Examining the Effects of Water Use Regulations on Agriculture in the
São Francisco River Basin, Brazil:
An Application of a Linked Hydro-Economic Model
Marcelo de O. Torres – Catholic University of Brasília, Brazila
Marco Maneta – University of California, Davis, USAc
Richard Howitt – University of California, Davis, USAb
Stephen A. Vosti – University of California, Davis, USAb
Wesley W. Wallender – University of California, Davis, USAc
Luís H. Bassoi – Embrapa, Semi-Arid Tropics Research Station
Lineu Rodrigues – Embrapa, Savannah Research Station
(a) Department of Economics; (b) Department of Agricultural and Resource Economics; (c)
Department of Land, Air and Water Resources.
Keywords: Water management, Agriculture, Hydro-Economic Model, Water Policy, São Francisco
River Basin, Brazil
Palavras-Chave: Economia dos Recursos Hídricos, Agricultura, Modelo Hidro-Econômico,
Irrigação, Bacia do Rio São Francisco
Summary
This paper presents a linked hydro-economic model and uses it to examine the effects of water use
regulations on the agriculture of the São Francisco River Basin, Brazil. The hydrologic effects of
weather on water availability are explicitly addressed using the hydrological model Mike-Basin, and
farmers’ adjustments to changes in the access to water and commodity prices are quantified with the
use of an economic model based on non-linear programming techniques. Both models are externally
linked. Results show that water use regulations may be binding depending on exogenous factors
such as commodity prices and precipitation regimes.
Sumário
Este artigo apresenta um modelo hidro-econômico para o exame dos efeitos da regulação do uso de
recursos hídricos na agricultura da bacia do Rio São Francisco. Efeitos de regimes alternativos de
precipitação na disponibilidade de recursos hídricos para irrigação são explicitamente considerados
no modelo hidrológico Mike Basin, assim como as reações dos produtores rurais a mudanças nos
preços agrícolas e no acesso a recursos hídricos são medidas com um modelo econômico baseado
em programação não-linear. Ambos modelos são externamente conectados. Os resultados mostram
que a regulação no uso e na disponibilidade de recursos hídricos pode ser “binding” dependendo de
fatores exógenos tais como preços das culturas e regimes de precipitação.
ANPEC: área 10.
JEL: Q-Q2.
1. Introduction
In many parts of the developed and developing world, water management policies have been
developed and implemented to deal with increasingly severe water scarcity, but the scientific basis
for testing and eventually guiding the deployment of these new policy instruments is often lacking.
For example, water rights are being allocated, water user associations are being formed, and water
pricing schemes are being discussed (e.g., Braga and Lotufo, 2008), but decision makers often have
little or no information about the effects of alternative policy actions on water use in agricultural or
the knock-on effects on rural employment or poverty.
This is understandable, because empirically examining the alternative water policies is
complex and necessarily interdisciplinary. Several studies have begun to address this complexity.
Early examples include Noel and Howitt (1982) and Vaux, H.J., and R. Howitt (1984) which study
water transfers and water market potential in California. Lefkoff and Gorelick (1990) adds water
quality and salinity issues in the study of the inter-relationships between water and crop production
in the Arkansas Valley; Rogers, Hurst, and Harshadeep (1993) links the water and agriculture to the
broader macroeconomy, and Beare, Bell and Fisher (1998) integrates hydrology and agriculture to
estimate irrigation water values in Australia. Evers, Elliot, and Stevens (1998) couple a crop growth
model with a hydrology model to evaluate cropping patterns, water and reservoir management
options in southwestern Oklahoma, USA.
More recent examples are Rosegrant et al. (2000) and Cai, McKinney and Lasdon (2003),
which use network flow and crop yield models applied to river basins. In the former, the model is
applied to water trading analysis in the Maipo river basin in Chile, and in the latter to evaluate soil
salinity and water availability usable for irrigation in the Syr Darya River basin in Central Asia.
Draper et al. (2003) focuses on optimal of water allocation, agriculture, and reservoir management
options in California, using a network flow approach and an economic optimization model with
multi-input crop-specific production functions. Alverez, et al. (2004) links gross agricultural
margins to irrigation using a water balance approach and agronomic production functions in a semiarid area in Spain. Cai and Wang (2006) , Cai, Ringler and You (2008), Marques et al. (2006), and
Ringler et al. (2006) all use network flow approaches coupled with multi-input multi-output
economic models to address theoretical and empirical issues in different parts of the world. And
finally, Guan and Hubacek (2007) that uses a water balance approach at the regional level linked to
an economic system represented by an input-output model with application to Northern China.
While the existing literature has made impressive contributions to our understanding of some
of the consequences of alternative water policy actions, gaps remain, especially as regards the
characterization of water-agriculture interrelationships. For example, the existing literature by and
large fails to adequately capture the multi-input, multi-output nature of agriculture. With the notable
exceptions of Draper et al. (2003), Cai and Wang (2006), Marques et al. (2006), Ringler et al. (2006)
and Cai, Ringler and You (2008), all studies have relied on a single water input (measured water or
proxies for water, such as evapotranspiration) in agronomic production functions, or on linear
programming based on fixed technical input-output coefficients. In reality, agriculture involves a
multi-input, multi-output non-linear production processes, and farmers react to changes in water
