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חקלאית בכלכלה למחקר המרכז
Agricultural for Center TheResearch Economic
וניהול סביבה לכלכלת המחלקה Environmental of Department
Management and Economics
Discussion Paper No. 4.20
Large-Scale Desalination and the External Impact on Irrigation-Water
Salinity: Economic Analysis for the Case of Israel
By
Yehuda Slater, Israel Finkelshtain, Ami Reznik and Iddo Kan
נמצאים המחלקה חברי של מאמרים :שלהם הבית באתרי גם
Papers by members of the Department can be found in their home sites:
http://departments.agri.huji.ac.il/economics/index.html
P.O. Box 12, Rehovot 76100, Israel 76100 רחובות ,12 .ד.ת
1
Large-Scale Desalination and the External Impact on Irrigation-Water
Salinity: Economic Analysis for the Case of Israel
Yehuda Slater, Israel Finkelshtain, Ami Reznik and Iddo Kan
Department of Environmental Economics and Management, The Robert H. Smith Faculty
of Agriculture, Food and Environment, The Hebrew University of Jerusalem, P.O.B. 12,
Rehovot 761001, Israel
Corresponding Author: Iddo Kan iddo.kan@mail.huji.ac.il
Key Points:
Subsidizing desalination is socially warranted because the associated irrigation-
water salinity reduction is an external effect of water consumption by all sectors
Irrigation with desalinated water is found optimal for Israel due to the large share of
water-intensive salinity-sensitive high-value crops
Ignoring the damage entailed by irrigation-water salinity benefits water suppliers at
the expense of consumers of water and agricultural products
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Large-Scale Desalination and the External Impact on Irrigation-Water
Salinity: Economic Analysis for the Case of Israel
Abstract
Recent agro-economic studies in water-scarce countries such as Spain, Australia, Saudi
Arabia, and Israel have revealed the economic viability of irrigating high-value crops
with desalinated water. However, the worldwide growth of large-scale desalination
capacities is primarily designed to resolve urban-water scarcity, disregarding the impact
of desalination on irrigation-water salinity. We develop a dynamic hydro-economic
programming model where infrastructure capacities and allocations of water quantities
and salinities in a regional water-distribution network are endogenous. We show that
subsidizing desalination is socially warranted because the associated reduction in
irrigation-water salinity is an external effect of water consumption by all water users.
Empirical application to the entire state of Israel indicates that large-scale desalination of
seawater and treated wastewater for irrigation is optimal. This result stems from the large
share of irrigation-intensive salinity-sensitive high-value crops, motivated by Israel’s
policies to support local agriculture. Ignoring salinity results in a 45% reduction in
desalinated irrigation water, a 29% reduction in farming profits, a 250% increase in
water-suppliers’ profits, and an average deadweight loss of $1,200 a year per hectare of
arable land.
Keywords: Desalination, Irrigation, Salinity, Economics, Agriculture, Water,
Externality, Policy, Model, Natural Resource
JEL Classification: Q15, Q25, Q28
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1. Introduction
Salts already affect about a third of the world’s arable areas, and a fifth of the world’s
irrigated lands (Nellemann et al., 2009; Qadir et al., 2014). Salinization is expected to
expand further through a range of processes driven by population growth; these include a
rise in irrigation with brackish water as a substitute for the freshwater amounts diverted to
domestic use, agricultural reuse of the growing treated wastewater (TWW) volumes
discharged from urban areas (Jimenez & Asano, 2008; Qadir et al., 2007), and
salinization of freshwater sources due to seawater intrusion and deep percolation of salts
from irrigated lands (Assouline et al., 2015). The integrative nature of these spatially and
intertemporally linked processes implies that salinity damage should be considered
intrinsic to the design of agricultural and water policies, as well as to the long-run
development of water infrastructures at the regional and state levels, in particular
desalination.
Worldwide desalination capacity is continuously growing, and is expected to be
nearly double by 2050 relative to the 2015 level of 97 × 106 (m3 day-1) (Darre & Toor,
2018). Nevertheless, due to high supply costs, adverse environmental effects, and
agronomic constraints, large-scale desalination is generally perceived as a technology for
relieving urban-water scarcity rather than agricultural water shortages and salinity
damage (Burn et al., 2015; Martínez-Alvarez et al, 2016; Sepehr et al., 2017). However,
recent field- and farm-level analyses have indicated that desalination can provide an
economically viable water source for irrigating high-value crops in water-scarce countries
such as Spain (Reca et al., 2018; Zarzo et al., 2013), Australia (Barron et al., 2015), Saudi
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Arabia (Multsch et al., 2017), and Israel (Hadas et al., 2016; Kaner et al., 2017). Thus, the
tendency to overlook the potential contribution of desalination to agricultural productivity
in the design of policies and water infrastructures may entail suboptimal water
management and deadweight loss.
Water economies at the basin, regional or state levels may comprise multiple water
sources with diverse qualities and supply costs (e.g., naturally recharged surface water
and groundwater, brackish water, desalinated seawater, and TWW), various consumers
(e.g., domestic, industrial, and agricultural users) with different demands for water
quantity and quality, and an ensemble of infrastructures that constitute a complex water-
distribution network to treat and convey water from sources to consumers, separated or
blended. Efficient management of such networks should account for the linkage of
scarcities across points in time and space, meaning that water use at a particular place and
time may have opportunity costs with respect to its usage for various purposes at
alternative locales and times (Fisher et al., 2005). Moreover, population growth, climate
change, and the long construction period for water infrastructures imply that water-
system designers should foresee scarcities and decide ahead of time which, when, where,
and to what extent infrastructural elements should be installed or extended.
Hydro-economic models are an efficient tool for integrating the economic,
hydrological, engineering, agronomic, and environmental aspects associated with water
policies and water-infrastructure blueprints of large-scale water systems (Booker et al.,
2012; Harou et al., 2009). However, despite the vast economic literature on irrigation-
water salinity (Connor et al., 2012; Feinerman & Yaron, 1983; Knapp, 1992; Letty &
Dinar, 1986; and Schwabe et al., 2006 are but a few examples for topics and modeling
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methods developed in the last decades), to date, the incorporation of salinity in hydro-
economic models has been limited. For example, Housh et al. (2011), Lavee et al. (2011),
Reznik et al. (2016), Saglam (2013) and Tanaka et al. (2006) refer to desalination as a
means of resolving water-quantity scarcities, overlooking the benefits of reducing
irrigation-water salinity. Howitt et al. (2010) and Welle et al. (2017) employed the van
Genuchten and Hoffman (1984) production function to internalize salinity’s agronomic
impact into a static analysis of agricultural irrigation-water management in the Central
Valley of California. However, that framework considered agriculture as a single water
consumer, and therefore did not capture interlinks with domestic and industrial water
users, for example, when agriculture consumes the TWW produced by urban regions. In
addition, economies of scale associated with water conveyance warrant a mixture of
water sources with different qualities for long-distance delivery. The economics of
blending irrigation-water sources with diverse salinities has been studied at the field and
regional levels (Dinar et al., 1986; Kan, 2008; Kan & Rapaport-Rom, 2012; Kan et al.,
2002); however, to our knowledge, less attention has been given to the policy and welfare
implications of salinity in spatially widespread water-distribution networks that supply
mixed water to both agricultural and urban sectors.
The objective of this paper is to assess the welfare contribution of large-scale
desalination through its impact on irrigation-water salinity. Specifically, we compare
optimal water management at the regional scale under two scenarios: in the first, termed
Salinity Internalized (SI), the salinity effects are considered in the design of water
infrastructures, whereas the second, Salinity Externalized (SE), presumes that temporal
and spatial changes in salinity are disregarded.
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The following section presents a general dynamic hydro-economic model that
optimizes water allocations and infrastructure development while accounting for water
salinity and its agricultural damage. Based on an analytical solution, we show that the
salinity reduction following desalination is an external effect of water consumption by all
sectors, which can be internalized by subsidizing the supplied water. Otherwise,
disregarding salinity leads to higher-than-optimal water prices and welfare loss, where
water suppliers benefit at the expense of urban and agricultural water users.
In Section 3 we develop an empirical version of the model based on the Israeli water
system. The case of Israel seems to correspond to the assertion that: “…for water-scarce
countries that already implement all other measures for freshwater generation,
desalination may serve as the only viable means to provide the water supply necessary to
sustain agriculture, support population, and promote economic development” (Elimelech
& Phillip, 2011, p. 717). Indeed, to cope with its growing water scarcity, Israel has
established a complex water-supply system, incorporating extraction of freshwater,
agricultural reuse of TWW, and extensive desalination of brackish water and seawater.
The empirical model tracks the dynamics of water salinity throughout the water-delivery
system, and controls the supplied water salinity by both the allocation and mixture of
water from different sources and the establishment of plants for the desalination of
seawater, brackish water and TWW. The model also comprises the farmers’ adaptation to
irrigation-water salinity through land allocation across crops in relation to the crops’ salt
tolerance.
Section 4 presents the empirical results. For the SI scenario, we obtain that the
negative effect of irrigation-water salinity on agricultural production in Israel warrants
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large-scale desalination of seawater and TWW for irrigation. We attribute this result to
the large share of high-value, salinity-sensitive fruit and vegetables in Israel’s vegetative
agriculture, where the Israeli farmers’ specialization in the production of these crops is
motivated by supporting regulations. We then show that disregarding the salinity effects
in the design of water infrastructures yields a considerable deadweight loss, evaluated at
$1,200 per average hectare of cultivable land. This estimate, which accounts for the
indirect salinity effects on domestic water supply and agricultural output prices, is nearly
three times larger than the direct salinity damage to agriculture of $440 ha-1 year-1
reported by Qadir et al. (2014). Section 5 summarizes with a discussion of the model’s
limitations and extensions.
2. General Framework
We first present a general dynamic hydro-economic model; then, to obtain theoretical
insights, we solve the optimization problem of a simplified static version analytically.
