Hyperspectral estimation of saline soil electrical conductivity based on fractional derivative

The integer-order differential (first-order or second-order) preprocessing method is often used in traditional electrical conductivity inversion models, but it ignores the hyperspectral reflectance information at the fractional-order differential. In this paper, a hyperspectral method based on fractional differential to estimate the electrical conductivity of saline soil was proposed. The salinized soil in Changji, Xinjiang was used as the research subject. The surface soil samples of 0-20 cm were collected in May 2017, the field hyperspectral of the saline soil was measured by a FieldSpec^®3 Hi-Res spectrometer, and physical and chemical parameters of soil electrical conductivity were tested in the laboratory. Next, the Grünwald-Letnikov fractional derivative calculation between 0.0-order and 2.0-order was programmed in MATLAB 2019a software (order interval is 0.1). Then, the variation law of the correlation coefficient curves between soil hyperspectral and electrical conductivity under 21 kinds of differentials was analyzed. When the maximum correlation coefficient of each fractional derivative was greater than 0.5, the corresponding wavelength was selected as the sensitive wavelength. Finally, the stepwise multiple linear regression model was used to predict the electrical conductivity. The results showed that the fractional derivative preprocessing method could display the variation details of the correlation coefficient curve under different fractional orders, and more peaks and troughs appeared in the whole band. The eight sensitive wavelengths of electrical conductivity were 400 nm, 418 nm, 567 nm, 1 667 nm, 2 132 nm, 2 193 nm, 2 257 nm, and 2 258 nm. The best model for estimating electrical conductivity was located at the 0.5^th-order. The relative percent difference (RPD) value of the verification set was 1.99, the determination coefficient (R²) was 0.81, and the root mean square error (RMSE) was 1.08. This model had the ability to estimate the electrical conductivity because the RPD value was greater than 1.8. This study explored the difference in electrical conductivity estimates under different fractional derivatives and provided a new method for electrical conductivity estimation, which could be of considerable value for research into improvement of saline soils in the arid regions of Xinjiang.