Quantitative Evaluation of the Performance of Water Management System in the
Washington Metropolitan Area
Roma Bhatkoti* and Konstantinos P. Triantis*’*
“Virginia Polytechnic Institute and State University
System Performance Laboratory
Grado Department of Industrial and Systems Engineering
Falls Church, VA 22043 USA
Telephone: 703-538-3765
E-mail: romal3@vt.edu, triantis@vt.edu
Abstract
The water management system for the Washington Metropolitan Area (WMA), like many other public utilities, is
reaching its maximum service potential in the face of this rapid growth and climate change. Frequent droughts have not only
prompted pricy withdrawals from reserve water supplies more than once, fall of 2010 being the latest case of such water
releases, but also have generated varied responses from different local governments that make up the WMA, reflecting lack
of cooperation. This also reflects that WMA water supply system is not adequate enough to meet daily demand using only
Potomac, Patuxent and Occoquan resources. Prior information about time and volume of releases will not only help in the
officient allocation of water but it will also help in well-informed decision making. Therefore, this paper does the following:
1) Model the demand and supply dynamics for the WMA, 2) Analyze the impact of historical droughts on water
availability; and 3) Assesses the performance of the system under various demand scenarios and drought conditions. Finally,
the paper concludes that WMA water supply system is susceptible to shortages in future and performance of the system is
expected to deteriorate in the coming years with recurrence of historical droughts.
Keywords: Water management, WMA, Performance Measurement
1. Introduction
The Washington Metropolitan Area (WMA) is the seventh largest U.S. metropolitan area and
is expected to grow by 25% by 2030. The Water Management System for the WMA, like many other
public utilities, is reaching its maximum service potential in the face of this rapid residential and
commercial growth. Projections place future steady-state consumption needs in excess of 26% over
current demand by 2020. For the present, episodic surges in demand, largely due to population and
economic growth, have already demonstrated they can exceed current capacity leading to off-
strategy spending and inefficient work-arounds. Moreover, climate change is expected to strain the
system further by increasing demand and reducing supplies. Frequent droughts have already
prompted pricy withdrawals from reserve water supplies of the region and associated water studies
confirm that further taxing of reserve supplies is not a viable longer-term strategy.
The objective of this paper is to assess the adequacy of current WMA water supply system to
meet the future water demand for the WMA region. This is accomplished by creating a water
demand-supply model to assist in water resource planning and decision making for the entire WMA
region that spans over 15 counties and 6 county-equivalent cities, plus the District of Columbia. The
* This paper is based in part on work supported by the National Science Foundation, while working at the
Foundation. Any opinion, finding, and conclusions and recommendations expressed in this paper are those of the
authors and do not necessarily reflect the views of the National Science Foundation.
* This work was supported in part by the Institute for Critical Technology and Applied Science (ICTAS).
1
model is developed within a system dynamics framework for the purposes of 1) quantitatively
assessing the adequacy of current water resources, available to the region, to meet future water
demand, 2) analyzing the impact of historical droughts and low flows on water availability and 3)
assessing the performance of the system under various demand scenarios and drought conditions.
The System Dynamic (SD) methodology is used for this research to build and assess quantitative
models. The SD methodology stands as a proven approach and tool used in the past both
domestically and globally to diagnose similar water systems. SD affords the engineering team the
ability to a) isolate key causal relationships between the system elements, and b) graphically represent
the constellation of subsystems for lay policy-maker comprehension and consideration. Moreover,
system dynamics is a continuous modeling process which allows for an examination of the effects of
multi-year droughts on different reservoirs.
This paper is organized as follows: Section (2) articulates the problem context. An overview of
the study area and its water resources is provided in section (3). Section (4) covers System Dynamics
methodology and previous research. Section (5) builds up the quantitative demand supply model,
section (6) assesses the performance of the current water management system and the last section
provides conclusions and future research.
2.Problem Context
The Washington metropolitan Area (WMA) is one of the fastest growing regions in US. This
growth can be attributed to the strength of the region’s economy and high rates of in-migration and
international immigration, becoming the seventh largest U.S. metropolitan area. Currently, WMA
has a population in excess of five million inhabitants and is expected to grow at the rate of
approximately 64,000 persons a year (COG 2008). Historically the WMA has experienced
population growth rates higher that the national average. Between 1980 and 1990 the WMA had a
population growth rate of 17% compared to the national average of 10% over the same time period
(Garling 1998). Population of the Washington metropolitan region is expected to grow by 25% by
2030. To meet the future demands of this growing metropolis, it is expected that nearly 1.5 million
housing units and 180 million square meters of commercial or institutional space will need to be
replaced or added. (see: http://www.nvta.com, www.demographia.com). Consequently, such high
growth will place a tremendous additional burden on WMA’s resoutces, i.e., more water and more
energy will be demanded.
Historically, periods of drought place an extra strain on the WMA region’s resources. The
WMA water supply system has made releases in three drought seasons since completion of the
Jennings Randolph Reservoir. In 1999, 2002 and 2010, low precipitation levels resulting in a water
supply which proved to be insufficient to fulfill the region’s demand projections during the summer
months of those years. Episodes like this, prompted authorities to pay premium prices for additional
water resources from Jennings Randolph and Little Seneca reservoirs, which are the reserve water
supplies for the WMA. These repositories are referred to as the “savings account” for the WMA.
The first release, totaling 2.9 billion gallons, was made during the summer of 1999 from the Jennings
Randolph Reservoir. The 1999 drought also highlighted the need for coordinated water conservation
measures and also highlighted the importance of knowing about the shortfall in advance. It was
observed that the water in the Potomac was not sufficient to meet water demands. Thus, prompting
releases. Also, Maryland imposed mandatory water restrictions in lieu of the impending drought
while Virginia and DC did not impose any such restrictions.
