© This is a copyright material and reproduction of this material without obtaining prior
permission is strictly prohibited. Plagiarism and other applicable laws could be enforced in
case of any violation.
1
1.
Introduction
2.
Water Pricing Models
3.
Water Allocation Models
1.
Introduction
An effective and holistic approach to water management requires an understanding of all
dynamics relating to water policies and it encompasses reasonable knowledge of models which
deals with water pricing, governance, etc. Consequently, this chapter presents a succinct
overview of literature on some of the leading economic models on water.
2.
Water Pricing Models
2.1
Paper by Monteiro (2005)
A paper by Monteiro (2005)1 provides a very good summary of important models on water
pricing. Interested readers may refer to the paper for detailed information on the economic water
pricing models included therein. We, however, reproduce below a table on questions addressed
by each of the water pricing models from Monteiro (2005) paper. It basically touches upon
almost all aspects on water pricing:
Questions Addressed
Average vs. Marginal Cost Pricing
Seasonal or temporal variations
Articles
Hirshleifer et al., 1960
Ryordan, 1971
Dandy et al., 1984
Zarnikau, 1994
Chambouleyron, 2003
Gisy and Loucks, 1971
Riley and Scherer, 1979
Manning and Gallagher, 1982
Dandy et al., 1984
Zarnikau, 1994
Monteiro, Henrique (2005), ‘Water Pricing Models: A survey’, Instituto Superior De Ciencias Do Trabalho E Da
Empresa, Portugal.
1
2
Capacity constraints or expansion decisions (Peakload pricing)
Scarcity
Revenue Requirements
Optimal number of metered connections
Efficiency of block tariffs
Second-best pricing
Optimal derivation of nonlinear pricing schemes
Customer heterogeneity
Storage
Groundwater
Conjunctive use of surface and groundwater
Utilization of water as an input
Constraints regarding water price changes
Pricing of wastewater services
Multi-product water supply
Dynamic programming techniques
Simulation techniques
Discounting
Elnaboulsi, 2001
Schuck and Green, 2002
Hirshleifer et al., 1960
Ryordan, 1971
Gysi and Loucks, 1971
Riley and Scherer, 1979
Manning and Gallagher, 1982
Zarnikau, 1994
Elnaboulsi, 2001
Griffin, 2001
Moncur and Pollock, 1988
Zarnikau, 1994
Elnaboulsi, 2001
Griffin, 2001
Schuck and Green, 2002
Hirshleifer et al., 1960
Freedman, 1986
Collinge, 1992
Zarnikau, 1994
Kim, 1995
Griffin, 2001
Schuck and Green, 2002
Barrett and Sinclair, 1999
Griffin, 2001
Chambouleyron, 2003
Gisy and Loucks, 1971
Elnaboulsi, 2001
Kim, 1995
Elnaboulsi, 2001
Schuck and Green, 2002
Elnaboulsi, 2001
Elnaboulsi, 2001
Chambouleyron, 2003
Riley and Scherer, 1979
Manning and Gallagher, 1982
Moncur and Pollock, 1988
Schuck and Green, 2002
Schuck and Green, 2002
Schuck and Green, 2002
Dandy et al., 1984
Elnaboulsi, 2001
Kim, 1995
Ryordan, 1971
Gysi and Loucks, 1971
Riley and Scherer, 1979
Schuck and Green, 2002
Manning and Gallagher, 1982
3
The most consensual result from the water pricing literature is that efficiency requires marginal
cost pricing. While this may be common sense for anyone with a minimum microeconomics
background, it has stirred up a lot of articles demonstrating the advantages of marginal cost
pricing in relation to the widely used average cost pricing practices of many water utilities.
There is, however, some divergence on whether we should consider short-run or long-run
marginal cost pricing. Some authors defend even in dynamic contexts multistage short-run
marginal cost pricing.
Intra-annual price changes or customer differentiation to reflect differences in marginal costs can
enhance efficiency. A marginal cost pricing mechanism may signal the value that consumers
attribute to further capacity expansions as the water supply system approaches its capacity limit
and marginal cost rises.
