Hyperspectral Estimation of Layer-Specific Leaf Nitrogen Content in Potato Canopy by Integrating Fractional-Order Derivatives and Three-Band Spectral Indices

To address the insufficient characterization of vertical heterogeneity in potato canopy leaf nitrogen content (LNC), this study developed a layer-specific LNC estimation framework based on canopy hyperspectral reflectance, fractional-order derivative (FOD) transformation, and two-band and three-band optimized spectral indices. Partial least squares regression (PLSR) was then used to evaluate the predictive ability of the selected spectral indices for Top, Middle, and Bottom LNC. Field experiments were conducted from 2022 to 2023 in the semi-arid region of Yulin, Shaanxi Province, China. Canopy hyperspectral reflectance from 350 to 1830 nm and LNC measurements of upper (Top), middle (Middle), and lower (Bottom) leaves were synchronously acquired during the tuber formation stage. The results showed that potato canopy LNC exhibited a clear vertical gradient, following the order Top LNC > Middle LNC > Bottom LNC. Traditional vegetation indices were significantly correlated with LNC, but their correlations decreased with increasing canopy depth, with the highest correlation for Bottom LNC being only 0.524. Compared with traditional vegetation indices, FOD-based two-band indices showed stronger Pearson correlations with layer-specific LNC. Under FOD1.5, the maximum absolute Pearson correlation coefficients (|r|) between the selected two-band indices and LNC reached 0.855, 0.849, and 0.814 for Top, Middle, and Bottom LNC, respectively. The three-band optimized spectral indices further enhanced spectral information extraction, with maximum |r| values of 0.893, 0.885, and 0.852, respectively. However, cross-year validation produced substantially lower R2 values, indicating limited temporal transferability of the selected indices and the need for further validation before broader application. Compared with the traditional vegetation index model, it increased the testing-set R2 for Bottom LNC by 0.279 and reduced RMSE from 0.159 to 0.113. These results suggest that FOD1.5-integrated three-band optimized spectral indices can improve the indirect estimation of layer-specific LNC from canopy reflectance, particularly for Bottom LNC, where the reflectance–LNC association is affected by canopy signal attenuation and mixing. The findings provide a methodological reference for describing canopy vertical nitrogen status and functional heterogeneity in potato, while their broader applicability requires further validation across growth stages, cultivars, sites, and nitrogen management conditions.