Approaches to Simulating Root-Water-Uptake Rate by Solving Inverse Problem of Richards' Equation

The inverse problem of Richards' equation incorporating plant water use is strongly nonlinear and improperly posed. Two present approaches to simulating root-water-uptake rate by solving the inverse problem of the equation were discussed, and a new iterative numerical method was developed. Two numerical experiments were conducted to demonstrate the uncertainty of root-water-uptake functions for simulating soil water flow. The result accuracy and the stability of the approaches were testified, respectively. The results show that the comparison between the measured and the simulated soil moisture content profiles is not enough to indicate the accuracy of the root-water-uptake function. The two present approaches could not be used to simulate water uptake rate by roots when the hydraulic gradient (including its direction and/or values) changed greatly in the profile, whereas the new proposed method was able to give a satisfied result——all the simulated water uptake rates in different time intervals between two successive measurements such as 1, 2, 5, 10 d and 15 d matched the real values well when the theoretical uptake rate was almost constant with time. The relative errors between the simulated and the actual transpiration rate in different time intervals were not more than 3%.