The application of economic-engineering optimisation for water management in Ensenada, Baja California, Mexico.

Abstract

Mathematical optimisation is used to integrate and economically evaluate wastewater reuse, desalination and other water management options for water supply in Ensenada, Baja California Mexico with future levels of population and water demand. The optimisation model (CALVIN) is used to explore and integrate water management alternatives such as water markets, reuse and seawater desalination, within physical capacity constraints and the region's water availability, minimising the sum of economic costs of water scarcity and operating costs within a region. The modelling approach integrates economic inputs from agricultural and urban water demand models with infrastructure and hydrological information, to identify an economically optimal water allocation between water users in Ensenada. Estimates of agricultural and urban economic water demands for year 2020 were used. The optimisation results indicate that wastewater reclamation and reuse for the city of Ensenada is the most economically promising alternative option to meet future water needs and make water imports less attractive. Seawater desalination and other options are not economically viable alone, but may have some utility if combined with other options for the Ensenada region.

Full text

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The application of economic-engineering optimisation
for water management in Ensenada, Baja California,
Mexico
J. Medellı ´n-Azuara*, L.G. Mendoza-Espinosa**, J.R. Lund* and R.J. Ramı ´rez-Acosta***
*Civil and Environmental Engineering, University of California, Davis, CA, USA
**Instituto de Investigaciones Oceanolo ´gicas, Universidad Auto ´noma de Baja California, Ensenada, Baja
California, Mexico (E-mail: lmendoza@uabc.mx)
***Facultad de Economı ´a, Universidad Auto ´noma de Baja California, Tijuana, Baja California, Mexico
Abstract Mathematical optimisation is used to integrate and economically evaluate wastewater reuse,
desalination and other water management options for water supply in Ensenada, Baja California Mexico with
future levels of population and water demand. The optimisation model (CALVIN) is used to explore and
integrate water management alternatives such as water markets, reuse and seawater desalination, within
physical capacity constraints and the region’s water availability, minimising the sum of economic costs of
water scarcity and operating costs within a region. The modelling approach integrates economic inputs from
agricultural and urban water demand models with infrastructure and hydrological information, to identify an
economically optimal water allocation between water users in Ensenada. Estimates of agricultural and urban
economic water demands for year 2020 were used. The optimisation results indicate that wastewater
reclamation and reuse for the city of Ensenada is the most economically promising alternative option to meet
future water needs and make water imports less attractive. Seawater desalination and other options are not
economically viable alone, but may have some utility if combined with other options for the Ensenada region.
Keywords Desalination; deterministic optimisation; wastewater reclamation; water management
Introduction
Baja California and California share many features, particularly a drought-prone climate
and growing water demands. Traditional water supply planning and analysis methods
were based on fixed water requirements and the concept of system water deliveries to
always achieve these fixed requirements. Increased costs for providing 100% water
supply reliability has led to more sophisticated views of water demands, moving to
economic water scarcity, rather than requirements. Economic valuation has proved to be
a simple, consistent and understandable principle to help evaluate complex integrated
infrastructure and policy options to rationally balance increased water supplies, reduced
water use and resource allocations, under hydrologic uncertainty (Jenkins et al., 2003,
2004; Pulido-Vela ´zquez et al., 2004).
CALVIN (CALifornia Value Integrated Network) is an economic-engineering
optimisation model that jointly considers water management and economic performance,
including water sources, storage and agricultural, environmental and urban water uses
(Draper et al., 2003). CALVIN has been used successfully in California to explore water
market behaviour and to facilitate economically driven managerial decisions. CALVIN
results go beyond simple cost benefit analysis by taking into account the economic value
of water for different users, water scarcity and supply costs. This information is then
used to identify and develop economically promising combinations of water management
activities including a broad array of options such as additional conveyance capacity,
Water Science & Technology Vol 55 No 1–2 pp 339–347 Q IWA Publishing 2007
339
doi: 10.2166/wst.2007.038

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water reuse and desalination, deregulation, water markets and reductions in water use
under different optimised scenarios.