It is apparent from numerous studies (ICPRB) that the WMA is facing problems of an
increasing water demand, limited resources and climate change. It is important to understand the
limitations of the current system and the petiods and frequency of water shortages so that policy
makers can plan for better reservoir operations in advance. WMA is already a very vast metropolitan
atea and with its heterogeneity and diversity it is becoming more difficult for water managers to
satisfactorily meet future water demand without causing unpleasant water use restrictions. And since
there is no unified authority to manage this region as a one cohesive entity, it poses a huge challenge
for policy makers and regional governments to include all stakeholders during strategic and
operational decision making in times of crises. Thus, it is important to model the area’s supply and
demand as a complete entity and to gauge its performance under different demand, drought and low
flow scenarios.
3.Overview of the Study Area and its Water Resources
The WMA is comprised of 15 counties, 6 county equivalent cities and the District of
Columbia. Figure 1 provides an overview of the study area. Since WMA is comprised of different
administrative units, the Metropolitan Washington Council of Governments (MWCOG) was created
in 1957 for the purpose of discussing regional issues and to guide the development of the region as a
whole. MWCOG, more commonly known as COG, is the regional organization comprised of 21
WMA local governments, members of the Maryland and Virginia state legislatures, the U.S. Senate,
and the U.S. House of Representatives. Other than that, there are numerous other local jurisdictions
in the WMA that have independent general purpose governments.
Figure 1: Water Supplier Service Areas in the Washington Metropolitan Area (Hagen and
Steiner 2000).
The main source of water in WMA is the Potomac River. There are around twenty water
utilities operating in the region. There are three main suppliers: the Fairfax County Water Authority
(FCWA), the Washington Suburban Sanitary Commission (WSSC), and the Washington Aqueduct.
Approximately 90 percent of the WMA’s population relies on water provided by these three main
agencies. The main suppliers also provide treated water to many wholesale or independent utilities.
The main suppliers are also called CO-OP suppliers because their function is coordinated by the
ICPRB (Interstate Commission on the Potomac River Basin) Section for Cooperative Water Supply
Operations on the Potomac (CO-OP). Other than coordinating between suppliers, the ICPRB also
manages water supply during droughts, forecasts demand, flood control, and facilitates source water
protection (see: http://www.potomacriver.org/cms, abouticprbdocs/staffexpertise.pdf).
The three major regional water suppliers have collectively paid for water storage in Jennings
Randolph and Little Seneca Reservoir. Jennings Randolph holds 13.4 billion gallons (bg) of water. It
is located 200 miles upstream of the utility water intakes located at Great Falls. Releases made from
Jennings Randolph take more than a week to reach intakes. The Little Seneca reservoir is a smaller
reservoir that holds 3.8 bg of water. It is used to “fine tune” the larger releases from the Jennings
Randolph. Releases made from Little Seneca take less than a day to reach the utilities’ intakes.
There are two additional reservoirs that are operated by the utilities separately. The WSSC
operates the Patuxent Reservoirs in the neighboring Patuxent River watershed. Total usable storage
available at these reserve water supplies is about 10.2 bg. The water stored in these reservoirs is used
along with Potomac River withdrawals throughout the year. Similarly, FCWA operates a reservoir on
the Occoquan River with a total storage volume of 8.0 bg. The Potomac River still remains the main
source of water for WMA residents. 75% percent of the water treated by the CO-OP suppliers
comes from the Potomac River. Patuxent and Occoquan reservoirs that do not fill from the
Potomac account for the remaining 25% of the regional demand (Hagen and Steiner 2000). Figure 2
gives a schematic of the WMA’s water resources.
{ii Mater Weter source
CO-OP Utlity
‘Wholesale / Independent UMllty
Figure 2: Overview of WMA’s Water Resource (ICPRB 2010a).
In summary, the WMA has a complex water management system that has to cater five
million residents spanning over 15,000 square kilometers. Being the nation’s capital with diverse
demographics and distinct local governments gives the WMA its unique character and provides
challenges for policy makers and regional government institutions.
4.Water System Modeling Addressing Demand, Supply, and Environmental Issues
Water resources are modeled on both global and local levels. Global water models, although
philosophically very intuitive and informative, provide little help to policy makers because global
models are highly aggregated and do not address day-to-day operational concerns of municipal water
managers (Winz, Brierley et al. 2009). So, local temporal and spatial models are developed to
facilitate decision making by local and regional governments since local governments have authority
to make water withdrawal, distribution and conservation related policies. Although local models are
more practical from a regional policy formulation and implementation point of view, it is important
to have a global perspective on water availability and to assess its impact on overall development of
human civilization. For that purpose, various global water scarcity studies have been conducted
(Saysel and Barlas 2001); (Alcamo and Henrichs 2002); (Chung, Kim et al. 2008). One such study
conducted by (Kojiri, Hori et al. 2008) depict that overall civilization development will be retarded if
there is a deficit in water resources.
Among the local water models, most have focused on managing water for droughts of
heavily populated regions. One such demand supply study was conducted in the Okanagan Basin,
Canada, where the research tried to investigate the impact of population growth and climate change
on water demand and supply. The mounting instances of water deficit trigger conservation policies
that come into play and balance the deficit. Groundwater pumping and water imports balance the
deficit by augmenting available supplies whereas municipal, agriculture and ecosystem demand
reinforces it (Langsdale, Beall et al. 2007).
