ࡱ > i n m bjbj X % n t t
e e e y y y 8 4 y D 8 !$ " C$ C$ Y$ ; ; , ; 3 5 5 5 5 5 5 $ Y e ; V: ; ; ; Y C$ Y$ FR FR FR ; @ l C$ e Y$ 3 FR ; 3 FR FR j Q 9 , # Y$ PʧM y $K 7 2 0 D i 2P d # # e lj X ; ; FR ; ; ; ; ; Y Y FR ; ; ; D ; ; ; ; ; ; ; ; ; ; ; ; ; t } : Examining the Effects of Water Use Regulations on Agriculture in the So Francisco River Basin, Brazil:
An Application of a Linked Hydro-Economic Model
Marcelo de O. Torres Catholic University of Braslia, 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
Lus 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, So Francisco River Basin, Brazil
Palavras-Chave: Economia dos Recursos Hdricos, Agricultura, Modelo Hidro-Econmico, Irrigao, Bacia do Rio So 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 So 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.
Sumrio
Este artigo apresenta um modelo hidro-econmico para o exame dos efeitos da regulao do uso de recursos hdricos na agricultura da bacia do Rio So Francisco. Efeitos de regimes alternativos de precipitao na disponibilidade de recursos hdricos para irrigao so explicitamente considerados no modelo hidrolgico Mike Basin, assim como as reaes dos produtores rurais a mudanas nos preos agrcolas e no acesso a recursos hdricos so medidas com um modelo econmico baseado em programao no-linear. Ambos modelos so externamente conectados. Os resultados mostram que a regulao no uso e na disponibilidade de recursos hdricos pode ser binding dependendo de fatores exgenos tais como preos das culturas e regimes de precipitao.
ANPEC: rea 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 semi-arid 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 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 So 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 So Francisco River Basin
The So Francisco River (see Figure 1) with 634.781 km (8% of countrys 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 basins 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.
Figure1 So Francisco River Basin and River
In part to deal with the increasing pressures on the Brazilian water resources, in the SFRB and elsewhere, Brazils 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 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.
Economic Model of Agriculture
The economic model proposed here is based on a class of models called Positive Mathematical Programming or PMP ADDIN EN.CITE Howitt199569669617Howitt, Richard EPositive mathematical programmingAmerican Journal of Agricultural EconomicsAmerican Journal of Agricultural Economics329-3427721995(Howitt, 1995), widely used in applied research and policy analysis ADDIN EN.CITE Howitt19866976975Howitt, Richard EGardner, B DCropping production and resource interrelationships among California crops in response to the 1985 Food Security ActImpacts of farm policy and technical change on US and Californian agriculture 271-2901986DavisHouse198771271227House, R MUSMP regional agricultural model1987Washington DCNational Economics Division Report, USDAERS 30Kasnakoglu19887137135Kasnakoglu, HBauer, SBauer, SHenrichsmeyer, WConcept and application of an agricultural sector model for policy analysis in TurkeyAgricultural sector modeling1988KielWissenschaftsverlag VaukLance199871171117Lance, H LMiller, D JEstimation of multioutput production functions with incomplete data: a generalized maximum entropy approachEuropean Review of Agricultural EconomicsEuropean Review of Agricultural Economics188-209251998(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; Rhm and Dabbert , 2003; Cai and Wang, 2006; Marques et al. 2006; and Cai, Ringler and You, 2008)).
The Objective Function
It is assumed that farmers in each municpio within the So Francisco River Basin seek to maximize net revenue derived from their farming activities in a given year. Therefore, the backbone of the analytical model is an objective function that explicitly sets out to maximize profits. That is:
EMBED Equation.3 Eq. SEQ Eq._ \* ARABIC 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 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, EMBED Equation.3 ; and the second term, in parenthesis, is the implicit cost associated with land allocation. It has a quadratic specification with parameters EMBED Equation.3 and EMBED Equation.3 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-makers 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. ADDIN EN.CITE Chatterjee199871571517Chatterjee, BHowitt, Richard ESexton, R JThe optimal joint provision of water for irrigation and hydropowerJournal of Environmental Economics and ManagementJournal of Environmental Economics and Management295-3133631998(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:
EMBED Equation.3 , Eq. 2
where the superscript r in EMBED Equation.3 stands for a rainfed production function, Ai represents the area share parameters, and bih are the production function parameters; EMBED Equation.3 , i s t h e e l a s t i c i t y o f s u b s t i t u t i o n a m o n g i n p u t s ; a n d i i s t h e r e t u r n s - t o - s c a l e p a r a m e t e r . T h e s u b s c r i p t h - 1 i n d i c a t e s t h a t r a i n f e d c r o p s c a n u s e a l l i n p u t s e x c e p t s u r f a c e w a t e r . P r e c i p i i s d e f i n e d a s t h e r a t i o b e t w e e n t h e e x p e c t e d l e v e l o f p r e c i p i t a t ion EMBED Equation.3 and the actual level of precipitation EMBED Equation.3 , that is, EMBED Equation.3 . Precipi therefore acts as a linear shifter in the production function.
