Model of water application under pivot sprinkler. I: Theoretical grounds

A model describing the application pattern produced by a single sprinkler i s proposed. Based on calibrated statistical distributions and free from any ballistic consideration, this model uses a mixture of beta probability dis tributions in which parameters are first estimated with water application d ata 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 o f 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 finall y 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 s prinklers attached to a center pivot or moving lateral irrigation machine.