
,.-. I ^ l UseNpMax,u,t \ I . l ConsUseP,u,t \
(QuseP,,u,t X ^1 — ) X ^1 — j
NWuser / p \ / P \ P /'co^
,.-. I ,. l UseNpMax,u,t \ l . l ConsUseP,u,t \ l Sep,u \J^^)
n=2
(^ . „, n . bPprice\ (. PuseNpMax,u,t^
x 11 + ElasPriceu x 1 - 11 -^—-
. 1 PconsUs
X I J.
,u,t\ Psep,u
/ion UseP,u,t
22
-------
P[JseNpMax,u,t\ ^ ( ^ PconsUseNp,u,t\ °Sep,u (53)
_ _ V"1 US6r fri (PuseNpMax,u,t\ I. PconsUseNp,u,t\
UuseNpSep,t ~ ^=2 WuseP,,u,t X ^ — J X ^1 — J WQ
bPprice\ (PuseNpMax,u,t\ I' PconsUseNp,u,t\
^1-
>
Sep,u
x(l + ElasPriceux ^ J ^ ^ ^..^ ^
100
where
, ,
UseNP'u't "DmRedJ
Qusepi,u,t = initial potable water use/demand
PuseNpMax,u,t = maximum percent of water demand that can be met by nonpotable water
PSep iU = percent of users serviced by septic systems draining within the study area
ElasPriceu = price elasticity for water user type, u,
bPprice = percent price change
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
r , PUseNpMax,u,t\ ( PconsUseP,u,t\ (54)
Wt/Sew,u,t X ^1 — J X ^1 — J
usePSepExt* ,n=2
PconsUseP,u,t\
100 / 100
,_ i"useNpMax,u,t\ f. "consUseNp,u,t\ "sepExt,u (55)
iVseNpSepExt,t — / (VusePl,u,t X ^ T^T I XII —- I X
x(l+ ElasPriceu x -^-J - (^^'"^ x f 1 - Pc°nst/seiVp'u^
p
rSepExt,u ^-, , -, >.
X TTTri X ^UseNp,u,t X 0(JDmRed)
1UU
Septic flows enter the groundwater system:
QusePSept + QuseNpSept = QsepGw,t (56)
where QsepGw,t = fl°w from septic systems to groundwater.
Aquifer Storage and Recovery Facility (Asr)
bQswAsr,t + bQResAsr,t + ^CVr/.Asr,t = C^lsrGw.t (57)
where QASTGW.I = fl°w from the ASR facility to groundwater.
-------
WMOST v1
2.2.2 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.
bQswWtp.t + bQResWtpjt < QswPumpI + "QswPumpAddl
bQcwWtp.t — QcwPumpI + "QcwPumpAddl
bQfiesWtp.t + "QswWtp.t + "QcwWtp.t — Qwtp.MaxI + "Qwtp,Addl
bQusePWwtp.t + "QuseNpWwtp.t + QcwWwtp.t — Qwwtp.MaxI + "Qwwtp,Addl
bQwwtpWrf.t — Qwrf.MaxI + "Qwrf,Addl
bQswAsr,t + bQResAsr,t + QwrfAsr,t ^ QAsr,Maxl
bQwrfUseNp.t — QNpdist.MaxI
(58)
(59)
(60)
(61)
(62)
(63)
(64)
where
Qwtp,Maxi
bQwtp,Addi
Qwwtp,Maxi
bQwwtp,Addi
Qwrf,Maxi
bQwrf,Addi
QAsr,Maxi
bQAsr,Addi
= 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
Limits for groundwater and reservoir storage volumes: For groundwater, the minimum storage
volume, VGW:Min, may be specified to reflect the maximum desired drawdown (e.g., to avert land
subsidence). The maximum volume, VGWiMax, may also be specified to reflect the size of the aquifer
and the maximum storage capacity. For the reservoir, the minimum storage volume, VReS:Min, 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, VRes :Maxi, maY b£
specified to reflect the physical size of the reservoir (note that additional surface water storage
capacity, bVReSiAddi, is one of the management options in Table 1-1).
24
-------
VGvfit < VGwMax (65)
VGWit > VGwMin (66)
^Res,t ^ VResMctx + ^ResMdl (67)
> VResMn (68)
Sustainable system: The final volume of the reservoir and groundwater are constrained to be equal to
their respective initial volumes. Therefore, no deficit can build up over the modeling time period.
New England, for example, is a region where many systems are within-year. However, the longer
time period that is modeled, the constraints become less binding because only the initial and final
volumes are forced to be equal.
VRes,t=i = VRes,t=tf (69)
Vcw,t=i = VCw,t=tf (70)
where tfis the last day in the time period optimized.
2.2.3 Constraints Associated with Management Options
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 f°r 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.
