Sizing of Terminal Units in Surface Irrigation Projects: I

Abstract

The problem of optimal turnout area size is analyzed using an approach common to the casual processes theory (CPT) of mathematical sociology and to the systems engineering approach. The three basic CPT models with different dependence structures are expanded for application to the problem. The general structure of the CPT model, which is based on the basic Bernoulli trials process, is presented, indicating the factors affecting the receipt of water by farmers. The phenomenon of human and physical interventions in CPT model 2 is characterized by the Bernoulli distribution of Poisson with different probabilities and with constant successive probabilities ratio. For the latter case, sets of parametric curves are given for three levels of prescribed success. In CPT model 3, a methodology is derived for obtaining a given or more fraction of visits to a particular state in a two‐state Markov chain model (MCM). These methods enable the parameterization of the level of success in obtaining water successfully by a group of farmers given the group size and the degree of intervention process. By prescribing satisfactory levels of the value for this success probability for a given value of the parameter for the degree of cooperation, the optimal group size is obtained. A mean value model is also developed for CPT model 3 with a four‐state MCM indicating a sample parametric application.