Similar demand and supply modeling was conducted for the Middle Rio Grande river basin,
where water deficit has been on a constant rise (Passell, Tidwell et al. 2003; Tidwell, Passell et al.
2004). This study explored demand and supply dynamics of the region where climate change and
population growth were key variables that affected supply and demand respectively. Various
competing management strategies were assessed including the reliability of the current system to
meet future water demand.
Various regions of the world have analyzed their water resources for climatic change
vulnerability and risks associated with possible water shortages. Like a study conducted in Las Vegas
concluded that reducing outdoor water consumption can reduce the vulnerability of the water
supply system and increase its robustness (Stave 2003). A similar study conducted by Marifio in 2008
have similar conclusions regarding current state of water policies for Zayandeh-Rud river basin in
Central Iran (Marifio 2008).
Many researchers have used different methodologies to understand the processes
responsible for spatial and temporal distribution of water resources in a river basin. Oel et al. 2010
use a multi-agent simulation approach to develop a model to represent local water use of the
Jaguaribe basin in Northeast Brazil. Various water supply system managers have used combination
of optimization and simulation techniques for improving water resource efficiency and effective
reservoir management (Sheer 1977; Palmer et al. 1979; 1982).
Once the water supply system has been accurately represented both temporally and spatially
through numerous methodologies like system dynamics, multi-agent modeling, etc. the system
performance should be evaluated under a wider range of feasible demand, supply and weather
scenarios. The literature discusses various performance metrics that are relevant for water
management systems, such as, reliability (the probability that the system will remain in a non-failure
state), resilience (the ability of the system to return to non-failure state after a failure has occurred),
vulnerability (the likely damage of a failure event), and robustness (flexibility to adapt to wide range
of scenarios) (Hashimoto et al. 1982; Kjeldsen and Rosbjerg, 2004; McMahon et al. 2006; Siminovic
et al. 1992). The literature also discusses the use of single metrics for performance assessment like a
drought risk index (DRI) or sustainability index instead of using multiple metrics like resilience,
reliability, vulnerability etc. concurrently. These single metrics are just a multiplicative or additive
combination of reliability, resilience and vulnerability concepts. (Zongxue et al. 1998; Loucks, 1997;
McMahon et al. 2006)
This paper uses the SD methodology to model the WMA water management system because
SD affords the engineering team the ability to a) isolate key causal relationships between the system
elements, and b) graphically represent the constellation of subsystems for lay policy-maker
comprehension and consideration. Moreover, system dynamics is a continuous modeling process
which allows for an examination of the effects of multi-year droughts on reservoir.
5.Modeling
In this study, the model has two main components: Water demand and supply. We provide a
discussion of both components subsequently.
5.1 Water Demand
Forecasting annual average water demand is a multi-step process. It requires data from
various agencies like the Metropolitan Washington Council of Governments (MWCOG), which is a
regional planning agency for Washington Metropolitan Area, utility providers like Washington
Aqueduct, WSSC, Rockville, etc.
MWCOG provides estimates of population, households, and employees for the Washington
Metropolitan Area from 2010 through 2040 (MWCOG, 2009) and the WMA utility suppliers like
WSSC, FCWA provide area specific billing information, water use data and demographic data along
with assumptions regarding changes in water use patterns in the region.
Figure 3 describes the annual average water demand forecasting process in detail. Firstly,
billing and production data is collected from each utility supplier along with the demographic data
specific to its area. The difference between the amount of water produced or purchased by the utility
and the amount billed to its customer gives a fairly good estimate of ‘unmetered water use’. The
ICPRB has come up with an estimate for unmetered water for all WMA water suppliers, which is
approximately 10 percent. This 10 percent value provides a conservative planning-level estimate of
future water demand that accounts for increased losses as infrastructure ages (ICPRB 2010a).
Second, billing information collected above is also used to calculate ‘unit use factors’ for each
category (single family, multifamily and employee). The unit use factor for each category is calculated
by dividing billing information for that category by its demographic data. Unit use factor basically
describes average daily water use. Future unit use factors are impacted by water use policies for the
region. For example, due to the Energy Policy Act of 1992 water use is expected to fall in future due
to the installation of water conserving fixtures and fittings. Other than that government keeps
coming up with numerous programs that promote voluntary water conservation that may also affect
consumet’s future water use behavior. Moreover, global climate change may result into significant
changes in regional temperature and precipitation trends and patterns that could impact summertime
outdoor water use, which is a significant component of annual average demand.
Similarly, the number of single family and multi-family households is obtained from each
county’s planning office. This information is then used to calculate ‘dwelling unit ratio’ (which is
calculated as the ratio of single family households to multi-family households) for each suppliet’s
service area. Later, the dwelling unit ratio is utilized to separate household forecasts made by
MWCOG into the number of single family and multi-family households for each suppliet’s service
area. Other than dwelling unit ratio, the above information is also an input for calculating unit use
factors.
According to the MWCOG forecast (MWCOG, 2009), households are expected to increase
by 29% by 2040, population by 24% and employees by 38%. The employee data is reflective of
economic growth of the region (see Table 1). The numbers reflect that the WMA economy is
growing due to its metropolitan character and federal job creation.
Similarly, unit use factors are also expected to exhibit long-term decreasing trends due to
changes in the water use behavior and the Energy Policy Act. ICPRB expects a total savings of 16
million gallon per day (mgd) per household by 2040 due to the provisions of the Energy Policy Act
of 1992 that require the use of more efficient plumbing fixtures. The figures given by ICPRB are
conservative because unit water use may fall further due to government led education campaigns like
“Water Use It Wisely” (ran by MWCOG) that promotes wise water use in the region (ICPRB
2010a).