2.1. Hydro-economic Model
Consider a water-distribution network that is centrally managed by a water master whose
objective is to maximize welfare throughout a planning horizon of 𝑇 discrete periods by
setting efficient prices and developing infrastructures. Let 𝕂 be a set of nodes
representing spatially linked water sources, treatment infrastructures, and water-use
regions, and 𝐪𝑡𝑘 = (𝑤𝑡
𝑘 , 𝑠𝑡𝑘) denote the pair of quantity (𝑤𝑡
𝑘) and salinity (𝑠𝑡𝑘) of the water
flowing through node 𝑘 ∈ 𝕂 during period 𝑡 (𝑡 = 1,… , 𝑇). The elements in 𝐪𝑡𝑘 are
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constrained by the vector of exogenous factors 𝐛𝑡𝑘 (i.e., a volumetric balance constraint in
a pipeline junction, the water salinity in groundwater sources, etc.), 𝐪𝑡𝑘 ≤ 𝐛𝑡
𝑘, where 𝐛𝑡𝑘 =
𝑓𝑡𝑘(𝐛𝑡−1
𝑘 , 𝐪𝑡−1𝑘 ) represents the intertemporal dependence between water flows and
constraints (e.g., the extractable aquifer stock depends on the initial stock and extraction
during the previous period). A related set of constraints, 𝐛𝑇+1𝑘 ≥ 𝐛𝑘, represents end
conditions; for example, minimum extractable stocks in an aquifer.
The vector 𝐪𝑡𝑘 is also constrained by the node’s capacity attributes 𝐳𝑡
𝑘 (e.g., the
maximum annual volume and minimum salinity level of a desalination plant’s outflow),
which are endogenous. We denote by Δ𝐳𝑡𝑘 the change in the capacity features of node 𝑘
during period 𝑡, such that, given the initial capacity 𝐳0𝑘, 𝐳𝑡
𝑘 = 𝐳0𝑘 + ∑ Δ𝐳𝜏
𝑘𝑡−1𝜏=1 . The total
per-period costs associated with the capacities incorporated in 𝐳𝑡𝑘 (i.e., maintenance and
capital costs) are denoted 𝐶𝑡𝑘(𝐳𝑡
𝑘).
We denote by 𝑉𝑡𝑘(𝐪𝑡
𝑘, 𝐱𝑡𝑘) the value associated with water flow through node 𝑘 ∈ 𝕂
during period 𝑡, where 𝐱𝑡𝑘 is a vector of non-water input variables (e.g., land allocation to
crops) which may be constrained from above by �̅�𝑡𝑘 (e.g., regional agricultural land). The
value function 𝑉𝑡𝑘(∙) may vary in time (e.g., due to population growth or climate change),
and it is negative when node 𝑘 is a water-treatment infrastructure (e.g., the variable costs
of a groundwater-pumping station, or a desalination or wastewater-treatment plant), and
positive if the node is an urban or agricultural water-consumption region.
Let 𝐐, 𝐗, 𝐁 and 𝐙 be the vectors incorporating 𝐪𝑡𝑘, 𝐱𝑡
𝑘, 𝐛𝑡𝑘 and 𝐳𝑡
𝑘 for all 𝑘 ∈ 𝕂 at all
the 𝑇 periods, respectively, and the vector 𝚫𝐙 represent all the capacity changes
throughout the planning horizon. Given the initial levels of the exogenous and capacity
constraints for all 𝑘 ∈ 𝕂, 𝐁0 and 𝐙0, the planner’s objective is to solve the problem
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max𝐐,𝚫𝐙,𝐗
𝑊 = ∑ (1 + 𝑟)−𝑡 ∑ [𝑉𝑡𝑘(𝐪𝑡
𝑘, 𝐱𝑡𝑘) − 𝐶𝑡
𝑘(𝐳𝑡𝑘)]𝑘∈𝕂
𝑇𝑡=1
𝑠. 𝑡. 𝐛𝑡𝑘 = 𝑓𝑡
𝑘(𝐛𝑡−1𝑘 , 𝐪𝑡−1
𝑘 ) ∀ 𝑘 ∈ 𝕂, 𝑡 = 1,… , 𝑇,
𝐳𝑡𝑘 = 𝐳0
𝑘 + ∑ Δ𝐳𝜏𝑘𝑡−1
𝜏=1 ∀ 𝑘 ∈ 𝕂, 𝑡 = 1,… , 𝑇,
𝐱𝑡𝑘 ≤ �̅�𝑡
𝑘 ∀ 𝑘 ∈ 𝕂, 𝑡 = 1,… , 𝑇,
𝐐 ≤ min(𝐁, 𝐙), 𝐁𝑇+1 ≥ 𝐁, 𝐐, 𝚫𝐙, 𝐗 ≥ 𝟎
(1)
where 𝑊 denotes welfare and 𝑟 is the discount rate. The solution defines the optimal
infrastructure-development plan and allocation of water throughout the distribution
network, induced by water quotas or prices. In the SI scenario, the water master accounts
for the impact of salinity changes embedded in the value function 𝑉𝑡𝑘(𝐪𝑡
𝑘, 𝐱𝑡𝑘) for all 𝑘 ∈
𝕂 and 𝑡 = 1, … , 𝑇, whereas the SE case implies 𝑠𝑡𝑘 = 𝑠0
𝑘 for all 𝑘 ∈ 𝕂 and 𝑡 = 1, … , 𝑇.
2.2. Theoretical Insights
To obtain an analytical solution, we consider a simplified static version of the
optimization problem expressed in equation (1). Figure 1 depicts a water economy in
which groundwater and desalinated seawater are two water sources with different
salinities, which are mixed and then delivered to two water-consumption zones—urban
and agricultural.
Figure 1 about here
We denote by 𝑠𝑔 and 𝑠𝑑 the salinities of the groundwater and desalinated water,
respectively, where 𝑠𝑔 > 𝑠𝑑. These salinity levels constitute minimum constraints for the
salinities of the water supplied by the respective sources: 𝑠𝑔 ≥ 𝑠𝑔 and 𝑠𝑑 ≥ 𝑠𝑑. The
extracted groundwater quantity, 𝑤𝑔, is limited by the availability constraint �̅�𝑔, whereas
the delivery of desalinated water, 𝑤𝑑, is unlimited. The total water supply, 𝑤 ≡ 𝑤𝑑 +
𝑤𝑔, is a mixture of the two sources with a salinity that is the volumetric weighted average
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𝑠 =𝑤𝑑𝑠𝑑+𝑤𝑔𝑠𝑔
𝑤. The blended water is split such that the urban and agricultural sectors
obtain amounts 𝑤𝑢 and 𝑤𝑎, respectively, and 𝑤𝑢 + 𝑤𝑎 = 𝑤.
We assume constant per-water-unit marginal costs, where the marginal cost of
desalination, 𝑐𝑑, exceeds that of the groundwater, 𝑐𝑔. Unlike groundwater, desalination is
also associated with fixed cost 𝐶𝑑, contingent on the supply of desalinated water. The
functions 𝑉𝑢(𝑤𝑢) and 𝑉𝑎(𝑤𝑎, 𝑠) are, respectively, the value of water consumed by
agents in the urban and agricultural zones (gross of water-purchasing expenses), where
water quantity is beneficial to both sectors (i.e., 𝑉𝑤𝑢(𝑤𝑢) > 0 and 𝑉𝑤
𝑎(𝑤𝑎, 𝑠) > 0),
whereas water salinity is harmful only to agriculture (𝑉𝑠𝑢(𝑤𝑢) = 0 and 𝑉𝑠
𝑎(𝑤𝑎, 𝑠) < 0).
A benevolent water authority manages water centrally by setting the capacities of
groundwater extraction and desalination, as well as the administrative water prices at the
consumption zones. As already noted, under the SI scenario, the planner solves the
problem in equation (1) which, with simplifying specifications, becomes
max𝑤𝑑,𝑤𝑔,𝑤𝑢,𝑤𝑎,𝑠𝑑,𝑠𝑔
𝑊 = 𝑉𝑢(𝑤𝑢) + 𝑉𝑎(𝑤𝑎, 𝑠) − 𝑐𝑑𝑤𝑑 − 𝑐𝑔𝑤𝑔 − 𝐶𝑑
𝑠. 𝑡. 𝑤 = 𝑤𝑢 + 𝑤𝑎 = 𝑤𝑑 + 𝑤𝑔, 𝑤𝑔 ≤ �̅�𝑔,
𝑠𝑑 ≥ 𝑠𝑑, 𝑠𝑔 ≥ 𝑠𝑔, 𝑠 =𝑤𝑑𝑠𝑑+𝑤𝑔𝑠𝑔
𝑤
𝑤𝑑, 𝑤𝑔, 𝑤𝑢, 𝑤𝑎, 𝑠𝑑, 𝑠𝑔 ≥ 0
(2)
By substituting the balance constraint 𝑤𝑢 = 𝑤𝑑 + 𝑤𝑔 − 𝑤𝑎 into 𝑉𝑢(𝑤𝑢) and optimizing
with respect to 𝑤𝑎 (assuming that the second-order conditions prevail), we get
𝑝SI = 𝑉𝑤𝑢(𝑤𝑢) = 𝑉𝑤
𝑎(𝑤𝑎, 𝑠) (3)
implying that a single optimal administrative water price (denoted 𝑝SI to indicate the SI
scenario) should be set for both consumption sectors. Optimization with respect to 𝑤𝑔
and 𝑤𝑑 subject to the condition in equation (3) yields
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𝑝SI = 𝑐𝑑 − 𝑉𝑠𝑎(𝑤𝑎, 𝑠)
𝑤𝑔(𝑠𝑑−𝑠𝑔)
(𝑤SC)2 (4)
𝑝SI = 𝑐𝑔 + 𝑉𝑠𝑎(𝑤𝑎, 𝑠)
𝑤𝑑(𝑠𝑑−𝑠𝑔)
(𝑤SI)2 + 𝜆𝑔 (5)
where 𝑤SI denotes the total water consumption under price 𝑝SI, and 𝜆𝑔 is the shadow
value of the groundwater constraint 𝑤𝑔 ≤ �̅�𝑔. Taken together, equations (4) and (5) yield
the efficiency condition underlying the price 𝑝SI
𝑉𝑠𝑎(𝑤𝑎,𝑠)
𝑤SI(𝑠𝑑 − 𝑠𝑔) = 𝑐𝑑 − (𝑐𝑔 + 𝜆𝑔) (6)
which requires the (left-hand-side) per-water-unit agricultural benefits associated with
reducing salinity from 𝑠𝑔 to 𝑠𝑑 to be equal to the (right-hand-side) difference between the
per-water-unit supply (plus scarcity) costs of the two sources.
