Toward the structure of a production function for wheat yields with dated inputs of irrigation water

The interdependence between the rate of water used by plants and the available stocks of moisture in the soil, the temporal interdependence between water use at different time points, and the consequences of these interdependencies for the relationship between time profiles as well as the quantities of water used by crop plants and yields have not generally been analyzed in a unified framework. We present one such unified framework for the analysis of optimal use of irrigation water. We have estimated from experimental data the mathematical form of a water use function and have used this function to compute the time profiles of actual water use for two crops: wheat in Delhi and alfalfa in Ohio. The estimated time profiles of consumptive use have been used to determine the relationship between wheat yields and dated inputs of water in Delhi.