Predicting the contents of soil salt and major water-soluble ions with fractional-order derivative spectral indices and variable selection

Abstract This study aimed to improve the potential of visible-near infrared (VIS-NIR) spectroscopy in predicting the contents of salt and major soluble ions in the topsoil at Hetao Irrigation District in Inner Mongolia, China. A total of 120 soil samples (sampling depth is 0–20 cm) were collected from the field. Fractional-order derivatives (FODs) (with intervals of 0.05 and range of 0–2) were used for soil spectral pretreatment. Coefficient of determination (R2) was used to determine the optimal FOD spectrums of the soil salt and major soluble ions. Extreme learning machine (ELM) models were calibrated with such spectral parameters as band reflectance, newly constructed two-band indices, and three-band indices from the optimal FOD spectrum, and the models were subsequently applied to estimate the contents of soil salt and soluble ions. Different algorithms including Monte Carlo uninformative variable elimination (MCUVE), iteratively retaining informative variables (IRIV), and bootstrapping soft shrinkage (BOSS) were applied to variable selection. The results indicated that the correlation between the contents of soil salt and soluble ions and FOD spectra increased as the derivative order increased. The optimal FOD spectrum of soil salt content (SSC), K+, Na+ and SO42− were the 0.9-order derivative spectrum while the optimal FOD spectrum of Ca2+, Mg2+, CO32–, HCO3– and Cl− were 1.65, 0.85, 1.90, 0.80 and 1.55 order derivative spectrum, respectively. The newly proposed three-band index (TBI4) showed a better correlation with ions content (e.g., TBI4 of Mg2+ had the best effect, and its R2 was 0.92). In most cases, the IRIV-ELM models outperformed MCUVE-ELM and BOSS-ELM models in estimating the contents of soil salt and soluble ions. Difference existed among the optimal prediction accuracy of the contents of soil salt and different ions: the prediction accuracy of SSC, Ca2+, Na+, Mg2+, Cl− and SO42− was very high while that of CO32− was high and K+ and HCO32− was relatively lower. However, these models have reached and even exceeded the quantitative prediction level. Therefore, we concluded that the contents of soil salt and soluble ions could be estimated using FOD algorithm and the optimal combination of spectral indices.