HESSHydrology and Earth System SciencesHESSHydrol. Earth Syst. Sci.1607-7938Copernicus PublicationsGöttingen, Germany10.5194/hess-20-2135-2016Sharing water and benefits in transboundary river basinsArjoonDianeTilmantAmauryamaury.tilmant@gci.ulaval.caHerrmannMarkusDepartment of Civil Engineering and Water Engineering, Université Laval, Québec, CanadaDepartment of Economics, Université Laval, Québec, CanadaAmaury Tilmant (amaury.tilmant@gci.ulaval.ca)3June20162062135215020January20168February201617May201618May2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://hess.copernicus.org/articles/20/2135/2016/hess-20-2135-2016.htmlThe full text article is available as a PDF file from https://hess.copernicus.org/articles/20/2135/2016/hess-20-2135-2016.pdf
The equitable sharing of benefits in transboundary river basins is necessary
to solve disputes among riparian countries and to reach a consensus on
basin-wide development and management activities. Benefit-sharing
arrangements must be collaboratively developed to be perceived not only as
efficient, but also as equitable in order to be considered acceptable to all
riparian countries. The current literature mainly describes what is meant by
the term benefit sharing in the context of transboundary river basins and
discusses this from a conceptual point of view, but falls short of providing
practical, institutional arrangements that ensure maximum economic welfare as
well as collaboratively developed methods for encouraging the equitable
sharing of benefits. In this study, we define an institutional arrangement
that distributes welfare in a river basin by maximizing the economic benefits
of water use and then sharing these benefits in an equitable manner using a
method developed through stakeholder involvement. We describe a methodology
in which (i) a hydrological model is used to allocate scarce water resources,
in an economically efficient manner, to water users in a transboundary basin,
(ii) water users are obliged to pay for water, and (iii) the total of these
water charges is equitably redistributed as monetary compensation to users in
an amount determined through the application of a sharing method developed by
stakeholder input, thus based on a stakeholder vision of fairness, using an
axiomatic approach. With the proposed benefit-sharing mechanism, the
efficiency–equity trade-off still exists, but the extent of the imbalance is
reduced because benefits are maximized and redistributed according to a key
that has been collectively agreed upon by the participants. The whole system
is overseen by a river basin authority. The methodology is applied to the
Eastern Nile River basin as a case study. The described technique not only
ensures economic efficiency, but may also lead to more equitable solutions in
the sharing of benefits in transboundary river basins because the definition
of the sharing rule is not in question, as would be the case if existing
methods, such as game theory, were applied, with their inherent definitions
of fairness.
Introduction
With growing water scarcity, as a result of expanding population demand,
environmental concerns and climate change effects, there is increased
international recognition of the importance of cooperation for the effective
governance of water resources. This is particularly evident in the case of
transboundary river basins in which unidirectional, negative externalities,
caused by the upstream regulation of the natural flow, often place some
parties at a disadvantage and result in asymmetric relationships that add to
the challenge of coordinating resource use . There is a
consensus among water professionals that the cooperative management of shared
river basins should provide opportunities to increase the scope and scale of
benefits , stepping beyond the
volumetric allocation of water that reduces negotiations between riparians to
a zero-sum game. In their seminal paper, discussed the
types of benefits that river basins can provide, assuming cooperation:
benefits to the river can result from sustainable cooperative
management of the ecosystem; efficient, cooperative management and
development of river flow can yield benefits from the river in the
form of increased water quality, quantity and productivity; policy shifts
away from riparian disputes/conflicts toward cooperative development can
reduce costs of non-cooperation arising because of the river; and
cooperation between riparian states can lead to economic, political and
institutional integration, resulting in benefits beyond the river.
A large proportion of past research has focused mainly on the economic
benefits of cooperation (benefits from the river). Focussing on benefits in
strictly economic terms does not lessen the importance of benefits from other
spheres . An economic perspective, however, may be an
effective method for encouraging cooperation because it may help riparian
countries to realize win–win situations .
The traditional approach to estimating the economic benefits of cooperation
relies on hydro-economic modeling . These studies present various
implementation strategies representing various levels of cooperation, but all
show that there are significant economic benefits to be had through
basin-wide cooperation. However, economic efficiency is not necessarily
compatible with equitability due to the different production abilities of
water users . Analytical methods, including game theory
solutions such as the Shapley value and bankruptcy theory , have been examined for use in
water allocation as equitable alternatives to the efficient economic
allocation produced by hydro-economic models. Analytical methods were also
used by , who looked at possible equitable criteria for
sharing water and developed allocation algorithms to operationalize these,
applying them to the Orange, Nile and Incomati rivers. It has been argued
that the notion of equity, or fairness, involves a cultural component that
should be incorporated into any type of water policy and, therefore,
stakeholder involvement in decision-making is a significant determinant in
the judgement of fairness . The explicit
provision of benefit-sharing arrangements that are collaboratively developed
and, thus, perceived as fair, is therefore necessary to help solve disputes
and to reach a consensus in transboundary river basin development and
management activities .
