Model of Water Application under Pivot Sprinkler. I: Theoretical Grounds

A model describing the application pattern produced by a single sprinkler is proposed. Based on calibrated statistical distributions and free from any ballistic consideration, this model uses a mixture of beta probability distributions in which parameters are first estimated with water application data measured in zero wind condition. Data measured in field conditions are then used to assess the wind effect on the shift of the center of gravity of the irrigated area, on the range of the sprinkler in various directions, and on the values of the beta distributions' parameters. The computation of the water application amounts at any point of the irrigated area is finally resolved in the use of a single equation, which can be easily implemented in a software package to simulate application patterns under a series of sprinklers attached to a center pivot or moving lateral irrigation machine.