However, pure marginal cost pricing may not be feasible while
respecting a revenue requirement because marginal costs may be higher or lower than average
costs. The most common ways of combining efficiency and revenue requirements are through
the use of two-part tariffs, adjusting the fixed charge to meet the revenue requirement, or through
the second-best pricing like Ramsey pricing. It is not evident from the survey whether the best
scheme is a two-part tariff or some other pricing mechanism. The role of black rate pricing,
increasingly more frequent in actual pricing practices, is yet to be fully investigated.
2.2.
Paper by Mohayidin et al. (2009)2
The study by Mohayidin et al. (2009) is somewhat is similar to Monteiro (2005) but with
additional citing of some latest papers. For the benefit of readers, we reproduce below table
from Mohayidin et al. (2009) paper:
Pertinent questions
Related articles
1. First best pricing versus second best Tsur and Dinar (1997); Zarnikau (1994); Thobani
pricing
(1998); Mitra (1997); Monteiro (2005); Lewis
(1969); Sahibzada (2002); Johansson (2000);
Dandy et al. (1984); Riordan (1971b); Garcia and
Reynaud (2004); Small and Carruthers (1991);
Mas-Collel et al. (1995).
2. Partial
equilibrium
versus
general Johansson et al. (2002) for PE. Berck et al. (1990)
equilibrium
for GE
3. Efficiency and fairness concerns
Lewis (1969); Seagraves and Easter (1983); Saliba
Mohayidin, Ghazali et al. (2009), ‘Review of water pricing theories and related models’, African Journal of
Agricultural Research Vol. 4 (13), pp. 1536-1544.
22
4
4.
5.
6.
7.
8.
9.
and Bush (1987); Sampath (1991 and 1992); Easter
(1997); Small and Rimal (1996); Dinar et al.
(1997); Johansson (2000 and 2002)
Temporal or seasonal rates
Gysi and Loucks (1971); Zarnikau (1994); Dinar et
al. (1997); Sahibzada (2002); Schuck and Green
(2002); Monteiro (2005)
Development decisions or capacity Riordan (1971b); Manning and Gallagher (1982);
restrictions
Riley and Scherer (1979).
Scarcity
Moncur and Pollock (1987); Einaboulsi (2001);
Griffin (2001); Zilberman (1997); Shah et al.
(1995); Easter (1997); Sahibzada (2002); Seagraves
and Easter (1983); Monteiro (2005); Sunding
(1994); Small and Rimal (1996); Laffont and Tirole
(1993).
Marginal value product pricing
Sahibzada (2002); Sunding (2005); Hussain et al.
(2007).
Storage
Riley and Scherer (1979)
Hedonic pricing model or implicit marginal Latinopoulos et al. (2004); Torell et al. (1990);
price
Faux and Perry (1999); Coelli et al. (1991); Griffin
(1985).
The theories, reviewed in this paper, explain different aspect of water pricing that can be used as
a means to address water scarcity issues in terms of quantity as well as quality. The empirical
findings reveal that the first best pricing3 is a widely accepted model for partial or full cost
recovery of the irrigation schemes as it considers inefficiencies in water use. On the other hand,
the second best pricing4 model sets price of water equal to the marginal cost of providing it or
incremental costs associated with incremental production. Most of the economists agree that if
water users pay the marginal cost of its supply water use, efficiency would be significantly
improved. The marginal product value from price represents inefficient use of input. Finally,
there exists currently a debate that while water pricing programs promote economically and
environmentally efficient water use, they may not always be appropriate as water pricing is often
perceived as a policy intervention that negatively affects poor farmers and small holders. It can
3
Consider a perfectly competitive open economy that no market imperfections or distortions, no externalities in
production or consumption, no public goods. The optimal government policy in this case is laissez-faire. Any type
of tax or subsidy implemented by the government under these circumstances can only reduce economic efficiency
and national welfare. Thus with a laissez-faire policy, the resulting equilibrium would be called first-best
equilibrium. Allocation maximizing the total net benefit is called Pareto efficient or first-best.
4
Introducing imperfections or distortions in first-best equilibrium will make it less efficient from a national
perspective than when the distortion was not present. In other words, the introduction of one distortion would
reduce the optimal level of national welfare. Equilibrium under such a situation is called second-best equilibrium.
5
be concluded that all of the mentioned theories consider water pricing as an important tool which
policy makers can apply for management of this valuable resource5.