Increasingly, efforts are focussing on the sharing of benefits generated
through cooperation in order to solve the problem of equitability. The
rapidly growing body of literature on benefit sharing mainly describes what
is meant by this in the context of transboundary river basins and discusses
benefit sharing from a conceptual point of view . This literature introduces and defines different
approaches but falls short of providing practical institutional arrangements
for the sharing of benefits. Recently, introduced a
methodology to address the problem of water allocation in the Nile River
through a revenue re-distribution mechanism that leads to a fairly allocated
revenue for each water user based on the proportion of its contribution to
the basin.
Analytical methods, such as game theory and related bankruptcy methods, may
also be useful for determining ways to fairly allocate generated benefits.
Game theory, which is the mathematical study of competition and cooperation,
can provide a somewhat realistic simulation of the interest-based behavior of
stakeholders . The framework that relates the preferences
of players to the observable features of a game is the hypothesis that
players care about nothing except their own payoffs . Fair
outcomes are captured in solution concepts such as the core, which
selects the payoff allocations that give each group of individuals no less
than their collective worth and the Shapley value in which payoffs
are related to the marginal contributions of individuals to a coalition
. The aim of bankruptcy methods is to distribute an
estate or asset among a group of creditors, all having a claim to the asset,
where the sum of the creditors' claims is larger that the amount available to
distribute . An overview of bankruptcy rules has been
presented by . Each bankruptcy rule defines
fairness based on the properties underlying the rule. The three most
well-known bankruptcy rules (the proportional rule, the constrained equal
awards rule and the constrained equal losses rule) all define equity through
the equal treatment of equals requirement in which agents with
identical claims should be treated the same
Equal treatment of
equals is one of the properties upon which these bankruptcy rules are
defined. For a complete discussion of all properties, refer to
.
. In other words, agents with the same
claim should receive the same compensation. The analysis and formulation of
properties and principles of distribution rules, such as those in cooperative
game theory and bankruptcy theory, are the object of the axiomatic method
.
The axiomatic method allows desirable properties to be translated into a
sharing rule. If a particular rule has been adopted to solve a problem
involving a group of agents, it is assumed that all agents have agreed on the
properties that such a rule fulfills. The concept of fairness, then, can be
embedded into a rule. The axiomatic approach is easily incorporated into
negotiations because the axioms can be interpreted quite naturally as
describing characteristics of a negotiation procedure .
As discussed previously, the economically efficient allocation of water is
not necessarily equitable. Axiomatic approaches, on the other hand, allow the
characterization of an equitable distribution of welfare, but do not
necessarily maximize the aggregated economic welfare over the basin.
Institutional arrangements that ensure maximum economic welfare, as well as
the equitable sharing of these benefits over the basin, are required.
In this study we define an institutional arrangement that distributes welfare
in a river basin by maximizing the economic benefits of water use and then
sharing these benefits in an equitable manner. The methodology relies on a
pseudo-market arrangement in the form of a highly regulated market in which
the behavior of water users is restrained to control externalities associated
with water transfers and to ensure basin-wide coordination and enhanced
efficiency. The term pseudo-market indicates that bulk water users are not
free to choose how much water will be moved in the system. Freedom of
contract and private property rights, which are necessary conditions for the
existence of a market, are restrained, giving rise to a
pseudo-market
One could also argue that a true market is created by
assuming that every agent agrees with, and respects, having to pay for
water.
. These restrictions are due to the flow characteristics of water and
to the need to account for externalities and third-party effects, which can
seldom be achieved within a traditional market.
The institutional arrangement described in this paper should encourage full
cooperation between water users because it is intended as a replacement for
traditional types of agreements on international river basins, which can lead
to distrust and tension between riparian countries. What we present is an
entirely different perspective that may help to avoid the pitfalls and
limitations of current agreements.
In the following section, we describe this arrangement, which uses a
hydro-economic model to determine the economically efficient allocation of
water and a collaboratively developed sharing method for the equitable
allocation of monetary benefits. Section 3 presents the application of this
framework to the Eastern Nile River basin. Section 4 presents and discusses
the results and Sect. 5 concludes the paper.
Methodology
In the proposed pseudo-market approach, a river basin authority (RBA) plays
the role of water system operator, identifying economically efficient
allocation policies that are then imposed on the agents (water users). The
agents are charged for water use and these payments are redistributed to
ensure equitability among the users. In this particular system, the mandate
of the RBA consists of (1) collecting information on water use and
productivity, (2) efficiently allocating water between the different agents
in the system based on the information collected in the first step,
(3) preserving the hydrologic integrity of the river basin, and
(4) coordinating the collection and redistribution of the benefits associated
with the optimal allocation policies.
Information collection
In this first step, the RBA collects information that is required to assess
the demand curves, or at least the productivity (unit net benefit), of all
users in the system, once at the beginning of each year. The information must
be validated to ensure that it is complete and reasonable since the
economically efficient allocation of water in the next step depends on it.
The collection of information can be the basis of a bidding process in which
agents offer to buy water at a given price. In the case of irrigation agents,
information such as crop area, crop type, yield, crop price and crop water
requirement over a period can be used to determine the bid for each agent
and, based on the bid information, the demand curve can be inferred using the
residual imputation method . This method
assumes that all input costs, except for the cost of water, are known. The
water value is then imputed as the residual of the observed gross benefits
after all non-water costs are subtracted .
