Optimizing First-order Rate Coefficients for Soil Nitrate Transformation Processes Applying an Inverse Method

It is extremely challenging to measure first-order rate coefficients for soil nitrate transformation processes directly, either in the laboratory or in the field. In this study, an improved inverse method was proposed to optimize the first-order rate coefficients by considering the intermediate changing processes of the integrated functions. A numerical experiment was designed to test the accuracy of the method in optimizing the coefficients. Comparisons between the optimized and theoretical results indicated that all the relative errors were within 10%. Data collected from a field experiment were used to validate the optimization procedure and to demonstrate its applications in practice. Using the established model and the estimated values by the inverse method, the simulated source-sink term (SST) distributions of September 2-12, 2007, were in good agreement, with the root mean squared error (RMSE) between them being as low as 0.00021 mg cm-3 d-1. Based on the established nitrate transformation model, the distributions of soil water content and nitrate concentration during September 2-12, 2007, were simulated, and compared well with the measured profiles, with the RMSE of 0.023 cm3 cm-3 and 0.017 mg cm-3, respectively. The improved inverse method should be useful for optimizing the first-order rate coefficients for nitrate transformation, establishing the nitrate transformation model, and simulating the nitrate transport in the soil-plant system.