Simulating and Monitoring the Temporal and Spatial Transfer of NPK Fertilizer in Agricultural Soils Using a Mathematical Model and Multi-Channel Electrical Conductivity Measurement

The distribution of nutrients in agricultural soils, which were generated from the dissolution of a mixed inorganic fertilizer on the soil surface, was simulated via the temporal and spatial variation of the soil electrical conductivity (EC). The conventional partial differential convection-diffusion equation describing the transport of solutes was developed to substitute the term of concentration with the term of EC. In addition, the term describing the dominance between the generation and degradation of ions in soil was also included. COMSOL software was used to simulate the temporal and spatial variation of the soil EC at various positions. Using the developed equation, the temporal and spatial variation of the soil EC caused by one and two fertilizer sources was simulated successfully. The accuracy of the simulation was verified by monitoring the transfer of ions which were generated from NPK fertilizer in an experimental model. The root mean square error (RMSE) between two methods was in the range from 0.001 to 0.048 for various positions. Influences of factors on the transfer of ions in soil were also simulated to support for selection of fertilizer appropriate to soil. By fitting data obtained from two methods, the dominance between the generation and the degradation of ions in two different types of agricultural soils was also estimated and consistent with the soil textures. The developed mathematical equation could be helpful for prediction of the temporal and spatial transfer of nutrients which were generated from NPK fertilizer in soil to reduce the environmental degradation of the excessive use of inorganic fertilizers.

Automated summary

This study simulated the distribution of nutrients in agricultural soils based on the temporal and spatial variation of soil electrical conductivity, and successfully developed an improved version of the traditional convection-diffusion equation to predict the transport of fertilizers in soil. The simulation results confirmed the accuracy of the model and supported the selection of appropriate fertilizers for soil.