Horbulyk (2010)6 suggests the following approach for water pricing for
2.3.
improving water management in Alberta: 1) the pricing of storage uses as well as of the
consumptive uses of water; and 2) the option to adopt a refundable or revenue-neutral financing
approach that returns fee revenues to the users while preserving users’ incentives to use water
efficiently.
3.
Forecasting Water Demand
Davis (2008)7 opines that a sound demand forecast is critical in water resources planning. He
suggests four types of approaches in Water Demand Forecasting viz. Trend Extrapolation, Per
Capita, Unit Use and Econometric.
In Trend Extrapolation approach, only historical demand data is required and it can be available
at a very low cost. However, the problem with this approach is that the model assumes that past
trend carries into the future. The approach also cannot account for changes in demographics,
weather or other factors.
Per Capita approach divides historical total demand by population to arrive at per capita use.
Then per capita use can be multiplied by projected population to arrive at the future demand of
water. The approach is simple to understand and allows the main driver, population to be
accounted for. However, demand may not always follow population growth. The model does
not account for factors such as price, income, types of housing, employment trends and other
factors.
Unit use approach suggests getting sector demands (e.g. single-family, multi-family, nonresidential) and dividing each sector demands by appropriate drivers (e.g. housing or
employment) to get unit use. Multiplying unit use by future number of units will give us future
Mohayidin et al. (2009), ‘Review of water pricing theories and related models’, African Journal of Agricultural
Research Vol. 4 (13), pp. 1536-1544.
5
Horbulyk, Theodore M. (2010), ‘ Water Pricing: An Option for Improing Water Management in Alberta’,
Department of Economics, University of Calgary, Alberta, Canada.
7
Davis, William (2008), ‘Forecasting Water Demand’, Paper presented at the American Water Works Association
(AWWA) Sustainable Water Source Conference , Reno, NV, USA
6
6
demand for water. The benefit of this approach is that it allows for majors sectors and drivers of
water demand to be accounted for. Also each sector demand can be projected independently.
However, water demand factors such as weather, income, price and others are not incorporated.
The Econometrics approach statistically correlates water demands with factors that influence
those demands:
Where
Qs = Water sector demand
I = median household income
H = average household size (persons)
L = average household density (units per acre)
T = maximum temperature
R = rainfall
P = marginal price of water
α = equation constant
β1 = elasticities8 of water use factors
The model has a significant ability to explain water use over time. However, it is very data
intensive and costly to produce.
In terms of specification errors, the ranking of the above four types of approaches is as follows
(in order of ranking – high to low) – Trend Analysis, Per Capita, Disaggregate Unit Use and
Multivariate Models.
In terms of cost, their ranking is as follows (from low to high) - Trend Analysis, Per Capita,
Disaggregate Unit Use and Multivariate Models.
8
A statistical rate of change that describes how a water use factor influences demand. A price elasticity of -0.10
means that a ten percent increase in real price will result in a one percent decrease in water demand.
7
4.
Predicting water quality in distribution systems
Deterministic models have been widely used to predict water quality in distribution systems, but
their calibration requires extensive and accurate data sets for numerous parameters. In a study by
D’Souza and Mohan Kumar (2010)9 alternative data-driven modeling approaches based on
artificial neural networks (ANNs) were used to predict temporal variations of two important
characteristics of water quality—chlorine residual and biomass concentrations.
The authors considered three types of ANN algorithms. Of these, the Levenberg-Marquardt
algorithm provided the best results in predicting residual chlorine and biomass with error-free
and “noisy” data. The ANN models developed here can generate water quality scenarios of piped
systems in real time to help utilities determine weak points of low chlorine residual and high
biomass concentration and select optimum remedial strategies.
5.
Modeling Water Quality in Drinking Water Distribution Systems by Robert Clark
and Walter Grayman
This comprehensive text discusses the use of water quality models and their potential for
enhancing and understanding the factors that affect water quality in distributed water. It
covers the development of the USEPA's EPANET and discusses its application to case studies.
The book outlines the major elements involved in water quality modeling. It discusses the
development and application of water quality models, and presents the results of applying these
models. Storage tank modeling is also covered.
Chapter topics include: Distribution system water quality, Modeling distribution systems,
Hydraulic analysis, Water quality models, Initial modeling studies, Modeling total
trihalomethanes and chlorine decay, Applying water quality models, Modeling waterborne
disease outbreaks, Modeling the effects of tanks and storage and Getting started in modeling.
