| The general problem of the advance and recession of irrigation water on an initially dry field was formulated using the kinematic-wave theory. Two comprehensive analytical models were developed to simulate all phases of one irrigation cycle on a sloping border.;In the first part of the study, the infiltration rate was assumed constant in time and space. Analytical solutions for the advance and recession, for this case, were used to derive expressions for the volumes in surface storage, and cumulative volumes of infiltration and runoff. This was performed for the advance, storage and recession phases. Two methods were proposed and used to estimate what the constant infiltration rate should be. One was based on the total infiltrated volume while the other used an infiltrometer test results.;The second part of the investigation was directed toward the development of a variable infiltration rate approach. The derivations and the forms of the equations used are similar to the first case. The infiltration rate for the process, however, was assumed to vary with time from the beginning of irrigation until the start of the recession phase. Expressions for the mean infiltration rate were derived using a volume balance approach. The derivations were carried out using three different infiltration equations: Horton, Kostiakov and the modified Kostiakov. The solutions for the recession are the same as in the case where the infiltration rate was constant.;The two analytical models were tested using field data. Both predicted, reasonably well, the volumes of water at different times during the process. The constant infiltration rate approach, however, has the severe limitation of a maximum distance reached by the advancing front. Its usefulness in predicting advance and recession times, opportunity times will depend on the particular conditions under which it is applied. The variable infiltration rate model estimates of advance and recession times, opportunity times, were reasonably close to field data. |