Table 1: The MWCOG Forecast for the Percentage Increase in Demographics for the WMA
Water Suppliers from 2010 to 2040. Source: ICPRB (2010a)
Households | Population | Employees
FWCA 36% 32% 54%
Aqueduct 28% 26% 24%
WSSC 22% 17% 42%
Average (Including Rockville) 29% 24% 38%
Hereafter, two demand scenarios are developed (Figure 5):
Demand Scenario 1: This scenario is based on MWCOG forecasts and assumes that both single
family household and multi-family household unit use will decrease throughout the forecast period
due to the effects of the Energy Policy Act of 1992.
Demand Scenario 2: This scenario is also based on MWCOG Round 7.2 growth forecasts but it
assumes that the reduction in single family unit use will be offset by increases in summertime
outdoor water use. Thus, we shall only see significant reduction in multi-family households water
use due to provisions of the Energy Policy Act.
Both demand scenarios were developed for the three major utility suppliers for the WMA and also
for the Rockville PWD. Both scenarios provide the average annual demand for water for each water
utility. But, water demand has very strong seasonal component. Summer water demand is much
higher than winter because more water is utilized to irrigate lawns, gardens, golf courses, etc. and for
keeping swimming pools full. Similarly, indoor water use also increases because people take more
frequent baths in summer. This becomes even more critical because stream flow rates ate typically
low in summer months (Figure 4). Therefore, ‘monthly production factors’ were used to convert the
annual demand forecasts to forecasts of monthly demand. The monthly production factor is
basically the ratio of average monthly to average annual production. The ICPRB has calculated
monthly production factors for each of WMA’s suppliers and they reflect typical seasonal variations
in water production.
The model developed for this study basically generates two demand scenarios and the supply system
is analyzed to see whether it is able to meet the 30 year projected demand for both scenarios.
| Data: | [Analyses: | [Resuits: |
Billing data (CY 2005 -
2008) by service area
Production data (daily
‘thru 2008)
Delineate curent &
‘Curent & future service |_| future service ereas
area information
Current & future ratios
Determine curent #SFH,
—— | | emastoees
dwelling unit ratios by service ares
(OUR)
‘Current & future Determine future #
Shouseholds & SFH, # MPH, and #
# employees by TAZ ‘empiayees by service
(Round 7.2) =
Figure 3: Annual Average Water Demand Forecasting Process (Source: ICPRB 2010a)
Monthly Mean Streamflow WMA Monthly Production Factors
Potomac River near Little Falls, MD (cubic feet (Dimensionless)
per second) 14
25000 12
20000 1
15000 on
08
410000 sa
5000 oP
0 °
tn ee ee SP EP OES SS SSS
FEE ELSES 8 & & ¥ sf & wre SK SF SS
¢ s
ve a rn, Oe
Figute 4: Monthly Mean Stream Flow for the Potomac River near Little Falls’, WMA
Monthly Production Factors
Household Forecast. Single Family
MWCOG-FCWA Forecast
\
Dwelling Unit Ratio Muti Family
Forecast
Mwedecewa ———— Forecast
i Saas
Average Annual
Demand Forecast -
Scenario 1-FCWA
System Loss Factor
(Unmetered Water Use %)
Employee Forecast ————
MWCOG-FCWA
Monthly Production
Single family Unit
Use-F CW Factor-FCWA
Use-F CWA, Savings Forecast Due to
‘Average Annual Energy Policy Act
Demand Forecast-
Mult family Unit
————> Scenario 2-FCWA
Use-FCWA
Employee Unit”
Use-FCWA
Figure 5: Demand Side Model: Demand Scenarios for the FCWA
5.2 Water Supply
The main source of water drinking supply for the majority of people in the WMA is the non-
tidal Potomac River. There are three main suppliers: FCWA, WSSC and the Washington Aqueduct.
Each of the three major suppliers withdraws water from the Potomac River upstream of Great Falls.
There is an additional intake at Little Falls which is used by Washington Aqueduct.
5.2.1 The Supply Side Model: Potomac River System
The average annual stream flow values for the Potomac River is around 7 billion gallons per
day (bgd), with higher flows typically occurring in the winter months and lower flows in the summer
months (Figure 4). For much of the year, water supply withdrawals from the Potomac remain a
small fraction of river’s flow because the average summer demand for water by WMA suppliers is
approximately 500 million gallons per day (mgd), or 0.5 bgd (ICPRB 2010a). This may give a false
% http://md.water.usgs.gov/surfacewater/streamflow/
sense of water security for the region. The critical aspect here is the stream flow variability. Potomac
stream flows may even drop to values as low as 530 cubic feet per sec (summer of 1966, the flow
was less than projected demand), which is quite low and about 22 times less than the average annual
flow. Over a course of a year a typical high discharge can be 11,000 cubic feet pet sec and typically
low discharge can be 2000 to 3000 cubic feet per sec. Due to such high flow variability, chances of
water supply system, relying solely on Potomac water, not meeting the daily demand targets may
increase. Therefore, during periods of low flow, which typically occur in summer and early fall, the
natural flow of the Potomac may require augmentation to satisfy predicted demand plus
environmental flow requirements.
The total available Potomac water is constrained by two factors: Minimum environmental
requirement and upstream consumptive demand. There is a minimum low-flow requirement of 100
med at Little falls and 300 mgd at Great Falls necessary for protecting aquatic life forms (Kiang and
Hagen 2003). Changes to the ‘Minimum Inflow Requirements’ will influence water availability in the
system. Other than that, water withdrawals from the Potomac River and its tributaries by upstream
users also have an impact on the amount of water available to meet demand in the WMA. Although
most of the water withdrawn upstream is returned to the Potomac River as wastewater treatment
plan discharge, some portion of this water is lost due to evaporation, transpiration, incorporation
into products, consumption by humans or livestock, etc. The portion of water that is not available
for downstream use is termed “consumptive use”. Figure 6 shows the Supply Side Model for the
Potomac River System.