D’Souza and Mohan Kumar (2010), ‘Comparison of ANN models for predicting water quality in distribution
systems’, e-journal AWWA, Vol. 102, Issue 7.
9
8
6.
6.1
Water Allocation Models
In a paper titled ‘Water Allocation Models for Alberta: What’s Available and
what are the Needs?, Ali et al. (201010) presents an overview of water allocation models around
the world. The authors reviewed the existing water allocation models in order to evaluate to
identify the available of suitable mathematical models that could be used to evaluate ways to
improve water use efficiencies in Canadian province of Alberta. They found that even the most
recent economic optimization model in Alberta is too narrow in scope and spatial coverage to
represent the intricacies of competing water users in southern Alberta. The authors identified at
least four general areas of improvement that could be made to a recently developed model to
improve its analytical capacity – expanding the model structure to include all irrigation districts
in southern Alberta, augmenting with modules of other water user sector demands, improving
capability to analyze alternative water licensing policies, and developing a field-scale model to
help understand the dynamics of micro level decision making on water rights transfers, irrigation
technology choices, crop choices, and other decision variables. The primary focus is on basinscale models since it is at this scale that sectoral competition for water can be adequately
analyzed to draw essential information for policymakers in their resource management decisions.
Although it is at the farm or field-scale where micro level decision making takes place regarding
irrigation equipment purchase, crop choice, and water application, extensive data requirement at
such fine levels often thwart modeling efforts.
Historically, water licenses and rights in Alberta have been based on a system of prior allocation
where priority is set by the date of application on the principle of first-in-time-first-in-right
(FITFIR). According to the author, the FITFIR system is an impediment to water market
development, a solution often touted for efficient allocation of water resources during scarcity,
since senior rights holders have little incentive to sell the rights to the newer or junior rights
holders. However, since the mid-nineties, there is a move toward transforming these historical
licenses and rights into tradable licenses with some government control on the nature of the trade
10
South Alberta Resource Economics Publications, University of Lethbridge, Department of Economics, Alberta,
Canada
9
and holdback options. The paper discusses various types of models – physical water allocation
models are discussed first, followed by the economic optimization models, and then a short
discussion follows with the applications and experiences from other international jurisdictions
for additional methodological insights. A summary of the most relevant models is presented in
the Table.
Table: Summary of the water allocation models at a glance
Study
Area
Scale
Southern Alberta:
IDM, AAFRD (2002a)
SSRB, Alberta
Irrigation
districts
WRMM, AENV (2002)
SSRB, Alberta and Basin
Saskatchewan
FFIRM, AAFRD (2002b)
SSRB, Alberta
Basin
Horbulyk and Lo (1998)
Mahan et al. (2000)
Cutlac and Horbulyk (2009)
He and Horbulyk (2010)
Australia:
Brooks and Harris (2008)
Zaman et al. (2009)
SSRB, Alberta
SSRB, Alberta
SSRB, Alberta
BRSB of SSRB
Victoria and
Southern New
South Wales
Northern Victoria
United States:
Vaux and Howitt (1984)
California
Booker and Young (1991,
Colorado
1994)
Chatterjee et al. (1998)
California
Chakravorty and Umetsu
California
(2003)
Wurbs (2003, 2004)
Texas
Brewer et al. (2009)
Western U.S.
