Devising a mathematical model for displacement estimation of the wetting pattern center from the emitter location resulting from the soil surface slope

This research aims to study the effect of land surface slope on the shape and size of the wetting pattern in the soil resulting from a dripping source, especially when there is a local surface runoff resulting from a water application rate higher than the soil infiltration capacity. As a result, it leads to a noticeable displacement of the center of the wetting pattern from the emitter position. The present research included finding this displacement mathematically and verifying its validity with the results of laboratory data. The studied data included 85 overlapping cases of the change in the water application rate and the slope of the soil surface for two levels of initial moisture and two soils of different textures. The results showed that the first devising equation could be used to estimate the wetting pattern center displacement from the emitter, resulting from the slope of the soil surface. The usage of the first devising equation was based on the of half the maximum horizontal surface advance (a), the maximum vertical advance under the emitter (b), and the soil surface slope, especially when the ratio (a/b) was within (0.9-1.1). The second devising equation can estimate the wetting pattern center displacement from the emitter resulting from the soil surface slope, regardless of the (a/b) ratio. That is, there was a considerable convergence between the displacement values of the center of the wetting pattern from the emitter position estimated by the first devising equation and the second devising equation when the value of (a/b) was close to one, which represents 87% of the 85 cases covered in this research.