Analytical solution for normal irrigation distribution parameters

The model most widely used to represent sprinkler irrigation distribution p arameters is based on numerical solutions to the normal cumulative probabil ity density function. For most practical irrigation design and management a pplications, numerical solutions are too laborious. One other study reporte d analytical approximations for several irrigation distribution parameters derived from the normal model. The estimation error resulting from those ap proximations were variable over the operational range of irrigation uniform ity and irrigation adequacy and were quite high in some ranges. In this not e, more accurate analytical approximations are presented for the distributi on coefficient, the application efficiency, the water requirement efficienc y, the deficiently irrigated volume, and the average deficit over the defic iently irrigated area. On average, over the entire operational range of irr igation uniformity and irrigation adequacy, the new approximations are abou t an order of magnitude more accurate than the previous approximations and introduce negligible error for most practical applications.