In order to control the declarations of agents in the agricultural sector,
the RBA can use techniques such as remote sensing to validate land
classification and cropping areas . As an example, the European Union uses an Integrated
Administration and Control System (IACS), which includes a land-parcel
identification system (LPIS), to control declarations from farmers for
financial aid grants . The LPIS uses orthophotos to
monitor the evolution of the land cover and the management of crops, and
enables more accurate declarations by farmers.
In the case of hydropower, information regarding energy production and
scheduling is important. For example, power plants might be offline for
maintenance or might be obliged to generate a minimum amount of energy to
meet their contractual commitments. Also, water use requirements such as
environmental flow and minimum domestic use supply will be required.
The unconstrained or expected net benefits (ENB) for a water user are the
consumer surplus (Fig. ), which is the area under the demand curve
above the price PD. The surplus is the private user cost of water and
corresponds to the willingness to pay for the last unit of water demanded in
a situation where allocation is unconstrained. This area is made up of three
regions (A, B and C) that will be discussed later.
Demand
curve. D: quantity of water demanded for a time period; x*: quantity of
water allocated for a time period; P: price of water.
Water allocation
Once water user information has been collected, allocation decisions are
identified by matching demand with supply in a cost-efficient way, i.e., by
giving priority of access to users with the highest productivity. In order to
do this, an aggregation of the demand curve is carried out, which means that
a distinction must be made between rival and non-rival water uses. When water
users are not in competition for the same unit of water, non-rivalness is
observed. For example, water flowing through a dam may be considered a
non-rival water use since a unit of water released through one dam can be
used downstream by another dam. In rival water use, units are consumed and
are no longer available to other water users (for example, water lost to
irrigation or water held in a reservoir during a period when it is required
downstream for irrigation). In this case, the demand curves are summed
horizontally (see Fig. ). Rival water uses need to be
coordinated to prevent conflicts. The decision to divert one additional unit
of water to any rival use depends on the at-source value
The
at-source value of water is observed at the location where bulk water is
diverted. The at-site value corresponds to the value of water delivered to
the users (for example, a farm at the end of a conveyance and distribution
system). At-site water values are generally larger than at-source values
because they include losses in the system and conveyance costs. In the study
of intersectoral allocation choices, at-source water values should be used
.
of water for that use. If this value is larger than the
at-source value of all downstream marginal users, then it will be diverted to
the rival use. See for a detailed description of rival
and non-rival water uses. The value of the last unit of water at any site,
then, is the sum of the marginal values of the non-rival users since the
demand curves can be summed up vertically (see Fig. ). This
aggregation of the demand curve is done automatically in hydro-economic
models. Hydro-economic models, then, can be used to determine the allocation
of water between users at the same site and over a basin (comprising a number
of sites) and to determine the marginal value of water and economic benefits
at each site. A description of the mathematical formulation involved is given
in the Appendix.
Aggregation of demand curves for rival and non-rival
water uses for a given time period.
Collection of bulk water charges
Based on the water allocation decisions and the corresponding water fluxes,
pseudo-market transactions occur between the RBA and the water users. Users
must pay the RBA for the water allocated to them. The cost of water is the
marginal water value or shadow price (λ) calculated by the
hydro-economic model at the site of water abstraction or use. Economic theory
indicates that for efficient water allocation to occur, the price that users
pay for the resource must be equal to the marginal value of still available
opportunities of water use, which reflects the social cost of using water at
a particular site. If the user pays less than this, the resource is
overconsumed or overutilized, as no efficient rationing occurs. Conversely, a
user price higher than the marginal value would result in
underconsumption/underutilization.
The RBA charges for the water entering the system in order to cover the costs
associated with its mandates (conservation, coordination, compensation). In
the case of consumptive users, water is purchased from the RBA at the
marginal water value (the value of a marginal unit of water) at the site of
abstraction. Non-consumptive users buy inflow from the RBA at a price equal
to the difference between the marginal value of water at the user site and
the marginal value of water at the downstream site (Fig. ). This
bulk water charge system is based on a dynamic water accounting framework
presented by .
Payment for bulk water use has been addressed, recently, by the United
Nations in their 2014 World Water Development Report in
which they state that economic instruments such as markets for buying and
selling a resource (such as water) or the imposition of water use tariffs
could create incentives for more efficient use. And, in fact, payment for
bulk water supply has been established in recent water laws in Zimbabwe,
Tanzania and Mozambique .
Collection of bulk water charges for a given time
period.
Once transactions are collected by the RBA, water costs (CW) for each water
user can be calculated along with the final net benefits (FNB), which are
equivalent to the consumer surplus shown, in Fig. , as the area
above the line Px* (area A). Line Px* is the social cost of
water where x* is the economically efficient water allocation.
The difference between the benefits expected by each agent (ENB) and the
final net benefits received (FNB) is the amount an agent will claim for
compensation in the next step (c) and is equal to the value of the
externalities (B+C in Fig. ). These claims are composed of the
difference in water costs between the unconstrained water demand (D) and
the actual water allocation (x*), which is area B in the figure, and the
cost of cooperation (CC), which is the loss in benefits due to the allocation
of fewer resources than what was demanded (area C in the figure).