policies by changing input and output mixes, the amount of irrigated area, and the amount of water
used per hectare. Existing studies do not allow for adjustments at these extensive and intensive
margins, and therefore may be under-estimating (or over-estimating) the impacts of proposed policy
changes. Also, agriculture in most settings is comprised of both rainfed and irrigated systems, and
2
the latter may take advantage of seasonal rainfall using irrigation to supplement when and where
needed. Existing models fail to capture this important aspect of heterogeneity in agriculture.
In this paper, we address these and other shortcomings by developing a hydro-economic
model for the São Francisco River Basin, Brazil. ,It treats separately, but allows for, the coexistence
of irrigated and rainfed agriculture, and takes into account seasonal precipitation levels as one of the
arguments of the crop specific multi-input, multi-output production functions. So water comes into
play through two sources: from the surface water bodies and from precipitation that falls directly
onto the crops. In this manner, the approach allows farmers to adjust product mix, production
technology, area under plow and water use in response to changes in relative input and product
prices, changes in the availability of surface water for irrigation and in the level of precipitation.
Moreover, the basin-wide hydrologic model allows researchers to predict the effects of weather on
model outcomes, thereby making the results more useful for the development and implementation of
policy instruments.The following sections describe the research site, the modeling framework, and
then present model simulations and results. The final section presents conclusions and discusses
their policy implications.
1.1. The São Francisco River Basin
The São Francisco River (see Figure 1) with 634.781 km² (8% of country’s area) and an
annual average flow of 2,850m3/second provides about 70% of the surface water in Northeast Brazil
and like much of Brazil the basin includes communities characterized by a broad range of incomes
and economic activities (ANA/GEF/PNUMA/OEA, 2004). The basin’s agricultural systems cover a
similar range between capitalized export-focused enterprises, mid-income and low-income
commercial farmers, and subsistence farms; the sector a a whole would clearly be characterized as
highly commercial (Timmer, 1988) and hence responsive to price and technology changes. The
basin also hosts several important water-dependent ecological zones. Increasingly, the complex web
linking water availability, water quality, water productivity, economic growth, poverty alleviation
and community and ecosystem health is coming into focus.
Sobradinho Dam
and Reservoir
Moxotó, Itaparica, Complexo
Paulo Afonso e Xingó Dams
Figure1 – São Francisco River Basin and River
In part to deal with the increasing pressures on the Brazilian water resources, in the SFRB
and elsewhere, Brazil’s Federal Law 9.433 was implemented to promote and guide public-sector
involvement in water management so as to integrate across the connections defined by the flow of
3
water to improve overall social welfare. More specifically, the Law clearly places hydrological
resources in the public domain (Article 1) and charges policymakers with the wise and sustainable
management of these resources (Article 3) via the use of water price policy and other policy
instruments (Article 5), some of which remain to be developed.
This law among other things places the river basin as the spatial scale unit for water
management and planning. In this context, river basins in Brazil were ranked according to the level
of complexity based on population density, natural resources base, economic activities and levels of
development and ecosystem vulnerability and the SFRB was in the most complex category and
considered as a special unit for planning and development of the country. Basins in this category will
face the widest scope of instruments for water management that go from the simple characterization
of its water bodies, water diversion plans and minimum flow requirements to the implementation of
water rights, allocation and pricing. Several other water and environmental and multiple use policies
are been considered and at the initial stages of implementation (ANA/GEF/PNUMA/OEA, 2004).
This places the SFRB as an ideal candidate for application of the model. In this context, this
paper uses a linked hydro-economic model to assess the joint effects of one policy change in the
minimum flows requirements at the Sobradinho dam (see Figure 1) and one economic shock. For the
policy change, we simulate a mandatory a minimum flow at the entrance of the Sobradinho reservoir
to maintain storage levels and to meet outflow requirements, and on the economic side we simulate a
large increase in the price of sugar cane. Results suggest that under these scenarios water for
irrigation will become scarce, especially in downstream areas, and that this policy-induced water
scarcity will lead to a non-uniform geographic distribution of the benefits associated with sugar price
increases, especially during dry years.
2. Economic Model of Agriculture
The economic model proposed here is based on a class of models called Positive
Mathematical Programming or PMP (Howitt, 1995), widely used in applied research and policy
analysis (House, 1987; Howitt and Gardner, 1986; Kasnakoglu and Bauer, 1988; Arfini and Paris,
1995; Lance and Miller, 1998; Chatterjee et al, 1998; Paris and Howitt, 1998; Heckelei and Britz,
2000; Preckel, Harrington, and Dubman 2002; Röhm and Dabbert , 2003; Cai and Wang, 2006;
Marques et al. 2006; and Cai, Ringler and You, 2008)).
2.1. The Objective Function
It is assumed that farmers in each município within the São Francisco River Basin seek to maximize
net revenue derived from their farming activities in a given year.1 Therefore, the backbone of the
analytical model is an objective function that explicitly sets out to maximize profits. That is:


