Development and verification of 3D Green-Ampt based membrane pore infiltration model

Film hole irrigation is an advanced low-cost and high-efficiency irrigation method, which can improve water conservation and water use efficiency. The study presented a three-dimensional infiltration model of film hole based on the one-dimensional Green-Ampt infiltration model and further explored the hypothesis that the generalized wetting front was flat in the one-dimensional formula. Given the characteristics of 3D infiltration of membrane pore irrigation, we discussed the shape of infiltration source, and proposed a line source of infiltration source. And the study presented hypothesis that water flowed from liner score of infiltration source to every point at wetting front. Based on the hypothesis, a three-dimensional Green-Ampt model for membrane pore irrigation including film hole diameter, characteristics of water conductivity and wetting front suction was established. Moreover, the model proposed in this study was validated and evaluated by laboratory experimental data of film hole diameter and Hydrus-2D model based on the theory for water movement in non-saturated soil. In the laboratory experiments, diameter were used to was designed with different levels of 4, 6, and 8 cm and the experiments carried out in Sated Key Laboratory Base of Eco-hydraulics in Northwest Arid Region. The infiltration was measured by difference of water level in Markov bottle. The water level was recorded every 1, 2, 3 and 5 min in the first 50 min, every 10 min from 50 to 100 min, and every 30 min from 100 to 180 min. Wetting front were recorded on soil box surface when water levels recorded. The experiment lasted for 5 h. Each treatment of laboratory experiment was replicated 3 times. In the case of different soil textures (sandy loam soil, loam soil and silty loam soil), the dynamic change of cumulative infiltration and wetting front was simulated by Hydrus-2D. The statistical comparisons (root mean square error-RMSE, percentage of bias-PBIAS, mean absolute error-MAE) of the estimated data with the measured and simulated data were conducted. The results showed that the variation of cumulative infiltration per unit film hole area with time obtained by the measured and simulated was consistent with the cumulative infiltration per unit film hole area of the proposed model. According to comparisons of the estimated values with the measured values, the root mean square error, mean absolute error, and percentage of bias were 0.96 cm, 0.54 cm and -4.8%, respectively. The root mean square error of measured and estimated values were 1.14 (6 cm) >0.93 (8 cm) >0.82 (10 cm). Besides, the simulated cumulative infiltration value of typical silt loam was more closer to the estimated values than typical sandy loam and typical loam. Comparing estimated wetting front with the measured and simulated ones, the difference was small in initial infiltration time and gradually increased with the increase of infiltration time. In addition, compared with the horizontal direction, the estimated generalized wetting front in the vertical direction was more closer to the measured and simulated value. In summary, the established 3-D infiltration model for film hole irrigation can be used to accurately calculate the cumulative infiltration of film hole and predicte the shape of wetting front. simulated value. In summary, the established 3-D infiltration model for film hole irrigation can be used to accurately calculate the cumulative infiltration of film hole and predicte the shape of wetting front.