Spatially Weighted Approaches to Estimating the Christiansen Uniformity Coefficient in Center Pivot Irrigation Systems

Center pivot irrigation systems are widely adopted for their operational efficiency and potential to achieve uniform water application. However, unplanned modifications to their hydraulic or structural components often reduce water distribution uniformity and compromise irrigation performance. This study evaluates the Christiansen uniformity coefficient (CU) in 12 center pivot systems operating under real field conditions in Colombia and introduces four spatially weighted alternatives to enhance the accuracy of uniformity assessment. The proposed weighting schemes account for the distance of each collector along the pivot transect: two unilateral approaches (favoring inner or outer sectors) and two bilateral approaches (emphasizing the central region or the extremes of the pivot arm). The results demonstrate that the weighted coefficients better capture the spatial variability inherent to center pivot irrigation, allowing a more realistic representation of field performance. In particular, the weighted CU values consistently provided higher and more robust estimates of irrigation uniformity, especially in systems with hydraulic modifications or emitter malfunctions. Additionally, Monte Carlo simulations revealed that the distribution of collected data significantly influences CU interpretation, suggesting that categorical scales for classifying irrigation uniformity (e.g., excellent, good, or poor) should be data set-–specific rather than universal. The methodology was implemented using open-source computational tools, ensuring replicability and practical applicability for irrigation managers and researchers.