2
max net    p i q i ( X ih , Pi )   p h X i h  ( i X i land  0.5 i X iland
)
i 
h

Eq. 1
The first term on equation 1 represents gross revenue, where pi is the output price of the perennial
crop, annual crop or livestock activity i, each of which is produced according to a production
function qi(Xih,Pi). Xih, described in more detail in the next section, is the matrix of i perennial crops,
annual crops and livestock, and h agricultural inputs, and sets the input requirements for producing
1
The lowest level of aggregation is the município (Brazilian counties); this is the spatial resolution used in the basinwide economic model of agriculture.
4
all crop and livestock products. Inputs include: land, surface water used in irrigation, hired labor,
family labor, and purchase inputs (e.g., fertilizers). Pi represents the amount of rainfall that falls
onto the land area covered by crop i during its growing season only. So, it has a seasonal temporal
resolution.
The cost to produce a unit of crop i is defined by two remaining terms: the first term is the
market price of the inputs, ph, multiplied by the quantity of inputs used, X ih ; and the second term, in
parenthesis, is the implicit cost associated with land allocation. It has a quadratic specification with
parameters  i and  i and captures the increasing marginal cost associated with allocating larger
amounts of land to a given crop. As a given farmer allocates increasing amounts of land to a specific
crop, the new land may be of inferior quality or not as suitable to grow that particular crop. More
generally, this term captures non-linear effects that may enter into the decision-maker’s problem and
that are not directly observable or measurable causing costs to rise non-linearly with area.
Before moving to the next section, a few caveats regarding model assumptions merit
mention. First, to incorporate perennial tree crops into the model, we follow Chatterjee et al. (1998)
and base tree crop off-take on ‘average’ production over the life cycle of trees. Second, changes in
land allocated to perennial tree crops in response to policy-induced (or other) changes in relative
output and input prices are assumed to occur as quickly as changes in annual cropland allocations.
Third, livestock (cattle, in this case) is produced using land (measured in terms of the carrying
capacity of established pastures), labor, and purchased inputs, and output is measured in terms of
harvested carcass weight which can be sold or consumed at home. Finally, no lags between
observed price changes and their realized impacts are explicitly included, and the decision-making
process captured in the model does not address issues of uncertainty.
2.2 The Production Function
The production function q(Xih,Pi), provides an estimate of output produced by an existing set of
inputs and given the level of precipitation for each cropping activity i. The functional form used for
q is a constant elasticity of substitution (CES) but distinct functions are used for rainfed and irrigated
crops. If the crop is rainfed, the function is:
i


qir  Ai Precip i   bih1 X ih 1  ,
Eq. 2
 h

r
where the superscript r in q i stands for a rainfed production function, Ai represents the area share
 1
parameters, and bih are the production function parameters;  
, σ is the elasticity of

substitution among inputs; and εi is the returns-to-scale parameter. The subscript h-1 indicates that
rainfed crops can use all inputs except surface water. Precipi is defined as the ratio between the
Pa
e
a
expected level of precipitation Pi and the actual level of precipitation Pi , that is, Precip i  i e .
Pi
Precipi therefore acts as a linear shifter in the production function.
If a crop is irrigated, the function is:

q  Ai   bi h 1 X i h 1  bw X i sw  Pi a
 h
ir
i



i


 ,
Eq. 3
5
ir
where the superscript ir in qi stands for an irrigated production function, Ai are the area share
parameters, bih-1 are the production function parameters for all inputs except surface water, bw is
the share parameter associated with water use whether it comes from surface water (Xisw ) or
a
precipitation ( Pi ), and  and εi are defined as in Eq. 2.
2.3 Shadow Values for Non-Marketed Limited Inputs
In the case of inputs with limited supplies such as family labor, surface water and land, the marginal
cost of an input is represented by the sum of its market price plus its shadow price, λ. The shadow
prices for each non-marketed or limited input are the Lagrange multipliers that solve a linear
programming model, which has as its explicit objective the maximization of net revenue using land
as the decision variable:
max land  pi yˆi X i land  ph aih X i land
i
i
Eq. 4
subject to município-level resource constraints:
Land :  X i land  Bland ,

