The San Francisco Integration Project is a Brazilian government project aiming to bring water to the semiarid region of the northeast. The project provides funding for two diversions of the San Francisco River, supplementing the supply of local water in four Brazilian states. The Piranhas-Açú and Jaguaribe basins will become the largest recipients of these water deliveries. In this paper, we propose methodologies to state in monetary terms the technical coefficients of water use for the economic sectors associated with urban supply (US) and agricultural irrigation (AI) in different regions of these basins. These coefficients show that for the US economic sectors, at a certain level of urbanization the productivity of water is decreasing. The coefficients of AI obtained are much lower than those of US. The coefficients of AI, when calculated by crop, showed that there is generally an inadequate crop mix in the two basins. When this is associated with the low efficiency of water use, the result is a low economic value per cubic metre of water allocated to the sector. This implies, for both sectors, a need for incentives to use water in a more efficient way.

## INTRODUCTION

The Piranhas-Açú watershed is an important river basin for two Brazilian states located in the northeastern region: Paraíba (PB) and Rio Grande do Norte (RN). Water management and planning at this basin is a very complex and there are many different water uses, both upstream and downstream from the reservoirs. Conflict over water use exists, involving users from both states. The Jaguaribe basin river is situated almost entirely within the boundaries of the State of Ceará (CE). This previously predominantly agricultural basin is experiencing rapid urban growth. Municipal and industrial demands require water reallocation for agriculture. In addition, the basin exports water to the Metropolitan Region of Fortaleza (MRF) through the Eixão or Channel Integration, designed to ensure water for the population and MRF industry for the next 30 years.

Technical coefficients of direct use of water measure the input of water use as a primary factor for various economic sectors. In this study, they were obtained in monetary terms for two sectors associated with urban supply (US) and for the agricultural irrigation (AI) sector. The coefficients used are a means of presenting the input coefficients of exogenous inputs. This is also called the intervention coefficients, one of the basic components of input–output analysis (Nakamura & Kondo 2009), in general measured using the unit cubic metres by quantities of the goods produced. Another configuration of these coefficients is presented in Hubacek & Guan (2008) as direct water consumption coefficients. Their coefficients are measured in the Chinese currency Yuan per unit of cubic metre of water, instead of goods produced per cubic metre. In the present study, the unit used is the Brazilian currency, the Real, the value of goods produced, per cubic metre of water. Our coefficients were obtained for both economic sectors, US and AI, and for different geographical regions of the basins having different hydrological and economic characteristics, called hydro-economic regions (HER). These economic sectors are the main water users in the two basins receiving water from the San Francisco Integration Project (SFIP).

## METHODS

The technical coefficients of direct water use represent the direct or the first round effects of the sectoral interaction in the economy (Hubacek & Guan 2008). These technical coefficients also have other uses, including the possible effects on the economy of a limitation in water resources resulting from changes in the management of supply or demand watersheds.

To start with, we divide the inputs necessary for production into endogenous and exogenous inputs. The endogenous inputs are economic and the exogenous zi′ are natural resources. In this work the exogenous ‘input’ is water. The output of the commodity or economic sector x is given by x′. If we divide the output of the commodity or sector by the endogenous and exogenous inputs, we will have the average amount of endogenous and exogenous input required to produce a unit of the final product of x′ given by: and , respectively.

If we consider a model with n sectors, dividing the demand for the output of each commodity or sector into two parts: the intermediate and final demand, we will have in a matricial form, the well known equations of basic input–output analysis:
1

2
where X = total output of all commodities or sectors (vector, −n × 1); Y = final demand of all commodities (vector, n × 1); A = endogenous inputs coefficient matrix (n × n); (IA)−1 = Leontief matrix (n × n).
In relation to the exogenous inputs, intermediate demand only is considered, i.e. demand for the exogenous inputs among the productive sectors in the economy, which is in a matricial form:
3
where Z = demand of exogenous input; given m exogenous inputs (m × 1); B = exogenous input coefficient matrix (m × n).
Substituting Equation (2) into Equation (3), we obtain
4

Equation (4) measures how much of the exogenous input (Z) is needed to meet the level of production X required by the demand Y.

As the exogenous inputs are usually scarce, their supply is limited. Using Equation (3) and considering that Z is limited, we will have a constraint on the level of production of the commodities, i.e. on the level of production in all sectors of the economy.
5

This means that production is limited by the water input. Using the technical coefficients (B−1) obtained for this study for each beneficiary region we can predict maximum economic return for all economic sectors (the vector X), depending on the different water distributions, i.e. different values of availability (Z) that can be simulated for different water management decisions.

The beneficiary regions that will receive water are not federal divisions, but sub-basins called HERs. Our study regionalized the technical coefficients of direct water use for each HER. These HERs are the ones that receive different amounts of water allocated to the various economic sectors, depending on the decisions made. They are defined by the area of its contribution to a large reservoir in each one of the two basins (Curemas-Mãe D’água and Armando Ribeiro in the Piranhas-Açú basin and in the Jaguaribe basin: Orós, Castanhão and Banabuiú reservoirs). In Piranhas-Açú basin, the HER2 was divided into two – HER2′ and HER2″- depending on the state (PB (HER2′) and RN (HER2″) to which it belonged. These HERs constitute the contribution of smaller water basins, associated with ottobacias, along the stretch of the main channel. These ottobacias are coded according to the methodology proposed by Brazilian engineer Otto Pfafstetter (Pfafstetter 1989; Verdin & Verdin 1999). Using an existing factor of proportionality relating the geographical area of the municipalities to these ottobacias (FUNARBE 2011), we were then able to relate the municipalities to the HERs. Thereafter, all data relating to municipalities and ottobacias – economic and hydrological – was regionalized by the HERs, which is why they are called hydro-economic units.

## CONCLUSIONS

Analysis of the individual technical coefficients obtained by type of crop allows us to conclude that in general in the two basins, there is a mix of unsuitable crops associated with inefficient water use, which results in low coefficients for water use in monetary terms. So, opportunities for improvement in the regional economy should be explored via incentives to plant crops with higher economic return per cubic metre of water applied, as well as to use more efficient irrigation technologies. In economic sectors associated with US in general, values and behavior of the technical coefficients were quite similar in all the HERs studied, initially increasing with higher urbanization and then decreasing after a certain point. This means that, also for the US sectors, there is a need for incentives to use water in a more efficient way.

Combination of these coefficients with water allocation model results might be useful in supporting policy makers in the design of water policies that improve demand management and encourage efficient use of water.

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