Potomac F Warm
Available Potomac
Minimum F low Resource (WMA Net
Requirement Resource)
Consumptive Use
Upstream of Potomac
Figure 6: Supply Side Model: Potomac River System
5.2.2 Supply Side Model: Additional Reservoir Systems
There are two additional reservoirs that are operated by the utilities separately. WSSC
operates the Patuxent Reservoirs in the neighboring Patuxent River watershed. Total usable storage
available at these reserve water supplies is about 10.2 bg. The water stored in these reservoirs is used
along with Potomac River withdrawals throughout the year. Similarly, FCWA operates a reservoir on
the Occoquan River with a total storage volume of 8.0 bg.
All of the above mentioned reservoirs have been modeled separately for this study. Figure 7
shows the Occoquan Reservoir System, The Occoquan Reservoir Model calculates daily storage
available in the Reservoir using the water balance approach that calculates the reservoir storage at
each time step (inflow-outflow = change in reservoir storage). Reservoir can be understood as a
stock having a fixed capacity (reservoir capacity) that accumulates the difference between its inflow
and outflow.
10
th
Stock(t) = | [Inflow(t) — Outflow(t)]dt + Stock (to)
to
Where: Svock(t) = the amount of stock at time 4 Inflow(t) = is the inflow at time 4, and Ovtflom(t) = the
outflow at time / and /is any time between /, and f, (¢, S /S ¢,). (Madani and Marino 2008)
Inflows to the reservoir typically consist of natural’ ‘reservoir inflow’ and water pouring into
the reservoir due to direct precipitation. The model incorporates ‘natural’ inflows because it allows
for separate accounting of natural flows and human influence activities. This is more advantageous
because it facilitates the user to modify inflows based on upstream diversions or return flows simply
by subtracting it from natural inflows (ICPRB Report 98-3). Another inflow to the reservoir is the
rain water pouring directly onto the reservoir. This inflow is calculated as the regional precipitation
rate multiplied by area of the reservoir.
Outflows to the reservoir typically consist of loss of water due to evaporation, water supply
releases and reservoir spill. It may vary from one reservoir to another. For example, unlike the
Patuxent reservoir, the Occoquan reservoir has to make releases for hydropower generation. But
care has to be taken while modeling outflows because reservoir stock cannot go negative. The
physical system has to be transformed into mathematical representation representing real physical
conditions. For example, outflow due to evaporation should drop to zero when reservoir is empty.
This condition is modeled by using table functions reflecting the impact of reservoir volume on
reservoir evaporation. Similarly, reservoir volume cannot go beyond its capacity. Any flow over and
above the capacity goes out in form of ‘reservoir spill’. Reservoir spill is calculated as:
Max (0,(Occoquan Reservoir storage- Reservoir Capacity)/ Reservoir Spill Time)
Which means any volume of water over and above reservoir capacity will be discharged with
a rate equal to ‘Reservoir Spill Time’. Similar constraints have to be placed on other outflows like
hydropower generation and water supply releases. Full releases cannot be made if there is not
enough water in the reservoir to satisfy water supply release requirements. Usually releases are made
in bulk instead of random amounts because the water also has to be treated before it is supplied to
homes and offices. Therefore, we have a ‘delta load shift’ for both Occoquan and Patuxent facilities
that determines the maximum water production that can be shifted from the Potomac water
treatment facilities to Occoquan and Patuxent water treatment facilities in any one day (in mgd). In
case of the Jennings Randolph reservoir, water has to be released in bulk (on the order of at least
100 to 200 mgd) to increase its travel time. Thus, in case of a predicted shortfall, an initial day’s
release of 200 mgd is made from the Jennings Randolph reservoir so that water reaches Potomac
intakes as a “wave.”
Other constraints on the reservoir storage capacity include the sedimentation rate’. Reservoir
sedimentation rates are highly variable and dependent on hydrologic conditions, with the majority of
* The inflow is called ‘natural’ because it represents those inflows to the reservoir that would have occurred
without any human influence like upstream withdrawals, return flows, or reservoir regulations (ICPRB Report 98-
3).
5 “Rivers carry different types of sediment down their riverbeds, allowing for the formation of riverbanks, levees
and shores. The construction of a dam blocks the flow of sediment downstream, leading to downstream erosion of
these Sedimentary depositional environment, depositional environments, and increased sediment build-up in the
11
sediment deposition occurring during very large storm events. Reservoir storage capacities decrease
with time due to the deposition of sediment. The model uses the data on sedimentation rates
compiled by the ICPRB for all the reservoirs.
Once supply and demand side was modeled, water withdrawals were modeled based on
reservoir rules and conditions.
O Effect of
Sedimentation on
Capacity
O Reservoir
Spill Time O Hydropower
oy Generation 2
O Reservoir A
Capacity oR O Hydropower
iv + Hydropower Generation 1
Generation
Delta load
shiftO
_\ Reservo <Remaining demand
arr canal Reservoir O Reservoiraa————__ for FCWA and WSSC>
fr Outflow \
ay —— as
OCh 7 nfulfilled Demand
cle, O Direct pap Resenoir for FCWA
Precipitation |f Evaporation
Inflow
oO & O Initial storage
§ volume
OF recibitation
10) NS neces
0 Area of the O Reservoir volume on Evaporation
reservoir Evaporation Rate rate
Figure 7: Supply Side Model: Occoquan Reservoir System
5.3. Balancing Demand and Supply
The ICPRB makes demand projections for the WMA region. Based on the demand projections
water is withdrawn from Potomac River or reservoirs. Each of the three major suppliers withdraws
water from the Potomac River upstream of Great Falls. There is an additional intake for Washington
Aqueduct at Little Falls.
