Nitrogen nutritional diagnosis of winter oilseed rape (Brassica napus L.) using fractional-order derivative hyperspectral indices: Field evaluation of dual nitrogen nutritional indices

In the rainfed Loess Plateau, diverse soil mulching practices alleviate water stress but complicate crop nitrogen diagnostics, which still rely on destructive sampling and inflexible models. From 2020–2024, we conducted field trials on winter oilseed rape ( Brassica napus L.) under ridge furrow mulching, straw mulching, and no mulching with graded nitrogen rates. At key growth stages, we measured leaf area index (LAI), leaf nitrogen concentration (LNC), seed yield, and canopy hyperspectral reflectance. First, using 2020–2023 data, we developed an integrated LAI– Nc dilution curve ( Nc =a × LAI −b ) to derive a theoretical nitrogen nutrition index ( NNI t ), which was validated against an empirical index ( NNI e ). Second, we applied fractional order differentiation (0.2–2.0) to the reflectance spectra, selected optimal spectral indices via correlation analysis, and combined them with a random forest model to invert NNI t . Third, we evaluated the “FOD index + RF” framework on independent 2023–2024 data and produced a spatiotemporal map of NNI t . Results showed that (1) the LAI– Nc curve robustly captured nitrogen dilution, with the mulched 210 kg ha -1 treatment achieving yields equivalent to 280 kg ha -1 at NNI t = 1; (2) the best FOD index correlated 0.698 with NNI t , and the RF inversion achieved R²= 0.769, RMSE= 0.131, MRE= 17.60 % for 2020–2023; and (3) 2023–2024 validation returned R²= 0.770, RMSE= 0.118, MRE= 12.93 %, while the spatiotemporal map vividly depicted nitrogen surplus–deficit dynamics. This framework overcomes model adaptability and sensitive band identification challenges, offering actionable spatiotemporal guidance for precision nitrogen management across multiple field practices. • Film mulching with 210 kg N ha⁻¹ boosts yield under reduced nitrogen conditions. • NNI theoretical values effectively reflect winter oilseed rape’s N status. • FOD with machine learning improves NNI theoretical values estimation accuracy. • The NNI map enables real-time assessment of nitrogen status in winter oilseed rape.