Food Water Energy for Urban Sustainable Environments (FUSE)

Agricultural Land and Water Use

Modeling Agricultural Land Use, Production, and Water Consumption

The agricultural module for Pune simulates land and water allocation among crops and computes several economic indicators (value of agricultural production, production costs, farmers’ profits, cultivated area by crop and irrigation system, and water use by source). Figure 1 shows the current distribution of sugarcane in Pune and linkages to reservoirs and command areas. The objective function of this module is to maximize farmers’ profits in the different irrigation districts, subject to various technical and resource constraints. These constraints include land availability, available land equipped with irrigation systems, monthly water resources availability from different sources (canal water, groundwater), energy availability for groundwater pumping, agronomic restrictions (e.g., succession, frequency), agricultural policy requirements (e.g., food security, crop diversification, set-aside), and labor availability, among others. Crop-water production functions are incorporated into the Pune agricultural module to optimize crop water application and yields. These functions represent the response of the crops to water applied under specific agronomic and climatic conditions. Crop-water production functions are developed here following the FAO method of crop coefficients and sensitivity indices that determine the response of each crop yield to water deficit. Other parameters required in the agricultural module includes crop prices, subsidies, crop water and labor requirements, irrigation efficiencies, water and production costs, land and labor availability, surface and groundwater extractions, and energy use for irrigation.

The use of mathematical programming models to analyze agricultural production at regional level such as the Pune agricultural module faces the problem of aggregation and overspecialization because farms in a region are different in terms of resources endowment, technologies, and management skills. Ideally, a regional model should include a component for every individual farm, but this is unfeasible because of the complexity of such a model. Many approaches have been taken to solve this problem and to calibrate regional models to observed conditions such as the representative farm approach (Day, 1963), the convex combination approach (Önal and McCarl, 1991), and the positive mathematical programming (PMP) approach (Howitt, 1995).

Pune agricultural module is calibrated to observed crop area using the PMP approach. The application of this approach as a mean for calibration has significantly increased during the last two decades. The main advantages of PMP compared to other approaches are the exact representation of the base conditions, lower data requirements, and a smooth response of the model to continuous changes in exogenous parameters when the model is used for analysis of policy changes. In this study, we follow the standard PMP approach to calibrate our model to observed crop area, which involves a two-step procedure for implementation. In the first step, optimized crop area is bounded by observed crop area by introducing a set of calibration constraints. In the second step, dual values associated with the calibration constraints are used to calculate calibration parameters, which represent the marginal cost coefficients of a convex cost function, and are incorporated into the objective function such that once the calibration constraints are removed, the modified model reproduces exactly the observed crop area.

References

  • Day R., 1963. On aggregating linear programming models of production. Journal of Farm Economics, 45: 797-813.
  • Howitt R., 1995. Positive mathematical programming. American Journal of Agricultural Economics, 77: 329-342.
  • Önal H., McCarl B., 1991. Exact aggregation in mathematical programming sector models. Canadian Journal of Agricultural Economics, 39: 319-334.