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,
^-, ^ *UseNpMax.u.t~~ ^ . T-.T r-i • (71)
usePMin,t = Wf«W,u,t X t1 -- - )) X t1 + ElasPrlCeu
u=2 to NUser
bPprice , PUseNpMax,u,t\
- 100 — \ 100 - / Usep,ut "Vomited)
ll}seNpMin,t / ^ \f,useri,uf • • inn
bPprice (72)
u=2 to NUser
PuseNpMax^t
7^ x fuseNp,u,t x
25
-------
WMOST '..1 T^=*ocetical
Minimum demand for potable and nonpotable water uses is set as:
QwtpUseP,t + bQlbtWUseP,t =5 QusePMin,t (73)
bQwtpUseNp,t + bQlbtWUseNp,t + bQwrfUseNp,t =5 QuseNpMin,t (74)
Consumptive water use
The final or adjusted percent consumptive use for potable water use, Pconsusep,u,t? is calculated based
on the initial percent consumptive use of potable water, PconsiisePi,u,t, PuseNpMax,u, and the percent
consumptive use of nonpotable water, PconsUseNp,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 _ PconsUsePI,u,t ~ 'UseNpMax.u X °Consl/seWp,u,t/100 (75)
ConsUseP,u,t ~
It is possible to enter input data for potable and nonpotable percent consumptive use and maximum
percent nonpotable use in a combination that result in an adjusted percent potable consumptive use
value being outside of the feasible range of 0-100%. Therefore, a third table in the "Nonpotable
Demand" input data worksheet pre-calculates the adjusted percent potable consumptive use values
and is highlighted red if the value is outside of the feasible range. The model will not run if any of
these values are outside of the feasible range and the user is provided with an error message to change
one or more of the input values.
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.
QswMint ^ QswRes,t where QSWMin,t= minimum in-stream flow for subbasin reach (76)
QswMax,t ^ QswRes,t where QSWMax,t= maximum in-stream flow for subbasin reach (77)
QswExtMin,t ^ QResExt,t where QSwExtMin,t= minimum flow exiting subbasin (78)
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.
QcwExtMin,t ^ bQcwExt,t (79)
Management limits:
The model user may specify limits on the social and/or physical limits of implementing four
management options - increasing water price, direct decrease in demand, fixing leaks in the water
distribution and wastewater collection systems, and inter-basin transfer.
2i
-------
bPPrice < PPriceMax * bPriceBin (80)
where
PprweMax = one time, maximum percent change in price
bQomRed — QomRedMax (81)
O'WtpLeakFix — 'WtpLeakFixMax (82)
where PwtpLeakFixMax = maximum physical limit of leakage reduction in distribution system (e.g.,
given age of system and the repair costs specified)
O'WwtpLeakFix — 'WwtpLeakFixMax (83)
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 timestep in the period of analysis,
bQibtWUseP,t + bQlbtWUseNpt ^ QlbtWMaxDay + ^QlbtWAddl (84)
bQusePlbtWw,t + bQuseNplbtWw,t ^ QlbtWwMaxDay + ^QlbtWwAddl (85)
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 + bQIbtwuseNp,t ^ (QibtwMaxoay + bQmwAdd{) x NDay(month(t)) (86)
bQusepibtww,t + bQUseNpIi,tww,t ^ (QibtwwMaxDay + bQjbtwwAddi^) x NDay(month(t)) (87)
where
QibtwMaxDay = maximum potable water transfers from/to outside the basin for each day in the
optimization period
QibtwwMaxDay = 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 monthly limit, if the time step is daily, then^or each month in the period of analysis,
Z
OQl
lbtWUseP,t
t=l to NdtM
NdtM
— QlbtWMaxMonth.m X TTT 7 , ,, >.\ + "QlbtW 'Addl
NDay(month(t))
-------
WMOST '..
cal
/^ bQusePIbtWw.t + "Qu
(89)
t=l to NdtM
NdtM
^ QlbtWwMaxMonth,m X 777; 7 . , x.xA + bQlbtWwAddl
777; 7 . , x.xA
NDay(month(t))
where
QibtwwMaxMonth,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 monthly limit, if the time step is monthly, then/or each month in the period of analysis,
bQibtWUseP,t + bQjhtWUseNp,t ^ QibtWMaxMonth,m + NdtM X bQIbtwAddi (90)
bQusePIbtWw.t + "QuseNplbtWwt — QlbtWwMaxMonth.m + NdtM X oy/btivw^ddl (°1)
For annual limit, for each year in the period of analysis,
,? OQlbtWUseP.t + OQlbtWUseNp.t — QlbtWMaxYr
Ndt (92)
x TT^- + NDaysYr x bQIbtwAddl
t=ltoNdt
,? bQu
sePlbtWw,t
t=l to Ndt
Ndt
S= QibtwwMaxYr x ,, ,.„ + NDaysYr x bQIbtWwAddi
where
C/fcttVAtovr = maximum potable water transfers from/to outside the basin for a given year in the
optimization period
QibtwwMaxYr = 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)
NDaysYr = number of days in the year that are modeled
28
-------
Internal Configuration
3. 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 and 3) 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 3-1 shows the flow of information and process links
between components of WMOST. Two modules are noted for future development - Sensitivity
Analysis and Trade-Off Analysis. These analyses can be performed manually as described in the User
Guide.
