Crop yield as affected by spatial variations of soil and irrigation

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Abstract
Crop yield is calculated for varying uniformities of seasonal available water. The variation is a consequence of both irrigation and soil heterogeneity. Analytical expressions and Monte Carlo simulations are used to calculate yields for an assumed linear response function. A comprehensive table from the Monte Carlo simulations includes results for 50, 100, and 200% of the water necessary for maximum yield. These are collated with five uniformities and three levels of effective available water. Uniformities of water are expressed as coefficients of variation ranging from 0 to 2. Variation in either irrigation or soil uniformity changes the results, but irrigation uniformity is likely more important, especially for surface systems. The effect of taking the two distributions—for irrigation and soil—to be correlated does not affect results greatly. When only cost of water is considered, the marginal rate of return is verified to be a maximum for smaller applications.

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