Equations (4) and (5) imply 𝑐𝑑 ≥ 𝑝SI ≥ 𝑐𝑔. Equation (4) expresses the price of the
supplied blended water in relation to the supply of desalinated water. The term
𝑉𝑠𝑎(𝑤𝑎, 𝑠)
𝑤𝑔(𝑠𝑑−𝑠𝑔)
(𝑤SI)2 in equation (4) reflects the marginal benefits accrued to the
agricultural sector by the decline in salinity of the mixed water due to the last unit of
desalinated water. However, from the perspective of any urban or agricultural water
consumer, this is an external effect, as she or he overlooks the salinity reduction
associated with the consumption of an additional unit of desalinated water. Therefore,
efficiency requires internalizing this external effect as a subsidy for the desalinated water
incorporated in the supplied blended water. The subsidy incentivizes the consumption of
desalinated-water quantities beyond the level equating the water price to the marginal
desalination cost 𝑐𝑑. Clearly, supplying the water quantity demanded under price 𝑝SI
requires the establishment of a sufficiently large desalination capacity.
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The optimal price 𝑝SI is also obtained in equation (5) by inspecting the effect of the
groundwater incorporated in the supplied blended water. The term 𝑉𝑠𝑎(𝑤𝑎, 𝑠)
𝑤𝑑(𝑠𝑔−𝑠𝑑)
(𝑤SI)2
in equation (5) represents the marginal damage caused to agriculture by an additional unit
of groundwater due to the increased salinity of the mixed water. This is a negative
external effect, which should be introduced as a tax to all water consumers in order to
render the optimal groundwater supply lower than that equating the water price to 𝑐𝑔
(even under an ineffective groundwater constraint; i.e., 𝜆𝑔 = 0).
The optimal solution is illustrated schematically in Figure 2a. It is assumed that
groundwater is supplied first at the marginal cost 𝑐𝑔, and water deliveries beyond the
groundwater constraint �̅�𝑔 require desalination at the marginal cost 𝑐𝑑. The brown
dashed curve denoted 𝑉𝑤𝑢(𝑤𝑢) is the inverse urban-water demand. The solid pink curve
marked by 𝑉𝑤(𝑤, 𝑠) represents the inverse aggregate demands of the urban and
agricultural sectors. At �̅�𝑔, the curve 𝑉𝑤(𝑤, 𝑠) kinks upward due to the increase in
agricultural produce resulting from the reduction in the blended water’s average salinity
𝑠, which occurs under positive supplies of desalinated water. The solid green curve
𝑉𝑤(𝑤, 𝑠𝑔) illustrates the inverse aggregate demand for the (hypothetical) case in which
the salinity of the blended water is unaffected by desalination, and remains similar to that
of the groundwater. The optimal conditions in equations (3), (4), and (5) imply that the
optimal water supply, 𝑤SI, is set such that 𝑉𝑤(𝑤SI, 𝑠) = 𝑐𝑑. Then, the water price can be
computed based on the equality 𝑝SI = 𝑉𝑤(𝑤SI, 𝑠𝑔).
Figure 2 about here
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Are the variable water-supply costs covered under the SI optimal price 𝑝SI? Based on
equation (5), the cost-recovery condition with respect to the variable costs, 𝑝SI𝑤SI ≥
𝑐𝑑𝑤𝑑 + 𝑐𝑔𝑤𝑔, becomes
𝑉𝑠𝑎(𝑤𝑎,𝑠)
𝑤SI(𝑠𝑑 − 𝑠𝑔) ≥ 𝑐𝑑 − (𝑐𝑔 + 𝜆𝑔 + 𝜆𝑔
𝑤𝑔
𝑤𝑑) (7)
which, in view of equation (6), indicates that the surplus of water suppliers is positive
provided that 𝜆𝑔𝑤𝑔
𝑤𝑑> 0; that is, provided that 𝑤𝑔 = �̅�𝑔 > 0.
The economic implications of changes in the salinities of the water sources can be
learned from the shadow values of the respective desalination and groundwater salinity
constraints 𝑠𝑑 ≥ 𝑠𝑑 and 𝑠𝑔 ≥ 𝑠𝑔, which are defined by 𝜆𝑠𝑑 = 𝑉𝑠𝑎(𝑤𝑎, 𝑠)
𝑤𝑑
𝑤SI and 𝜆𝑠𝑔 =
𝑉𝑠𝑎(𝑤𝑎, 𝑠)
𝑤𝑔
𝑤SI, respectively. Thus, the larger the share of a water source in the total water
supply, the larger the negative agricultural impact associated with a marginal increase in
the salinity of that source.
Turning to the SE scenario, suppose that the groundwater source is exhausted (i.e.,
𝑤𝑔 = �̅�𝑔), and desalinated water is supplied (𝑤𝑑 > 0); alas, the water master refers to
desalination as an instrument for resolving water-quantity scarcity while ignoring its
impact on salinity; that is, she or he erroneously assumes that the salinity of the supplied
blended water is fixed at 𝑠𝑔. Consequently, when determining the administrative water
price (denoted 𝑝SE for the SE case) according to equations (4) and (5), the terms
𝑉𝑠𝑎(𝑤𝑎, 𝑠)
𝑤𝑔(𝑠𝑑−𝑠𝑔)
(𝑤𝑑+𝑤𝑔)2 and 𝑉𝑠
𝑎(𝑤𝑎, 𝑠)𝑤𝑑(𝑠𝑑−𝑠𝑔)
(𝑤𝑑+𝑤𝑔)2 , respectively, are dropped; hence, 𝑝SE =
𝑐𝑑, and equation (5) implies 𝜆𝑔 = 𝑐𝑑 − 𝑐𝑔. Nevertheless, the actual salinity of the mixed
14
water, 𝑠, will be lower than 𝑠𝑔 when desalinated water is supplied, and the actual levels
of 𝑤𝑑 and 𝑤𝑎 can be computed by the conditions
𝑐𝑑 = 𝑉𝑤𝑢(𝑤𝑑 + �̅�𝑔 − 𝑤𝑎) = 𝑉𝑤
𝑎(𝑤𝑎, 𝑠) + 𝑉𝑠𝑎(𝑤𝑎, 𝑠)
�̅�𝑔(𝑠𝑑−𝑠𝑔)
(𝑤𝑑+�̅�𝑔)2 (8)
which follow from equations (3) and (4), together with the water-balance constraint 𝑤𝑢 =
𝑤𝑑 + �̅�𝑔 −𝑤𝑎.
Figure 2b illustrates the SE solution. The policy maker mistakenly refers to the
(green) curve 𝑉𝑤(𝑤, 𝑠𝑔) as the inverse aggregate demand, and therefore sets 𝑝SE =
𝑉𝑤(𝑤, 𝑠𝑔) = 𝑐𝑑. Since 𝑝SE > 𝑝SI, the desalination capacity and the surpluses of the urban
and agricultural consumers are lower than their SI counterparts, whereas the surplus of
the water suppliers is positive, and equals (𝑐𝑑 − 𝑐𝑔)�̅�𝑔. The area marked F indicates the
deadweight loss associated with ignoring the desalination impact on salinity.
So far, we have assumed that desalination is warranted under both scenarios; that is,
the welfare with desalination exceeds the welfare without it. It may well be that this
condition holds under the SI scenario, but not under that of SE, as illustrated in Figure 2c.
The total water-consumption value associated with desalination under the SI scenario
(i.e., the area of the dashed-yellow-line trapezoid underneath the (pink) inverse aggregate
demand curve 𝑉𝑤(𝑤, 𝑠) in the segment 𝑤 ∈ [�̅�𝑔, 𝑤SI]) exceeds the total desalination cost
(the area of the pink rectangle, 𝑐𝑑(𝑤SI − �̅�𝑔) + 𝐶𝑑). In the SE case, however, the total
consumption value erroneously perceived by the water master (the area of the dashed-
brown-line trapezoid below the (green) inverse aggregate demand curve 𝑉𝑤(𝑤, 𝑠𝑔) in the
segment 𝑤 ∈ [�̅�𝑔, 𝑤SE]) is smaller than the respective desalination costs (the area of the
green rectangle, 𝑐𝑑(𝑤SE − �̅�𝑔) + 𝐶𝑑). Therefore, in the SE case, the water master
would reject desalination altogether, and may set a market-clearing water price according
15
to 𝑝SE = 𝑉𝑤(�̅�𝑔, 𝑠𝑔). The deadweight loss under SE increases relative to the case in
which the desalination infrastructure is warranted or already in place, as assumed in
Figure 2b.
To conclude, we show that overlooking the effect of desalination on the supplied-
water salinity leads to higher water prices, lower desalination, and lower consumer
surplus, whereas the water suppliers’ profits increase. Moreover, the establishment of
desalination infrastructures may be wrongly perceived as economically unwarranted.
Thus, in a dynamic framework, where water demands increase over time, the
development rate of desalination capacities will be slower under SE than under SI.
3. Empirical Model of Israel’s Water Economy
Our objective is to evaluate empirically the economic implications of ignoring the salinity
impact of large-scale desalination in the design of Israel’s water economy.
3.1. Israel’s Water Economy
Israel faces three water-management challenges: first, while precipitation is relatively
abundant in the north, the population is concentrated in the center, and most of the
agricultural lands are located in the south; second, whereas rainfall events occur only in
winter, summer is the main irrigation season; third, natural freshwater is scarce,
successive drought years are common, and water scarcity is steadily increasing due to
rapid population growth (Kislev, 2011).
16
Israel has confronted these challenges by establishing a complex water-distribution
network that spans most of the country’s regions, in particular based on a national water
carrier that essentially turns almost the entire state into a single basin in terms of water
management. Severe water scarcity motivated the exploitation of brackish water and
TWW for irrigation, and in recent years, extensive seawater desalination has been
employed (Burn et al., 2015; Martínez-Alvarez et al., 2016) (see Appendix A). However,
desalination capacities were primarily designed to meet the growing water demand for
domestic uses, whereas the impact of desalination on irrigation-water salinity was not
considered explicitly (see Israel Water Authority, 2012a).
3.2. Empirical Model
By virtue of the Israeli Water Law (Israel Ministry of National Infrastructures, 1959),
water is a public property that is centrally managed by the government, which designs
water-supply infrastructures and sets administrative water prices and quotas to control
consumption; accordingly, the model’s objective is to characterize the optimal levels of
these policy instruments from the point of view of a welfare-maximizing benevolent
government.