Transfer payments
At this point in the methodology, the RBA has collected an amount of money,
referred to as the estate (E), that can be shared among the water
use agents. Using an axiomatic approach, a method of sharing this estate
should be determined. The aim of the axiomatic approach is to find and
capture the notion of fairness that water users could agree upon. The
approach then sets out axioms (properties) that fairness should or should not
satisfy. Finally, these properties are translated into a sharing rule that
quantifies the particular definition of fairness. How the benefits are shared
depends entirely on this definition as agreed to by water users. For example,
a simple proportional sharing method may satisfy the properties of equity
defined by the users, or an egalitarian method, or some other form of sharing
may be required. Since each river basin will have a different definition of
fairness (depending on conditions in the basin and the outcome of
negotiations with the water users), each river basin will likely have its own
unique sharing rule.
A flowchart of the complete methodology, including information obtained at
each step, is shown in Fig. .
Flowchart of methodology including information obtained
at each step.
Case studyEastern Nile River basin
The Eastern Nile River basin is used to illustrate the methodology described
in the previous section. Covering an area of approximately 330 000 km2
and with a length of 1529 km, the Blue Nile originates in the highlands of
Ethiopia and flows into Sudan, where it joins the White Nile at Khartoum to
form the Main Nile. The Main Nile then flows out of Sudan, into Egypt, and
discharges into the Mediterranean Sea. The Eastern Nile River basin is
composed of the Blue Nile, the Tekeze-Atbara, the Baro-Aboko-Sobat, the White
Nile downstream from Malakal and the Main Nile sub-basins (Fig. ).
Eastern Nile River basin
The dominant uses of water in the Eastern Nile River basin are irrigated
agriculture and hydropower generation, mostly in Sudan and Egypt. This is,
however, likely to change in the near future with the completion of the Grand
Ethiopian Renaissance Dam on the border of Ethiopia and Sudan.
There is a long history of unsuccessful negotiations over water allocation
and development of Nile water resources. Attempts at cooperation and benefit
sharing within the Eastern Nile basin go back to the early part of the 20th
century. The 1929 Nile Waters Agreement between Sudan and Egypt prioritized
Egyptian water needs and reportedly gave Egypt the right to veto future
hydroelectric projects along the Nile . Sudan and Egypt
subsequently replaced the 1929 treaty, in 1959, with the Agreement for the
Full Utilization of the Nile Waters, which essentially allocated the entire
flow of the Nile at the Aswan Dam to Sudan and Egypt. Unsurprisingly, this
has caused regional tension with the other riparians, who invoke the Nyerere
Doctrine
The Nyerere Doctrine of state succession, founded by the
first President of Tanzania, states that a new nation should not be bound to
international agreements dating back to colonial times and that these
agreements should be re-negotiated when a state becomes independent.
, and
general principles of international water law, to contest the 1959 agreement
and claim a share of the Nile waters.
In 1999 the Nile Basin Initiative (NBI) was undertaken with the goal being to
adopt a comprehensive, permanent, legal and institutional agreement on the
Nile River basin. So far there has been little success in negotiations
leading to an agreement. However, a Cooperative Framework Agreement (CFA) was
signed by a number of the Nile basin countries, with the notable exceptions
of Egypt, Sudan and South Sudan.
Regional tensions have further complicated Nile cooperation efforts. For
example, Ethiopia and Egypt have a long history of distrust and Egypt and
Sudan, as well as Eritrea and Ethiopia, have long unresolved border disputes.
Additionally, many Nile riparians have been broken by internal conflicts and
instabilities that result in challenges to international relations.
In recent years, the construction of the Grand Ethiopian Renaissance Dam has
been a source of concern and conflict among the three riparian countries. It
should be noted, however, that in early 2015, Egypt, Sudan and Ethiopia
signed an agreement on the declaration of principles with respect to the
project.
It is pretty much agreed, at this point, that benefit sharing may offer a
solution to the stalemate surrounding water use and allocation in the Eastern
Nile River basin. While the concept of benefit sharing can be appreciated by
most riparian countries, questions regarding methods of sharing benefits have
emerged. The three Eastern Nile River basin countries need to, first and
foremost, identify the bundle of benefits that can be generated, and then
agree on a mechanism for sharing these ).
Information collection
Given the lack of accurate data with respect to irrigated agriculture in the
Nile River basin, a net return of 0.05 USD m-3 is chosen as in
. For hydropower it is assumed that each MWh generated
has an economic value averaging 80 USD MWh-1 for firm power and
50 USD MWh-1 for secondary power. These values are consistent with
feasibility studies of hydroelectric dams in Ethiopia. Using these values the
unconstrained ENB are determined for each water use agent as
ENBj=Dj⋅Pj,
where Dj is the unconstrained quantity of water demanded by agent j and
Pj is its productivity. Note that the assumption is made that users do not
currently pay for water.
The water demand for the irrigation agents is equal to the crop water demand.
For the hydropower agents the water demand is equal to the amount that they
are allocated in the next step. Since the allocation is economically
efficient, the hydropower agents are assumed to be satisfied with the amount
of water flowing through the turbines.