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.
Figure 3-1. WMOST Internal Configuration
WMOST Internal Configuration
Flow of information
Process links
Excel Worksheets: User Interface
Links to all input
and output
worksheets
Initiate running
optimization and
other analyses
Visual Basic Modules
Soluer
Input Setup
Setup input worksheets according
user specifications
Main
Read input
Define linear programming
problem using equations of mass
balance, costs, revenues, &
constraints
Write input fite for Lp_solve and
Trade-Off Analysis
(future development)
Run model multiple time varying
in-stream flow
Track results and create trade-off
curve with cast
Lp_solve
Lpsolve55.dll
(stand-alone file]
*
Sensitivity Analysis
(future development)
Run model multiple times varying
input parameter(s)
Track results and provide ranking
of most influential parameters
Table Outputs
Populate output worksheets with
table of results from Lp_solve
Graphical Outputs
Produce streamftow graphs
29
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WMOST v1 Theoretical Documentation
4. Summary of Input Data
Variables
Units
Description
Land Use: Conservation and Stormwater Management
As,i
Aminsl
Amaxsl
CCASil
C°mAs'1
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
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
Potable Demand
QusePI,u,t
'ConsUsel,u,t
PuseNpMax,u,t
MOD
%
%
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
Nonpotable Demand
p
r ConsUseNp,u,t
%
Percent consumptive use for nonpotable water
for each user for an average month for each
month
Demand Management
Eu
^C,Price
% demand reduction / % price
increase
$
Price elasticity for each user
Capital cost to implement price increase
' Recharge and runoff rates may be derived from a calibrated/validated simulation model such as Soil Water Assessment Tool,
Hydrological Simulation Program—Fortran or Storm Water Management Model.
30
-------
August 2013
of
Variables
r
'-'Omfrice
p
'PriceMax
QomRedMax
Qom
c
uOmDm
Units
S/yr
%
MOD
S
$/yr
Description
O&M cost to administer price increase (e.g.,
resurvey for appropriate price etc.)
Maximum percent price change
Maximum/total direct demand reduction
Initial cost for direct demand reduction
O&M cost for direct demand reduction
Septic System Users
Psep.u
p
rSepExt,u
%
%
Percent septic use for each public water user
that drains within modeled watershed
Percent septic use for each public water user
that drains outside modeled watershed
Groundwater Storage
kb
VGW,,
*Gw,Min
Vcw,Max
QcwExt.t
QcwExtMin.t
QsxtGw.t
QptGw,t
QcwPt.t
I/time step
MG
MG
MG
MG/time step
MG/time step
MG/time step
MG per time step
MG per 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
Flow from private point source to groundwater,
i.e., discharge
Flow from groundwater to private point source,
i.e., withdrawal
Surface Water/Stream Reach and Reservoir/Surface Storage
QsxtSw,t
QswResMlnf
QswResMax.t
QswExtMin.t
QptSw,t
fi/sec
ftj/sec
fi/sec
ft3/sec
MG per time step
Inflow from external surface water to study area
stream reach
Minimum in-stream flow in reach
Maximum in-stream flow in reach
Minimum surface water flow out of study area
Flow from private point source to surface water,
i.e., discharge
31
-------
WMOST '..
