Raising the dead without a Red Sea-Dead Sea canal ? Hydro-economics and governance

Introduction Conclusions References

A central hydro-economic model concept is that water demands are not fixed delivery requirements but rather functions where volumes of water use at different times and places have varying total and marginal economic values (Harou et al., 2009). The model identifies water allocations to nodes and through links that maximize systemwide net benefits with net benefits quantified as the area between the demand and 5 cost curves. Allocations are subject to physical, hydrologic, engineering, operational, and policy constraints and limits.
Models include environmental water uses -such as flow to the Dead Sea -in two ways. Where possible, quantify environmental demand curves using revealed preference, travel cost, hedonic pricings, stated preference, or other econometric estimation 10 methods (Young, 2005). Then, locate demand curves at model nodes like other economic demands. This first approach is often only partial and controversial (Becker and Katz, 2009;Young, 2005). A second approach, adopted here, instead specifies environmental water use as a constraint on flow at a model node or along a link. Then (i) change the constraint level through sensitivity analysis, or (ii) examine the shadow 15 value associated with the constraint to identify the opportunity cost of environmental water (Harou et al., 2009). Shadow values (Lagrange multipliers; dual variables) are model outputs and specify how system-wide net benefits change were the constraint relaxed one unit (such as 1 m 3 ).
This second approach to environmental water use parallels other constraint-based 20 methods to represent operating rules, policies, or proscribe delivery requirements to certain nodes or demand sectors. Thus, the hydro-economic model does not make water policy nor recommend environmental water use levels; rather, it identifies water allocations that perfectly obey imposed policies and environmental uses and reports resulting hydrologic, economic, and other impacts. Introduction

WAS model and extensions
The hydro-economic WAS model is a steady-state, nonlinear optimization program that identifies withdrawals from sources, deliveries through conveyance links between districts, and allocations to water use sectors within districts that maximize regional net benefits (Fisher et al., 2005). The single-year version for Israel, Jordan, and Palestine 5 includes demands of 17.4 million people in urban, industrial, and agricultural sectors spread across 45 districts, 109 links, and 91 supply sources (Fig. 1), fresh and recycled water qualities, and country-specific price policies (Fisher et al., 2005). A stochastic version adds hydrologic variability, leak reduction, water conservation programs, plus conveyance, recycling, desalination, and source capacity expansion decisions 10 (Rosenberg et al., 2008). The work here extends the single-year and stochastic versions to include and allow return flows from agriculture, brine waste from desalination, multiple water quality types to meet a minimum in-stream flow requirement, and fixed-increment infrastructure capacity expansions. These extensions represent important components of flow 15 balance for the Dead Sea, flow requirements to restore the Dead Sea level, and limits to build large infrastructure such as the Red-Dead projects. These extensions are needed to assess Dead Sea restoration alternatives, implemented as one or more new optimization program constraint(s), and discussed further below. 20 In the single-year and stochastic versions of WAS, agricultural wastewater (return flows) cannot be reused, is assumed to have no economic value, and is not considered or quantified. However, agriculture wastewater is currently a large component of lower Jordan River flows and Dead Sea inflows. When increasing flow to the Dead Sea in a water scarce region or reallocating water away from agriculture, return flows 25 do have a use and economic value. Thus, it is important to quantify and account for them. The extended model adds a third water quality type, return flow, to the fresh and recycled water qualities already included. This addition generates a new mass balance constraint in each district i for the new water quality type q return flow :

Return flows from agriculture
∀i ,q ∈ returnflow.
(1) 5 We can then enter data to (i) restrict sectors from using return flows to satisfy economic demands, and (ii) indicate there is no leakage or local sources of this quality type. These conditions reduce Eq. (1) to: Here, imports, exports, and reused wastewater are the only active terms in the re-10 turn flow accounting. The former two terms are included by specifying conveyance links for return flows among districts and nodes; in this case, the districts near or that can deliver return flows to the Jordan Valley and Dead Sea. The later term is defined by only allowing the agriculture sector to contribute wastewater and specifying a non-consumptive fraction of the original use that becomes available as the return 15 flow. This definition mimics an existing constraint that allows the agricultural sector to reuse treated wastewater from the urban and industrial sectors (for return flows, there is no physical wastewater treatment infrastructure). I use a non-consumptive fraction of 33% -as suggested by the literature -and test this assumption by comparing computed return flows to the lower Jordan River under the existing management regime to 20 observed flows. Together, the additional constraint, data entry, and parameter specification allow us to include and model returns flows from agriculture.