Water allocation
The stochastic multistage decision-making problem (Eqs. to
defined in the Appendix) was solved using stochastic dual dynamic
programming (SDDP). Details of this algorithm can be found in
and in . The hydro-economic model of
the Eastern Nile basin is based on the schematization shown in
Fig. . In this study the assumption is made that the Grand
Ethiopian Renaissance Dam (located at H8 in Fig. ) is online.
Allocation decisions are chosen to maximize expected net economic returns
from irrigated agriculture and hydropower generation over a planning horizon
of 10 years and for 30 hydrologic sequences (see for a
description of the model).
Model schematic of the Eastern Nile River basin.
Irrigation agents (I) and hydropower agents (H) for this case study are
shown. Note that the numbering is not consecutive because there are nodes
that represent agents that are not part of the case study.
Once the allocation decisions are determined, the actual gross benefits (GB)
can be calculated as
GBj=xj*⋅Pj,
where xj* is the water allocation decision for agent j. The
difference between the ENB and GB is the cost of cooperation (CC) to the
agent due to the efficient allocation of water. In other words, it is the
difference between the amount of benefits the agent is expecting to get if
their unconstrained water demand is met and the actual benefits the agent
receives given the allocation decision, excluding water costs.
Collection of bulk water charges
The total of the transactions collected by the RBA (E), minus yearly
operating expenses of 3 million USD, will be used to compensate the agents
for a percentage of the benefits lost either through efficient allocation
(cost of cooperation) or water costs. Operating expenses of
3 million USD yr-1 are in line with those published by power pools
and river commissions .
Final net benefits for each agent can be calculated as
FNBj=GBj-CWj,
where CWj is the cost of water for agent j.
Transfer payments
Once the final net benefits have been determined, transfer payments can be
calculated for each agent. To do this, the total cost for each agent needs to
be calculated, which will give the upper limit to the claim (c) of an agent
to the estate.
Figure shows the annual demand curve for an irrigation agent in
this case study. In this study, we implicitly assume that the input demand is
horizontal (perfectly elastic) with the price (P) = marginal
productivity. The area to the left of line D (comprising areas A, B and C) is
the ENB (we see that the agent does not pay for water) resulting from
unconstrained water use. When water is constrained, area A is the FNB. The
claims (c) are divided into two parts: area B is the cost of water (CW) to
the agent and area C is the cost of cooperation (CC) due to the efficient
allocation of water. Area B also represents the amount of money that the RBA
collects from this agent. As previously mentioned, for hydropower agents the
water demand and the water allocation are equal; therefore, there is no cost
of cooperation. The claim (c), then, for a hydropower agent, is the cost of
water (CW). Over the whole basin the amount that the RBA collects (and is
available for transfer payments) is enough to reimburse the agents for the
actual cost of water; however, as mentioned, USD 3 million are held back
for annual operating expenses. Therefore the shortfall between the amount the
RBA has to share and the claims of the agents is the total cost of
cooperation for irrigation agents (∑CCj) plus operating
expenses.
Demand curve for the case study. D: quantity of water
demanded for a time period; x*: quantity of water allocated for a time
period; P: price of water.
The situation in which the amount available to share between agents is less
than the total claims of the agents is, by definition, a bankruptcy problem.
In this case study, the collected benefits are shared among the water use
agents following a rule that was developed based on a number of well-defined
properties in the bankruptcy literature (feasibility, non-negativity, claims-boundedness) as well as some that are specific to the problem
(solidarity, security of minimum benefits).
It should be noted that, for this study, the properties of this rule were not
developed with stakeholder input, as this was beyond the scope of this
research project. Although stakeholder involvement is imperative in this
institutional arrangement, in this case study, we are giving an objective
viewpoint, and this analysis serves as a benchmark or reference point.
Benefits are shared in such a way as to ensure that each agent has the same
proportion of final costs (ENBj- (FNBj+ tpj)) to benefits
demanded (ENBj) (where tpj is the monetary transfer payment made to the
agent) and that these are minimized. By extension, this rule also ensures
that each agent receives an equal proportion of final benefits (FNBj+
tpj) to benefits demanded (ENBj) and that these are maximized. This
rule also applies a solidarity property in which all agents take
equal responsibility for the shortfall in benefits at certain nodes due to
the efficient economic allocation of water over the basin, and a property of
security of minimum benefits in which the benefits obtained from the
use of water (FNBj) are uncontested.
The compensation rule is defined as follows:
tpj=ENBj-(FNBj+γENBj),
where γ is chosen such that
∑tpj≤E.
Equation () ensures the property of feasibility, which is
the requirement that the sum of the transfer payments not exceed the amount
available to share.
The following constraints also apply:
tpj≥0,tpj≤cj.
Equation () ensures non-negativity, which requires that
each agent receive a non-negative amount, and Eq. () ensures
claims boundedness, which requires that each agent receive, at most,
the amount of its claim.
Rewriting Eq. () to read
γ=(ENBj-(FNBj+tpj))/ENBj
shows that the property of solidarity is supported by ensuring that
the final cost (ENBj-(FNBj+ tpj)) to expected benefit (ENBj)
ratio for all agents is the same.