If a crop is irrigated, the function is:
EMBED Equation.3 ,Eq. 3
where the superscript ir in EMBED Equation.3 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 a s s o c i a t e d w i t h w a t e r u s e w h e t h e r i t c o m e s f r o m s u r f a c e w a t e r ( X i s w ) o r p r e c i p i t a t i o n ( E M B E D E q u a t i o n . 3 ) , a n d E M B E D E q u a t i o n . 3 a n d i a r e d e f i n e d a s i n E q . 2 .
2 . 3 S h a d o w V a l u e s f o r N o n - M a r k e t e d L i m i t e d I n p u t s
I n t h e c a s e o f i n p u t s w i t h l i m i t e d s u p p l i e s s u c h a s f a m i l y l a b o r , s u r f a c e w a t e r a n d l a n d , t h e m a r g i n a l c o s t o f a n i n p u t i s r e p r e s e n t e d b y t h e s u m o f i t s m a r k e t p r i c e p l u s i t s s h a d o w p r i c e , . T h e s h a d o w p r i c e s f o r e a c h n o n - m a r k e t e d o r l i m i t e d i n p u t a r e t h e L a g r a n g e m u l t i p l i e r s t h a t solve a linear programming model, which has as its explicit objective the maximization of net revenue using land as the decision variable:
EMBED Equation.3 Eq. 4
subject to municpio-level resource constraints:
EMBED Equation.3
EMBED Equation.3
and a model calibration constraintEq. 5
Eq. 6
EMBED Equation.3 , Eq. 7
where in Eq. 4 pi is defined as before, w i s t h e y i e l d p e r h e c t a r e o f l a n d d e d i c a t e d t o c r o p i
( E M B E D E q u a t i o n . 3 ) , p h i s t h e u n i t c o s t o f i n p u t h u s e d i n t h e p r o d u c t i o n o f c r o p i , a n d a i h a r e i n p u t s p e r h e c t a r e E M B E D E q u a t i o n . 3 . B l a n d a n d B f l r e f l e c t t h e t o t a l a v a i l a b i l i t y o f land and family labor, respectively. Eq. 6 assures that the total amount of surface water used in month m, EMBED Equation.3 , is less or equal to the total amount of surface available for irrigation in that month, EMBED Equation.3 . In REF _Ref172463826 \h \* MERGEFORMAT Eq. 7, EMBED Equation.3 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 non-marketed inputs.
The shadow values associated with constrained resources represented by Eqs. 5 and 6
( EMBED Equation.3 ) 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 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 EMBED Equation.3 , 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 municpio 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 ADDIN EN.CITE Allen19982932936Allen, Richard GPereira, L SRaes, D Smith, MCrop evapotranspiration, guidelines for computing crop water requirements.FAO irrigation and drainage paper300561998RomeFood and Agriculture Organization of the United Nationspaper 56internal-pdf://FAOirrigation-1505075200/FAOirrigation.pdf(Allen et al., 1998), the total annual agronomicaly optimal evapotranspiration for each crop i in day n is EMBED Equation.3 . For those days in which EMBED Equation.3 > EMBED Equation.3 (actual precipitation level), we called Zin the difference between EMBED Equation.3 and EMBED Equation.3 , that is, EMBED Equation.3 . On the other hand, for those days in which EMBED Equation.3 , Zin is truncated at 0. The sum of EMBED Equation.3 annually takes then the form of EMBED Equation.3 , where n=1 refers to September the 1st; and monthly, the form of EMBED Equation.3 , 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 between the sums. That is, EMBED Equation.3 Where m = 1,,12 (month 1 refers to September, 2 to October, 3 to November and so on).
The total amount of surface water used in month m, is then
EMBED Equation.3 , Eq. 8
where EMBED Equation.3 is the annual amount of surface water per hectare EMBED Equation.3 . Eq. 8 together with Eqs. 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 EMBED Equation.3 and the crop specific parameter Ai in Eq. 2; and 5 parameters bih, one for the return-to-scale parameter EMBED Equation.3 and the crop-specific parameter Ai in Eq. 3. For the estimation of the 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 ADDIN EN.CITE Jaynes195767467417Jaynes, E TInformation theory and statistical mechanicsPhysical ReviewPhysical Review171-1901081957Paris199867367317Paris, QHowitt, Richard EAn analysis of ill-posed production problems using maximum entropyAmerican Journal of Agricultural EconomicsAmerican Journal of Agricultural Economics124-138801998Golan19966756756Golan, A Judge, G GMiller, D JMaximum entropy econometrics: robust estimation with limited data1996Chichester, EnglandJohn Wiley and SonsMittelhammer20006726726Mittelhammer, R CJudge, G GMiller, D JEconometric foundations2000CambridgeCambridge University Press(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, EMBED Equation.3 . Regarding the value of land, however, in addition to the market and shadow prices, the calibration cons t r a i n t r e p r e s e n t e d b y E q . 7 f u r t h e r i n c r e a s e s t h e v a l u e o f t h i s f i x e d i n p u t . I n o t h e r w o r d s , t h e t r u e m a r g i n a l c o s t a s s o c i a t e d w i t h l a n d a l l o c a t i o n t o t h e i t h c r o p i s t h e s u m o f : 1 ) t h e m a r k e t p r i c e o f l a n d ; 2 ) t h e s h a d o w v a l u e o f l a n d , L a n d ; a n d 3 ) E MBED Equation.3 .