Brine waste from desalination
Brine waste from desalination is also not included in the single-year and stochastic versions of WAS because the waste is assumed to have no use nor economic value. However, brine waste from the Red-Dead project could be delivered to Dead Sea and used in lieu of fresh, recycled, or agricultural return flows to raise the Dead Sea level. In this situation, brine waste does have economic value; it is important to include and quantify these effects. We can further modify constraint Eq.
(1) to include the volume of brine waste of water 5 quality type q available at district i : and define this available volume with a new constraint that ties the brine waste volume to a user-specified fractional amount of the desalinated water produced: Here, the desalinated water produced is one of several terms embedded in the Local Sources term in Eqs.
(1) and (3). The brine fraction is a unitless ratio that represents the volume of brine generated for each 1 m 3 of desalinated water produced. DQ(q) is a user-specified set of source water quality types (q 2 ) that, when desalinated, generate 15 brine quality q. For simplicity, we can lump brine waste and agricultural return flows into one water quality type, return flows. Current proposals suggest the Red-Dead project will generate 1 m 3 of brine waste for each 1 m 3 of desalinated water produced.
I use this brine fraction value and also test the assumption through sensitivity analysis. 20 A third extension allows multiple water quality types to, on average, meet a minimum in-stream flow-requirement. The single-year WAS model hard-coded a flow requirement to ensure Israel supplied Gaza with freshwater; Rosenberg et al. (2008)  the requirement general to allow the user to specify a minimum required flow for any quality q along any conveyance link from district i to district j in each stochastic water availability event e:

Multiple water qualities can meet an in-stream flow requirement
Conveyance Flow qi j e ≥ minimum required flow qi j , ∀qi j e.
We can extend this constraint to allow multiple flows of different quality types to count 5 towards the minimum required flow and further, the expected flow to satisfy the minimum flow requirement rather than in each and every event: In Eqs. (6) and (7), probability e is the likelihood that event e will occur and Q(i ,j ) is a user-specified set of water quality types whose flows can count towards the expected minimum required flow along the link from i to j . For required deliveries to the Dead Sea, Q(i ,j ) includes all water quality types (fresh, recycled, and return flows). 15 A fourth and final extension adds additional constraints and integer decision variables to limit infrastructure capacity expansion decisions to fixed increments. Prior work allowed continuous expansions of desalination, local source, conveyance, and wastewater treatment infrastructure up to a maximum capacity (Rosenberg et al., 2008). That approach works when proposed expansions are small and/or capital costs for expan- for large capacity expansions such as coastal desalination plants or the Red-Dead project that can only be built in phases, to full capacity, or not at all. Here, we can use integer decision variables and constraints to limit expansions to fixed increments. For expansion of local sources or desalination facilities, these limits are:

Fixed-increment infrastructure expansions
where Local Source Expansion is the expansion size (MCM/year) for district i and water quality type q used elsewhere in the model, Capacity Interval is the fixed capacity expansion interval associated with each expansion level (MCM/year/level), and LEVEL is an integer variable that represents the number of expansions implemented 10 and takes values [0, 1, 2, ...] up to the maximum allowed expansion levels. Equation (8) forces Local Source Expansion to take step capacities 0, 1*Capacity Interval, 2*Capacity Interval, ..., Maximum Expansion Level*Capacity Interval. And when a particular capacity expansion project can only be built to maximum capacity or not built (such as for the Red-Dead project), LEVEL becomes a binary variable that takes the 15 values [0, 1]. Including these constraints and decision variables turns the model into a mixed-integer, non linear program that can be formulated and solved in the General Algebraic Modeling System (GAMS) with DICOPT (Brooke et al., 1998;Grossmann et al., 2002). Notation for the full optimization program, including the objective function, constraints, 20 and decision variables, is available online at http://www.engr.usu.edu/cee/faculty/ derosenberg/documents/Rosenberg-RaiseTheDeadwithoutARedDeadCanal-SM.pdf.

Model data
The extended WAS model uses supply, conveyance, demand, wastewater treatment, and policy data for Israel, Jordan, and Palestine collected between 1995 and 2003 25 (Fisher et al., 2005) and updated for Jordan in 2006 (Rosenberg et al., 2008 section presents updated data for each country, costs for the Red-Dead project, and describes how the three countries' inter-tied water systems are represented.

