An Inverse Method to Estimate the Source-Sink Term in the Nitrate Transport Equation

摘要

The source-sink term (SST) in the convection-dispersion equation (CDE) to simulate nitrate (NO₃––N) transport integrates several NO₃––N transformation processes in soils. The term is affected by considerably complicated micro-environmental conditions and is difficult to be measured directly. In this study, the average SST distribution was estimated by solving the CDE with an unknown SST iteratively using an inverse method. The required input information for the SST estimation was easily obtained, including soil hydraulic properties, two successively measured NO₃––N concentration distributions, and the boundary and initial conditions. Numerical experiments were designed to examine the accuracy and stability of the inverse approach, considering spatial intervals of measurement data along the soil profile, time intervals between the successive measurements of soil NO₃––N concentration, boundary conditions, layered soils, and measurement errors of NO₃––N concentration. Comparisons with theoretical results showed that the inverse method was reliable for estimating the SST in the CDE. Data from a column experiment with winter wheat (Triticum aestivum L. ) growth were used to demonstrate applications of the inverse method. The root-nitrate-uptake (RNU) rate distributions were estimated according to the proposed inverse procedure and the soil NO₃––N transport with RNU in the columns was simulated. The simulated soil NO₃––N concentration distributions were comparable with the measured values. The relative errors between the simulated and measured values of the total N mass extracted by winter wheat were <10%.