Sprinkler Uniformity Measures and Skewness

The measures of uniformity of sprinkler irrigation like Christiansen's coefficient of uniformity, Wilcox-Swale's coefficient and pattern efficiency has, in the past, been related to each other assuming that the precipitations are distributed according to the symmetric Gaussian distribution. Sprinkler irrigation patterns are known to always possess some skewness. This paper establishes the relationships between the uniformity coefficients utilizing the asymmetric gamma distribution. A comparison with the experimental data confirms the effect of skewness on the uniformity coefficients. Both theory and data show that pattern efficiency is very sensitive to skewness. It is concluded that the conversions between the uniformity coefficient may be risky if the skewness of the precipitation distribution is disregarded.