Studying uniform and variable rate center pivot irrigation strategies with the aid of site-specific water production functions

• Novel site-specific water production functions (WPFs) were developed and tested.
• New zoning procedures for variable rate irrigation were established.
• The k-NN WPF accurately predicted cotton yield under supplemental irrigation.
• Sector zoning was predicted to enhance cotton yield under supplemental irrigation.

Irrigation management has evolved into a top priority issue since available fresh water resources are limited. Water production functions (WPFs), mathematical relationships between applied water and crop yield, are useful tools for irrigation management and economic analysis of yield reduction due to deficit irrigation. This study aimed at (i) designing and evaluating site-specific WPFs (using k nearest neighbors (k-NN), multiple linear regression, and neural networks), (ii) simulating yield maps for uniform, sector control VRI, and zone control VRI center pivot systems using the site-specific WPFs, (iii) using the best WPF to investigate different cotton irrigation and zoning strategies using integer linear programming, and (iv) comparing soil-based and WPF-based zones for sector control VRI systems. A two-year cotton irrigation experiment (2013–2014) was implemented to study irrigation-cotton lint yield relationship across different soil types. The site-specific k-NN WPFs showed the highest performance with root mean square error equal to 0.131 Mg ha−1 and 0.194 Mg ha−1 in 2013 and 2014, respectively. The result indicated that variable rate irrigation with limited sector control capability could enhance cotton lint yield under supplemental irrigation when field-level spatial soil heterogeneity is significant. The temporal changes in climate and rainfall patterns, however, had a great impact on cotton response to irrigation in west Tennessee, a moderately humid region with short season environment. We believe site-specific WPFs are useful empirical tools for on-farm irrigation research.