Formally, the optimality equations for each input can then be defined as:
EMBED Equation.3 , for unconstrained inputs;
EMBED Equation.3 , for irrigation and non-irrigation family labor;
EMBED Equation.3 , for land;
EMBED Equation.3 , for surface water. 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 EMBED Equation.3 , and Ai , EMBED Equation.3 and EMBED Equation.3 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 ( EMBED Equation.3 ) and a value of 0.4 for the elasticities of substitution ( i ) . A n a p p e n d i x c o n t a i n i n g t h e d e r i v a t i o n a n d c a l c u l a t i o n o f p a r a m e t e r s E M B E D E q u a t i o n . 3 , a n d A i , a s w e l l a s E M B E D E q u a t i o n . 3 a n d E M B E D E q u a t i o n . 3 o f E q . 1 m a y b e r e q u e s t e d t o t h e a u t h o r s .
2 . 5 E c o n o m i c S i m u l a t i o n M o d e l
R E F _ R e f 1 8 5 7 6 0 8 82 \h \* MERGEFORMAT Eq. 11 uses the parameterized CES production function EMBED Equation.3 to find the optimal set of inputs that maximizes net revenue:
EMBED Equation.3 Eq. 10
When municpios are subject to resource and water vailability constraints
Land: EMBED Equation.3
Family Labor: EMBED Equation.3
Surface Water: EMBED Equation.3
EMBED Equation.3 Eqs. 11
3. The Hydrologic Model
The hydrologic component is based on a semi-distributed modeling and water accounting approach implemented in MIKE Basin ADDIN EN.CITE Danish Hydraulic Institute200563463427Danish Hydraulic Institute, MIKE Basin 2005. User's guide2362005(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.
Figure 2 Hydrologic Model of the SFRB, with Discharge Data from Selected Watersheds
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 municpio-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 municpio 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 municpio 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: EMBED Equation.3 , where Xwcnm is the amount of water in watershed c used for irrigation on 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 municpio i , located in watershed c, on the irrigation of crop n, in month m (Xwicnm) , is calculated as EMBED Equation.3 , where EMBED Equation.3 is the percentage of total irrigated area in municpio i that is allocated to crop n. EMBED Equation.3 .
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: Boqueiro which is located upstream and Juazeiro, downstream of the So Francisco River. The area encompassed by these two watersheds includes the Sobradinho Dam (Figure 1) and 59 municpios and has experienced (although not uniformly) above-average increases in area dedicated to diversified commercial agriculture over the past 10 years. The Boqueiro watershed, located upstream from Juazeiro, includes the municpio of Barreiras which is home to large-scale grain farmers (especially soybeans) practice irrigated agriculture using center-pivot technology. The other downstream watershed ( Juazeiro) include part of the municpios 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 (Boqueiro 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, (Produo Agrcola 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.
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 Boqueiro under these two scenarios. We also assume that official rules guarantee agriculturalists at least 10 m3s-1 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 Boqueiro under Wet (Optimistic) and Drought (Pessimistic) Weather Scenarios (Baseline Sugar Cane Prices)
Wet-Year Water (m3/sec)Drought-Year Water (m3/sec)JuazeiroBoqueiroJuazeiroBoqueiroJanuary5477.3463.32991.8220.2February5471.1557.22955.0167.9March5718.0483.82364.9210.0April3130.6418.11578.3221.2May1724.2336.2681.8196.6June1573.5286.7274.0176.7July1391.7266.966.9171.9August919.1252.710.0166.8September380.7244.610.0161.7October621.2267.510.0170.3November1740.4320.0627.7194.9December3863.4410.72153.5218.7
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-sugar-price scenario; note that during dry years water available for agriculture essentially goes to zero during the period July through October.
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 Boqueiro during Wet (Optimistic) and Drought (Pessimistic) Weather Scenarios, assuming the High-Sugar-Price Scenario
Wet Year (m3/sec)Drought Year (m3/sec)January54422973February53882927March57232154April31751585May1743650June1483222July136610August82710September29610October54310November1718574December37942016
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.
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.
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.
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.
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.
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 So 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, 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 type-specific 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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