i

Family labor :  ai fl X i land  B fl ,
i

Eq. 5

Surface Water :  X isw m  B sw m ,
i

Eq. 6
and a model calibration constraint
X i land  Xˆ i land ,
Eq. 7
where in Eq. 4 pi is defined as before, ŷ is the yield per hectare of land dedicated to crop i
( X iland ), ph is the unit cost of input h used in the production of crop i, and aih are inputs per hectare
 X ih
 . Bland and Bfl reflect the total availability of land and family labor, respectively. Eq. 6


X
iland 

assures that the total amount of surface water used in month m, X isw m , is less or equal to the total
amount of surface available for irrigation in that month, B swm . In Eq. 7, X̂ i land is the total amount
of land allocated to crop i that is observed by researchers; this constraint prevents specialization and
preserves observed crop allocation patterns while estimating shadow values of limited or nonmarketed inputs.
The shadow values associated with constrained resources represented by Eqs. 5 and 6
( land , FamilyLabo r ,  SurfaceWater ) have the usual conceptual definition. That is, they measure by
how much net revenue would increase at the margin if farmers had one more unit of land, water, or
family labor available. In Eq. 7, the Lagrange multiplier measures the change in farm profits
6
associated with a one-unit reallocation of land from the least profitable crop to a more profitable
crop, and are needed in the calibration of the production function (Appendix A). For the model
calibration constraint (Eq. 7), the associated Lagrange multiplier, say i land , measures how much
farmers gain by re-allocating one unit of land from the least profitable crop to a more profitable crop
i. Notice that although the shadow values associated with the fixed inputs such as land, family labor,
and water may change from farmer to farmer, they are not crop specific. However, the Lagrange
multiplier associated with Eq. 7 is both farmer- and crop-specific.
To operate with constraints in Eq. 6 at a monthly time step, information is collected on the dates
of planting and harvesting for each crop i and for each município during the 365 days (n) of the year.
Then, assuming that each crop has four growth stages, each with an associated crop water coefficient
kc and using the reference crop evapotranspiration Eto method (Allen et al., 1998), the total annual
agronomicaly optimal evapotranspiration for each crop i in day n is kci n Eton . For those days in
which kci n Eton > Pna (actual precipitation level), we called Zin the difference between kci n Eton and
Pna , that is, Z in  kc in Eton  Pna . On the other hand, for those days in which kc in Eton  Pna , Zin is
365
truncated at 0. The sum of Z in annually takes then the form of
Z
n 1
in
, where n=1 refers to
f
September the 1st; and monthly, the form of
Z
n s
in
, where s and f are, respectively, the starting
and ending day of each month.
Therefore, using these annual and monthly sums of Zin we then calculate the Metin as the ratio
f
between the sums. That is, Met im 
Z
n s
365
Z
n 1
in
. Where m = 1,…,12 (month 1 refers to September, 2
in
to October, 3 to November and so on).
The total amount of surface water used in month m, is then
X
i
isw m
  Met i m * ai sw *X iland ,
Eq. 8
i
 . Eq. 8 together with Eqs.
where ai sw is the annual amount of surface water per hectare  X isw
X iland 

