Modeling Scattering Power of Soil Particle Based on K-M Theory

Soil particle size is an important indicator in soil systems, it can provide important assistance for the agricultural work. In order to address the weakness of traditional soil particle size measuring work, which are time-consuming, labor-intensive, and have limited applicability. This study utilizes the Mie theory and the Kubelka–Munk theory as the precondition, establish an empirical formula between the scattering power and the soil particle size. The study collected surface soil samples from Nong'an, Changchun City, Jilin Province, including black soil, brown soil, sandy soil, and each saline sample, based on visible and near-infrared spectroscopy. Prepare soil samples with a particle size range of 2.5–0.15 mm through drying, grinding, and sieving operations, combining scattering power parameters in the K-M theory to construct an empirical formula for it and soil particle. After verified by comparing different empirical formulas are suitable for the measured data, assume the inverse proportion formula added correction term is the most appropriate. The conclusion is there is a strong linear relationship between the scattering power and the reciprocal of particle size. The average fitting accuracy of the 400–2400 nm wavelength band reaches 94.45%, root mean square error ($\text{RMSE}$) reaches 0.0354 mm. After removing outliers, the fitting accuracy can reach up to 95.77%, $\text{RMSE}$up to 0.0337 mm. Proved there is a very high analytical relationship between soil particle size and scattering power parameters in K-M theory. The empirical formula also can find supported by Mie theory and S-shape R(D) function, and has a high transferability from the laboratory to Landsat8 satellite board, the accuracy can reach to about 90% on SWIR band, showed good generalization ability.