The population of Northern Baja California has grown rapidly and water transfers and
water marketing should begin to play a key role in major regional water plans. Ensenada,
located 100km south of Tijuana, relies entirely on groundwater as its potable water
source. According to estimates made by the local water utility (CESPE), water demand
can only be met in a sustainable manner until the end of 2006. Currently, Ensenada is
one of the few cities in Mexico treating all of its wastewater. Although Ensenada’s waste-
water meets Mexican environmental standards for reuse, it is currently being discharged
into the sea (Mendoza-Espinosa et al., 2004). Besides urban water demand, two
agricultural regions were included: Guadalupe and Maneadero. Guadalupe, is the most
important wine producing region in Mexico. Maneadero is located 8km south of
Ensenada where a great variety of high value crops are produced, most of which are
exported to the USA. In both cases, reclaimed wastewater could be used for irrigation as
a substitute for groundwater. Alternatively, to meet Ensenada’s future water demands, the
National Water Commission (CNA) is considering seawater desalination and a new
aqueduct to deliver water from the Colorado River. Both alternatives involve major
capital investments and, for desalination, high operation costs.
This study employed economic analysis within an engineering optimisation framework
to evaluate the promising use of these water management alternatives, independently and
in combination, for the Ensenada region, within regional hydrologic and infrastructure
constraints. Estimates of agricultural, residential and industrial economic water demands
by year 2020 were used. Management alternatives included enhanced wastewater
treatment facilities, reclaimed water conveyance infrastructure (for irrigation) and
desalination capacity. The modelling approach, implemented using CALVIN, proved to
be effective for identifying promising water management alternatives. Results show that
wastewater reclamation and reuse is the most cost-effective alternative for meeting future
water needs in the Ensenada region if groundwater overdraft is not an option. Further-
more, water imports either from Tijuana or from the proposed branch from the Colorado
River aqueduct are less attractive when reuse is available. Seawater desalination is only a
promising option when the cost of treatment is low and comparable to groundwater
extraction.
Methods
Economic-engineering optimisation model
The study focused first on the quantitative understanding of the water resources situation
in Ensenada. This quantification took place within the framework of a computer model,
called CALVIN that offers a systematic approach to study such complex water resource
management problems. CALVIN model applications in California include users’ willing-
ness to pay for additional water, the economic values of conjunctive use, economic cost
of environmental restrictions, economic impacts of dam removal, facility expansions,
conveyance and water transfers (Tanaka et al., 2003; Jenkins et al., 2004; Pulido-Vela ´z-
quez et al., 2004). More recent applications of the model include the potential effects of
climate change on California water management (Tanaka et al., in press).
A region in CALVIN is represented as a system of nodes and links (Figure 1). Nodes
include reservoirs, aquifers, agricultural region, urban centres, water treatment facilities
and pumping stations. Links are physical connections between two nodes and may have
associated costs or gains/losses associated with water flows. Links can also be restricted
to a maximum flow such as a conveyance capacity or a minimum environmental or man-
dated flow. The model is a network flow optimisation model which integrates an
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Figure 1 General schematics of the CALVIN model for the Ensenada region
GWMIS
La Mision
aquifer
Ensenada
Urban
MT16
MT14
MT15
M12
GWGPE
Guadalupe
aquifer
Maneadero
aquifer
El Sauzal
El Gallo
El Naranjo
SR
ZAM
Zamora
reservoir
Desalination
Arroyo El
Gallo
M19
Evaporation
losses
Inflows to La Mision aquifer
Ensenada
aquifer
Inflows to
Ensenada aquifer
Inflows to
Maneadero
aquifer
Guadalupe
agriculture
M23
Pacific
Ocean
Inflows to Zamora
M9
Maneadero
agriculture
GWMAN
GW
ENS
M15
Inflows to
Guadalupe
aquifer
Pacific
Ocean
Inflows to
arroyo El
Gallo
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engineering description of a water management system, economic descriptions of water
use demands and its costs, and specific environmental and water allocation policies to
identify promising solutions to regional water resource problems (Draper et al., 2003).
The network flow optimisation problem is solved using the HEC-PRM optimisation soft-
ware developed by the US Army Corps of Engineers.