5, 6 and 7, form the set of constraints of the linear optimization problem.
2.4 Estimation of Production Function Parameters
Estimation of the full set of parameters for the production function with 4 inputs in Eq. 2 and
5 inputs in Eq. 3 requires each crop i to be parameterized in terms of 4 parameters bih-1 , one for the
return-to-scale parameter  i and the crop specific parameter Ai in Eq. 2; and 5 parameters bih, one for
the return-to-scale parameter  i and the crop-specific parameter Ai in Eq. 3. For the estimation of the
7
parameters in Eq. 2, actual precipitation is set equal to expected precipitation, defined as the amount
of precipitation seen in the baseline year; the shifter parameter Precipi therefore is assumed to take
on the value of 1.
Typically, the few degrees of freedom included in the farmer- and crop-specific parameter
estimation process may require their estimation by methods such as maximum entropy (Golan et al.,
1996; Jaynes, 1957; Mittelhammer et al., 2000; Paris and Howitt, 1998). In this paper we follow an
analytical rather than an econometric method in which the parameters are calculated using the
economic optimality conditions for the use of each input and some prior values for some key
parameters such as the elasticity of substitution. These conditions seek maximization by setting the
value of the marginal product of each input equal to its unitary cost. In which the former is is defined
by its output price multiplied by the derivative of the production function (Eq. 2 and 3) with respect
to each input. For the unconstrained inputs, the unitary cost is simply their market price; for the
constrained inputs, each unitary cost is the sum of their purchase prices and their respective shadow
values, land, FamilyLabor , SurfaceW ater . Regarding the value of land, however, in addition to the
market and shadow prices, the calibration constraint represented by Eq. 7 further increases the value
of this fixed input. In other words, the true marginal cost associated with land allocation to the ith
crop is the sum of: 1) the market price of land; 2) the shadow value of land, λLand; and 3)
i land
.
Formally, the optimality equations for each input can then be defined as:
qi
 pu , for unconstrained inputs;
X iu
qi
pi
  fl , for irrigation and non-irrigation family labor;
X i fl
pi
qi
 pland  land  i land , for land;
X i land
qi
pi
 psw  sw , for surface water.
X i sw
pi
Eqs. 9
Subscript u in the previous equation indicates the unconstrained inputs in X, i.e., materials and hired
labor. By algebraically manipulating the optimality equations we reach expressions for each of the
parameters b̂ih , and Ai ,  i and  i in Eq. 1 as a function of values on input prices, output prices, and
input quantities. For this exercise we assume constant returns to scale for all crops (  i    1 ) and
a value of 0.4 for the elasticities of substitution (σi). An appendix containing the derivation and
calculation of parameters b̂ih , and Ai, as well as  i and  i of Eq. 1 may be requested to the authors .
2.5 Economic Simulation Model
Eq. 11 uses the parameterized CES production function
maximizes net revenue:
8
q̂ to find the optimal set of inputs that
 [ p qˆ
max net
i
X
r
i
i
2
( X ih , Pi )  pi qˆ iir ( X ih , Pi )   p h X ih  (ˆ i X i land  ˆ i X iland
)]
i
Eq. 10
When municípios are subject to resource and water vailability constraints
Land:
 X i land
i
Family Labor:
 Bland
 X i fl  B fl
i
Surface Water:
X
isw m
 Bsw m
i
X
i
isw m
  Met i m * ( X i sw )
Eqs. 11
i
3. The Hydrologic Model
The hydrologic component is based on a semi-distributed modeling and water accounting approach
implemented in MIKE Basin (Danish Hydraulic Institute, 2005). In this model the basin is
characterized as a network of interconnected elements (catchments, channels, water users or
reservoirs) that can store, transfer or use water. A mass balance equation is solved for each of these
elements and time step given the supplied inflow and outflow information provided by the users. In
this approach the SFRB is divided in 16 sub-catchment areas and the inputs to each catchment is the
sum of the outflows of the immediately upstream catchments. River discharges include catchments’
contribution measured by the difference between immediately upstream catchments inflows and
outflows. Outflows from reservoirs are controlled via release rules. Figure 2 depicts the SFRB and
the watersheds (outlined in grey) contained in the model. For each watershed, monthly average
discharges are reported; several examples of mean discharges (horizontal bars) are provided in
Figure 2 with red lines reporting standard deviations derived from historical discharge data.
Petrolina
Barreiras
Paracatu
Rio Paranaíba
Figure 2 – Hydrologic Model of the SFRB, with Discharge Data from Selected Watersheds
9
4. Hydrologic and Economic Models: Linkages
As regards of model interactions, the hydrologic model provides the economic model with
estimates of surface water available for use in irrigation in each month for each watershed during a
given scenario. This information is then ‘fed into’ the economic model of agriculture where it
appears as a constraint on cropping activities, Eqs. 6 and 11. That is, first the Hydrologic model
provides the economic model with the flows for the upstream subcatchment. The economic model
incorporates this information and allows upstream farmers to adjust their input and output mixes.
