Two exponential relationships (1- from the beginning to the midpoint of the field, 2- from the beginning to the endpoint of the field) were considered for the advance curve of surface irrigation water along a field. The constant coefficients of these advance relationships were determined using the least squares optimization method. These relationships were compared with the advanced relationships obtained by the Elliott and Walker method (EW) using the advanced data related to 14 irrigation events and using root mean square error deviation (dRMS) and Nash-Sutcliffe (NSE) indices. The results of this evaluation showed that the advanced relationships obtained from the presented method in this research (TR) have better accuracy, with average values of 7.05 min and 0.984 for dRMS and NSE, respectively. Then, using the TR method for deriving the advance relationships and using the volume balance method, the coefficients of the Kostiakov-Lewis infiltration relationship were determined. The infiltration relationships derived from the TR method were compared with the infiltration relationships obtained from the two-point method of EW. The results of this investigation showed that the TR method predicts the average infiltration depth with an average absolute relative error of 6%, which is more accurate than that of EW
