Analytical Solution for Normal Irrigation Distribution Parameters

Abstract

The model most widely used to represent sprinkler irrigation distribution parameters is based on numerical solutions to the normal cumulative probability density function. For most practical irrigation design and management applications, numerical solutions are too laborious. One other study reported analytical approximations for several irrigation distribution parameters derived from the normal model. The estimation error resulting from those approximations were variable over the operational range of irrigation uniformity and irrigation adequacy and were quite high in some ranges. In this note, more accurate analytical approximations are presented for the distribution coefficient, the application efficiency, the water requirement efficiency, the deficiently irrigated volume, and the average deficit over the deficiently irrigated area. On average, over the entire operational range of irrigation uniformity and irrigation adequacy, the new approximations are about an order of magnitude more accurate than the previous approximations and introduce negligible error for most practical applications.