The results are a set of monthly optimal water demand upstream. Remaining outflows from the
upstream subcatchment are then used as the inflows for the midstream subcatchment and so on until
this optimization process reaches the downstream subcatchment.
5. Data
For this exercise, the calibration of the economic model uses município-level data on inputs,
outputs, and relative prices from the Brazilian Agricultural Census1995/96 and 2006/2007
(preliminary statistics) - (IBGE). Methods for estimating water use at the crop and município levels
is detailed below. The hydrological model relies on discharge data from DSS522.1 dataset
(DE/FIH/GRDC and UNESCO/IHP, 2001) and on data of precipitation and evapotraspiration at the
sub-watershed level from CRU_TS_2.10 dataset (Mitchell and Jones, 2005).
5.1 Water Use Data
The database on water use for irrigation at the município level is calculated in the following
way. First, we calculate the water use in irrigation at the watershed level. Information on monthly
reference evapotranspiration (ETo) and precipitation at each yellow polygon Figure 2 has been
collected (Mitchell and Jones, 2005). An average irrigation efficiency of 70% is assumed and crop
water coefficients (KC), available from Allen (1998), for the 10 most important crops in terms of
irrigated area within each watershed: soybeans, corn, beans, rice, melons, onions, tomatoes,
sugarcane, bananas, grapes and mangos. A crop calendar provides the most probable dates of
planting and harvesting for each of crop grown in each watershed. These data allow us to calculate
the amount of irrigation water used in each watershed c by using the formula:
ET  precip cm
Xwcnm  cnm
, where Xwcnm is the amount of water in watershed c used for irrigation on
IEff
month m on crop n, ETcnm is the evapotranspiration in watershed c associated with crop n on month
m. Precipcdm is the amount of rainfall in watershed c on month m, and IEff is average irrigation
efficiency. If in a given month, Precipcm > ETcnm , Xwcnm is assumed to be zero. The amount of
water used in município i , located in watershed c, on the irrigation of crop n, in month m (Xwicnm) ,
is calculated as Xwicnm   in * Xwcnm , where  in is the percentage of total irrigated area in município i
that is allocated to crop n. Xwicnm  Xwinm .
6. Simulations and Results
In this paper we examine the impacts of minimum flow regulations and of an exogenous
price shock on the agricultural activities and income in two contiguous watersheds located in the
north-central part of the SFRB: Boqueirão which is located upstream and Juazeiro, downstream of
the São Francisco River. The area encompassed by these two watersheds includes the Sobradinho
Dam (Figure 1) and 59 municípios and has experienced (although not uniformly) above-average
increases in area dedicated to diversified commercial agriculture over the past 10 years. The
10
Boqueirão watershed, located upstream from Juazeiro, includes the município of Barreiras which is
home to large-scale grain farmers (especially soybeans) practice irrigated agriculture using centerpivot technology. The other downstream watershed ( Juazeiro) include part of the municípios of
Petrolina and Juazeiro, which have several irrigation districts and highly diversified agricultural
systems that produce a broad array of tropical fruits and grapes.
As regards of water use regulations, ANA, the Brazilian agency for water resources,
currently stipulates 1815m3/s as the minimum outflow flow from the Sobradinho Dam. Our Monte
Carlo simulations, based on historical data on discharge in the SFRB (DE/FIH/GRDC and
UNESCO/IHP, 2001) reveal, however, that in circumstances such as a drought, it would be difficult
to meet this outflow flow and still have the reservoir at a constant level. We therefore simulate the
effects on the agriculture in the two subcathments (Boqueirão and Juazeiro) in case ANA puts also a
mandatory regulation on the inflows at the upstream entrance to the Sobradinho reservoir stipulating
a minimum inflow of 2000m3/s during all months of the year. Figure 3 depicts continuous water
availability at the entrance to the dam ‘net’ of the 2000m3/s required by law. The cluster of grey
curves report the simulated flows under different weather conditions; all flows at or above the red
line are for very wet years, while those at or below the dashed line are for very dry years. The cluster
of grey curves report the simulated flows under different weather conditions; all flows at or above
the red line are for very wet years, while those at or below the dashed line are for very dry years. The
reader will note that during the dry months (e.g., July through October) very little water is available
for agriculture, once the ANA in-stream flow requirements have been met.
Figure 3 – Baseline Water Availability at the Entrance of Sobradinho Reservoir
Notes: Estimates at and above the red line represent flows during the 5% wettest years;
estimates at or below the dashed line represent flows during the 5% driest years.
We also simulate an increase in the price of sugar cane. Brazil has been experiencing a boom
in sugar cane production due to high international prices, and steady increases in domestic and
international demand for ethanol. In fact, sugar cane area has increased 23% and production 32%
over the past 10 years, (Produção Agrícola Municipal – IBGE). In this context, we simulate the