This software seeks water operations and allocation decisions which minimise the
total cost of operation in a system (the sum of operating costs and water scarcity costs in
urban and agricultural demand areas). In minimising this total cost, the water
management decisions are limited by hydrologic, infrastructure and institutional
constraints. The objective function is to minimise overall system costs over the entire
modelled time period, represented mathematically by:
X
MinZ ¼
i
h
X
cijXij
ð1Þ
where Z: total cost; cij, cost coefficient; and Xij, flow from node i to node j (arc ij).
In this formulation, each node represents a location in time and space. Constraints in
CALVIN include maximum and minimum flow limits and conservation of overall mass
(Jenkins et al., 2001). These constraints represent the physical and institutional bounds
on water operations and allocations. Mathematically, constraints can be represented as:
X
massconservation
i
Xji¼
i
X
aijXijþ bj;
forallnodesj;
ð2Þ
amaximumflow Xij# uij;
forallarcs;
ð3Þ
ð4Þ
aminimumflowXij$ lij
forallarcs;
where bjare external inflows to node j; aij, gains or losses on flows in arc; uij, upper
bound on arc; and lij, lower bound on arc.
Results from optimisation using CALVIN are not limited to flows between nodes and sto-
rage levels in reservoirs for every time step modelled. The combined use of an
economic objective function with a mathematical optimisation algorithm provides, for each
location and time step, the marginal economic willingness to pay of users for additional
water (the Lagrange multiplier for constraint 2). Similarly, the economic value of a unit
expansion of infrastructure capacity is estimated by the Lagrange multiplier for uij in
equation (3), for each arc and time step. The economic value of environmental uses or pre-
viously allocated by government mandates is not valued directly in CALVIN. Instead, these
water uses are represented as minimum flows in equation (4), and their economic opportunity
costs for other water users are evaluated with the Lagrange multiplier on this constraint.
Scenarios in CALVIN are created by modifying the parameters in equations (1–4)
above. An aqueduct expansion would increase the upper bound uijfor that particular link.
It is also possible to prevent overdraft of aquifers by establishing an end-of- period sto-
rage. Operation costs are included in the cijparameter of equation (1), thus having water
flowing from a desalination facility may have unit cost, as would flow from an artificial
recharge facility.
The modelling alternatives examined in this paper represent the following water
management options at year 2020 water demand levels:
1. Current operating and allocation policies, referred to as status quo;
2. Seawater desalination as a new source of potable water;
3. Wastewater reuse for aquifer recharge and irrigation; and
4. Combined seawater desalination and wastewater reuse.
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The status quo would continue to provide water at projected 2020 levels to the city
and the agriculture in Guadalupe and Maneadero. Yet, expansion in conveyance capacity
and water treatment would have to occur for the urban sector. It is assumed that water
demands for the city of Ensenada will increase from its current 22 million cubic meters
per year (Mm3/y) to 39.5. Mm3/y (CNA, 2005). Agricultural water demand is assumed to
be constant. Furthermore, it is assumed aquifer overdraft would continue to be allowed.
Seawater desalination has been advocated as an alternative water supply (CNA, 2004).
In this study a new desalination plant with a capacity of 12.6Mm3/y for the city of
Ensenada is considered. Two cost levels (low and high) for seawater desalination were
used. The low price mimics current CESPE costs for groundwater delivered to the city.
High water desalination costs in this study where established at 1.6 US dollars per cubic
meter.
The city has three wastewater treatment plants: El Sauzal, El Gallo and El Naranjo.
All plants use activated sludge as treatment processes and the effluents are disinfected
with chlorine before being discharged to local creeks that eventually reach the ocean.
The effluent from El Naranjo could be used for the irrigation and/or aquifer recharge in
the agricultural valley of Maneadero (Mendoza-Espinosa et al., 2004). Effluents from El
Gallo and El Sauzal comply entirely with Mexican legislation related to the reuse of
wastewater for activities where the public is in direct and indirect contact with the
wastewater. With some additional conveyance capacity, the reclaimed water could be
used for crop irrigation or recharge of the Guadalupe Valley aquifer (Mendoza-Espinosa
et al., 2005).
For wastewater reuse, four new projects were considered (see Figure 1):
1. Up to 9.4Mm3/y of artificial recharge of the Maneadero aquifer using treated
wastewater from El Naranjo wastewater treatment plant.