Our model is based on a partial-equilibrium setup, integrating a water-distribution
module and an agriculture module, as depicted schematically in Figure 3. Adopting a
holistic approach (Brouwer & Hofkes, 2008), the variables of both modules are solved
simultaneously. The water-distribution module determines the allocation of water from
sources to regions of urban and agricultural consumers, sets the development trajectories
of infrastructure capacities, and computes the salinities, the shadow values of constraints,
17
and (assuming price-based water allocations) the efficient water prices throughout the
water-distribution network during the simulated period. The agriculture module
characterizes the optimal allocation of agricultural land across crops in each of the
agricultural regions subject to constrained regional land, foreign-labor quotas, and the
quantity and salinity of the water allocated to that region by the water-distribution
module. The irrigation water’s salinity affects crop yields in relation to crops’ tolerance
to salinity. In addition, the agricultural module includes demand functions for vegetative
agricultural products, such that the prices of those products constitute equilibria in the
local markets for fresh fruit and vegetables—the latter protected by import tariffs.
Figure 3 about here
We calibrate the model to a base year (2015) and run it for a 30-year period. The
demands for urban water and agricultural products shift along the years in relation to a
projected population growth—this incentivizes the extension of water-supply
infrastructures, particularly the supply of desalinated water, which affects the irrigation-
water salinity and thereby yields optimal agricultural land allocation, equilibrium prices
and quantities in the different markets for vegetative agricultural products, and the
allocation of surpluses among the urban-water users, farmers, consumers of agricultural
products, and water suppliers.
The model is programmed in GAMS (General Algebraic Modeling System), with
links to input-data and output-data Excel files (see supplemental materials), and solves
simultaneously for all variables throughout the entire planning horizon. The GAMS code
describes the model components in detail; here, we outline the main empirical elements.
18
3.2.1. Water-Distribution Module
The water-distribution module extends the hydro-economic model MYWAS (Multi-Year
Water Allocation System) (Fisher & Huber-Lee, 2011; Reznik et al., 2017), which is an
Israeli multiyear version of the one-period WAS (Water Allocation System) model
developed in the 1990s for the areas of Israel, Jordan and the Palestinian Authority
(Fisher et al., 2005). Appendix B presents schemes of the water network embedded in
MYWAS. There are 19 naturally enriched freshwater stocks (15 aquifers, the Sea of
Galilee, and 3 regional arrays of artificial reservoirs), 5 seawater-desalination plants in
the center of the country, 4 non-enriched brackish-water aquifers which are connected to
desalination plants, 18 wastewater-treatment plants (WWTPs) that apply secondary
treatment, and 1 which applies tertiary treatment to the sewage of the Tel Aviv
metropolis. Water users include 21 urban regions and 18 agricultural zones. Urban zones
obtain freshwater for domestic and industrial uses from natural freshwater sources,
desalinated seawater and desalinated brackish water, and generate sewage outflows that
undergo mandatory treatment at the WWTPs. The agricultural zones can consume
irrigation water from all sources. The prevailing base-year water system includes 163
freshwater pipelines and 74 pipelines for wastewater and brackish water.
We introduce infrastructures that are nonexistent in the base year, the timing and
extent of which can be set as determined endogenously; these include an optional
desalination plant in the northwest region of Acre, 12 pipelines that connect seawater-
desalination plants directly to agricultural areas located close to the Mediterranean
shoreline, and deliveries of desalinated TWW to agricultural zones (which necessitates
tertiary wastewater pretreatment). For the wastewater-desalination activities we introduce
19
an output/input rate parameter of 0.85, meaning that the brine needed to be disposed of
constitutes 15% (Pérez-González et al., 2012). We also allow discharge of TWW from
WWTPs to the environment (at zero cost or benefit), conditional on being reclaimed to
the level of tertiary treatment to meet regulated quality standards. Together with these
potential activities, the water network includes 118 nodes, connected by 289 pipelines.
The extractions from naturally enriched freshwater sources are limited by stock
constraints. Let (𝑗 = 1,… ,19) denote a freshwater-source node, and 𝑤𝑡𝑗 (m3 year-1) be the
extraction from source 𝑗 during year 𝑡. The amount 𝑤𝑡𝑗 is limited by the extractable stock
�̅�𝑡𝑗 (m3 year-1), which is a state variable defined by �̅�𝑡
𝑗= max(0, 𝑅𝑡−1
𝑗− �̅�𝑡−1
𝑗− 𝑒𝑡−1
𝑗),
where 𝑅𝑡−1𝑗
(m3 year-1) is the previous year’s recharge, and 𝑒𝑡−1𝑗= max(0, �̅�𝑡−1
𝑗+ 𝑅𝑡−1
𝑗−
𝑤𝑡−1𝑗− �̅�𝑗) (m3 year-1) is the spillover from the source to the environment when the stock
exceeds its maximum extractable content �̅�𝑗 (m3 year-1). In addition, we set a minimum
extractable stock for the last period, 𝑏𝑇+1𝑗
, such that �̅�𝑇+1𝑗≥ 𝑏𝑇+1
𝑗.
The water salinity is defined for each pipeline as the average salinities of the inflows
into the pipe, weighted by the respective inflow volumes. The source salinities are 1 dS
m-1 for freshwater from naturally enriched sources, 0.25 dS m-1 for desalinated water
(Yermiyahu et al., 2007), and 4 dS m-1 for brackish water. The salinity of freshwater
pumped from the Sea of Galilee decreases linearly with the lake's water stock. Pursuant
to regulations, the salinity of urban inflows is constrained to not exceed 1.4 dS m-1. The
salinity of the sewage produced in any urban region is 0.7 dS m-1 higher than the salinity
of the inflow into that region (Israel Water Authority, 2012b).
Variable and fixed water-supply costs of all infrastructural elements are taken from
Reznik et al. (2017). Note that the desalination cost of TWW ($0.63 m-3 on average) is
20
higher than that of seawater ($0.56 m-3) due to the multiple TWW-desalination
pretreatments and the need to dispose of the brine produced by plants located away from
the seacoast. To define the benefits of urban-water users we denote by 𝑖 (𝑖 = 1,… ,21) an
urban-region node, and by 𝑤𝑡𝑖 (m3 year-1), the respective water consumption. The total
benefits associated with 𝑤𝑡𝑖 equal the integrated inverse constant-elasticity demand
function 𝑉𝑡𝑖(𝑤𝑡
𝑖) = (𝜂 + 1)−1𝜐𝑡𝑖(𝑤𝑡
𝑖)𝜂+1
($ year-1), where 𝜂−1 is the demand elasticity
and 𝜐𝑡𝑖 is computed for any year 𝑡 by 𝜐𝑡
𝑖 = 𝑝0𝑖 (𝑤0
𝑖(1 + 𝜌)𝑡)−𝜂
, wherein 𝜌 is the
population-growth rate and 𝑝0𝑖 ($ m-3) is the observed base year (𝑡 = 0) urban-water
price. The parameter 𝜂 = −0.1 is taken from Bar-Shira et al. (2007).
3.2.2. Agriculture Module
Our analysis incorporates the 55 main crops grown by the Israeli agricultural sector on
about 300,000 ha, supplying vegetative products to the processing industry, export, and
the local fresh-produce markets. Nearly 60% of the arable area is devoted to high-value
fruit and vegetable crops (Israel Central Bureau of Statistics, 2019), requiring intensive
irrigation and a large labor force; the latter is highly dependent on foreign workers
(Kemp, 2010), who are allocated to farmers based on cropping-acreage declarations.
Whereas most of the field-crop outputs (particularly grains) are exempted from import
tariffs, the production of fruit and vegetables is protected by import tariff-rate quotas
(Finkelshtain & Kachel, 2009; Finkelshtain et al., 2011); we assume that the local-market
prices and quantities of fruit and vegetables constitute a competitive equilibrium.
Figure 4 about here
21
Apparently, the fresh-product crops grown in Israel are also relatively sensitive to
salinity. Figure 4 presents the aggregate agricultural land, water use, and production value
of the 55 crops in the base year, categorized into production to the local market,
processing industry, and export. In addition, each value is separated into four crop
bundles that classify the crops according to their salinity tolerance (Maas & Hoffman,
1977). Consider the salinity-sensitive and moderately sensitive crop bundles delivered to
the local market, where the demand is steadily growing due to population growth, and
where prices may rise due to the presence of import tariffs: while only 20% of the total
arable land in the country is allocated to these two bundles (Figure 4a), their water
consumption constitutes 46% of the total irrigation-water use (Figure 4b), and their
production value amounts to 59% (Figure 4c). These patterns can potentially incentivize
large allocations of desalinated water to the agricultural sector to reduce irrigation-water
salinity, increase the yields and per-hectare profits of these crops, and in turn, the land
allocated to them and their total production value. To capture these effects, we base the
agriculture module on the VALUE (Vegetative Agriculture Land-Use Economics) model.
VALUE is a positive mathematical programming (PMP) partial-equilibrium model
of Israel’s agriculture, used to analyze rural landscape amenities (Kan et al., 2009),
organic-waste policies (Kan et al., 2010; Raviv et al., 2017), climate change (Palatnik et
al., 2011; Zelingher et al., 2019), and water management (Baum et al., 2016; Kan &
Rapaport-Rom, 2012). The decision variables in VALUE are the cultivated lands
allocated to the 55 crops in each of the 18 nodes specified in MYWAS as agricultural
water-consumption regions. We denote by 𝑥𝑜𝑡𝑎 (ha) the land assigned in year 𝑡 to crop 𝑜
22
(𝑜 = 1, … ,55) in agricultural region 𝑎 (𝑎 = 1, … ,18). The output 𝑦𝑜𝑡𝑎 (ton ha-1 year-1) is
given by the production function
𝑦𝑜𝑡𝑎 (𝑤𝑜
𝑎, 𝑠𝑜𝑡𝑎 ) =
�̅�𝑜𝑎
1+𝛼𝑜1𝑎 (𝛼𝑜5
𝑎 𝑠𝑜𝑡𝑎 +𝛼𝑜2
𝑎 (𝑤𝑜𝑎)𝛼𝑜3
𝑎)𝛼𝑜4𝑎 (9)
where 𝑤𝑜𝑎 (m3 ha-1 year-1) is the total water available to the crop, including irrigation
water and rainfall during the crop’s growing season, both of which are assumed constant;
𝑠𝑜𝑡𝑎 (dS m-1) is the salinity of 𝑤𝑜
𝑎, which is a weighted average of the salinities of the
water supply set by MYWAS for irrigation in region 𝑎 and the rainfall salinity (assumed
to be 0.1 (dS m-1)); �̅�𝑜𝑎 (ton ha-1 year-1) is the maximum potential yield obtainable under
zero salinity and no water deficit; 𝛼𝑜1𝑎 through 𝛼𝑜5
𝑎 are crop- and region-specific
parameters.