Israel
Since 2003, Israel has embarked on an ambitious program to build seawater desalination plants along its Mediterranean coast (Dreizin, 2006;Dreizin et al., 2008). Currently, Project tender amounts serve as the upper bound on capital costs to further expand 10 these plant capacities towards Israel's desalination target of 750 MCM/year. Capital costs for these expansion options are included in a scenario that examines optimal infrastructure and conservation program expansions. Israel groundwater availability is represented as constant from year to year whereas availability of Upper Jordan River surface water sources (to the districts of Golan, 15 Hula, and the Sea of Galilee) are variable with variability characterized by sorting into increasing order the 60-year record of water availability to the Sea of Galilee between 1950 and 2010 (Givati and Rosenfeld, 2007) (availability=stream flow+spring flows+direct rainfall-evaporation; excludes upstream consumptive use). I partition the distribution of water availability into a discrete set of 6 availability events whose mass 20 probabilities correspond to the mass probabilities used previously for Jordan (Rosenberg et al., 2008). For each event, I pull the representative availability value from the sorted distribution and divide by the mean observed availability over the 60-year record (443 MCM/year). This division gives an event-specific availability factor and allows use of a single-set of water availability events for diverse locations in Jordan and Israel 25 that have different probability distributions of water availability. Finally, we can multiply source availabilities by event-and source-specific availability factors to estimate source availability in each event. stored only a paltry 7 to 30 MCM/year (Namrouqa, 2009, 2010. Low storage is likely due to significant upstream abstractions and consumptive use by Syria (Rosenberg, 2006) and has prompted Jordan to ask Syria to release water to fill the dam (Namrouqa, 2010). Given the dam's low storage levels and yield to date, the extended model only allows up to 146 MCM/year abstraction from the Yarmouk River as a local supply to 15 Irbid. Finally, the model keeps water efficiency improvements for urban users, leak reduction programs, Disi aquifer and conveyance to Amman and Aqaba, wastewater treatment for Aqaba and Zarqa, and local source developments for Aqaba as potential water conservation programs and infrastructure capacity expansions (Rosenberg et al., 20 2008). These programs are examined in a scenario that represents new, decentralized infrastructure expansions and conservation program developments.

Palestine
Despite difficult political circumstances, there have been notable water resources developments in the West Bank and Gaza since 2003 (Fisher et al., 2005) with capacities that range from, respectively, 0.44 to 8.9 and 15 to 40 MCM/year. Recent studies by the Palestinian Water Authority (PWA) and others call to expand conveyance, desalination, and wastewater treatment and reuse in Gaza at capital costs of, respectively, $0.3, $2.7, and $1.2 million/MCM. Although the Palestinian water distribution system has many leaks, the current analysis assumes PWA will reduce physical 5 leakage to 20%.

Red-Dead project
This study locates the Red-Dead project and it's conveyance, desalination, and hydropower generation facilities entirely in Jordan. It considers two project configurations and optimistically estimates capital and operating costs from recent newspaper reports 10 and official Jordanian statements (Table 1). Actual costs are likely larger so optimistic estimates provide a lower-bound basis to determine project feasibility. The first Red-Dead project configuration includes the canal, desalination at Balqa (near the Dead Sea), delivery of brine waste to the Dead Sea, conveyance from Balqa to Amman, and represents the current proposal by Jordan, Israel, and the Palestinians. A second con- 15 figuration includes only the canal and hydropower generation at Balqa with tail water delivered to the Dead Sea. Here, operational costs are negative and represents profits of approximately $0.05 per kWh generated (Hrayshat, 2009(Hrayshat, , 2008. We test the effect of hydropower operational cost through sensitivity analysis. 20 Representing the Red-Dead project, Dead Sea, and return flows in a combined, intertied model for the three countries ( Fig. 1)  links for return flows at no operational cost were also added from West (Israel) to East Jerusalem (Palestine) and from East Jerusalem (Palestine) to Jericho (Palestine). These links all represent conveyance by gravity flow through existing wadis and channels to the Jordan River and Dead Sea. The new expected minimum flow requirement presented in Sect. 3.3 was specified along the last link from the Jordan River to the 5 Dead Sea and used to make the hydro-economic analysis.