2. Up to 6.3Mm3/y of artificial recharge of the Guadalupe aquifer using treated
wastewater from either El Naranjo or El Gallo wastewater treatment plants.
3. Up to 9.4Mm3/y of treated wastewater from El Naranjo wastewater treatment plant
for irrigation in Maneadero.
4. Up to 6.3Mm3/y of treated water from El Sauzal for irrigation in the Guadalupe Valley.
Finally, seawater desalination and the preceding wastewater reuse option were com-
bined into a last water management alternative for Ensenada. Only variable costs were
considered for all water management options. Desalinated seawater was restricted to be
used solely for urban consumption, whereas recycled wastewater could be used for irriga-
tion and groundwater recharge.
Data requirements
The CALVIN Ensenada regional model required gathering a great amount of information
for the model database. The schematic is presented in Figure 1. The model included four
aquifers that supply water to the city of Ensenada, one reservoir (Zamora), two aque-
ducts, several pumping stations, three wastewater treatment plants, one urban demand
and two agricultural demands (Maneadero and Guadalupe).
Data for the present study comes from the National Water Commission (CNA) data-
bases, the local utility company (CESPE) and interviews with local farmers. Monthly
hydrologic data from 1983 to 1993 were collected to estimate inflows to the aquifers.
The city of Ensenada receives water from four aquifers (Ensenada, La Mision, Guada-
lupe and Maneadero) and a reservoir (Zamora). Estimates of storage capacity, water
extractions, evaporation rates and natural recharge were made using data from CNA.
CESPE provided information on potable water and wastewater treatment capacities and
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costs, conveyance capacity, pumping costs, water tariffs and existing physical connec-
tions between network elements.
Agricultural production costs were estimated using local farmer’s reports on the
region’s crops, planted area, crop yield, water use, labour use per crop, wages, off-farm
labour opportunities, pumping costs and historical institutional rules. A microeconomic
agricultural production model was used to derive economic water demands for irrigation
water.
Urban scarcity costs were calculated with water demand projections for 2020 obtained
using population growth estimations from SAPROF (1999). Following Jenkins et al.
(2001), water scarcity value for urban demand nodes was obtained. A constant (20.2)
price-elasticity of demand for urban water was assumed. Observed water consumption
and prices, and a constant per capita consumption rate were used to derive year 2020
economic water demands.
The collected data were incorporated into a database for input to the optimisation
solver, which uses a generalised network flow optimisation algorithm to find the set of
water operations and allocations for maximising regional economic net benefits (minimis-
ing net costs).
Results and discussion
Results of this study indicate that flexible and integrated water management schemes can
reduce the probability of water shortages and overall costs. Currently, all four aquifers
are being overdrafted, yet water reuse may reduce dependence on groundwater. Model
runs in this study allow overdraft at current rates.
In addition, overall results from this study show that water reuse is a superior water
management option compared to low-cost seawater desalination and the status quo. Table
1 shows a breakdown of water use in the Ensenada region by source. As an expensive
source, desalted seawater would be used only in the city of Ensenada (column 2 Table 1).
When both water reuse and desalination are available, the use of desalted water drops by
8.2 per cent points (column 4).
Other findings include:
1. The status quo is unsustainable. Expansions in conveyance capacity are needed to
meet future demands even if overdraft of aquifers is allowed. Therefore, either new
sources of water or measures to limit groundwater extraction are needed. Continuing
to overdraft aquifers such as Maneadero will increase saline intrusion and jeopardise
Table 1 Water supply share by source
Supply Options considered (share in per cent)
Current policyLow cost desalination Water reuseReuse and LC desalination
Urban
Groundwater
Surface
Desalinated
Recycled
Sum
Agricultural
Groundwater
Surface
Desalinated
Recycled
Sum
97.0
3.0
0.0
0.0
100.0
72.3
3.0
24.7
0.0
100.0
97.0
3.0
0.0
0.0
100.0
80.5
3.0
16.5
0.0
100.0
100.0
0.0
0.0
0.0
100.0
100.0
0.0
0.0
0.0
100.0
77.7
0.0
0.0
22.3
100.0
77.7
0.0
0.0
22.3
100.0
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its long-term availability as a water source for both agricultural and urban uses (Daes-
sle ´ et al., 2005). Wastewater treatment facility expansions will be needed to accom-
modate increases in wastewater generation. If no action is taken, a compromise
between the agricultural use and the urban use of water will have to be made. Current
tendency seems to be in favour of urban growth thus, the agricultural sector would
shrink significantly, as water sources currently used for agriculture are shifted to urban
uses with higher economic values.
