Analysis of Clements First Formula for Irrigation Distribution Networks

The aim of this article is to determine with real data to what extent the hypotheses on which Clementʹs first formula is based are fulfilled, and to compare the results of applying this formula. To this end the flow demand in the peak period was studied in two distribution networks with different irrigation methods and crops located in the Ebro River basin (northeast Spain). The calibration procedure for this formula proposed by the Centre Technique du Génie Rural des Eaux et des Forets (CTGREF) in 1977 was also analyzed. The result was that most of the hypotheses were not fulfilled. Furthermore, the discharge distributions obtained in the period of study did not correspond to a normal distribution. However, comparing the real accumulated probability curve and that calculated by Clementʹs formula, it was found that the differences between the two curves for probabilities greater than 90% (a wide range of application of the formula) were lower than 9.4%. The reason for this result was found. It was shown also, that the CTGREF adjustment procedure did not provide substantial improvement in the estimation of flows because the aim of the fit was to achieve a normal distribution rather than an accumulated distribution function.