We develop the production functions by a four-stage meta-analysis procedure. First,
we use the yield–water salinity model developed by Shani et al. (2007) to generate a
dataset of plant-level relative yields (i.e., relative to �̅�𝑜𝑎) under different combinations of
water and salinity levels, adopting crop salinity-tolerance parameters from Tanji and
Kielen (2002), and region-specific soil and climate parameters from Kan and Rapaport-
Rom (2012); second, to account for intra-field spatial irrigation heterogeneity, we
calculate field-level relative-yield levels by applying the log-normal distribution function
(Knapp, 1992), calibrated for a Christiansen uniformity coefficient of 85; third, we apply
a nonlinear regression to the generated dataset to estimate the parameters 𝛼𝑜1𝑎 through
𝛼𝑜5𝑎 ; finally, we calibrate �̅�𝑜
𝑎 using the observed base-year yield 𝑦𝑜0𝑎 and salinity 𝑠𝑜0
𝑎 :
�̅�𝑜𝑎 = 𝑦𝑜0
𝑎 (1 + 𝛼𝑜1𝑎 (𝛼𝑜5
𝑎 𝑠𝑜0𝑎 + 𝛼𝑜2
𝑎 (𝑤𝑜𝑎)𝛼𝑜3
𝑎)𝛼𝑜4𝑎
). The resultant functions exhibit the
23
expected properties of 𝜕𝑦
𝜕𝑤> 0 and
𝜕𝑦
𝜕𝑠< 0. In addition,
𝜕2𝑦
𝜕𝑠2> 0, meaning that the higher
the salinity of the water applied to a crop, the lower the salinity’s marginal damage.
The statewide production of each crop 𝑜 in year 𝑡, 𝑌𝑜𝑡 = ∑ 𝑥𝑜𝑡𝑎 𝑦𝑜𝑡
𝑎18𝑎=1 (ton year-1), is
allocated to the local food-processing industry and export markets based on the respective
constant market shares 𝜇𝑜𝐿, 𝜇𝑜
𝐼𝑛 and 𝜇𝑜𝐸𝑥, where 𝜇𝑜
𝐿 + 𝜇𝑜𝐼𝑛 + 𝜇𝑜
𝐸𝑥 = 1. The prices of crop
𝑜’s outputs supplied to the industry and to export, denoted, respectively, 𝑝𝑜𝐼𝑛 and 𝑝𝑜
𝐸𝑥 ($
ton-1), equal their corresponding (exogenous) import prices, whereas the price of the
local-market product, 𝑝𝑜𝑡𝐿 , is determined in equilibrium subject to the import-tariff-rate
quotas. We use a constant-elasticity demand function to represent the benefits to local
consumers of crop 𝑜’s products, 𝑉𝑜𝑡(𝑌𝑜𝑡, 𝐼𝑚𝑜𝑡) = 𝐴𝑜𝑡(𝜇𝑜𝐿𝑌𝑜𝑡+𝐼𝑚𝑜𝑡)
𝜗𝑜+1
𝜗𝑜+1 ($ year-1), in which
𝐼𝑚𝑜𝑡 (ton year-1) is import, 𝜗𝑜−1 is the demand elasticity, and 𝐴𝑜𝑡 = 𝑝𝑜0
𝐿 ((𝜇𝑜𝐿𝑌𝑜𝑡 +
𝐼𝑚𝑜𝑡)(1 + 𝜌)𝑡)−𝜗𝑜
($ year-1) is an inverse-demand-function parameter, calibrated for the
base year based on the observed local price 𝑝𝑜0𝐿 and output 𝑌𝑜𝑡. The total import is given
by 𝐼𝑚𝑜𝑡 = 𝐼𝑚𝑜𝑡0 + 𝐼𝑚𝑜𝑡
1 , with 𝐼𝑚𝑜𝑡0 and 𝐼𝑚𝑜𝑡
1 denoting the amounts imported free of
tariff and with the tariff, respectively, where 𝐼𝑚𝑜𝑡0 cannot exceed the free-of-tariff quota
𝐼𝑚̅̅̅̅ 𝑜0. For the import price of each crop, we select the country from which the import cost
(including transportation to Israel) is the lowest. The cropping acreage, per-hectare
yields, imports, prices and tariffs are from the Israel Ministry of Agriculture and Rural
Development, and the crop-specific output-demand elasticities (𝜗𝑜) are adopted from
Fuchs (2014).
Following the PMP approach, we assume a quadratic regional profit function, 𝜋𝑜𝑡𝑎 =
𝑥𝑜𝑡𝑎 (𝑝𝑜𝑡𝑦𝑜𝑡
𝑎 − 𝛄𝑜𝑎 − 𝜙𝑜
𝑎 − 𝛿𝑜𝑎𝑥𝑜𝑡𝑎 ) ($ year-1), where 𝑝𝑜𝑡 = 𝜇𝑜
𝐿𝑝𝑜𝑡𝐿 + 𝜇𝑜
𝐼𝑛𝑝𝑜𝐼𝑛 + 𝜇𝑜
𝐸𝑥𝑝𝑜𝐸𝑥 ($
24
ton-1) is the average price of crop o, 𝛄𝑜𝑎 ($ ha-1 year-1) is a vector of input costs, and 𝜙𝑜
𝑎 ($
ha-1 year-1) and 𝛿𝑜𝑎 ($ ha-2 year-1) are parameters representing unobservable costs,
calibrated by the two-stage procedure proposed by Howitt (1995). The calibration
accounts for the base-year constraints of regional agricultural land, foreign labor, and
water: ∑ 𝑥𝑜0𝑎55
𝑜=1 ≤ 𝑥𝑎, ∑ 𝑥𝑜0𝑎 𝑓𝑙𝑜
𝑎55𝑜=1 ≤ 𝑓𝑙𝑎, and ∑ 𝑥𝑜0
𝑎 𝑤𝑜𝑎55
𝑜=1 ≤ 𝑤0𝑎, respectively, where
𝑥𝑎 (ha) is region 𝑎’s total arable land, 𝑓𝑙𝑜𝑎 (day ha-1 year-1) and 𝑓𝑙𝑎 (day year-1) are,
respectively, crop 𝑜’s consumption and regional aggregate quota of foreign labor, and 𝑤0𝑎
is the base-year total irrigation water allocated to the region.
3.2.3. Integrated Model
The integrated MYWAS–VALUE model solves the problem expressed in equation (1),
the elements of which incorporate the empirical specifications of benefits, costs, and
constraints described above. We employ a social discount rate (𝑟) of 3.5%, as suggested
by Nordhaus (2007), and adopt the Israel Central Bureau of Statistics (2014) prediction of
1.8% annual population growth rate (𝜌). As an end condition, we mandate retaining a
minimum of 5% of the extractable stock from each naturally enriched freshwater source.
The historical average annual precipitation and enrichment of natural freshwater sources
(taken from Weinberger et al., 2012) are assumed for every year during the simulated
period. Monetary values are in 2015 US dollars, discounted to the 15th year (2030).
Note that while the demands for urban water and agricultural products are calibrated
for 2015 based on the assumption of market-clearing prices, the observed base-year water
prices and the associated water distributions and infrastructures are not optimal! This is
because of the Israeli Balanced Budget Water Economy legislation (Reznik et al., 2016);
25
therefore, as shown in Appendix C, the model does not reproduce the observed values of
the decision variables in the base year. Thus, the base-year conditions do not serve as a
reference in our analyses. Instead, we compare the optimal solutions under the SI and SE
scenarios.
While the solution for the SI case is obtained by solving the problem in equation (1),
the SE scenario requires a two-stage procedure: first, we run the model with the water
salinity in each agricultural region fixed at its base-year level (i.e., in equation 9, 𝑠𝑜𝑡𝑎 =
𝑠𝑜0𝑎 for all 𝑡 = 1,…30); the output of this simulation is an infrastructure-development
plan that the planner erroneously considers optimal given her or his presumption of
nonresponsive irrigation-water salinity. However, as already noted in the theoretical
analysis, salinity will change, and in turn affect crop production, agricultural output
prices, farming profitability, land use, and surpluses of producers and consumers in the
agricultural sector. Therefore, in the second stage, we rerun the model while allowing
salinity to change, but at the same time forcing the development of infrastructures to
follow the infrastructure plan that resulted from the first stage. Thus, the SE scenario
represents the expected evolution of the water and vegetative-agriculture sectors under
efficient prices, given a non-optimal water-infrastructure blueprint.
4. Economic Implications of Externalizing Salinity
We first evaluate the differences between the SI and SE scenarios with respect to water
supplies, salinities, prices, and surplus allocation across sectors. Then, we assess how
these differences are affected by changes in precipitation and in the agricultural product
26
import tariffs and foreign-worker quotas. Appendix D provides detailed results tables;
here, we present the main findings.
Figure 5 about here
4.1. Internalized versus Externalized Salinity
Figure 5 presents optimal trajectories of statewide water supply to the agricultural regions
and discharge of tertiary-TWW to natural waterways under the two scenarios. The SI
optimal solution suggests massive delivery of desalinated water to the agricultural zones,
mostly from seawater-desalination plants, and to a lower extent by desalinating TWW
(Figure 5a). It is found optimal to install 8 out of the 12 optional pipelines connecting
seawater-desalination plants directly to agricultural regions, as well as the optional
seawater-desalination plant in the north of the country. Irrigation with natural freshwater
and secondary-TWW is stable throughout the period, seawater desalination for irrigation
increases slightly with time, and most of the growing amount of sewage produced by the
urban zones (not shown) is discharged to nature after tertiary wastewater treatment.
Compared to the SI scenario, the total irrigation water under the SE scenario is 45%
lower (Figure 5b), particularly because of the lower capacity of the infrastructures
supplying desalinated seawater to the agricultural zones, and because desalination of
TWW becomes unwarranted due to the higher costs relative to that of seawater
desalination. Concomitantly, a larger share of the TWW is used for irrigation, such that
lower amounts are discharged to nature. Moreover, the water-supply trends differ from
the SI solution: seawater desalination for agriculture declines over time, continuously
27
replaced by the growing amounts of TWW produced in the urban zones and by
freshwater from natural sources.