Hydro-economic model results
I ran the extended model for a base case representing existing infrastructure, demands forecast in 2020, fresh and recycled water use, and a Dead Sea flow requirement of 100 MCM/year (A1 in Figs. 2 to 4 and Table 2). Scenario analysis shows impacts 10 when considering agricultural return flows (A2 and A3), return flows with two Red-Dead project configurations (B and C) and with new decentralized water infrastructure plus conservation programs (D). Sensitivity analysis shows how scenario net benefits and allocations change when increasing the expected required flow to the Dead Seathe environmental water use constraint attached to the lower Jordan River conveyance 15 link. System-wide expected net benefits fall and expected costs rise as the required flow to the Dead Sea increases (Fig. 2). Rising expected costs reflect increasing water scarcity and reduced benefits as water is reallocated from users to the Dead Sea. When the existing system (A1, using only fresh and recycled waters) returns approxi-20 mately 800 MCM/year to the Dead Sea, cost increases surpass a $US 658 million/year benchmark that represents likely benefits from restoration as measured by prior estimates of Israeli, Palestinian, and Jordanian willingness-to-pay (WTP) to restore the Dead Sea (Becker and Katz, 2009). This result suggests the existing system can flexibly reallocate and deliver additional water to the Dead Sea but cannot -even ac-  (Yechieli et al., 1998). Expected costs associated with the Red-Dead project (B, configured to desalinate new supply and deliver brine waste to the Dead Sea as currently proposed by Jordan, Israel, and the Palestinians) are lower than the reallocation alternatives and the WTP 5 benchmark. However, expected costs are lower still for a smaller Red-Dead project configuration (C) that only generates hydropower and delivers tail water to the Dead Sea or alternative (D) that builds new, decentralized local infrastructure and conservation programs across the three countries (Fig. 2). These alternatives are more economically viable than the Red-Dead project currently proposed by the three countries. 10 The three viable restoration alternatives distribute benefits and desalination responsibilities differently among the three countries (Fig. 3). Jordan principally bears costs to operate the Red-Dead project and satisfy larger Dead Sea flow requirements whiles Israel cuts back some Mediterranean coastal desalination (B). With a smaller Red-Dead project that just generates hydropower (C), Jordan still exclusively bears the project 15 costs. Costs, benefits, and desalination responsibilities switch with a decentralized mix of new local infrastructure and conservation programs (D). Initially, Israel cuts back coastal desalination while expected benefits accrue mostly to Jordan. However, as required flows to the Dead Sea increase, Israel increases coastal desalination and faces increased expected costs.

Implications for governance
For all alternatives, expected costs rise as the required flow to the Dead Sea increases (Figs. 2 and 3). Increases reflect increasing water scarcity and show each country currently has little or no individual economic incentive to deliver water to the Dead Sea. Absent a requirement, countries would rather put water to beneficial use and have Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | current full use of Jordan River water and will likely continue should new infrastructure like a Red-Dead project be built. New infrastructure alone will not raise the Dead Sea level. Third parties and institutions outside the basin -such as the World Bank or environmental groups -that seek to raise the Dead Sea level must also create incentives for countries to deliver water to 5 the Dead Sea. First, outside institutions could offer countries financial incentives such as pay the full capital cost of the Red-Dead project (annualized at $US 320 million/year, 5% interest, continuous compounding, 20-year project life) to encourage the countries to agree on the water volumes each will deliver to the Dead Sea. Even with this incentive, a decentralized mix of new local infrastructure and conservation programs is still 10 a more economically viable alternative to raise the Dead Sea level.