FCWA and WSSC also rely on water stored in reservoirs that are outside of the drainage area
above their Potomac River intakes, on the Occoquan River and the Patuxent River, respectively. But
they first make withdrawals from the Potomac River from their water treatment plants located at
reservoir. The rate at which these sediments build up in a reservoir is called rate of sedimentation.”
http://en.wikipedia.org/wiki/Environmental_problems_of_dams
12
Great Falls. The short fall is augmented by their other water treatment plants located at the
Occoquan and Patuxent reservoirs respectively. However, the Washington Aqueduct and Rockville
PWD only have Potomac River as their only source of water. Therefore, the model assumes priority
for Washington Aqueduct’s and Rockville PDW’s withdrawals. The left over water is utilized to
fulfill FCWA and WSSC water demand. If there is still some shortfall, releases from Jennings
Randolph and Little Seneca can be used to augment Potomac River’s flow during times of drought.
Figures 8a and 8b show how demand and supply equations are balanced in the WMA water supply
system. The “Total WMA unfulfilled demand’ and ‘Demand Component still remaining after all
resources for WMA are completely exhausted’ are key variables to assess WMA water supply system
performance.
Switch for Choosing
ae
= and
FCWA Demand
Aquaduct and
Rockville Demand
PRES toatwima
/ —> "Demand
|
Remaining Potomac
Remaining demand
fecrewasndwese Water after FOWA and
WSSC withdrawals
Unflufiled demand for
Aquaduct and Rockville
Remaining Potomac Water
after Aquaduct and
Rockville withdrawals
Figure 8a: Balancing Demand and Supply
JRR Reservoir
Spill Time
JRR Effectof
JRR Change in
Reservoir Natural
Inflow
JRR Reservoir
Inflow
JRR
Precipitation rate
JRR Reservoir
Spill
J RR Reservoir
JRR Direct
Precipitation
JRR Area of the
reservoir
Sedimentation on
Capacity
J RR Reservoir
Capacity
JRR Reservoir
Outflow.
J RR Reservoir
Evaporation
Total WMA
Unfulfilled Demand
JRR Reservoir
Evaporation Rate
| -Unflufiled demand
for Aquaduct and
ey
F Rockville>
Figure 8b: Balancing Demand and Supply
13
5.4 The Simulation
The model is run for a 30 year simulation period, from the year 2011 to year 2040. The data
for the demand projections are taken from the MWCOG and WMA utility suppliers. The model is
run for two demand scenarios. The supply side is run for three scenarios: one normal condition and
two drought conditions. There have been two instances of significant droughts in the history of the
WMA. The first being the drought of 1930-31, which is the longest drought recorded in history. It is
noteworthy since it lasted from the summer of 1930 through the winter of 1931 (Kame’enui et al.
2005). Another instance of low flows occurred in 1966. The WMA demand levels exceeded the 1966
low-flow of the Potomac River 41 times during 1971 through 1982 (Ways, 1993). The model was
run to examine the impact of such extreme weather conditions and to determine the ability of the
WMA water supply system to fulfill future demand (2010-2040). Moreover, system dynamics is a
continuous modeling process which allows for an examination of the effects of multi-year droughts
on reservoir.
The Simulation Results
The model’s results for each scenario are shown in Figures 9a through 9f. The first two
gtaphs simulate the WMA water supply system for normal weather conditions where there is no
drought in the WMA region. In that situation, the WMA water supply system will be sufficient to
meet the predicted water supply demand through year 2040, Although, the system is able to fulfill
future year demands for both scenarios, it will require pricy withdrawals from the Jennings
Randolph reservoir a few times.
The third and fourth graph show that the water supply system will not be able to meet future
supply demand if low flow conditions of the year 1966 are repeated. In that case, not only will the
system require frequent withdrawals from Jennings Randolph reservoir, but it will not be able to
meet the WMA demand for specific low flow periods. This will cause triggering of the Low Flow
Allocation Agreement’s (LFAA) low-flow stages. The LFAA establishes a set of stages for low river
flow that would prompt action by the agreement signatories to monitor and eventually restrict water
withdrawals’. It also established a formula that allocates the amount of water each supplier can
withdraw from the Potomac River in the event that the total flow is not sufficient to meet all needs.
Although, LFAA's low-flow stages have never been triggered in the past, the model predicts that it
will be triggered if low flow conditions of the year 1966 are repeated in future (2030's). Similarly,
during a repeat of the worst drought of record (1930-1931), model predicts that WMA water system
will fail to meet future demand (Figures 9c and 9f)
What is more important here is the behavior of the system, not the numbers generated in
model runs. Different scenarios were developed merely to understand the system behavior. Thus,
they are mostly qualitative and may not represent any realistic future scenario since the population
forecast (and corresponding demand forecast) beyond the 2030 horizon is only a rough
approximation (Hagen and Steiner 2000).