In this final step, the transfer payments are calculated and the total final
benefits (FNB + tp) for each agent are determined.
Results
The analysis of results was carried out on year 4 of the 10-year planning
horizon. This ensures a steady-state condition that is not influenced by
initial hydrological and storage conditions or by any end-effect distortion
due to reservoir depletion that occurs as the end of the planning period
approaches . As previously explained, the amount of water
allocated to hydropower agents is equal to the amount demanded. This means
that all hydropower agents receive 100 % of the water demanded. The
efficient allocation of water results in most irrigation agents also
receiving their unconstrained demand. The exceptions are agents I1, I4 and
I14, who receive, on average, 1, 0 and 94 % of their unconstrained demand,
respectively (see Fig. ). This result is not
unexpected because, from an economic standpoint, irrigation in the Eastern
Nile River basin should take place downstream after water has been used for
hydropower generation upstream . These three
irrigation agents have cooperation costs as well as, possibly, water costs.
Looking at the cumulative distribution of the proportion of the allocated
amount of water to the amount received for these agents
(Fig. ), we see that 95 % of the time, agent I1 does not
receive any water. Agent I14, on the other hand, receives its full demand
about 75 % of the time. Agent I4 (not shown in Fig. ) always
receives 0 %. The rationing of water for upstream irrigation users is a
result of the horizontal demand curve used for irrigation. If more detailed
economic/agricultural data were available, a non-horizontal demand curve
could be produced. This may result in irrigation schemes with high value
crops having priority to water and those areas with low value crops not being
irrigated. This means that the irrigation water users that are rationed may
change and they may be more spread out over the basin.
Average proportion of water allocation to
unconstrained demand for all agents. Only the values for those agents in
which the proportion is less than 1 are shown.
Cumulative distribution function for the proportion
of water allocation to unconstrained demand for agents I1 and I14.
Overall, the agents with the smallest claims are all hydropower agents in
Sudan (H9, H11, H14, H15) with marginal values that are almost equal to
marginal values at the downstream sites (see Fig. ). This means that
they sell water downstream at about the same price that they paid for it,
resulting in lower water costs. Figure gives a
basin-wide view of the percentage of the unconstrained benefits claimed by
each agent, by agent type, on average. The irrigation agents upstream claim a
larger percentage of their expected benefits because, first, they pay more
for water and, second, they also have cooperation costs. With respect to
hydropower agents, H8 and H19 (Grand Renaissance and High Aswan,
respectively) claim the largest percentage of their expected benefits. In
both cases, the cost of water at these sites is much greater than the cost of
water at the respective downstream sites.
Marginal water value – Blue Nile and Main Nile
Percentage of unconstrained benefits
claimed by agents.
From the collection of bulk water charges for the period analyzed (year 4),
the RBA ends up with USD 3894 million to allocate between the agents (after
subtracting USD 3 million for operating costs). The total claims amount for
all agents, for the year, is USD 4266 million, which means that there is a
shortfall of USD 372 million between the amount available to share and the
claims, or about 9 % of the total claims.
Using the bankruptcy rule developed for this example, the average amount of
transfer payment is calculated for each agent. The ratio of FNB to ENB,
referred to as the initial ratio, and final net benefits plus
transfer payments (FNB+tp) to ENB, referred to as the final ratio,
are determined and analyzed. These results were analyzed over the 30
different hydrologic sequences to assess how this rule performs under varying
hydrologic conditions.
Figure shows the mean values for initial ratios (shown as
large filled squares) and final ratios (shown as large filled diamonds) for
irrigation agents as well as the values for each of the hydrologic sequences.
Agents I1 and I4 receive little or no irrigation water, on average, as
discussed previously. Agent I14 initially receives about 23 % of its
expected net benefits, on average. This agent is located at the Kashm El
Girba dam, on the Tekeze-Atbara River. The flow of this river is highly
seasonal, with annual flows entering Sudan from Ethiopia restricted to the
flood period of July to October. The design storage capacity of the reservoir
at this site is about 10 % of the inflow; however, high sedimentation in
the reservoir dropped the storage capacity by 50 % as of 1977. This loss of
storage capacity has resulted in severe water shortages during drought years
and an associated decline in the crop area cultivated. As a result, the
restriction of water for this irrigation agent is more probably due to the
hydrology as opposed to being economic in nature. Due to flow variation, the
marginal water values are highly variable at this site, resulting in a wide
spread of initial ratios over the hydrologic sequences (as indicated by a
large vertical spread of data points on the graph for this agent). All other
agents always receive their full unconstrained demand. Variability in the
initial ratios of these agents is due to variability in the marginal water
values over the hydrologic sequences.
Initial and final ratios for irrigation agents.
Results for hydropower agents are shown in Fig. . Here we see
more variation in the initial ratio than for the irrigation agents. The
upstream hydropower agents (H2, H3), and those on the Tekeze-Atbara River
(H13, H14), have large variations in initial ratios as a result of large
inter- as well as intra-year variations in flow (and subsequently in marginal
water values), which occurs because these sites are all upstream of flow
regulating infrastructure. The agents with the smallest claims are the four
smallest hydropower agents in Sudan (H9, H11, H14, H15). These agents have
the largest initial ratios and, therefore, often do not receive monetary
transfers. This also results in the final ratios for hydropower agents not
being equal because the property of non-negativity, which is used to define
the sharing rule, allows an agent to keep its initial benefits from water use
even if this results in its final ratio being larger than those of the other
agents.
