Estimation model of soil moisture content in root domain of winter wheat using a fractional-order differential spectral index

Soil moisture content (SMC) is one of the most important conditions to affect crop growth and development in the irrigation of agricultural production. Monitoring SMC of crop roots is much more conducive to guiding precise crop irrigation. This study aims to investigate the effect of fractional-order differentiation (FOD) combined with the spectral index on the hyperspectral inversion of SMC in the winter wheat root domain. The winter wheat was selected as the research object in the Water-saving Irrigation Experimental Station. The data was also measured for the hyperspectral reflectance and soil water content. The hyperspectral reflectance was smoothed by Savitzky-Golay (SG). Then the typical spectral index was calculated to construct the partial least squares regression (PLSR), random forest (RF), and back propagation neural network (BPNN) inversion models of soil water content. The hyperspectral reflectance was processed by fractional differentiation of 0-2.0 order (step of 0.2), in order to calculate the ratio index (RI) and normalized difference index (NDI). A systematic analysis was made to determine the two-dimensional correlation between the RI of different orders, the normalized index and SMC. The sensitive spectral index was screened and grouped to construct three inversion models (PLSR, RF, and BPNN). The results show that: There was a very different correlation between different typical spectral indices and soil moisture content. The correlation coefficient fluctuated between 0.2 and 0.6, the highest of which with the SMC was the near-infrared spectral RI (about −0.6). The best effect was achieved in the SMC inversion model using the typical spectral index, followed by RF and BPNN models. The coefficient of determination of the improved model was 0.55, the root mean square error (RMSE) was 0.027 g/g, and the relative analysis error was 1.64. There was a high correlation coefficient between the sensitive spectral index and SMC after the fractional-order differential processing. The correlation coefficient between the sensitive spectral index and SMC showed a step change at different fractional orders. The correlation coefficient between the sensitive spectral index and SMC was higher at the order 0.2-1.0, and then fluctuated around 0.76, finally gradually decreasing from the order 1.2. The correlation between the sensitivity spectral index and SMC fluctuated around 0.65 after the order of 1.6. The optimal SMC inversion model was the RF model using the normalized sensitivity index after FOD treatment. The determination coefficient of the improved model was 0.75, the RMSE was 0.024 g/g, and the relative analysis error was 2.08. SMC inversion model with the improved fractional differential shared a significantly improved effect (the coefficient of determination from 0.55 to 0.75), compared with the typical spectral index one. The spectral details were mined as much as possible, while the noise was effectively removed more thoroughly without the information variables. As such, an SMC monitoring model was established using the optimal variable set. The findings can provide a reliable way for the hyperspectral monitoring of soil water content in the winter wheat root domain.