effects of even higher demand for sugar-cane/ethanol represented by five-fold increase in the
price/ton.
11
6.1 Scenarios
The minimum flow requirements and the increase in prices are simulated under two scenarios
derived from Figure 4, one optimistic and one pessimistic. Under the optimistic scenario, surface
water available for agriculture in each month is the average of flows in a given month over the 5%
wettest years, after the 2000m3/s is deducted. Under the pessimistic scenario, this average is
calculated under the 5% driest years. Table 1 reports, for example, the monthly flows in Juazeiro and
Boqueirão under these two scenarios. We also assume that official rules guarantee agriculturalists at
3 -1
least 10 m s of water for irrigation. Notice how little water would be available for agriculture in
Juazeiro, the downstream watershed, in the months of August to October in the event of a drought
(sugar cane prices held constant at baseline prices.)
Table 1
Baseline Monthly Water Availability in Juazeiro and Boqueirão under Wet (Optimistic) and
Drought (Pessimistic) Weather Scenarios (Baseline Sugar Cane Prices)
Wet-Year Water (m3/sec)
Drought-Year Water (m3/sec)
Juazeiro
Boqueirão
Juazeiro
Boqueirão
January
February
5477.3
5471.1
463.3
557.2
2991.8
2955.0
220.2
167.9
March
5718.0
483.8
2364.9
210.0
April
3130.6
418.1
1578.3
221.2
May
1724.2
336.2
681.8
196.6
June
1573.5
286.7
274.0
176.7
July
1391.7
266.9
66.9
171.9
August
919.1
252.7
10.0
166.8
September
380.7
244.6
10.0
161.7
October
621.2
267.5
10.0
170.3
November
1740.4
320.0
627.7
194.9
December
3863.4
410.7
2153.5
218.7
Now under the effects of the price-induced changes, water availability downstream would be
reduced even more substantially. Figure 5 depicts changes in water availability under the high-sugarprice scenario; note that during dry years water available for agriculture essentially goes to zero
during the period July through October.
12
Figure 4 –Water Availability at the Entrance to Sobradinho Reservoir after Upstream and
Downstream Agricultural Adjustments to High Sugar Prices
Notes: Estimates at and above the red line represent flows during the 5% wettest years;
estimates at or below the dashed line represent flows during the 5% driest years.
In particular these effects are even more visible in Table 2, which reports flows at the two scenarios
to Juazeiro. Downstream water availability is clearly binding on agriculturists during a lager time
spam, July-October, and maybe even June.
Table 2
Monthly Water Availability in Juazeiro and Boqueirão during Wet (Optimistic) and Drought
(Pessimistic) Weather Scenarios, assuming the High-Sugar-Price Scenario
Wet Year (m3/sec)
Drought
Year
(m3/sec)
January
February
March
April
May
June
July
August
September
October
November
December
5442
5388
5723
3175
1743
1483
1366
827
296
543
1718
3794
2973
2927
2154
1585
650
222
10
10
10
10
574
2016
6.2 Effects on Cultivated Area, Agricultural Employment, and Farm Profits
Figure 5 through Figure 8 report baseline land use, area dedicated to sugar care, agricultural
employment, and farm profits, and the effects of the sugar price increase on these agricultural
outcomes under different extreme weather scenarios. Note that SC in the figures mean sugar-cane.
13
In both upstream and downstream areas, rainfed agriculture dominates the landscape prior to
the increase in sugarcane prices, and continues to do so after the price increase (see Figure 5). That
said, total area under plow increase in response to the price increase in both the upstream and
downstream areas, and proportional increases in irrigated agriculture are larger than those for rainfed
agriculture on both areas. Finally, cultivated area is not particularly influenced by the extreme
weather patterns included in this set of simulations.
Upstream - Boqueirão
500,000
400,000
Hectares
300,000
200,000
100,000
0
Baseline SC price SC price
Drought Wet
Dowstream - Juazeiro
1,000,000
800,000
Hectares
600,000
400,000
200,000
0
Baseline SC price SC price
Drought
Wet
total
rainfed
irrigated
Figure 5 –Cultivated Area (Total, Rainfed and Irrigated), Upstream and Downstream, by
Weather and Price Scenario
Predictably, area dedicated to sugarcane increases substantially in both the upstream and
downstream areas as a result of the price increase, with the largest absolute increases in both areas
occurring in rainfed production (Figure 6). Extreme weather does not seem to influence upstream
sugarcane production, but the same is not true for the downstream area which has to dramatically cut
back on irrigated sugarcane cultivation during the dry year.
14
Dowstream - Juazeiro
50,000
40,000
Hectares
30,000
20,000
10,000
0
Baseline SC price SC price
Drought
Wet
Total
Irrigated
Figure 6 –Area Dedicated to Sugar Cane, Upstream and Downstream, by Weather and Price
Scenario
As expected, rainfed agriculture is the dominant source of employment for rural laborers in
both the upstream and downstream areas, and the price shock does not alter employment patterns
greatly (see Figure 7). Weather does make a different in employment in irrigated agriculture,
especially in the downstream area during a dry year.
15
Upstream - Boqueirão
Full Time
and
Temporary
Workers
6000
4000
2000
0
Baseline
SC price
Drought
SC price
Wet
Downstream - Juazeiro
50,000
Full Time
and
Temporary
Workers
40,000
30,000
20,000
10,000
0
Baseline
Total
SC price
Drought
SC price
Wet
Irrigated
Figure 7 – Agricultural Employment, Total and Irrigated Agriculture, Upstream and
