Retrieval of Soybean SPAD at Different Vertical Canopy Scales Based on Fractional-Order Derivatives and Spectral...

Vertical heterogeneity in soybean canopies may lead to differences in the relationships between SPAD values at different canopy positions and canopy hyperspectral information, thereby affecting prediction performance. To characterize these spectral relationships and compare SPAD predictability, field experiments were conducted during the soybean flowering stage in Yangling, Shaanxi, China, in 2022 and 2023, with nine irrigation-nitrogen combinations and a rainfed control. A total of 120 paired observations of plant-level SPAD and canopy reflectance spectra were obtained from 20 fixed plots. Upper-layer SPAD, lower-layer SPAD, and their equal-weight arithmetic mean were used as estimation targets. Difference indices (DIs), soil-adjusted vegetation indices (SAVIs), and their combined feature set (ZU) were derived from fractional-order differentiated spectra and used with random forest (RF), support vector regression (SVR), and backpropagation neural network (BPNN) models to compare prediction performance among the three targets. The optimal differentiation orders and wavelength combinations varied among SPAD targets. Upper-layer SPAD showed its strongest association at an order of 0.4 (maximum |r| = 0.737), whereas lower-layer and mean SPAD showed their strongest associations at an order of 1.2, with maximum |r| values of 0.733 and 0.810, respectively. Across the spectral input-algorithm combinations, mean SPAD generally achieved higher prediction accuracy. Its best out-of-fold R² was 0.636, with an RMSE of 2.450 SPAD units, compared with maximum R² values of 0.461 and 0.510 for upper- and lower-layer SPAD, respectively. Further evaluation showed that mean-SPAD models maintained relatively favorable performance under repeated grouped validation and bidirectional cross-year testing. The SAVI-RF model achieved a repeated-validation R² of 0.597 ± 0.064 and cross-year R² values of 0.655 and 0.611 in the two directions. These findings indicate that SPAD predictability from canopy hyperspectral data varies with the sampling target, with the equal-weight mean of upper- and lower-layer SPAD showing relatively higher and more stable predictive performance within the current experiment. The study highlights the importance of vertical canopy sampling in hyperspectral SPAD estimation and provides evidence to inform sampling design and hyperspectral monitoring of soybean at flowering.