In this study, a new advance relation (TR) was presented, which has only one constant coefficient. To determine the value of this coefficient, the water advance information at the midpoint and endpoint along the field is used. Field data from six irrigation events were used to evaluate this relationship and compare it with Elliott and Walker's (EW) exponential advance relationship. EW and TR advance relationships were compared using the relative error, Root Mean Square Deviation (RMSD), and Nash-Sutcliffe Efficiency (NSE) indices. The result of this comparison showed that the two advance relationships have equal accuracy in a number of irrigation events, and the EW advance relationship has more accuracy in other events. Then, using the TR advance relationship, a new method was presented to determine the subsurface storage coefficient in different lengths of the field and as a result to determine the coefficients of the Kostiakov infiltration relationship. The error-index for the average infiltration depth was used to compare the infiltration relations obtained from the EW and TR methods. The results of this comparison showed that the infiltration relationships of the two methods had equal accuracy in numerous irrigation events, and in some cases, the infiltration relationships obtained from the TR method were more accurate