Figure 6 presents per-annum statewide averages of water supply, use and salinity
under the two scenarios. Clearly, the total water deliveries (Figure 6b) are lower under
SE, and the average irrigation-water salinity (Figure 6c) is 0.2 (dS m-1) higher due to the
larger shares of natural freshwater and TWW in the supplied water (Figures 5a, 5b, and
6a).
Figure 6 about here
Figure 7 reports average shadow values of water availability at the sources (Figure
7a), infrastructure-capacity constraints (Figure 7b), water prices in the urban and
agricultural zones (Figure 7c), and shadow values of the salinity of the water sources
(Figure 7d). In the SE case, water is scarcer due to the lower water-infrastructure
capacity; hence, the higher water prices compared to SI. Notice the switch in sign of the
shadow value of the inflow–outflow balance constraint imposed on the WWTP (Figure
7a), meaning that instead of subsidizing TWW to encourage farmers to consume it under
SI, farmers are willing to pay for TWW in the SE case. In addition, while irrigation
salinity is higher under SE (Figure 6c), the shadow value of the salinity in the irrigation
water is slightly lower (Figure 7d), which is attributed to the aforementioned positive sign
of the second derivative of the production function with respect to salinity (𝜕2𝑦
𝜕𝑠2> 0).
Also notable is the relatively large negative shadow value of the salinity of the
desalinated TWW under SI, which can be explained by the fact that this water source
supplies low-salinity water only for agricultural irrigation, whereas the salinity of the
TWW supplied to agricultural regions is high, and desalinated brackish water and
28
seawater are also supplied to the urban users who are assumed immune to salinity
changes (up to the maximum urban-water salinity limit of 1.4 (dS m-1)). Thus, as TWW
desalination vanishes under the SE scenario, the share of the other sources rises and
therefore, their salinity shadow values become higher.
Figure 7 about here
As already noted, we assume that prices are set efficiently, and use the demand
functions and shadow values to compute the water and agriculture-product prices, and the
corresponding allocation of surpluses across sectors. Figure 8a presents average yearly
surplus allocations under the SI and SE scenarios (consumer surpluses are normalized to
0 under the SI scenario). As shown analytically, all sectors except for water suppliers face
a welfare loss under the SE vs. SI scenario, where the overall annual deadweight loss is
$366 million. On average, this damage amounts to about $1,200 per hectare of arable
land, caused by the salinity rise (of 0.2 (dS m-1) on average, Figure 6c), of which farming
losses are $1,087 ha-1 year-1 (29% of farmers’ profit under the SI scenario).
Figure 8 about here
4.2. Sensitivity Analyses
We commence by analyzing a change in precipitation. On a per-annum average, Israel’s
arable lands obtain 375 mm and 333 mm of water from naturally enriched freshwater
sources and direct rainfall, respectively. However, climatological studies (Bentsen et al.,
2013; Gent et al., 2011; Watanabe et al., 2010) predict a precipitation reduction of 10–
30% throughout Israel in the coming decades. In Figure 8b, we present the impact of a
20% reduction in precipitation for every year of the 30-year period on the allocation of
29
surpluses under the SI and SE scenarios. All sectors except for the water suppliers lose
from the change, farmers in particular. The overall deadweight loss is 37% and 38%
under the SI and SE scenarios, respectively. Regarding water management (not shown),
in both scenarios, increasing seawater desalination is the main means of offsetting the
reduction in availability of natural freshwater sources, as well as cuts in agricultural
irrigation.
As already noted, Israel employs import tariffs to support local agriculture and
controls the allocation of foreign labor. In Figures 8c and 8d we present, respectively, the
surplus change caused by the abolishment of import tariffs on vegetative products and
dismissing the control of foreign labor by quotas (for the latter, we assume no change in
the regulated minimum wage of the foreign workers or in the crop-specific per-hectare
employment of foreign and local workers). Both policy changes effectively transfer
surpluses from farmers to consumers of agricultural products in both the SI and SE cases,
raising the overall welfare, with a larger effect under the SE scenario.
The agricultural intervention policies employed in Israel are continuously criticized
economically (Organization for Economic Co-operation and Development [OECD],
2018), and are the subject of public and political debate (Hendel et al., 2017). The overall
producer-support estimate for Israel is 17.7%, slightly below the OECD average of 19.2%
(OECD, 2019). However, the share of domestic price support, border measures, and other
market-distorting interventions is relatively high (91%); therefore, the effect of changes
in such policies is expected to be larger than in other countries with similar semiarid
conditions (e.g., Australia, Spain, and California).
30
5. Limitations and Extensions
This study shows that, under the specific circumstances of Israel, large-scale supply of
desalinated water for irrigation is economically warranted, and overlooking the impact of
desalination on irrigation-water salinity entails significant deadweight loss. Nevertheless,
“no model solves all problems” (Draper et al., 2003, p. 156), and the economic valuations
provided herein may vary with the inclusion of a range of exempted factors; a few
examples follow.
Our ability to introduce salinity impacts on agricultural outputs into our hydro-
economic model builds on decades of theoretical and experimental agronomic research.
However, aside from irrigation, salinity has additional economic implications, such as
health effects associated with drinking water (Dasgupta et al., 2016). Moreover, salinity
is but one of a large set of water-quality measures that determine the economic value of
water in various water uses. For example, the contents of Mg2+ and SO42– in desalinated
seawater are lower than recommended for drinking and irrigation water (Yermiyahu et
al., 2007), and desalination removes nutrients that might otherwise save on fertilization
expenses (Ben-Gal et al., 2009; Dawson & Hilton, 2011). On the other hand, TWW
desalination also eliminates various contaminants (Gur-Reznik & Dosoretz, 2015) that
damage irrigation systems (Tarchitzky et al., 2013) and cause environmental and health
risks (Fatta-Kassinos et al., 2011; Kasprzyk-Hordern et al., 2009) which, in turn, may
affect the demand for agricultural products (Messer et al., 2017). In addition, while our
model allows for environmental discharge of tertiary-TWW and spillovers from
31
freshwater aquifers, we do not assign values to these flows because there are as yet no
monetary valuations of the associated impacts on ecosystem services (Tsur, 2020).
Our modeling approach is suited to centrally managed water systems, as in Israel.
We assume benevolent policy makers; however, centralization attracts political pressure
to bend policies in favor of interest groups. Such distortions can be captured in a
political-equilibrium analytical framework (Finkelshtain & Kislev, 1997). For the case of
decentralized water systems, one should account for imperfections of water markets and
water-right allocations, asymmetric information, and transition and transaction costs
(Garrick et al., 2013; Richter et al., 2013).
Finally, our model does not explicitly incorporate uncertainty with respect to key
factors, such as population growth, climate conditions, and environmental effects, some
of which may be associated with deep uncertainty. Moreover, we maximize a single
objective, whereas water systems may involve multiple objectives. The analysis provided
here may be extended by employing many objective robust decision-making procedures
(e.g., Kasprzyk et al., 2013; Moallemi et al., 2020; Trindade et al., 2017).
Acknowledgments
This study was partly funded by the Israel Ministry of Agriculture and Rural
Development (grant number 12-04-0011) and the Center for Agricultural Economics
Research at the Hebrew University of Jerusalem. The authors thank the Editor, Associate
Editor, and three anonymous reviewers for valuable comments, and to Yael Kachel from
the Israel Ministry of Agriculture and Rural Development for providing data. The
32
empirical hydro-economic model developed in this study (entitled MYWAS-VALUE) is
available at: 10.5281/zenodo.3702053.
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Yermiyahu, U., Tal, A., Ben-Gal, A., Bar-Tal, A., Tarchitzky, J., & Lahav, O. (2007).
Rethinking desalinated water quality and agriculture. Science, 318(5852), 920–921.
Zarzo, D., Campos, E., & Terrero, P. (2013). Spanish experience in desalination for
agriculture. Desalination and Water Treatment, 51(1–3), 53–66.
Zelingher, R., Ghermandi, A., De Cian, E., Mistry, M., & Kan I. (2019). Economic
impacts of climate change on vegetative agriculture markets in Israel. Environmental
and Resource Economics, 74(2), 679–696.
39
Figure 1. A water economy with urban and agricultural zones in which water consumers
obtain a mixture of groundwater and desalinated water.
Groundwater
Desalination
Urban Zone
Agriculture Zone
�̅�𝑔, 𝑠𝑔, 𝑐𝑔
𝑤𝑔, 𝑠𝑔
𝑠𝑑 , 𝑐𝑑 , 𝐶𝑑𝑤𝑑 , 𝑠𝑑
𝑤𝑢, 𝑠
𝑤𝑎, 𝑠
𝑉𝑢 𝑤𝑢
𝑉𝑎 𝑤𝑎, 𝑠
40
𝑉𝑤𝑢 𝑤𝑢 - Inverse urban demand
𝑉𝑤 𝑤, 𝑠 - Inverse aggregate demand under average salinity 𝑠
𝑉𝑤 𝑤, 𝑠𝑔 - Inverse aggregate demand under groundwater salinity 𝑠𝑔
𝑉𝑤 𝑤, 𝑠𝑔
𝑉𝑤𝑢 𝑤𝑢
�̅�𝑔𝑤 = 𝑤𝑔 +𝑤𝑑
𝑐𝑑
𝑐𝑔
𝑝SI
𝑝
𝑤SI
𝑉𝑤 𝑤, 𝑠
𝑤𝑔 𝑤𝑑 0
Salinity Internalized
B
C
𝑉𝑠𝑎 𝑤𝑎, 𝑠
�̅�𝑔 𝑠𝑑 − 𝑠𝑔
𝑤SI 2
(a)
𝑉𝑠𝑎 𝑤𝑎, 𝑠
𝑤𝑑 𝑠𝑑 − 𝑠𝑔
𝑤SI 2+ 𝜆𝑔
A
Consumer surplus = A+B
Producer surplus = C-B
Welfare = A+C
Consumer surplus = D
Producer surplus = E
Welfare = D+E
Deadweight loss due to disregarding salinity = F
𝑉𝑤 𝑤, 𝑠𝑔
�̅�𝑔𝑤 = 𝑤𝑔 +𝑤𝑑
𝑐𝑑
𝑐𝑔
𝑝
𝑤SE
𝑉𝑤 𝑤, 𝑠
𝑤𝑔 𝑤𝑑 0
Salinity Externalized
E
(b)
𝑝SE=
D
F
𝑉𝑤𝑢 𝑤𝑢
41
Figure 2. Schematic illustration of water prices, quantities and surplus allocations under
(a) the Salinity-Internalized scenario, (b) the Salinity-Externalized scenario, and (c)
where water-use benefits from desalinated water exceed the desalination variable and
fixed costs under the Salinity-Internalized scenario, but not under the Salinity-
Externalized scenario.