cal
Variables
QswPt.t
VRBS,I
*Res,Min
'Res,Max
QExtSwOutMin.t
Cc,Res
^Om,Res
RuseP
RuseNp
RWW
Units
MG per time step
MG
MG
MG
ftj/sec
$/MG
$/MG
$/100ftJ
$/100ftJ
$/100ft3
Description
Flow from surface water to private point source,
i.e., withdrawal
Reservoir volume
Minimum reservoir volume
Current maximum reservoir volume
Minimum flow out of study area
Capital construction cost
O&M costs
Customer's price for potable water
Customer's price for nonpotable water
Customer's price for wastewater
Interbasin Transfer
Ccibtw
CdbtWw
ClbtW
ClbtWw
QlbtWMaxDay.t
QlbtWwMaxDay ,t
QlbtWMaxMonth,t
QlbtWwMaxMonth.t
QlbtWMaxYr,t
QlbtWwMaxYr,t
QlbtWAddlMax
QlbtWwAddMax
S/MGD
S/MGD
S/MGD
S/MGD
MGD
MGD
MGD
MGD
Initial cost for obtaining rights to and building
infrastructure for interbasin transfer of potable
water
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
Maximum additional interbasin transfer flow
for water and wastewater on a daily basis
General
TPlan
i
yrs
%
Planning horizon
Interest rate
Water Treatment Plant
R
usePF
S/month
Consumer's price for potable water: Fixed
monthly fee
32
-------
August 2013
of
Variables
"useP
r
'-CjGwPump
r
^"OmfiwPump
QcwPumpI
T
1 GwPump,Exist
T
1 GwPump,New
r
'-C,SwPump
r
^"Om^wPump
^cSwPumpl
T
1 SwPump, Exist
T
1 SwPump, New
Cc,wtp
C()m,Wtp
Twtp,Exist
Twtp,New
Qwtp.Max
(•C.WtpLeak
Com,WtpLeak
'WtpLeakFixMax
Units
S/HCF
S/MGD
$/MGD/yr
MOD
yrs
yrs
S/MGD
$/MGD/yr
MGD
yrs
yrs
S/MGD
$/MGD/yr
yrs
yrs
MGD
$
$/yr
%
Description
Consumer's price for potable water: Variable,
volume-based fee
Gw pumping: Capital construction cost
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
O&M costs for continued leak repair
Maximum percent of leaks that can be fixed
Wastewater treatment plant
RWWF
RWW
Cc.wwtp
c
^Om,Wwtp
'Exist, Wwtp
T
1 New, Wwtp
Qwwtp,Max
S/month
S/HCF
S/MGD
S/MGD/yr
yrs
yrs
MGD
Consumer's price for waste water: Fixed
monthly fee
Consumer's price for wastewater: Variable,
volume-based fee
Capital construction cost
O&M costs
Lifetime remaining on existing construction
Lifetime of new construction
Current maximum capacity
33
-------
WMOST '..
cal
Variables
P
'WwtpLeakFixMax
'WwtpLeakl
Cc.WwtpLeak
^Om,Wwtpleak
Units
%
% of WW Inflow
$
$/yr
Description
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
$MGD
S/MGD/yr
yrs
yrs
MOD
Capital construction cost
O&M costs
Lifetime remaining on existing construction
Lifetime of new construction
Current maximum capacity
Nonpotable water distribution system (NpDist)
RuseNpF
RuseNp
Cc,Npdist
r
l-Om,Npdist
QNpDistl
'NpDist.Exist
T
1 NpDist,New
S/month
S/HCF
S/MGD
S/MGD/yr
MGD
yrs
yrs
Consumer's price for nonpotable water: Fixed
monthly fee
Consumer's price for nonpotable water:
Variable, volume-based fee
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
Aquifer Storage and Recovery
CC,AST
c
^Om,Asr
T
1 Exist,Asr
T
1 New,Asr
QAST.MUX
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
34
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Future Development
5. Future Development
The following model enhancements may be implemented in future development efforts. These
suggestions are based on reviewer and stakeholder feedback.
5.1 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 26
26 Non-linear functions can be approximated by a set of linear equations to keep the model a linear programming
optimization problem.
35
-------
WMOST '..1 T^=*ocetical
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)
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 GREAT27 or other climate
projections to facilitate sensitivity and uncertainty analyses
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 Stormwater module that is run as a pre-processor for generating managed runoff and
recharge rate time series
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.
27 http://water.epa.gov/infrastructure/watersecurity/climate/creat.cfm
3i
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Future
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 Planning28 by screening
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
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
5.2 User Interface and User Support
• Input features
o Provide generic runoff and recharge rates for various combinations of land cover/land
use, soil, and slope HRUs (i.e., for various precipitation/weather regions) so that user
does not need an existing, detailed simulation model to derive input values for runoff
and recharge rates
o Direct linking and interoperability with simulation models for importing baseline
runoff and recharge rate time series (e.g., Hydrological Simulation Program Fortran
(HSPF),29 Soil Water and Assessment Tool (SWAT)30
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
28 http://cfpub.epa.gov/npdes/integratedplans.cfm
http://water.usgs.gov/software/HSPF/
30 http://swat.tamu.edu/
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WMOST '..1 T^=*ocetical
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)
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Appendix A
6. 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 with case studies as a source of default data.
6.1 User Error Checks
The user is informed with a message box if any of the following are encountered in the entered input
data:
• 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, and
• adjusted percent consumptive use for potable water values are between 0-100%.
6.2 User Manual, Case Studies and Default Data
Two case studies are provided with the model user guide 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% depending on the infrastructure or
management practice.
Many federal and state websites provide data for geographic information systems 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.
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