Initial and final ratios for hydropower agents.
Overall, the average final ratios for all agents (irrigation and hydropower)
are equal, with the exception of agents H9, H11, H14 and H15, as mentioned
above. There is also very little variation in final ratio values with respect
to hydrologic sequence. The final ratio for irrigation agents varies from
93.5 to 95 % of their uncontested benefits. For hydropower agents the
statistical distribution of final benefit ratios is shown in
Fig. . We see that these final ratios also vary between 93.5
and 95 % with the exception, again, of agents H9, H11, H14 and H15, which
have high initial ratios that vary with inter- and intra-annual variations in
the marginal value of water. These results indicate that the sharing rule
used is predictable in that agents can expect similar final benefits
regardless of the hydrologic conditions.
Final benefit ratio for hydropower agents.
Results that warrant a closer look are those for the upstream irrigation
agents I1 and I4. We can conclude that, in this case study, given the
economic information used in the model, it is economically inefficient to
irrigate upstream in the basin regardless of the hydrologic sequence (meaning
that even in situations of high flow years, there is no irrigation water
allocated to these agents). However, these two irrigation agents consistently
demand fairly substantial transfer payments even though they do not
contribute economically to the basin. This becomes an obvious problem of
fairness for the other agents. If these results persist over a number of
years, the RBA could use this information for better management by ensuring
that agriculture is developed downstream or that upstream agricultural sites
have a high productivity value.
Finally, it should be noted that we make no attempt to compare the results of
the case study with current water use in the basin. While the presented case
study is hypothetical and is not consistent with the actual, current
situation, it represents a possible long-term future scenario in the basin,
and the results reflect these assumptions. In the case study, we assume
complete cooperation; there is expanded irrigation in the basin and the Grand
Ethiopian Renaissance Dam is online.
Conclusions
The sharing of benefits among agents in a transboundary river basin is based
on three fundamental questions: (i) how can the benefits of water use be
quantified and monetized, ii) what mechanism can be used to allocate
benefits, and (iii) upon what criteria should the sharing of benefits be
based to ensure efficiency and equitability. It should be noted that there is
no unique response to these questions. In this paper, we propose one approach
for distributing the benefits of cooperative management in a river basin
system comprised of rival and non-rival uses. To illustrate the approach, we
used the Eastern Nile River basin as a case study due to the important
hydropower and agricultural sectors spread over three countries.
The methodology described in this paper is based on the welfare distribution
for each agent being equal to the sum of its benefits from water use plus a
monetary transfer. First, efficient water allocation is implemented through
the application of a hydro-economic model in order to maximize the benefits
in the river basin. Second, a charge for the use of water is established. The
price that agents pay for the use of water is equal to the marginal value of
water at the site at which the agent receives its allocation. The total of
the water charges is equivalent to the overall value of water in the basin
that is used in the sectors being studied. Finally, the total of the water
charges are reallocated over the basin to ensure that all agents pay the same
ratio of costs to benefits, using an axiomatic approach. The whole system is
overseen by an RBA.
The two main goals of benefit sharing, efficiency and equitability, are the
foundation of this methodology. The hydro-economic model results are the
efficient water allocations for each agent. Efficiency is also inherent in
the benefit-sharing rule used to implement the monetary transfers in that all
of the available money is shared among the agents. The defined properties of
fairness are embedded in the sharing rule through the axioms.
This methodology can be useful to policy-makers in that the solution is more
likely to be perceived as equitable, resulting in water use agents being more
open to cooperation. An additional advantage of this method is the
predictability of the final results. These results, over varying hydrological
sequences, are shown to be relatively constant.
The importance of this methodology is that it can be adopted for application
in negotiations to cooperate in transboundary river basins. The methodology
is flexible in that there is no set way to allocate the water over the basin.
Any hydro-economic model (or another method) can be used as long as the
amount of water allocated to each agent, as well as the marginal value of
water for each agent, is available. Also, the development of the sharing rule
can be based on stakeholder input and will depend on specific conditions in
specific river basins.
One obvious constraint of this method is its dependence on the existence of a
strong basin-wide authority to impose fees and that can enable negotiations
between stakeholders for the development of a sharing rule. Allowing all
stakeholders a place at the table might prove challenging, especially for
large systems with diversified water use activities. In the irrigation
sector, for instance, farmers could be represented by a water user
association. For uses of water as a public good, such as for environmental
flows, the representative could be the Ministry of Environment of the country
of interest. For municipal uses, the system could be designed in such a way
that a minimum amount of allocated water is guaranteed (a fixed constraint in
the allocation system), while quantities beyond that minimum would be part of
the pool for which municipalities would have to bid. Industrial and power
companies are easier to handle. All users that can be rationed (mainly
private water users) are allowed a place at the table for the purpose of
defining fairness with respect to transfer payments. Another possibility is
that the government (or at least a high level representative of the
stakeholders) has the ultimate negotiation power, akin to negotiations on
trade liberalizations. Clearly, different lobbies exist that would try to
influence the government, implying, ultimately, some form of compensation
(the analysis of which is outside the scope of this paper).