Shttp://www.mwcog.org/environment/water/watersupply/aggreements.asp
14
Total WMA Unfulfilled Demand
Demand Component still remaining afterall resources for WMA are completely exhausted
02
270 360
181
2011-2040 (360 Months)
Figure 9a: Model Simulation Results - Normal Condition Figure 9d: Model Simulation Results - Normal Condition
Total WMA Unfulfilled Demand
600
Demand Component still remaining afterall resources for WMA are completely exhausted
400
200
200
| 100
oLy | | |
1 o Ta 20 360 =
2011-2040 (360 Months) mm “eo
Figure 9b: Model Simulation Results — Drought - 66 Figure 9e: Model Simulation Results - Drought - 66
Total WMA Unfulfilled Demand
600
Demand Component sil remaining after all resources for WMA are completely exhausted
00
00
0 |
I oT ToL 20
2011-2040 (360 months) oo “0
Figure 9c: Model Simulation Results ~ Drought ~ 31-32 Figure 9f: Model Simulation Results - Drought ~ 31-32
Figure 9: Model Simulation Results
6.The Performance Analysis
WMA was faced with severe drought in the summer of 1966, which forced Washington DC
to declare its first “water emergency”. Other than that, population forecast generated in 1960's
indicated that demand would exceed supply in the future (natural low flows in the Potomac River).
15
To address the future water deficit, the U.S. Army Corps of Engineers conducted a study that
identified 16 potential dam sites on the Potomac River upstream of Washington, D.C., which led to
considerable public opposition due to environmental concerns regarding the building of these dams.
Concurrent research conducted at Johns Hopkins University concluded that the WMA future water
supply could be met through the cooperation amongst WMA water suppliers and the coordinated
operation of the Jennings Randolph, Occoquan and Patuxent reservoirs. This was how the WMA
water management system came into being, which basically involves managing the reservoirs and the
cooperation amongst the WMA water supply system entities through various agreements among
agencies including the U.S. Army Corps of Engineers, the states of Maryland and Virginia, the
District of Columbia, local water utilities, and the Interstate Commission on the Potomac River
Basin (Sheer and Flynn 1983).
To gauge whether the system is doing what it was intended for, it is necessary to assess its
performance under the wide range of scenarios expected during their operating life. Also,
performance has become an important issue over the past decade or so since environmental flows
have been considered a component of system yield (McMahon et al. 2006).
This study gauges the WMA water supply system’s performance using various performance
mettics including time based reliability, volumetric reliability, resilience and vulnerability. They are
discussed in the following sections along with their values for the WMA water supply system.
6.1 Reliability
Reliability of a water supply system is one of the most important matrices for performance
assessment. It is defined as the probability that water supply system is able to meet the target
demand. McMahon et al. (2006), calculates time-based reliability as proportion of intervals during
the simulation period that the water supply system can meet the target demand. Mathematically, it is
expressed as:
N.
Reliability, ==, 0 < Reliability, <1 re)
Where Reliability, is the time-based reliability, N is the number of intervals that the target
demand was fully met and N is the total number of intervals in the simulation.
We also calculate volumetric reliability, which is based on the volume of water demand met
by the water supply system divided by the total target demand during the entire simulation period.
Mathematically, it is expressed as (McMahon et al. 2006):
Y_,(D; — Di
Reliability, = 1— Be 0 <Reliability,<1 (2)
=i Vt
Where Reliability, is the volumetric reliability, Dj is the target demand during the i”
period, Dj is the volume supplied during the i” period and N is the number of intervals in the
simulation.
16
6.2 Resilience
Resilience of any system is defined as the ability of the system to recover from any shock.
For a water supply system, it is an indicator of how readily a water supply system will recover from a
failure. Hashimoto et al. (1982) define the resilience of water supply system as:
Resilience = £ fa#0; O0<@sil (3)
a
Where Resilience is the resilience, f; is the number of individual failure periods and fg is
the total duration of all failures. Resilience therefore can also be understood as the inverse of the
average failure duration. When fy is zero, by definition, g , should be 1.
6.3 Vulnerability
Finally, vulnerability measures the average volumetric severity of failure during a failure
period. Mathematically, Hashimoto et al. (1982) define vulnerability as:
fs
max (s;)
Vulnerability’ =
_ Sum of maximum shortfall during each failure period (4)
Number of continuous sequences of failure
Where, s; is the volumetric shortfall (Dj — Dj) during the J continuous failure sequence
and f, is the number of individual failure periods. This measure of vulnerability has same unit as
volume therefore it has to be normalized diving it by the target demand (D) to create a
dimensionless measure similar to other performance criteria:
Vulnerability’
Vulnerability = D
; 0<Vulnerability<1 (5)
Finally, all the three concepts of reliability, resilience and vulnerability are combined into one
single metric termed the drought risk index (DRI), which is dimensionless and is expressed as
(Zongxue et al., 1998):
DRI = &,(1 — Reliability) + €,(1 — Resilience) + €,(Vulnerability ); 0< DRI<1
Where, € is the weight associated with each performance dimension and é; + & + 3 = 1.
In this study, the weights are set equal to 0.33.
Tables 2a and 2b give the performance matrices for the WMA water supply system. Table 2a
gives performance matrices for the WMA supply system without its “savings account” (Jennings
Randolph and Little Seneca Reservoir). Table 2b expresses the performance matrices for the whole
system. As expected, reliability of the system goes down as the severity of drought increases. The
drought of 1930-31 was the longest and most severe and longest drought in history of the WMA, It
is noteworthy that it lasted from the summer of 1930 through the winter of 1931. Therefore, we
observe reliability and resilience of the system to be lower for 1931-32 drought conditions when
17
compared with normal conditions and 1966 low flow conditions. Reliability and resilience values are
also lower for scenario 2 because this scenario assumes a higher demand. The model simulation runs
and performance indices reveal that the WMA water supply system will require frequent releases
from their savings accounts in the future if historical drought conditions are repeated. There are
instances expected in the future when water will not be enough to meet WMA demands. This is also
reflected by the increasing vulnerability of the system as the severity of drought increases from
normal to drought conditions of 1931-32. We also observe that the vulnerability ratio is
approximately the complement of resilience values.