Other regions:
Cortignani and Severini (2009) Central Italy
Methodology
Calculation of daily water
requirements
Calculation of physical allocation
and deficits based on IDM needs
Economic optimization and
simulation
Basin
Economic optimization
Basin
Economic optimization
Basin
Economic-hydrologic integrated
Irrigation Economic optimization with PMP
districts calibration
Region
Econometric analysis
Basin
Economic-hydrologic integrated
optimization and simulation
Region
Basin
Regional trade
Economic-hydrologic integrated
Basin
Basin
Dynamic programming
Spatial, optimal control
Basin
Basin
Institutional perspective
Model comparison
Farm
Economic optimization with
improved PMP
Economic optimization with
extended PMP
Economic-hydrologic integrated
Economic optimization
Rohm and Dabbert (2003)
Germany
Region
Rosegrant et al. (2000)
Pujol et al. (2006)
Maipo, Chile
Basin
Southern Spain and Basin
Italy
10
Qubaa et al. (2002)
Benli and Kodal (2003)
South Lebanon
GAP project,
Turkey
Farm
Economic optimization
Economic optimization
Other relevant studies:
Tsur (2005)
Theoretical and mathematical
derivation of water allocation and
pricing
Zilberman and Schoengold
Mathematical and graphical
(2005)
overview of water allocation
Schoengold and Zilberman
Mathematical and graphical
(2007)
overview of water allocation
Howitt (1995, 2005)
PMP calibration
McKinney and Savitsky (2006)
Setting-up water allocation
problems, GAMS codes, solutions
Howe (2005)
Comparison of water pricing
policies in U.S. and Canada
Grafton et al. (2009)
Comparison of water rights,
markets, and trading in
southwestern U.S. and MurrayDarling Basin, Australia
Notes: IDM = Irrigation District Model; WRMM = Water Resource Management Model;
FFIRM = Farm Financial Impact and Risk Model; AAFRD = Alberta Agriculture, Food and
Rural Development; AENV = Alberta Environment; SSRB = South Saskatchewan River Basin;
BRSB = Bow River Sub-Basin; PMP = Positive Mathematical Programming; GAP = Southeastern Anatolian Project.
6.1.1 Physical Allocation Models
One type of model that has been applied to the water allocation problem in Alberta deals with the
physical aspects of water allocation – starting from the diversion of water at the head works,
through the networks of storage basins, canals and pipelines, to the distribution of water at the
irrigated fields. Two such models are known as the Irrigation District Model (IDM) and the
Water Resources Management Model (WRMM) (Alberta Environment, 2002). The IDM utilizes
two integrated modules – the Irrigation Requirements Module that contains weather and field
level data, and the Network Management Module that contains data on canal/pipeline network
characteristics in each irrigation districts, storage reservoirs, return flows, and losses. Together,
they determine daily farm delivery requirements based on crop growth parameters and translate
them into canal flow and diversion requirements. It is the IDM that helps to develop alternative
water requirement scenarios depending on the crop mix, irrigation methods, expansion
potentials, future demands, and climate predictions.
11
The WRMM is a basin-scale simulation model that takes the irrigation requirements from
the IDM as inputs and determines if those requirements could be met following the license
priorities and given other major delivery requirements in the non-irrigation sectors such as
municipal, industrial, recreation, wetlands, instream flows, and inter-provincial apportionment
commitments. The output of the WRMM informs the frequency and magnitude of the irrigation
water deficits on a weekly basis. These deficits form the inputs of a third model, the Farm
Financial Impact and Risk Model (FFIRM) that analyzes the risk and water shortage impacts on
the income for representative farms across the basin.
The FFIRM is the only model currently being used by the water managers in Alberta
Irrigation that incorporates crop yield-water functions and economic parameters (crop prices,
labor, capital, repair & maintenance, and energy costs) to help understand how the water
availability and climate conditions translate into economic impacts. It includes two components
– an optimization component dealing with the optimal allocation of water demand and supply
derived from the IDM and WRMM among four typical farm enterprises across the basin. In case
of water shortages, this component of the model allocates water to the most profitable farm
enterprise on a priority basis. The other component of FFIRM simulates long term financial
viability of these farm enterprises considering risk and crop-water management choices. The
FFIRM model does a good job of budgeting farm costs and revenues for given situations but
since the IDM and WRMM are not based on farmer responses to economic incentives and price
signals, the analyses are non-optimizing and thus, may not represent very well actual farmer
behavior.
6.1.2 Economic Optimization Models:
Apart from the FFIRM, which involves both economic optimization and simulation approaches,
a second type of model applied to the water allocation problem in Alberta involves economic
optimization using mathematical programming techniques. Usually, these models have been at
the basin scale, involve a high level of aggregation in the input data, have welfare or profit
12
maximization objectives, and assume fully functional water markets in a potential water shortage
situation. He and Horbulyk (2010)11 developed mathematical programming model to test the
impacts of (i) volumetric water pricing, and (ii) short-term water trading policies among three
irrigation districts (Bow River (BRID), Eastern (EID), and Western (WID)) in the Bow River
Sub-basin (BRSB) of Alberta. These two market based policies are implemented in a way that
treats water pricing as a substitute for the existing seniority-based (FITFIR) transfer allocations.