Another constraint is the availability of reliable data. Some information
such as market prices, either national or international, can be observed and
transportation costs can be estimated, allowing for an approximation of the
mark-up that may accrue to farmers, for example. This paper describes a
system in which it is assumed that there is cooperation over the whole basin
and that water users have agreed to bid for water and to supply the
information that is necessary to make the methodology work. Increasingly, the
information required is becoming available through the use of remote sensing
and monitoring of river basins.
Incentives for water users to cheat, with respect to the data they provide,
will remain even if the river basin authority is able to audit the bids. For
industrial uses, including hydropower generation, cheating might be more
difficult because the market prices and production functions are often well
characterized. The main challenge is to be found in the agricultural sector
because (a) it is often the largest water use in a basin (and, hence,
cheating might have serious basin-wide consequences), and (b) the
heterogeneity in terms of cropping patterns and irrigation efficiency
requires that significant data be collected and analyzed to audit the
demands. We argue that the incentives to cheat might not be eliminated, but
they can be suppressed, or at least kept within limits, through a robust
monitoring system and a strong RBA to negotiate disputes. An example of how
this has worked, with good success, is the Indus River basin.
, in discussing the Permanent Indus Commission, states
“The commission's ability to monitor development of the shared river system
has permitted it to ease member states” fear of cheating and confirm the
accuracy of all exchanged data. Finally, its conflict resolution mechanisms
have permitted the commission to negotiate settlements to disputes and
prevent defection from cooperation.
This paper adds to the analysis of the sharing of economic benefits in
transboundary river basins by describing a methodology for efficient and
equitable benefit sharing based on operating the river basin as a water
pseudo-market with the advantages of resource use optimization, improved
resource reliability and enhanced security of resource supply. Also, we
impose specific axioms, based on a stakeholder vision of fairness, on the
compensation scheme and derive a unique solution for the distribution of
monetary payments. This technique may lead to a sharing solution that is more
acceptable to shareholders because the definition of the sharing rule is not
in question, as would be the case if we applied existing bankruptcy rules or
other game theory solutions with their inherent definitions of fairness.
Hydro-economic modeling is a common tool used to analyze river basin systems
and, specifically, water resources allocation problems. These models use a
network representation of the system in order to physically connect various
sources of supply with scarcity-sensitive water demands. Reviews of
hydro-economic models can be found in Harou et al. (2009) and Brouwer and
Hofkes (2008). Two classes of hydro-economic models exist: optimization-based
and simulation-based. Both approaches have advantages and disadvantages, but
the allocation decisions and the marginal costs of the binding constraints
(the limiting resources or factors that prevent further improvement of the
objective function) determined by an optimization model make this type of
model attractive in the proposed methodology. In the system network, a water
balance is evaluated at each node to determine the amount of water available
for the demand sites connected to that node. The mass balance equation
ensures that water is allocated to the connected water users to the extent
permitted by water availability at the node. In the case of water scarcity,
the marginal cost associated with the water balance indicates the shadow
price of water or what the users would be willing to pay for an additional
unit of water (Young, 2005).
In a hydro-economic water resource optimization problem, the objective
function Z to be maximized includes the economic net benefits across
all water uses over a given planning period.
Z*=maxxtEqt∑tTαtbt(wt,xt)+αT+1ν(wT+1),
where bt are the basin-wide net benefits at time t, xt the
vector of allocation decisions, wt the vector of state variables,
α a discount factor, ν a terminal value function, E the
expectation operator capturing he uncertainty that governs the hydrologic
inflow qt and Z the total benefit associated with the optimal
allocations (x1*, x2*, ..., xT*).
This function is maximized to the extent permitted by physical, institutional
or economic constraints:
gt+1(xt+1)≤0,ht+1(wt+1)≤0,wt+1=ft(wt,xt,qt),
where g is a set of functions constraining the allocation decision, h a
set of functions constraining the state of the system and f a set of
functions describing the transition of the system from time t to time
t+1.
Included in the functions in Eq. () are the mass balance equations
for the river basin:
st+1-R(rt+lt)-I(it)+et(st,st+1)=st+qt,
where st is the storage at time t, rt the controlled outflows, lt
the uncontrolled outflows, it the water withdrawals, R and I the
connectivity matrices representing the topology of the system (including
return flows), and et the evaporation losses.
At the optimal solution of the problem (Eqs. to
), the solver provides the allocation decisions (x1*,
x2*,..., xT*) and the marginal values of water (shadow prices)
(λ1, λ2,...,λT) of the constraints. For the
constrains in Eq. (), the shadow prices correspond to the marginal
resource opportunity cost at the sites where water balances are computed.
Acknowledgements
The authors are grateful to Yasir Mohamed (HRC-Sudan) and Erik Ansink
(Utrecht University) for valuable discussions early in the development of
this work, and would like to thank the Institut Hydro-Québec en
environnement, développement et société (EDS) for their financial
support (grant 03605-FO101829).Edited by: P. van der Zaag
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