Simulation of Full Shape of Wetting Bulb in Subsurface Drip Irrigation System with Nonlinear Regression Model

 
The wetted profile pattern is an important factor to consider when designing and managing a surface and subsurface drip irrigation systems. The knowledge of the pattern dimensions is imperative in choosing the suitable spacing between emitters and the correct distance between laterals. The experiments were carried out in a transparent plexiglass tank (0.5 *1.22 *3 m) using three different soil textures (sandy clay, sand clay loam, and sandy loam). The drippers were installed at 3 different soil depths (15, 30 and 45 cm). The emitter outflows were 2.4, 4 and 6 Lhr^-1 with irrigation duration of 6 hr. In this study, using the data obtained from the laboratory experiments and conducting the nonlinear regression analysis using Microsoft Excel Solver tool 2010, an empirical model was developed to predict the horizontal distribution of the wetting front for different application times. The suggested model includes estimation of the wetted radius at the top and bottom of the emitter horizontal axis as a function of emitter discharge, saturated hydraulic conductivity, water application time, soil bulk density, emitter installation depth, initial soil moisture content, and the percentages of sand, silt, and clay in the soil. We pursued a similar procedure in developing empirical formulas for estimating the wetted radius at different soil depths (by optimizing the coefficients of Equations) to predict the full shape of the wetting pattern. The best performance of the model was related to the depth of zero (on the emitter positioning axis), where the values of RMSE, MAE,  and R² were 2.15, 1.7 cm, 14.85 % and 0.92, respectively. The lowest performance of the model was related to the depth of 20 cm from the emitter, where values of  RMSE, MAE,  and R² were 3.93, 3.26 cm, 37.55% and 0.75, respectively (R² coefficient was significant at 5% level). The results of this research showed that the suggested model predicted the full shape of wetting pattern with acceptable accuracy. Considering these models in designing subsurface drip irrigation systems could improve system performance.