Unified nitrogen diagnosis in winter oilseed rape (Brassica napus L.): Integrating Bayesian critical N dilution curves and fractional-order three-dimensional spectral indices

Unified and management-oriented nitrogen (N) diagnosis in mulched dryland crops requires a physiologically consistent baseline that can support consistent interpretation across tested management scenarios and be retrieved non-destructively. To address this, we conducted multi-season field experiments on winter oilseed rape (Brassica napus L.) on the Loess Plateau using three mulching treatments (no mulching, straw mulching, and film mulching) and five N rates (0-280 kg N ha(-1)). Specifically, we aimed to integrate Bayesian physiological modeling with hyperspectral sensing. Aboveground dry matter (DM), leaf N concentration (LNC), canopy hyperspectral reflectance, and seed yield were measured across key growth stages. A Bayesian framework was used to estimate the critical N dilution relationship and quantify parameter uncertainty, supporting pooling across years and mulching treatments (posterior probability of practically negligible differences > 0.95). The resulting unified critical curve was LNCc = 35.732 & times; DM-0.15, enabling a consistent nitrogen nutrition index (NNI) threshold interpretation across mulching scenarios. To enable rapid diagnosis, canopy spectra were transformed using 0.8-order fractional derivatives, and tri-band three-dimensional spectral indices were optimized to predict NNI with machine learning. The best model (XGBoost) achieved R-2 = 0.682 with RMSE = 0.092 on a held-out validation set. Agronomically, film mulching increased mean seed yield by similar to 31.6% relative to no mulching, and yield response exhibited a clear N plateau: FMN3 produced yields only 1.05%-1.74% lower than FMN4 while reducing N input by 25%. The spectral NNI showed a consistent linear-plateau relationship with relative yield, with the plateau occurring near NNI approximate to 1.0. Overall, combining Bayesian N-c-NNI standardization with hyperspectral NNI retrieval provides a unified, management-oriented pathway for N diagnosis within the tested multi-year mulching conditions; however, further external validation across sites, cultivars, and independent years is still required, together with additional assessment of phenology-specific spectral bias, canopy vertical N redistribution, and uncertainty associated with large 3D-OSI feature screening.