There is one unexpected observation; we expected that resilience of the WMA water supply
system without Jennings Randolph reservoir would be lower than the system with it because it
provides additional source of water to the system. But, the outcome was contrary to our expectation.
It is observed that resilience actually went down for the system when it included additional resources
(Jennings Randolph reservoir). The reason behind it could be the method by which resilience is
calculated. Equation 3 defines Resilience as the ratio of f, and fq where, f, is the number of
individual failure periods and fy is the total duration of all failures. If we observe model runs in
Figures 9e, 9f we shall see that the system with additional resource has just one failure in both runs,
whereas, the system without additional resources had multiple failures scattered through time. Thus,
when we have just one failure scattered over few time periods contrary to multiple failure periods,
resilience for the single failure case will go down. These results are contrary to each other and can be
misleading for policy makers.
In order to remove the confusion caused by such contradictory performance indices, we can
use a single measure for evaluating the overall performance of reservoirs. Therefore, we also
calculate drought risk index (DRI) (Table 2a and 2b) using equal weights (& = & = &3 = 0.33). The
convenience of these metrics is that they offer a single measure for evaluating the overall
performance of reservoirs rather than having to consider each of the constituent metrics, a situation
complicated by the numerous trade-offs between them (McMahon et al. 2006). Moreover, since DRI
is an additive metric, hence, it is not so easily nullified by any of its constituent metrics being zero.
The drought risk index (DRI), as calculated in Table 2, gives the expected outcome. It increases as
severity of drought increases.
Table 2a: Performance Matrices for WMA Water Supply System (Without Jennings
Randolph Reservoir)
WMA Water Supply System (Potomac River + Occoquan Reservoir
+ Patuxent Reservoir)
spas heren Bi sa Drought
Reliability, | Reliability, | Resilience | Vulnerability | Rio Tadex*
Scenario 1 9 99 7
iSipereetlttert tern 0.9833 0.9983 0.888 0.1340 0.0867
Scenario 2 0.9833 0.9979 0.888 0.1599 0.0952
Scenario 1 0.9388 0.9968 0.857 0.1750 0.1251
Drought 66 : = 2 a
Scenario 2 0.9722 0.9935 0.857 0.2064 0.1245
Scenario 1 0.9694 0.9920 0.833 0.1818 0.1252
Drought 31-32 - u ~
Scenario 2 0.9694 0.9911 0.833 0.2040 0.1325
*& =&=& = 033
18
Table 2b: Performance Matrices for WMA Water Supply System (With Jennings Randolph
Reservoir)
WMA Water Supply System (Potomac River + Occoquan Reservoir
+ Patuxent Reservoir + Jennings Randolph Reservoir)
Baten heren Bi sa Drought
Reliability, | Reliability, | Resilience | Vulnerability | pio Tadext
Scenario 1 1 1 1 0 0
Normal Condition
Scenario 2 1 x 1 0 0
Scenario 1 0.9861 0.999 0.833 0.274 0.1501
Drought 66 =
Scenario 2 0.9944 0.9981 0.833 0.351 0.1728
Scenario 1 0.9888 0.9975 0.75 0.297 0.3492
Drought 31-32
Scenario 2 0.9888 0.997 0.75 0.324 0.1931
* 8 = $2 = os = 0.33
7.Conclusions and Future Research
To sum up, we conclude that the WMA water supply system is susceptible to shortages in
future caused by increasing customer demand for water and alarming trends in climate. The
performance of the system is expected to deteriorate in the coming years and the recurrence of
historical droughts and low flow conditions can strain the system even further. Current resources are
not sufficient to meet the demand and there is a very high probability that water restrictions will be
imposed due to the triggering of Low Flow Allocation Agreement (LFAA).
The model predicts that frequent releases will be made from the Jennings Randolph
reservoir even during normal conditions. Drought will further increase the frequency of releases.
The releases are often coupled with coordinated water conservation measures that are not very
popular with consumers. Thus, knowing when the releases will be required in future may help in
coordinating the operations of all the three major reservoirs of the region. The policy makers can
plan reservoir operations in such a way that the Patuxent and Occoquan reservoirs are full in the
beginning of the period of expected shortfall. This can be done by exploiting the Potomac River
flow to meet water supply demands during its periods of high flows while letting the Patuxent and
Occoquan reservoirs get filled in the meantime.
Finally, this model is part of an ongoing research effort to understand and assess the
Washington Metropolitan Area’s water resource management system. The next step to this research
would be to incorporate institutional interactions among various entities of the water supply system
and to simulated and test competing policy alternatives for the WMA.
The methodology used in this paper to address the future of WMA water supply system can
be utilized for various other water supply systems. System dynamics can be used to simulate supply
demand dynamics any water supply system. The scope can be expanded further to explicitly capture
the dynamic feedbacks between institutions responsible for managing water resources and water
availability, demand management strategies, growth and climate factors, and hydrological and
environmental concerns.
19
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9.Glossary
CLD Causal Loop Diagram
CO-OP Cooperative Water Supply Operations on the Potomac
FCWA Fairfax County Water Authority
GCM General Circulation Models
ICPRB Interstate Commission on the Potomac River Basin
LFAA Low Flow Allocation Agreement
MWCOG/COG Metropolitan Washington Council of Governments
USGS US. Geological Survey
WMA Washington Metropolitan Area
WSSC Washington Suburban Sanitary Commission
22