2. Low-cost seawater desalination is a better water management option compared to the
status quo, since willingness to pay for imported water is reduced (Table 2).
(Willingness to pay in the context of this study means how much a user would pay for
one additional unit of water). Nevertheless, this would be the case only if the cost of
desalinated water compares favorably to current water production costs using ground-
water. High seawater desalination costs were never used in these model runs.
Currently, most water utilities in Mexico are state owned and operate at zero profit
level. Therefore, investment on research and development of new technologies is not
pursued and the water utilities rely mostly on water tariffs. High cost desalted
seawater may only exacerbate financial issues, since a strong increment in the water
tariff may encounter strong social and political opposition.
3. Wastewater reuse on its own can reduce shortages and willingness to pay for imported
water from the Colorado River system (In this context, imported water means water
that has to be brought from a separate region). By increasing local supplies of water,
local wastewater reuse for irrigation or aquifer recharge would greatly reduce the
costs of water scarcity, leaving a much smaller amount of local water scarcity to be
accommodated by water allocation, water conservation, and increased water use effi-
ciency. In this case, increased wastewater reuse would reduce the value of imported
water by 57%, avoiding considerable capital and operating costs for such a new
supply. If the required wastewater reuse infrastructure is built, seawater desalination
may not be cost-effective. Table 2 shows that the willingness to pay for this imported
water decreases as seawater desalination and wastewater reuse options are available.
At current extraction and water consumption levels in Ensenada, new water sources
would have to be found to keep up with water demand projections. Therefore, there is an
inherent willingness to pay for imported water to avoid shortages. Table 2 shows that
desalination alone would lead to little reduction in the value of imported water. However,
wastewater reuse alone and wastewater reuse combined with desalination would reduce
substantially both water scarcity costs and the value of additional water imports.
All models have limitations and this is not less true for CALVIN. Main limitations are
data quality, system simplifications and a non-exhaustive economic representation (see
Jenkins et al., 2004). In particular, the model assumes that operational and allocation
changes suggested are possible institutionally. Yet this might not be possible due to the
complexity of water management decisions.
Nevertheless, having this type of analytical tool for Baja California allows more
definitive answers to many water and environmental issues for this region. Precise
Table 2 Reduction in economic value of imported water
Options considered (percent with respect to current policy)
Desalination (low cost)Wastewater reuse Wastewater reuse and desalination
(low cost)
Reduction in economic value
of imported water
1.4% 15.8%16.1%
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applications of optimisation insights will require further testing and refinement by more
detailed simulation studies. Further work will also link a larger model of Baja California,
Mexico to an existing California model to allow a better quantitative exploration of
cross-border water management issues.
Conclusions
This study demonstrates that economic-engineering optimisation can provide insights
regarding the best combination of water technology applications and the potential of
newer water management practices, such as wastewater reuse over older practices such as
increased water imports. Traditional water management and planning can prescribe
excessive expansions of supply by considering only supply costs and not the economic
costs of water scarcity. Optimisation methods, such as those demonstrated here, also
provide a rational engineering basis for design of a mixed portfolio of water supply
actions for future conditions. With growing water demands for Ensenada, Mexico, new
water sources would be needed in the near future. Wastewater reclamation and reuse for
the city of Ensenada is potentially the most economically promising option for guarantee-
ing a reliable and economical supply of water to the city. Seawater desalination alone
appears economically inferior and would need to be combined with other management
activities, including wastewater reuse, to become more economical.
Acknowledgements
This material is based in part on work supported by a grant from the University of Cali-
fornia Institute for Mexico and the United States (UC MEXUS) and the Consejo Nacional
de Ciencia y Tecnologı ´a de Me ´xico (CONACYT).
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