Besides generating some interesting and fairly intuitive results with a rather simple set-up, the
He and Horbulyk (2010) model distanced itself from others models with regard to its calibration
method. While all previous models were calibrated through modifying the constraints, this model
was calibrated through modifying the objective function, a procedure commonly known as
positive mathematical programming or PMP. The PMP utilizes dual values of the calibration
constraints to modify the objective function such that the base year observed activities are
reproduced without the calibration constraints.
6.1.3 Models in other jurisdictions
6.1.3.1 United States
The semiarid southwestern United States has been the subject of numerous studies on
interstate water allocation, regional water transfer, third-party effects, transaction costs, etc. with
a range of trade models, mathematical programming models, and optimal control models. Over
80% of surface and ground water in this region is used for agriculture and the rest for municipal
and industrial use.. Vaux and Howitt (1984)12 used a regional trade model with nonlinear
regional demand and supply functions to show that regional water transfer could be an effective
mechanism to deal with water scarcity in California until 2020. Booker and Young (1991,
1994)13 used a non-linear economic-hydrologic optimization model to estimate economic gain
11
He, L. and T.M. Horbulyk (2010): Market-based policy instruments, irrigation water demand, and crop
diversification in the Bow River basin of southern Alberta. Canadian Journal of Agricultural Economics, 1-23.
12
Vaux, H.J. Jr. and R. Howitt (1984): Managing water scarcity: An evaluation of interregional transfers. Water
Resources Research, 20(7), 785-792.
13
Booker, J.F. and R. Young (1994): Modeling intrastate and interstate markets for Colorado River water resources.
Journal of Environmental Economics and Management, 26, 66-87.
13
from intra- and inter-state trade of consumptive and non-consumptive uses of fourteen water
demand sectors in the Colorado River Basin under two water flow regimes. Results indicate that
within state water transfers yield more economic benefit in the short flow regime induced by a
severe drought or climate change. One interesting result of the model is that if on-farm irrigation
technology is traditional rather than modern and efficient, basin-wide optimization leads to a
significantly higher aggregate economic gain. This is because higher return flow from traditional
irrigation technology (e.g., gravity) replenishes groundwater, which appears as a backstop
technology for the downstream users.
An excellent handbook on setting up the optimization problems, GAMS codes, and
illustrative solutions for water allocation among users, optimal management of a single reservoir
or a river system, upstream-downstream problems, water rights and markets, etc. is provided by
McKinney and Savitsky (2006)14.
Howe (2005)15 provides a comparison of water pricing
policies in the U.S. and Canada while Grafton et al. (2009)16 provides a comparison of water
rights, markets and trading in the U.S. and Australia.
6.1.3.2 Australia
Brooks and Harris (2008)17 provide estimates of the magnitude of efficiency gains from water
markets operating on weekly basis in three trading zones in Australia. Results indicate a
substantial gain in economic efficiency can be obtained by reallocation of water from low to high
value uses, which could be further improved if trade restrictions are progressively removed.
Another recent study on Australian water markets used an integrated economic-hydrologic
14
McKinney, D.C. and A.G. Savitsky (2006): Basic optimization models for water and energy management.
Revision 8. http://www.ce.utexas.edu/prof/mckinney/ce385d/lectures/McKinneySavitsky.pdf
15
Howe, C.W. (2005): The functions, impacts and effectiveness of water pricing: Evidence from the United States
and Canada. Water Resources Development, 21(1), 43-53.
16
Grafton, R.Q., C. Landry, G.D. Libecap, and R.J. O’Brien (2009): Water markets: Australia’s Murray-Darling
basin and the U.S. southwest. Paper presented at the Water Economic Consortium Meeting, UC Berkeley, Nov
6-7, 2009. http://www.icer.it/docs/wp2009/ICERwp15-09.pdf
17
Brooks, R. and E. Harris (2008): Efficiency gains from water markets: Empirical analysis of Watermove in
Australia. Agricultural Water Management, 95, 391-399.
14
model to simulate the short and long-term impacts from water trading (Zaman et al., 2009)18. The
authors argue that an integrated model is necessary to improve estimates from market trading as
it can induce sudden changes in the demand and/or supply from one region to another that results
in significant bottleneck and pressure on the water delivery infrastructure.