Pay countries to deliver water to the Dead Sea
Alternatively, outside institutions could pay countries to deliver water to the Dead Sea. The outside institution purchases water from the countries with purchases occurring only when purchase prices (i) exceed the scarcity (and other) costs borne by users in the country selling the water, but are (ii) less than the environmental value of water returned to the Dead Sea.
There are several common objections to market-based water purchases (Richards and Singh, 2001) and responses (Fisher and Huber-Lee, 2009;Fisher et al., 2005). Here, I address issues to purchase water for environmental purposes (Murphy et al., 20 2009). First, the most effective market will involve a grand coalition of all countries (although one or more countries may only nominally participate) (Fisher and Huber-Lee, 2009). Second, no countries may choose to sell. Although, at some (possibly large) price, a country will find the payment sufficient compensation for the scarcity costs it incurs and sell water. Third, countries could collude to raise prices. While possible, collusion will likely be temporary. As offer prices rise, a country will have a strong incentive to defect and sell. Fourth, the sale price need not stay constant and can vary with environmental, hydrological, and other conditions such as the water volume already purchased. Setting appropriate sale prices is key to establish a successful market for environmental purchases. And WAS model shadow values for water associated with the Dead Sea flow constraint can help guide price setting (Fisher and Huber-Lee, 2009;Fisher 5 et al., 2005). These shadow values represent the scarcity value of water and minimum price an outside institution must offer to successfully purchase water from a country. A regressive schedule (Table 2) could set prices at or above the shadow value associated with the delivery volume still remaining to meet the annual target.
The present values of annual payments to countries to deliver water to the Dead 10 Sea are large and typically exceed capital costs for new infrastructure (Fig. 4). Payments under the existing system (A2) and with the Red-Dead project proposed by the three countries (B) exceed the estimated $US 6.9 billion present value of the annual WTP benchmark representing benefits to restore the Dead Sea (20 year life, 5% interest, continuous compounding). Lower payments and capital costs for a decen- 15 tralized mix of new local infrastructure and conservation programs (D) still approach the WTP benchmark. Costs are lowest for the smaller Red-Dead project configured to only generate hydropower (C) and are principally to build new infrastructure (canal, turbines, and generators). Here, payments are needed only to purchase flows up to 300 MCM/year before the project is built. Above this level, Jordan builds and profitably 20 generates hydropower at full capacity, the Dead Sea flow constraint does not bind, and the associated shadow value is zero. hydropower operating cost (Fig. 5). Should either the sale price for generated energy fall or we include project operations and maintenance costs, Jordan would still build the Red-Dead project, but operate the project at less than capacity and only to meet the Dead Sea flow requirement. There would be a shadow value associated with delivering water to the Dead Sea and Jordan would likely seek annual payments to deliver the 5 water to the Dead Sea. The present value of these payments would comprise several billion dollars and approach payments associated with other Dead Sea restoration alternatives. These results suggest the economic viability of a smaller Red-Dead project that only generates hydropower is sensitive to the sale price of generated electricity, operations and maintenance costs; these project aspects require further study.

Limitations
The hydro-economic model results and implications for governance do not consider the environmental effects of mixing Red-and Dead Sea waters, adding brine waste from desalinated Red Sea water to Dead Sea water, or locating a large project intake facility at the north end of the Red Sea in the Eilat/Aqaba environmental and tourist 15 zone. Currently, the World Bank is identifying effects and remediation strategies and quantifying remediation costs. Still, even with small remediation costs, model results show other alternatives are more economically viable than the Red-Dead project currently proposed by the three countries. Further, remediation costs would exacerbate existing governance that encourages full use of Jordan River water and make it more Introduction the Dead Sea level. The project would build a large, expensive canal from the Red Sea to the Dead Sea and also generate hydropower and desalinated water. Hydro-economic model results for the three countries' inter-tied water systems show two Dead Sea restoration alterantives -a (i) mix of decentralized new infrastructure and conservation programs in each country, or (ii) smaller Red-Dead project that only gen-5 erates hydropower -are more economically viable than the larger Red-Dead project proposed by the three countries. These assessments consider important components of flow balance for the Dead Sea, flow requirements to restore the Dead Sea level, and limits to build large infrastructure such as the Red-Dead project.
Results for all restoration alternatives show rising deliveries to the Dead Sea trig-10 ger increasing water scarcity and suggest each country has little individual incentive to allow water to flow to the Dead Sea. Beyond new infrastructure, outside institutions that seek to raise the Dead must also develop new governance that provides countries incentives to deliver water to the Dead Sea. One incentive -pay countries to deliver water -ties environmental water purchases to model shadow value results and the 15 scarcity value of water. Payments will substantially raise actual Dead Sea restoration costs above the current estimated $US 5 billion capital costs for the Red-Dead project. Although payments are large, restoration benefits measured by willingness-to-pay estimates are larger still and identify several viable approaches to raise the Dead beyond the Red-Dead project proposed by the three countries.  Figure 3. Economic impacts for six restoration alternatives when increasing required flow to the Dead Sea. Change on the y-axis is quantified as expected net benefits observed for the base case alternative A1 that allows reallocations, uses only fresh + recycled water, and delivers just 100 MCM/year flow to the Dead Sea minus expected net benefits for the specified alternative at the specified Dead Sea flow requirement. Payments to countries are based on the shadow value price schedule in Table 1. 5 Fig. 4. Present value costs for each alternative including capital costs for new infrastructure and programs and payments to countries to deliver the specified flow to the Dead Sea. Payments to countries are based on the shadow value price schedule in Table 1