Downstream, by Weather and Price Scenario
Finally, the large increase in sugarcane prices has a large, positive effect on farm profits in
both the upstream and downstream areas, and under both extreme weather scenarios (Figure 8).
However, downstream farmers are forced to reduce irrigated sugarcane production (and other forms
of irrigated agriculture) during the dry year, and their profits suffer as a consequence. The same is
not true for upstream farmers who have ‘first claim’ to surface water, which they use at the expense
of downstream farmers during the dry year.
16
Upstream - Boqueirão
120,000,000
100,000,000
80,000,000
Brazilian
60,000,000
Reais
40,000,000
20,000,000
0
Baseline
SC price
Drought
SC price
Wet
Downstream - Juazeiro
300,000,000
250,000,000
200,000,000
Brazilian
150,000,000
Reais
100,000,000
50,000,000
0
Baseline
SC price
Drought
SC price Wet
Total Ag.
Total Ag. Irrigated
Total Sugar Cane
Total Sugar Cane Irrigated
Figure 8 –Agricultural Profits and Sugarcane Profits, Upstream and Downstream, by Weather
and Price Scenario
7. Conclusions and Policy Implications
An expanding set of policy instruments for managing water use in agriculture is available to
policymakers, but effective and equitable implementation of these instruments requires tools that can
predict the affects of alternative policy actions. This paper uses linked hydro-economic models to
explore, in the context of a large watershed within the São Francisco River Basin (SFRB), the effects
of the implementation of the Brazilian water use regulations and (simultaneously) a large rise in the
price of sugarcane. The application of water use regulations has the expected effect of dramatically
reducing the surface water flows available to agriculture for irrigation, in all areas. More
specifically, in the watersheds examined in this study, a minimum flow at the entrance of
Sobradinho Dam of 2000 m3s-1 reduces the amount of water available for agriculture, in particular in
Juazeiro, the downstream watershed. This policy-mandated retention of water flows in the SFRB
system constrains downstream farmers’ cropping options, especially during dry years.
However, the economic, rural employment, and other consequences of minimum flow
regulations will depend on (among other things) the product mix and irrigation technologies in place
when the regulations are implemented, the location of agricultural activities, weather conditions, and
input and product prices. Moreover, credibly predicting the consequences of policy actions require
methods the incorporate the multiple ways in which changes in weather affect agriculture (namely,
17
reductions in rainfall, increases in ETo, and reductions in surface water flows) and the multiple ways
in which farmers respond to policy changes, price changes, and weather shocks (namely, but
adjusting product mix, production technologies, and area under plow). The economic model of
agriculture when linked with the basin-wide hydrologic model addresses all of these issues. More
specifically, the linked hydro-economic models are used to predict the site-specific and farm typespecific effects of the application of water use regulations, and, since the effects are not likely to be
spatially uniform, help locate the ‘winners’ and the ‘losers’ associated with this specific policy
action, measure their respective gains and losses, provide estimates of the willingness of ‘losers’ to
pay ‘winners’ for additional water, and (hence) provide information useful to the establishment of
water markets or other efficiency- or equity-enhancing policies.
The linked hydro-economic models also provide insights into the effects of a large increase
in sugarcane prices. Upstream and downstream farmers react (as expected) to the price increase by
increasing the area dedicated to rainfed and irrigated sugarcane production, and agricultural profits
increase substantially. However, during dry years, downstream farmers do not have access to
sufficient water to retain as much area in irrigated sugarcane as they would have liked, so profits fall;
upstream farmers, having ‘first claim’ on surface water for irrigation are able to retain larger areas in
sugarcane even during dry years, and hence do not suffer lower profits during drought periods.
Finally, the effects of the price shock and the implementation of water use regulations on
rural employment are not large, so the effects on rural poverty will not be, either. The expansion of
irrigated sugarcane production in both the upstream and downstream areas does lead to some
increases in employment in sugarcane in both areas, but since sugarcane does not intensively use
labor (except during harvest) and some new sugarcane area is replacing crops previously cultivated,
the net gains are small. The encouraging news is that the expansion of sugarcane area does not
completely ‘crowd out’ other irrigated crops (e.g., fresh fruits and vegetables) that small-scale
agriculturalists and rural laborers are most likely to participate in and benefit from.
Acknowledgements – This research project is sponsored in part by the Challenge Program on Water
and Food (CPWF) of the Consultative Group on International Agricultural Research (CGIAR), in
collaboration with the International Water Management Institute (IWMI). The opinions expressed in
this paper are not necessarily those of the supporting agencies.
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