Sprinkler irrigation uniformity assessment: Relational analysis of Christiansen uniformity and Distribution uniformity

Christiansen uniformity (CU) and Distribution uniformity (DU) are the most commonly used irrigation quality evaluation indicators, focusing on overall uniformity and local water deficit, respectively. Clarifying the quantitative relationship between the CU and DU has important production value for determining the water distribution characteristics of whole and localized areas in the evaluation of sprinkler irrigation water uniformity and improving the quality of sprinkler irrigation. This paper analyses the relationship between the calculation formulas of CU and DU based on mathematical analysis. The results reveal a prominent linear relationship between CU and DU, and the sum of the slope coefficient and the constant term of the linear relationship equation is 1. The value of the slope coefficient of the CU–DU linear relationship characterizes the differentiated form of the sprinkler water distribution. The slope coefficient is determined by the nozzle type, operating parameters and working scenarios. Notably, the specific form of the linear relationship obtained by fitting the experimental results in the literature is not universal. The mapping relationship between the value of the slope coefficient and the distribution form of sprinkler irrigation water quantity was established, and the influence of the value range of the slope coefficient on the DU of the overall and local sprinkler irrigation water quantity was demonstrated. The results show that the deviation rates of CU and DU decrease with increasing slope coefficient. When the slope coefficient is less than 1, CU is greater than DU; and the slope coefficient ranges from 0.46 to 1.36. When the slope coefficient is 0.625, the possibility of uniform irrigation is the highest. This research helps to overcome the limitations of CU and DU for irrigation uniformity evaluation and provides a reference for carrying out sprinkler irrigation uniformity evaluation with comprehensive characterization capabilities. L'uniformité de Christiansen (CU) et l'uniformité de distribution (DU) sont les indicateurs d'évaluation de la qualité de l'irrigation les plus couramment utilisés, mettant l'accent sur l'uniformité globale et le déficit hydrique local respectivement. La clarification de la relation quantitative entre le coefficient de l'uniformité de Christiansen (CU) et le coefficient de l'uniformité de distribution (DU) possède une valeur productive importante pour la détermination des caractéristiques de distribu