An Inverse Method to Estimate the Root Water Uptake Source-Sink Term in Soil Water Transport Equation under the Effect of Superabsorbent Polymer

The widespread use of superabsorbent polymers (SAPs) in arid regions improves the efficiency of local land and water use. However, SAPs' repeated absorption and release of water has periodic and unstable effects on both soil's physical and chemical properties and on the growth of plant roots, which complicates modeling of water movement in SAP-treated soils. In this paper, we proposea model of soil water movement for SAP-treated soils. The residence time of SAP in the soil and the duration of the experiment were considered as the same parameter t. This simplifies previously proposed models in which the residence time of SAP in the soil and the experiment's duration were considered as two independent parameters. Numerical testing was carried out on the inverse method of estimating the source/sink term of root water uptake in the model of soil water movement under the effect of SAP. The test results show that time interval, hydraulic parameters, test error, and instrument precision had a significant influence on the stability of the inverse method, while time step, layering of soil, and boundary conditions had relatively smaller effects. A comprehensive analysis of the method's stability, calculation, and accuracy suggests that the proposed inverse method applies if the following conditions are satisfied: the time interval is between 5 d and 17 d; the time step is between 1000 and 10000; the test error is ≥ 0.9; the instrument precision is ≤ 0.03; and the rate of soil surface evaporation is ≤ 0.6 mm/d.