6.2
A Model for Optimal Allocation of Water to Competing Demands19
The study develops a simple interactive integrated water allocation model (IWAM), which can
assist the planners and decision makers in optimal allocation of limited water from a storage
reservoir to different user sectors, considering socio-economic, environmental and technical
aspects. IWAM comprises three modules—a reservoir operation module (ROM), an economic
analysis module (EAM) and a water allocation module (WAM). The model can optimize the
water allocation with any of two different objectives or two objectives together. The two
individual objectives included in the model are the maximization of satisfaction and the
maximization of net economic benefit by the demand sectors. Weighting technique (WT) or
simultaneous compromise constraint (SICCON) technique is used to convert the multi-objective
decision-making problem into a single objective function. The single objective functions are
optimized using linear programming. The model applicability is demonstrated for various cases
with a hypothetical example.
6.3
Optimal Allocation of Reservoir Water20
The purpose of the paper is to determine the optimal allocation of reservoir water among
consumptive and non-consumptive uses. A non-linear mathematical programming model is
developed to optimally allocate Lake Tenkiller water among competing uses that maximize the
net social benefit. A mass balance equation is used to determine the level and volume of water in
the lake. The paper examines the effect of water management on lake resources when
18
Zaman, A.M., H.M. Malano, and B. Davidson (2009): An integrated water trading-allocation model, applied to a
water market in Australia. Agricultural Water Management, 96, 149-159.
19
Babel et al. (2005), ‘A Model for Optimal Allocation of Water to Competing Demands’, Water Resources
Management (2005) 19: 693–712.
20
Debnath, Deepayan (2009), ‘Optimal Allocation of Reservoir Water’, Department of Agricultural Economics,
University of Oklahoma, Stillwater, Oklahoma
15
recreational values are and are not included as control variables in the optimization process.
Results show that maintaining lake level near ‘normal lake level’ of 632 feet during the summer
months and shifting releases for hydropower generation to other months increased overall
benefits including recreational benefits with only a slight reduction in hydropower generation.
6.4
Basin21
Scenario Analysis of Water Allocation Based on ET Control in Haihe River
Rational water allocation is important branch of decision making on water planning and
management in Haihe River Basin. Considering condition of water scarcity in Haihe River
Basin, ET quota is taken as objective for water allocation in provinces to realize the requirement
of water inflow into the Bohai Sea. To make qualified ET distribution and water allocation in
various regions, a framework is put forward in the paper, in which two models are applied to
analyze the different scenarios with predefined economic growth and ecological objective. The
first model figures out rational ET objective with multi-objective analysis for compromised
solution in economic growth and ecological maintenance. The second one provides hydraulic
simulation and water balance to allocation the ET objective to corresponding regions under
operational rules. The scenario analysis could discover the relations between economy and
ecology.
Models by the United States Environmental Protection Agency (EPA)22
7.
EPA is the world leader in developing modeling techniques and software for Drinking Water,
Surface Water and Ground Water as is evident from the following:

Centre for Subsurface Modeling Support (CSMoS) provides users with models used
to assess ground-water patterns

EPANET Drinking Water Model models the hydraulics and water quality of water
distribution piping systems

Ground Water Compendium contains fact sheets about models that can be used to
analyze ground water quality and quantity
Jinju, You et al. (2005), ‘Scenario Analysis of Water Allocation Based on ET Control in Haihe River Basin’,
Department of Water Resources Research, China Institute of Water Resources Research and Hydropower
Research, P.R. China.
22
EPA (www.epa.gov)
21
16

Office of Water Models lists models, databases, and other resources developed at the
EPA Office of Water

OWA Water Quality Models contains several models that assess different aspects of
water quality

Storm Water Management Model simulates rainfall runoff in urban areas for single
events or long-term data

Watershed and Water Quality Modeling Technical Support Center provides access to
models and tools that can be used in the development of Total Maximum Daily Loads
(TMDL), waste load allocations, and watershed protection plans

Watershed Management Tools contains several models that assess different aspects of
water quality on a watershed scale.

Watershed Mapping tools lists two models that map and simulate watershed
development over time.
17