𝑉𝑤 𝑤, 𝑠𝑔
�̅�𝑔𝑤 = 𝑤𝑔 +𝑤𝑑
𝑐𝑑
𝑐𝑔
𝑝
𝑤SE
𝑉𝑤 𝑤, 𝑠
𝑤𝑔 𝑤𝑑 0
Desalination Fixed Cost Effect
H
(c)
𝑝SEG
𝑉𝑤𝑢 𝑤𝑢
𝑤SI
Consumer surplus = G
Producer surplus = H
Welfare = G+H
42
Figure 3. Scheme of the integrated water and agriculture modules of the hydro-
economic model.
Seawater
Brackish
Water
Aquifers
Natural
Freshwater
Sources
Water Module
Agriculture Module
Labor
Land
Local Market
Export
Industry
Agricultural Zones
Import
Urban ZonesWater flow
Agriculture output
Agriculture input
TWW
Desalination
Wastewater Secondary Treatment
Precipitation
Environment
Desalination Wastewater Tertiary Treatment
43
Figure 4. Base-year statewide allocation of (a) land use, (b) water consumption, and (c) production value across four crop bundles
with different salinity-tolerance levels, separated into production for the local fresh-produce, industry and export markets.
0
20
40
60
80
100
120
140
160
180
200
Lo
cal
Indu
stry
Ex
port
10
3h
ecta
re
Land
Tolerant
Moderately Tolerant
Moderately Sensitive
Sensitive
(a)
0
100
200
300
400
500
600
700
Lo
cal
Indu
stry
Ex
port
10
3m
3year
-1
Water(b)
0
500
1,000
1,500
2,000
2,500
3,000
3,500
Lo
cal
Indu
stry
Ex
port
10
6$
year
-1
Production Value(c)
44
Figure 5. Optimal trajectories of statewide annual water supplies to agriculture and
discharges of tertiary-TWW to nature under (a) the Salinity-Internalized and (b) the
Salinity-Externalized scenarios.
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
(10
6m
3year
-1)
Year
Salinity Internalized(a)
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30
(10
6m
3 y
ear
-1)
Year
Salinity Externalized (b)
Fresh Groundwater Seawater Desalinated
Brackish Water Desalinated TWW Desalinated
Secondary TWW to Agriculture Tertiary TWW to Nature
Total Agriculture Total Urban
45
Figure 6. Optimal average (a) annual water supplies, (b) annual water uses, and (c)
supplied-water salinities under the Salinity-Internalized and Salinity-Externalized
scenarios.
0
200
400
600
800
1000
1200
Natu
ral F
resh
water
Tre
ated W
astew
ater
Desa
linated
Seaw
ate
r
Desa
linated
Brac
kish
Desa
linated
TW
W
10
6m
3year-1
Water Supply
Salinity Internalized
Salinity Externilized
(a)
0
200
400
600
800
1000
1200
Urb
an
Agric
ultu
re
Natu
re
10
6m
3year-1
Water Use(b)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Urb
an
Agric
ultu
re
Natu
re
dS
m-1
Water Salinity(c)
46
Figure 7. Average (a) water-source shadow values, (b) shadow values of infrastructures,
(c) water prices at consumption points, and (c) shadow values of water-source salinity
(per supplied cubic meter of water) under the Salinity-Internalized and Salinity-
Externalized scenarios.
-0.2
0
0.2
0.4
0.6
0.8
1
Natu
ral F
resh
water
Tre
ated W
astew
ater
Desa
linated
Seaw
ate
r
Desa
linated
Brac
kish
Desa
linated
TW
W
$ m
-3
Water Shadow
Value
Salinity Internalized
Salinity Externilized
(a)
0
0.1
0.2
0.3
0.4
0.5
Natu
ral F
resh
water
Tre
ated W
astew
ater
Desa
linated
Seaw
ate
r
Desa
linated
Brac
kish
Desa
linated
TW
W
$ m
-3
Infastructure
Shadow Value(b)
0
0.3
0.6
0.9
1.2
1.5
1.8
Urb
an
Agric
ultu
re
$ m
-3
Water
Price(c)
-0.45
-0.4
-0.35
-0.3
-0.25
-0.2
-0.15
-0.1
-0.05
0
Natu
ral F
resh
water
Tre
ated W
astew
ater
Desa
linated
Seaw
ate
r
Desa
linated
Brac
kish
Desa
linated
TW
W
Agric
ultu
re
$ (
dS
m-1
)-1m
-3
Salinity Shadow
Value
(d)
47
Figure 8. (a) Average annual surplus allocation under the Salinity-Internalized and
Salinity-Externalized scenarios. Surplus change caused by (b) 20% reduction in
precipitation, and (c) and (d) policy reforms in which agricultural import tariffs and
foreign-labor quotas, respectively, are abolished.
-600
-300
0
300
600
900
1200
1500
Urb
an W
ate
r Con
sum
ers
Agri. P
rodu
ct Co
nsu
mers
Farm
ing
Pro
fits
Wate
r Sup
pliers
So
cial W
elfa
re
10
6$ y
ear-1
Surplus
Salinity Internalized
Salinity Externilized
(a)
-600
-500
-400
-300
-200
-100
0
100
200
Urb
an W
ate
r Con
sum
ers
Agri. P
rodu
ct Co
nsu
mers
Farm
ing
Pro
fits
Wate
r Sup
pliers
So
cial W
elfa
re
10
6$ y
ear-1
Surplus Change Due to
Precipitation Reduction(b)
-600
-400
-200
0
200
400
600
800
1000
1200
Urb
an W
ate
r Con
sum
ers
Agri. P
rodu
ct Co
nsu
mers
Farm
ing
Pro
fits
Wate
r Sup
pliers
So
cial W
elfa
re
10
6$ y
ear-1
Surplus Change Due to
Import Tariff Abolishment(c)
-400
-300
-200
-100
0
100
200
300
400
500
600
Urb
an W
ate
r Con
sum
ers
Agri. P
rodu
ct Co
nsu
mers
Farm
ing
Pro
fits
Wate
r Sup
pliers
So
cial W
elfa
re
10
6$ y
ear-1
Surplus Change due to Foreign-
Labor Quota Abolishment(d)
48
Appendix A. Water and Agricultural Production in Israel
Figure A1 presents the evolution of water sources and uses (Israel Water Authority,
2016), population growth and vegetative agricultural production (Israel Central Bureau of
Statistics, 2017) in Israel during the period 1996–2016. Fresh groundwater extractions
declined dramatically, and were partly substituted by seawater desalination (Figure A1a).
At the same time, the population increased by 50% (Figure A1c), generating larger
amounts of sewage, which was reclaimed (Figure A1a) and reused by irrigation (Figure
A1b). The population growth also increased the demand for food; however, while the
index of local vegetative agricultural production increased until 2010, it stabilized
thereafter.
49
.
Figure A1. Trends of (a) water sources, (b) water uses, and (c) population growth and vegetative agricultural production in Israel
during 1996–2016.
