Table 1.
Selection of parameters for numerical testing.
Fig 1.
Theoretical moisture and calculated water uptake distribution in the soil profile at different times.
(a) Theoretical moisture distribution; (b) Calculated water uptake distribution. Use inverse method to calculate distribution of moisture (apply SAP after 0, 1, 3, 5, 8, 10, 13, 15, 17, 20d) and water uptake (from apply SAP 3d to 5d, 3d to 8d, 3d to 10d, 3d to 13d, 3d to 15d, 3d to 17d, 3d to 20d) in the soil profile at different times. Theoretical values are calculated from the root water uptake model developed by Shao AJ et al [33,34] (S = ET×A×[e^-B(lnZ-C)2]/Z).
Table 2.
Error analysis between theoretical and calculated values.
Fig 2.
Calculated water uptake distribution in the soil profile at different time steps.
Use inverse method to calculate distribution of water uptake in the soil profile at different time step (10, 100, 1000, 10000). Theoretical values are calculated from the root water uptake model developed by Shao AJ et al [33,34] (S = ET×A×[e^-B(lnZ-C)2]/Z).
Fig 3.
Calculated water uptake distribution in the soil profile at different levels of unsaturated hydraulic conductivity.
Use inverse method to calculate distribution of water uptake in the soil profile at different unsaturated hydraulic conductivity (100K, 10K, 5K, 0.5K, 0.1K, 0.01K, 0.001K). 100K means the value of unsaturated hydraulic conductivity is increased by 100 times than the normal K, and 0.01K means the value of unsaturated hydraulic conductivity is reduced by 100 times than the normal K, Theoretical values are calculated from the root water uptake model developed by Shao AJ et al [33,34] (S = ET×A×[e^-B(lnZ-C)2]/Z).
Fig 4.
Calculated water uptake distribution in the soil profile at different levels of unsaturated diffusivity.
Use inverse method to calculate distribution of water uptake in the soil profile at different unsaturated diffusivity (100D, 10D, 5D, 0.5D, 0.1D), 100D means the value of unsaturated diffusivity is increased by 100 times than the normal D, and 0.01D means the value of unsaturated diffusivity is reduced by 100 times than the normal D, Theoretical values are calculated from the root water uptake model developed by Shao AJ et al [33,34] (S = ET×A×[e^-B(lnZ-C)2]/Z).
Fig 5.
Calculated water uptake distribution in the soil profile at different test errors.
Use inverse method to calculate distribution of water uptake in the soil profile at different test errors (per = 0.95, per = 0.90, per = 0.85, per = 0.80, per = 0.70), The bigger the value of per, the smaller the test error. Theoretical values are calculated from the root water uptake model developed by Shao AJ et al[33,34] (S = ET×A×[e^-B(lnZ-C)2]/Z).
Fig 6.
Calculated water uptake distribution in the soil profile at different instrument precisions.
Use inverse method to calculate distribution of water uptake in the soil profile at different instrument precisions (w = 0.01, w = 0.03, w = 0.05, w = 0.1), The bigger the value of w, the smaller the instrument precisions. Theoretical values are calculated from the root water uptake model developed by Shao AJ et al[33,34] (S = ET×A×[e^-B(lnZ-C)2]/Z).
Fig 7.
Theoretical moisture and calculated water uptake distribution in the profile of layered soil.
(a) Theoretical moisture distribution; (b) Calculated water uptake distribution. Use inverse method to calculate distribution of water uptake in the profile of layered soil (sandy loam+silty soil), Theoretical distribution of moisture and water uptake are calculated from the root water uptake model developed by Shao AJ et al [33,34] (S = ET×A×[e^-B(lnZ-C)2]/Z).
Fig 8.
Theoretical moisture and calculated water uptake distribution in the soil profile at different rates of soil surface evaporation (a) Theoretical moisture distribution (b) Calculated water uptake distribution. Use inverse method to calculate distribution of water uptake in the soil profile at different rates of soil surface evaporation (E = 0.03, E = 0.1, E = 0.3, E = 0.6), The “E” stands for evaporation. All the distribution of water uptake in the soil profile are calculated from applying SAP 3d to 15d. Theoretical distribution of moisture and water uptake are calculated from the root water uptake model developed by Shao AJ et al[33,34] (S = ET×A×[e^-B(lnZ-C)2]/Z).