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

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 R