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
10
9m
3yea
r-1
Water Sources
Agri. Brackish Water
Agri. Treated Wastewater
Seawater Desalination
Natural Freshwater
(a)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
10
9m
3 y
ear-1
Water Uses
Agri. Brackish Water
Agri. Treated Wastewater
Agri. Freshwater
Urban Freshwater
(b)
80
90
100
110
120
130
140
150
160
5.0
5.5
6.0
6.5
7.0
7.5
8.0
8.5
9.0
Veg
. Agri. P
rod
uctio
n In
dex
Po
pu
lati
on
(10
6)
Population & Agri. Production
Population
Veg. Agri. Prod. Index
(c)
50
Appendix B. Schemes of the MYWAS Model
5000Zalmon
5001Menashe
5002 Metzer
5003 Rosh Haain
5004 Achisemech
5005 Holda
5006 Zohar
Natural Fresh
Water Sources
Urban
Demand
Nodes
Agricultural
Demand Nodes
Waste Water
Treatment
Plants
Sea Water and
Ground Water
Desalination
Plants
1101Hadera
1102Palmachim
1103Ashkelon
1100Carmel Coast
1105Negav
1104Southern
Coast
Model TopologyNational
Carrier
Junctions
1000Sea of Galilee
1002Western Kineret
GW
1003Western Galilee
1008Northern Coast
1009Central Coast
1006North Mountain
1010Central Mountain
1011Southern Coast
1012Negev Coastal GW
1013Southern Mountain
1001Golan
1004Lower Galilee
1005Eastern Aquifers
1015Arava
1014Negev Aquifer
1106Arava
1107Eilat
1007Carmel Coast
3114Jerusalem
3101Tzfat
3102Kineret
3105Jeezrael Valley
3100Golan
3104Haifa
3108Hadera
3109Sharon
3110Petah Tikva
3112Ramle
3113Rehovot
3111Tel Aviv
3115Ashkelon
3107Judea and Samaria
3116Negev
3106Jordan Valley
3103Acco
3117Arava
1212Southern
Coast
1216Negev
1218Arava
1211Shafdan
1215Negev Coast
1200Golan
1206Jordan Valley
1217Dead Sea
1205Western Galilee
1204Kishon
1207North Coast
1208Central Coast
1202Kineret
1201Tzfat
1203Beit Shean
1209Yarkon
1210Nesher
1213Judea and Samaria
1214Shfela
3001Eastern Galilee
3015Western
Negev
3016Lachish
3014Granot
3013Adolam
3012Modieen
3009Tel Aviv
3011Jerusalem
3007Sharon South
3010Lod
3006Hadera
3002Western Galilee
3005Carmel Coast
3003Lower Jordan
River
3004Jordan Valley
3008Judea and Samaria
3018Dead Sea
3019Arava
3017Ramat Negev
3000Golan
3020Eilat
Brackish and
Surface Water
Sources
Golan Local
WG Local
Eastern Local
Southern Coast
Brackish
Carmel Coast
Brackish
Negav Brackish
Arava Brackish
51
Rosh Haain
Achisemech
Holda
Zohar
Zalmon
Menashe
Metzer
Sea of GalileeWestern Kineret
GW
Hadera SWD
Northern Coast
Northern Mountain
Central Coast
Central Mountain
Ashkelon SWD
Negev Coastal GW
Southern Mountain
Palmachim SWD
Southern Coast GWD
Southern Coast
3001Eastern Galilee
3016Western Negev
3018Lachish
3015Granot
3014Adolam
3013Modieen
3010Tel Aviv
3012Jerusalem
3008Sharon South
3011Lod
3007Hadera
3002Western Galilee
3006Carmel Coast 3003
Lower Jordan River
3004Jordan Valley
3009Judea and Samaria
3005Dead Sea
3020Arava
3019Ramat Negev
3000Golan
3021Eilat
Golan GWGolan Local
Western GalileeWG Local
Lower Galilee
Eastern Aquifers
Eastern Local
Fresh water system
Carmel Coast
Arava
Negev Aquifer
Carmel Coast GWD
Negav GWD
Arava GWD Eilat S/GWD
52
Fresh and Brackish water for
Agriculture
3114Jerusalem
3101Tzfat
3102Kineret
3105Jeezrael Valley
3100Golan
3104Haifa
3108Hadera
3109Sharon
3110Petah Tikva
3112Ramle
3113Rehovot
3111Tel Aviv
3115Ashkelon
3107Judea and Samaria
3117Negev
3106Jordan Valley
Rosh Haain
Achisemech
Holda
Zohar
Zalmon
Menashe
Metzer
Sea of GalileeWestern Kineret
GW
Northern Coast
Northern Mountain
Central Coast
Central Mountain
Negev Coastal GW
Southern Mountain
Southern Coast
Brackish
Southern Coast
Golan GWGolan LocalWestern GalileeWG Local
Lower Galilee
Eastern Local
Carmel Coast
Arava
Negev Aquifer
Carmel Coast
Brackish
Negav Brackish
Arava Brackish
3103Acco
Eastern Aquifers
3118Arava
53
1200Golan
1206Jordan Valley
1214Dead Sea
1205Western Galilee
1204Kishon
1207North Coast
1208Central Coast
1212Southern Coast
1216Negev
1218Arava
Waste water system
3001Eastern Galilee
3016Western Negev
3018Lachish
3015Granot
3014Adolam
3013Modieen
3010Tel Aviv
3012Jerusalem
3008Sharon South
3011Lod
3007Hadera
3002Western Galilee
3006Carmel Coast
3003Lower Jordan
River
3004Jordan Valley
3009Judea and Samaria
3005Dead Sea
3020Arava
3019Ramat Negev
1211Shafdan
3000Golan
3021Eilat
1202Kineret
1201Tzfat
1203Beit Shean
1209Yarkon
1210Nesher
1213Judea and Samaria
1214Shfela
1215Negev Coast
3114Jerusalem
3101Tzfat
3102Kineret
3105Jeezrael Valley
3103Acco
3100Golan
3104Haifa
3108Hadera
3109Sharon
3110Petah Tikva
3112Ramle
3113Rehovot
3111Tel Aviv
3115Ashkelon
3107Judea and Samaria
3117Negev
3118Arava
3106Jordan Valley
54
Water-Distribution Network
55
Appendix C. Calibration Data vs. Optimization Results
Figure C1 presents the statewide patterns of Israel’s water economy for the first year of
the optimal solution under the Salinity-Internalized scenario in comparison to the
observed base-year calibration data.
Figure C1. (a) Water supplies, (b) water uses, (c) water prices, and (d) salinities of the
supplied water in the first year of the Salinity-Internalized scenario and the base-year
calibration data.
As already shown by Reznik et al. (2016), the water supply costs in Israel are
characterized by economies of scale. Since water prices are set subject to a regulatory
requirement to recover variable and fixed costs, water prices in the urban sector are higher
than their optimal counterparts (Figure C1c), and hence the larger water supply in the
Salinity-Internalized case relative to that of the base year (Figure C1a). The larger share
0
100
200
300
400
500
600
700
800
900
1000
Natu
ral F
resh
wate
r
Tre
ated
Waste
wate
r
Desa
linate
d S
eaw
ate
r
Desa
linate
d B
rack
ish
Desa
linate
d T
WW
10
6m
3year-1
Water Supply
Salinity Internalized
Calibration
(a)
0
200
400
600
800
1000
1200
1400
Urb
an
Agric
ultu
re
Natu
re
10
6m
3year-1
Water Use(b)
0
0.5
1
1.5
2
2.5
3
3.5
Urb
an
Agric
ultu
re
$ m
-3
Water Price(c)
0
0.5
1
1.5
2
Urb
an
Agric
ultu
re
Natu
re
dS
m-1
Water Salinity(d)
56
of desalinated water in the total water supply causes the lower salinity under the Salinity-
Internalized scenario (Figure B1d).
57
Appendix D. Results of the Salinity-Internalized and Salinity-Externalized Scenarios
Table D1
Per-Annum Statewide Average Water Volumes
Salinity
Internalized
Salinity
Externalized
All Water Consumers
Water Supply (106 m3 year-1)
Natural Freshwater 1,124 1,153
Brackish Groundwater 0 0
Brackish Groundwater Desalinated 106 63
Treated Wastewater 626 714
Treated Wastewater Desalinated 81 0
Seawater Desalinated 865 652
All 2,802 2,582
Water Consumption (106 m3 year-1)
Urban 1,263 1,242
Agriculture 1,149 9 8
Nature 390 3 2
All 2,802 2,5 2
Agricultural Sector
Water Supply (106 m3 year-1)
Natural Freshwater 262 270
Brackish Groundwater 0
Brackish Groundwater Desalinated 0 0
Treated Wastewater 236 373
Treated Wastewater Desalinated 81 0
Seawater Desalinated 569 355
All 1,149 9 8
Agricultural Labor (106 day year-1)
Foreign 9.5 9.4
Local 5.1 5.0
58
Table D2
Per-Annum Statewide Average Shadow Values of Water-Quantity and Water-
Infrastructure-Capacity Constraints at Supply Points; Water Prices at the Consumption
Points ($ m-3); Shadow Values of Land and Foreign Labora
Salinity
Internalized
Salinity
Externalized
Water Supply Constraint ($ m-3)
Natural Freshwater 0.27 0.87
Brackish Groundwater
0.11 0.00
Brackish Groundwater Desalinated
0.10 0.75
Treated Wastewater
-0.09 0.14
Treated Wastewater Desalinated
0.38 0.82
Seawater Desalinated
0.00 0.00
Consumption Price ($ m-3)
Urban
1.54 1.77
Agriculture
0.41 0.72
All
0.86 1.13
Capacity Constraint ($ m-3)
Natural Freshwater 0.01 0.07
Brackish Groundwater
0.01 0.00
Brackish Groundwater Desalinated
0.47 0.25
Treated Wastewater
0.05 0.15
Treated Wastewater Desalinated
0.27 0.10
Seawater Desalinated
0.05 0.38
Water Conveyance
0.00 0.01
Non-Water Agricultural Production Factors
Agricultural Land ($ ha-1) 5.12 2.49
Foreign Labor ($ day-1)
59.3 45.7
a Shadow values and prices were discounted to the 15th year, and then averaged.
59
Table D3
Per-Annum Statewide Average Salinity Levels and Salinity Shadow Values at the Water
Supply and Consumption Points
Salinity
Internalized
Salinity
Externalized
Salinity (dS m-1)
Supplya
Natural Freshwater 1.05 1.06
Treated Wastewater
1.46 1.49
All
0.83 0.95
Consumption
Urban
0.82 0.84
Agriculture
0.60 0.82
Nature
1.55 1.73
All
0.83 0.95
Shadow Value ($106 (dS/m)-1 year-1)b
Supply
Natural Freshwater -19.3 -31.3
Brackish Groundwater
0.0 0.0
Brackish Groundwater Desalinated
-6.6 -8.6
Treated Wastewater
-17.5 -43.1
Treated Wastewater Desalinated
-33.5 0.0
Seawater Desalinated
-95.5 -98.0
Consumption
Agriculture
-77.4 -68.1
a The salinity of brackish water and desalinated water is 4 and 0.25 dS m-1, respectively.
b Shadow values were discounted to the 15th year, and then averaged.
60
Table D4
Per-Annum Statewide Average Welfare Elements ($106 year-1)a
Salinity
Internalized
Salinity
Externalized
Agricultural Products
Production Value 5,577 5,229
Import Valueb 662 724
Variable Costs 3,999 3,765
Capital Costs 336 322
Water-Supply Costs
Variable Costs 1,432 1,291
Capital and Operation Costs 472 421
Total 1,903 1,712
Water Purchase Expenses
Urban 1,855 2,100
Agriculture 442 655
Water to Nature 131 115
Total 2,297 2,755
Surpluses
Urban Water Consumersc 0 -465
Agricultural Product Consumersc 0 -241
Farming Profits 1,136 810
Water Suppliers 263 929
Social Welfare 1399 1032
a Annual welfare-element values were discounted to the 15th year, and then averaged.
b The import value includes only imports of products associated with the 55 crops incorporated in the
model.
c Since the computation of the areas beneath the calibrated constant-elasticity demand functions of urban
water and agricultural products involves extrapolations, we normalize the surpluses of urban-water and
agricultural-product consumers to 0 under the Salinity-Internalized scenario, and report their changes
under the Salinity-Externalized scenario in comparison to the Salinity-Internalized one.
61
Table D5
Laspeyres Quantity and Price Indices, and Value Index, of Agricultural Production by
Salinity-Tolerance Crop Bundles, under the Salinity Externalized Scenario Relative to the
Salinity-Internalized Scenario (i.e., Salinity Internalized = 100)
Crop Bundle Sensitivity to Salinitya Quantity Price Value
Sensitive (36%) 92 104 95
Moderately Sensitive (47%) 94 102 97
Moderately Tolerant (14%) 95 100 95
Tolerant (3%) 64 102 66
All crops 92 102 94
a Values in parentheses indicate the share of the crop bundle in the production value under the Salinity-
Internalized scenario.
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